EFFECTS OF OUT- OF- CLASS- ACTIVITY AND 
COUNSELLING STRATEGIES ON LEARNING OUTCOMES 
IN GEOMETRY AMONG LOW-ACHIEVING SECONDARY 
SCHOOL STUDENTS IN IBADAN 
 
 
 
BY 
 
 
 
MARY OKWUCHUKWU AKUJIEZE 
 
NCE (POLYTECHNIC), B.ED G&C/MATHEMATICS (IBADAN), 
M.ED EDUCATIONAL EVALUATION (IBADAN) 
MATRIC NO: 112858 
 
 
 
A THESIS IN THE INTERNATIONAL CENTRE FOR EDUCATIONAL 
EVALUATION (ICEE), INSTITUTE OF EDUCATION, UNIVERSITY OF IBADAN, 
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF 
DEGREE OF DOCTOR OF PHILOSOPHY IN EDUCATIONAL EVALUATION, 
UNIVERSITY OF IBADAN, IBADAN, NIGERIA 
 
 
 
 
APRIL, 2013 
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ABSTRACT 
Literature in mathematics education shows that the teaching methods being applied by many 
mathematics teachers are teacher-centered. Furthermore, the methods do not relate classroom activities to 
out of class real life experiences. Most often, low-achieving secondary school students (LASSS) do not 
gain from the method of instruction and consequently develop poor attitude towards mathematics, 
particularly in the area of Geometry. It is on the basis of this that the study examined the extent to which 
Out-of-Class-Activity (OCA) and Group Counselling Strategies (GCS) enhance learning outcomes in 
Geometry among LASSS in Ibadan, with students‘ mathematics self-efficacy (MSE) and gender as 
moderator variables. 
A pretest, posttest control group experimental design with 3x2x2 factorial matrix was adopted for 
the study. Multistage random sampling technique was used to select 110 LASSS from six Junior 
Secondary Schools in three Local Government Areas in Ibadan. These students were distributed into three 
groups viz: Group I (OCA), Group II (GCS) and Group III (Control). Four validated instruments: Students‘ 
Selection Test (r = 0.70); Achievement Test in Geometry (ATG) (r = 0.81); Mathematics Self-Efficacy 
Scale (r = 0.85); and Geometry Attitude Scale (GAS) (r = 0.73) were used to collect data. Seven 
hypotheses were tested at 0.05 level of significance. Data were analysed using Mean, Standard Deviation, 
and Analysis of Covariance.  
  There was a significant main effect of treatment on achievement in Geometry (F (2, 97) = 35.77, p < 
0.05) and attitude towards Geometry (F (2, 97) =108.21, p < 0.05). In ATG, OCA Group performed best (  = 
19.10; SD =3.99) followed by GCS (  = 19.03; SD = 3.57), while Control Group performed worst (  = 
12.58; SD = 3.75). In Geometry Attitude Scale, Out-of-Class-Activity group performed best ( =220.20; 
SD =28.58) followed by GCS ( =205.87; SD = 21.86), while Control Group performed worst (  = 157.92; 
SD = 27.40). Mathematics Self-Efficacy had statistically significant effect on achievement in Geometry (F 
(1, 97) = 4.07, p < 0.05), but no significant effect on attitude towards Geometry. Students who held strong 
beliefs in their abilities performed better ( = 17.27; SD = 5.13) than those who did not believe in their 
abilities ( = 16.05; SD = 4.58.).  There was no significant difference between the male and female students 
in their achievement in and attitude towards Geometry.  There were no significant 2 and 3-way interaction 
effects of treatment, gender and MSE on learning outcomes in Geometry. This implies that the effects of 
treatments on learning outcomes in Geometry can be generalised across male and female and students with 
low and high levels of mathematics self-efficacy. 
Both Out-of-Class-Activity and Group Counselling strategies were effective in enhancing learning 
outcomes in Geometry among low-achieving secondary students. Based on the efficacy of the 
interventions, mathematics teachers, counsellors and school administrators should employ these strategies 
in enhancing learning outcomes in Geometry among students. 
 
Key words: Out-of-Class-activity, Cognitive behaviour therapy, Mathematics self-efficacy, Low- 
  achieving secondary school students, Learning outcomes in Geometry                             
Word count:  473 
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CERTIFICATION 
 
I certify that this work was carried out by Mary Okwuchukwu AKUJIEZE in the 
International Centre for Educational Evaluation (ICEE), Institute of Education, University of 
Ibadan. 
 
 
 
 
 
 
 
 
 
………………………………     …………..………….. 
Supervisor                                                                             Date  
Dr. Benson Adesina Adegoke                                                         
Research Fellow 
Institute of Education,  
University of Ibadan, Nigeria.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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ACKNOWLEDGEMENTS 
 
The actualisation of a doctoral degree aspiration cannot be singularly accomplished. 
Therefore, it is necessary to acknowledge the efforts of many people who helped in one way 
or the other for the successful completion of the course. First of all, I want to thank the 
Almighty God through whose grace I was able to start this long journey and He did not 
abandon me on the way.  I sincerely thank God for His faithfulness, protection, provision, 
care and readiness to answer my calls.  
My sincere appreciation goes to my supervisor, Dr. Adegoke, B. A. for his relentless 
supervision and keen interest in this work. Despite his very busy schedules, he still made 
himself available for regular and prompt consultation on this work. He was never tired of 
guiding, giving useful suggestions and objective comments, scrutinizing as well as taking his 
time to go over the drafts of this work whenever they were presented to him. Words are not 
enough to express my profound gratitude to him. He is a good example of a conscientious 
and hardworking teacher. His insistence on getting the best out of his students has contributed 
in no small measure to the writing of this thesis.  My prayer is that God Almighty in His 
infinite mercies will continue to shower His blessings on him.            
Also words are not enough to express my profound gratitude to my first supervisor, 
Bishop (Prof.) E.J. Ibeagha who was instrumental to my proceeding to Ph.D programme. I 
thank him for his encouragement, assistance, motivation and prayers at all times and even 
when he was away from Ibadan on transfer to Enugu State on ministerial work.  
My unreserved thanks go to all the research fellows in the International Centre for 
Educational Evaluation for their contributions, support, expert advice, suggestions, input and 
constructive criticisms. This work was really enhanced through their immense contributions: 
Director of Institute of Education, Prof. M.A. Araromi,who  was always giving me moral 
support; Prof. T.W. Yoloye, who from time to time was encouraging me to speed up the 
work, Prof.Adenike,E. Emeke who played the role of a mother to me, the Head of ICEE Dr. 
Ifeoma, Isiugo-Abanihe for her assistance at various stages, Drs. Georgina. N. Obaitan, 
Folajogun.V. Falaye for their great help on abstract writing, J. G. Adewale was equally 
acknowledged for his suggestion durng post field seminer, Modupe.M. Osokoya (Sub-Dean 
of ICEE) for her help and counselling, J.A. Adegbile who played a wonderful role in my life, 
Eugenia.A. Okwilagwe, Ven. Umoru Adams-Onuka, Monica.N. Odinko, F.O. Ibode, B.A. 
Adegoke, J.O. Adeleke who proofread my pre-field Seminar papers, Serifat.F.Akorede, 
Ikmot O.Junaid,  J.A. Abijo  and V Abe  for their encouragemet.  
I must also place on record the significant role played by Prof. I. Nwazuoke. His 
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motivating words that encouraged me to rise up to the challenges I experienced during the 
course of the programme, will always be remembered. Thank you sir. 
My journey to the university began with the ―prodding‖ of Dr. Abimbade.  He was a 
pivot upon which my academic foundation was laid. May the Almighty God reward you 
abundantly sir. I also acknowledge the significant contributions of other lecturers from other 
departments of university of Ibadan who assisted, supported and encouraged me in different 
ways. These include Prof. C. Uwakwe, Drs D.A. Adeyemo ,A.O. Aremu, D. A Oluwole and 
J.O.Fehintola. 
I owe much debt as well to Dr. Waheed Yinyinola for his invaluable patience, 
suggestions, encouragement, advice, guidance and provision of materials throughout my 
research study. I thank him again for finding time out of his very tight schedule of numerous 
duties to read through my work at different stages.  
I am grateful to many students of the Institute of Education who encouraged me and assisted 
me in one form or the other, colleagues like pastor Ashamu, Pastor Bolu, Mrs Nwazuoke, 
Mrs Oni, Mrs Nwazota and Dr. Opateye. My work colleagues at Methodist Grammar School 
II, Bodija Ibadan, especially Pastor A. Orimolade and Mrs A.O. Adeseye have been 
immeasurably supportive.  
I especially, owe thanks to my sisters and brothers Ngozi, Rebecca, Joy, Moses and 
James respectively for their financial support, prayers and encouragement. I greatly 
appreciate the support received from my mother, Comfort, her motivating words and prayers 
inspired me a lot. Thank you ma for all your support. May God grant you long life to witness 
more glorious events. 
I am grateful to Faith for her selfless effort in typing all the works. The sleepless 
nights and times she sacrificed in order to ensure that the work was typed and submitted at 
the right time was highly appreciated. God bless you abundantly. I also acknowledge the 
immense contributions of non-teaching staff of Institute of Education and Educational 
Management. May God bless you all.  
Last but not the least, my special thanks go to my family. My husband, Edmund 
Akujieze, children: (Unoma, Nkiru, Obiora, Chidinma and Chinyere) and sons-in-law. Their 
constant prayers and belief made these efforts positive. Without their unconditional love, 
financial and technical supports, I could not have accomplished my dream.  
 
       
 
 
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DEDICATION 
 
I dedicate this thesis to 
 
The Beginning and the End. The First and the Last. The lion of the tribe of Judah. The God of 
Abraham, Isaac and Jacob.  The Alpha and Omega. I am that I am. The Sovereign ruler of the 
kingdom of heaven and earth. The God of gods. The king of kings. The only wise God, The 
Omnipotent, the Omniscient and Omnipresent God. The one who was, who is and who will 
ever be world without end, Amen. Holy is your name. I sincerely thank you Lord for your 
faithfulness in my life.        
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TABLE OF CONTENTS 
           Page  
Title page           i 
Abstract           ii  
Certification          iii  
Acknowledgements         iv 
Dedication          vi 
Table of contents          vii 
List of Tables          xii   
List of Figures          xiii 
 
CHAPTER ONE: INTRODUCTION       1  
1.1 Background to the study        1 
1.2 Statement of the problem        10 
1.3 Hypotheses          10 
1.4 Scope of the study         11 
1.5 Significance of the study        11 
1.6 Operational definition of terms      12  
      
CHAPTER TWO: LITERATURE REVIEW       13 
2.1 Introduction         13 
2.2 Theoretical framework         14 
2.2.1 Constructivist theory         14 
2.2.2 Ausubel‘s Theory of Organization of Knowledge     15 
2.2.3 Theory of Causation (REBT)       16 
2.2.4 Operant Conditioning        18 
2.2.5 Modelling or Social Learning theory      18 
2.2.6 Cognitive Behaviour Therapy      19  
2.3 Low-Achieving Secondary Students       22 
2.4 Teaching and Learning of Geometry in Secondary School using OCA        22 
2.4.1  The Concept of Out-of-Class-Activity (OCA) Strategy   24 
2.4.2 Summary of the related principles of the social and cognitive strategy 26                                                    
2.5 Out- of- Class- Activity Strategy and Achievement    27 
2.6 The Concept of Group Counseling (CBT)       29 
2.6.1 Counselling and Academic Achievement      30 
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2.7 Cognitive Behaviour Therapy (CBT) and Self-Efficacy          31 
2.7.1    Mathematics Self-Efficacy and Mathematics Achievement    32 
2.7.2 Mathematics Self-Efficacy and Attitude towards Mathematics  33  
2.8 The Concept of Gender         35     
2.8.1 Gender and Geometry Achievement             37             
2.8.2 Gender and Attitude towards Mathematics      39  
2.9 The Concept of Attitude        41  
2.10 Appraisal of Literature       43 
         
CHAPTER THREE: METHODOLOGY       45 
3.1 Research Design         45 
3.2 Outline of Design        45 
3.3 Variables in the study        46 
3.3.1 Independent variable        46  
3.3.1.1 Out-of-Class-Activity Group (Out-of-Class-Activity + Instruction)  46 
3.3.1.2 Counselling Group (Group Counselling strategy +instruction)  46 
3.3.1.3 Control Group (which received instruction only)    46 
3.3.2 Dependent variables         46 
3.3.2.1 Achievement Test in Geometry (ATG)      46 
3.3.2.2 Geometry Attitude Scale (GAS)      46 
3.3.3 Moderator variables         46 
3.3.3.1 Mathematics Self-efficacy varying at two levels    46 
3.3.3.2 Gender varying at two levels        46 
3.4 Population          47 
3.4.1 Participants         47 
3.5 Sample and Sampling procedure       48 
3.6 Instrumentation         48 
3.6.1 Students‘ Selection Test (SST)      49 
3.6.2 Achievement Test in Geometry (ATG)      49 
3.6.3 Mathematics Self-efficacy Scale (MSES)      50 
3.6.4 Geometry Attitude Scale (GAS)      51 
3.6.5 Researcher‘s Instructional Guide in Geometry (RIGG)   51  
3.7 Procedures for the Experiment       51 
3.7.1 Experimental Group I        54 
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3.7.2 Experimental Group II        57 
3.7.3 The Control Group        59 
3.8 Control of Extraneous Variable      59  
3.9 Data Analysis         60 
 
CHAPTER FOUR: RESULTS AND DISCUSSION   62 
4.0 Results and Discussion       62  
4.1 Hypothesis 1: There is no significant main effect of treatment    
On participants‘         62 
(a) Achievement in geometry         
       (b) Attitude towards geometry       
4.2      Hypothesis 2: There is no significant main effect of self-efficacy   66 
On participants‘ 
(a) Achievement in geometry        
        (b)  Attitude towards geometry       
4.3     Hypothesis 3: There is no significant main effect of gender   68 
  On participants‘ 
  (a) Achievement in geometry        
(b) Attitude towards geometry         
4.4  Hypothesis 4: There is no significant 2-way interaction effect of treatment  70 
 By self-efficacy          
On participants‘ 
(a) Achievement in geometry         
 (b) Attitude towards geometry.          
 4.5 Hypothesis 5: There is no significant 2-way interaction effect of treatment   
 By gender          71 
 On participants‘ 
  (a) Achievement in geometry           
(b) Attitude towards geometry.        
4.6 Hypothesis 6: There is no significant 2-way interaction effect of  
 Self-efficacy by gender        71 
On participants‘ 
(a) Achievement in geometry         
(b) Attitude towards Geometry        
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4.7  Hypothesis 7: There is no significant 3-way interaction effect of:    
 Treatment, self-efficacy and gender      71 
  On participants‘ 
(a) Achievement in Geometry       
 (b) Attitude towards geometry.        
4.8 Discussion         72 
4.9 Hypothesis 1: The hypothesis stated there is no significant main effect  
Of treatment on participants‘:       72 
 (a) Achievement in geometry; and  
 (b) Attitude towards geometry  
4.10 Hypothesis 2: There is no significant main effect of self-efficacy on  
 Participants‘:          76  
 (a) Achievement in geometry and  
 (b) Attitude towards, geometry  
4.11 Hypothesis 3: There is no significant main effect of gender on  
 Participants‘:          77  
 (a) Achievement in geometry and  
 (b) Attitude towards geometry 
4.12 Hypothesis 4: There is no significant 2-way interaction effect of  
 Treatment by self-efficacy on participants‘ Achievement in and  
 Attitude towards geometry        78 
4.13 Hypothesis 5: There is no significant 2-way interaction effect of  
 Treatment by gender on participants‘ Achievement in and  
 Attitude towards geometry        78 
4.14 Hypothesis 6: There is no significant 2-way interaction effect of  
 Self-efficacy by Gender on participants‘ Achievement in and  
 Attitude towards geometry        79 
4.15 Hypothesis 7: There is no significant 3-way interaction effect of  
 Treatment, Self-efficacy and Gender on participants‘ Achievement in and  
 Attitude towards geometry        79 
 
 
 
 
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CHAPTER FIVE: SUMMARY AND CONCLUSIONS       
5.1 Introduction          80 
5.2 Summary of findings         80 
5.3 Implications of the findings        81 
5.4 Recommendations        82 
5.5 Limitations of the study        83 
5.6 Suggestions for Further study       83 
5.7 Contributions to knowledge        84 
 References           85 
 Appendix I         119 
 Appendix II         121 
 Appendix III         123 
 Appendix IV         130 
 Appendix V         133 
 Appendix VI         145 
 Appendix VII         159  
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LIST OF TABLES 
           Page  
Table 3.1 3x2x2 factorial design       46 
 
Table 3.2 Information for the 110 participants in the study    47 
 
Table 3.3 Distribution of schools and students used for the study  48 
 
Table 3.4 Table of Specification for Geometry      50 
 
Table 3.5  Showing the Time-Table for the Training of Teachers   52 
 
Table 3.6 The Hypothesis and the method of Analysis     61 
 
Table 4.1 Mean and Standard deviation of participants‘ scores on    
  Achievement in Geometry      62  
  
Table 4.2 ANCOVA of between subject effects      63 
             
Table 4.3 Scheffe Post-Hoc Means for group in Homogeneous  
 Subsets by Treatment.                              63 
 
Table 4.4 Shows the Mean and Standard deviation of self-efficacy   
on participants‘ achievement in Geometry     64                                                                                                
 
Table 4.5 ANCOVA of Students‘ Attitude Scores by Treatment,  
 Self-Efficacy and Gender      65 
 
Table 4.6a Scheffe Post-Hoc Multiple Comparison of Participants‘  
 Attitude by Treatment       66 
 
Table 4.6b Scheffe Post-Hoc Means for Groups in Homogeneous  
 Subsets on Attitude by Treatment.            66 
 
Table 4.7 Shows the Mean and Standard deviation of self-efficacy   
 on participants‘ achievement in Geometry     67                                                                                     
 
Table 4.8a Scheffe Post-Hoc Multiple Comparison of Participants‘  
 Achievement in Geometry       67 
 
Table 4.8b Homogenous subsets by Self-Efficacy    68 
 
Table 4.9 Mean and Standard deviation of self-efficacy on participants‘   
attitude towards geometry      68 
 
Table 4.10 Mean and Standard deviation of gender  on participants‘  
 achievement in geometry       69 
 
Table 4.11 Mean and Standard deviation of gender  on participants‘  
           Attitude towards geometry       70
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LIST OF FIGURES 
           Page  
 
Figure 3.1 Outline of Design        45 
Figure 3.2 Experimental Group I       56  
Figure 3.3 Experimental Group II      58 
  
 
    
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CHAPTER ONE 
INTRODUCTION 
 
1.1 Background to the Study  
 Geometry, a branch of Mathematics, has received a substantial attention since 2000BC. 
The importance of geometry in the lives of people cannot be overemphasized. This is because 
geometry is used by engineers and architects in planning building and other structures such as 
bridges and tunnels. In addition, it helps people to acquire abilities such as making new 
discoveries, analyzing problems and making connections between mathematics and real life 
situations (Bindak, 2004). Moreover, the National Council of Teachers of Mathematics 
(NCTM, 2000), the largest organisation for teachers of Mathematics in the world, attests to the 
importance of geometry in school Mathematics by stating ―geometry is a natural place for the 
development of students‘ reasoning and justification skills (p. 40).  Surveyors, artists and other 
professional men and women use geometry in their work (Adegoke, 2002) as it is being used 
by human beings to specify quantities and to measure figures and lands.  The widely known 
quote of Plato,‖ Let no man ignorant of geometry enter here‖ over the door of his academy 
(Burton, 1999; p79) and the fact that ‗Elements‘, the famous geometry book written by Euclid 
around 300 BC, has more editions than any other book except for Bible (Malkevitch,1998) 
attests to the importance given to geometry. Geometry maintains its importance in 
Mathematics curriculum (Adegoke; 2002, Duatepe, 2004) as it helps to develop spatial 
perception.  Learning geometry prepares students for higher Mathematics courses and sciences 
and for a variety of occupations requiring mathematical skills and general thinking skills as 
well as problem-solving abilities are facilitated by geometry. It is used to represent and solve 
problems in other topics of mathematics, and daily life situations. Geometry is found to be 
useful in other disciplines such as arts and science.   
Every human being from a housewife to an engineer needs some geometry intuition to 
understand and interpret the world (Adegoke, 2002; Duatepe, 2004). This is because geometry 
as a branch of mathematics is an intellectually stimulating subject that affects every facet of 
human activity such as economy, politics, science and technology. Sherrard (1981) as cited by 
Duatepe (2004)  labeled geometry as a basic skill in Mathematics that is significant for every 
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student since it is an important help for communication, as geometry terms are used in 
speaking.  Adegoke (2002) and Duatepe (2004) noted that geometry can enhance cultural and 
aesthetic values as Artists use various geometric forms are used in making attractive patterns  
for textiles, household items, advertising  and  in box designs.     
It is interesting to note that in spite of the importance of geometry, numerous researches 
(Clements & Battistssa, 1992; Mitchelmore, 1997; NCTM, 1989; Senk,1985; 
Thirumurthy,2003; Ubuz & Ustun,2002 ) make it clear that students are not learning geometry 
as they are expected to learn.  TIMSS (1999) has also reported that students‘ geometry 
achievement have been found to be lower than the other areas of mathematics (Mullis, Martin, 
Gonzalez, Gregory,Garden, O‘Cannor, Chrostowski, & Smith, 2000).  Duatepe (2004) and 
Uwadiae (2010) noted that analysis of school certificate mathematics examination results show 
that students have consistently low performance in geometry, as less than 42% of registered 
candidates obtain credit pass. West African Examinations Council (WAEC) Chief Examiners‘ 
Reports (2005,2006, 2007), indicated that students areas of deficiency in school certificate 
examinations showed that, students least understood geometry concepts, as shown by their 
achievement. It was further reported that most students avoid geometry questions or 
haphazardly attempt them.  Adegoke (2002) and Adeleke (2007) noted that students find 
geometry difficult to learn and teachers find it difficult to teach. This probably might have 
accounted for the general poor performance of students in Mathematics and hence, the research 
on it. A need for increasing geometry achievement of students has been realized by 
Mathematics educators (NCTM, 1989, NCTM, 2000).     
 The achievement of students in Geometry could be influenced by learners‘ 
characteristics such as gender. However, researchers (for instance, Etukudo, 2002; Ezeugo & 
Agwagah, 2000) have divergent views on gender in relation to roles, ability, attitude, and 
achievement in specific tasks. In fact, findings on gender difference in Geometry vary 
significantly. Some scholars claim that males perform better than females (Adeyegbe, 2000; 
Olatundun, 2008); while others such as Olowojaiye (2001) and Yinyinola (2008) claim that no 
difference exists in the achievement of male and female students in Mathematics.  Abiam and 
Odok (2006) found that there is no significant relationship between gender and achievement in 
number and numeration, statistics, algebra but a weak relationship between gender and 
achievement in geometry and trigonometry. Amelink (2009) noted that male students 
th
performed better in geometry and measurement among 8  graders, while numbers and 
operation were better performed by female students.   
 
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Another factor that is found to affect achievement is attitude. Nkwe (1985) argues that 
pupils who are positively inclined towards a subject tends to do well in that subject.  Melihan, 
Seher and Ramazan (2010) noted that attitudes play an important role in geometry 
achievement. Ma and Kishor (1997) indicated that there is a general belief that children learn 
more effectively when they are interested in what they learn and that they will achieve better in 
mathematics if they like mathematics. Similarly, if students have positive attitude towards 
geometry, they are expected to like geometry, participate in the classroom activities and to be 
high achievers in geometry (Bindak, 2004). According to Adebowale (2000), a student‘s 
attitude could relate to all the facets of his or her education. The researcher opines that, the 
attitude of a student towards Mathematics and Mathematics-related subjects will determine the 
measure of the student‘s attractiveness or repulsiveness to Mathematics. This tends to 
influence the learner‘s choice and achievement (Adetunji, 2000; Ayedun, 2000; Mohd, 
Mahmood & Ismail, 2011; Osborn & Simon, 2003).  Studies on the relationship between 
students‘ attitude and the students‘ academic performance show a positive relationship (Mohd, 
Mahmood & Ismail, 2011; Bramlett & Herron, 2009; Nicolaidou & Philippou, 2003). 
However, Mogari (2012) remarks that it cannot be concluded that positive attitude will always 
affect good performance. Kiely (1990) reports that on average, a small number of pupils who 
were not good enough in mathematics obtained high score in the attitude test. 
Aiken (1970) as cited by Mogari (2012) opined that assessment of attitude would be of 
less concern if attitudes were not thought to affect performance in some way. Kulm (1980) 
concluded that achievement depends on attitudes, hence the ongoing search for a relationship 
between the two variables. The needs and interest of today‘s children are far more different 
than the children of the past decades.  The traditional instructional methods do not seem to be 
responsive to the potential of today‘s children (Battista & Clement 1999; Garrity, 1998).   
 Research report indicated that poor teaching approach accounts for students‘ poor 
achievement in geometry (WAEC, 2007; Olunloye, 2010). Uloko and Usman (2008) reported 
that there is a positive correlation between good teaching approach and students‘ achievement 
in mathematics. Also Iji (2005) stated that good strategy improves both low and high ability 
students in geometry at the upper basic education class. That is good teaching approach 
produces high achievement among learners while poor teaching approach will lead to poor 
learning and low achievement.  Generally, instruction in geometry has been teacher-centered, 
procedure-based, and prescriptive (Baynes, 1998; Keiser, 1997). This method is lacking in 
creativity, visualization, and conceptual development (Keiser, 1997; NCTM, 2000). 
Schoenfeld (1983) as cited by Duatepe (2004) noted that students cannot be creative enough in 
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a traditional class. Furthermore, this approach was problematic for many students and teachers, 
and both groups considered geometry to be the most frightening subject (Malloy & Friel, 
1999).  This might have resulted in students losing interest in geometry. Schoenfeld (1983) as 
cited by Duatepe (2004) associated the limitations of traditional teaching in geometry with the 
teacher-oriented instruction and ―ready-made‖ mathematical knowledge presented to the 
students. Most formal school experience never gives students the opportunity to do anything 
with Mathematics except for lean back and listen. Students are not given a chance to be 
involved in the teaching and learning process to learn meaningfully. According to Olunloye 
(2010), teachers should improve their teaching methods in order to enhance better 
understanding and application of geometry among the students so that their interest could be 
aroused. Thus, there is need to explore approaches that will improve students‘ achievement as 
current results (WAEC, 2010) indicate that the conventional teaching approach is deficient in 
meeting the needs of majority of learners.  The conventional teaching approach is described as 
teacher centered and didactic with learners simply listening, copying notes, doing class work 
and doing assignments. Furthermore, with conventional teaching approach, gap between high 
and low ability students is very wide. 
According to Clements and Battissa (1992), effort should be made to conduct 
teaching/learning research that leads students to get geometry concepts meaningfully and 
excitingly. During the last decade, researchers have studied on how geometry topics should be 
presented so that students‘ difficulties can be overcome.  Many researchers  (Arcavi & Hadas, 
2000; Baharvand, 2001; Bobango,1988; Borrow, 2000; Chazan,1998; Choi-Koh,1999; 
Flanagan,2001; Furinghetti & Paola, 2000; Healy, 2000; Hodanbosi, 2001; Holzi, 2001; Ives, 
2003; Jones,1998; Johnson, 2002; July, 2001; Laborde, 2002; Marrades & Guiterrez, 2000; 
Moses, 2000; Scher, 2002; Ustun, 2003; Washington-Myers,2001) have studied the use of 
technology on geometry. Some of them (Din & Whitson, 2001; Round, 1998; & Velo, 2001) 
studied the effect of computer programmes in geometry and some researchers (Dixon, 1997; 
Duatepe & Ersoy, 2002; Ryan, 1999) conducted studies on usage of calculators in geometry. 
These studies revealed that the use of technology is beneficial to students in developing their 
understanding of geometric concepts.  
A different aid for geometry teaching other than technology is barely seen in the 
literature. Nichols and Hall (1996) studied the effects of cooperative learning method in 
geometry lessons and found that it has positive effects. The effects of manipulative besides 
cooperative learning were investigated by Garrity (1998).  The result indicated that it improved 
the students‘ attitudes towards Mathematics and achievement.  
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There still occurs a need to find different teaching methods in geometry instruction that 
can meet the students‘ needs and make them engage in geometry to provide meaningful 
learning. Constructivist learning theory basically claims that in order for learning to be 
meaningful, learners should actively construct knowledge. The teacher should assist learning 
by creating a stimulating learning environment for students, asking questions that require 
students to think critically, and allowing them to investigate, discover and question the 
concepts they are learning. Researchers in Mathematics education such as Folk and Dierking 
(1992) and NCLB (2002), suggest the use of Out-of-Class-Activity  (OCA) and Counselling  
strategies to improve the learning outcomes of the low-achieving students. Considering these 
facts, this study investigated an alternative teaching method in geometry; Out-of-Class-
Activity based instruction. 
 Out-of-Class-Activity Strategy (OCA) encompasses Mathematics learning that takes 
place outside the traditional classroom walls, for example, on the field, in the garden, market, 
in the community and in the laboratory. OCA is a therapeutic strategy by which students are 
taught Mathematical knowledge systematically through connectivity to the real life situation. 
In this study, the Out-of-Class-Activity strategy was based on constructivist ideas. The 
constructivist learning theory (Piaget, 1963; Vygotsky, 1987) holds that learning should build 
upon the knowledge that a student already has acquired; this prior knowledge is called schema. 
The theory suggests that learning is more effective when a student is actively engaged in the 
construction of knowledge rather than passively receiving it. The goal of using Out-of-Class-
Activity strategy is the development of Mathematics (geometry included) teaching innovations 
in which students and teachers engage in mathematically rich situations through the creation of 
learning modules that capitalize on students‘ knowledge and experiences in their everyday life 
experiences. OCA is characterized by the following:  
 The learners are actively involved; 
 The environment is democratic; 
 The activities are interactive and student-centered; and 
 The teacher guides, directs and facilitates the process of learning in which the  students are 
encouraged (Gray, 1999).  
 Mathematics is hierarchical in nature. That is, complex concepts are built cumulatively 
on simple ones. For this reason, Kemeny (2006) advocates that Geometry should be taught 
systematically, relating the classroom concepts to the real life experiences of the learners. 
Traverse, John and Garth (1971) state that teachers of low-achieving students should be well 
experienced in the teaching of Mathematics. According to Traverse et al, the teachers should 
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be acquainted with what students are doing in their industrial arts (local environments) and use 
the knowledge acquired in their local environment as sources of application of learning 
Mathematics. Similarly, Weil and Calhain (2004) assert that teachers must not only be 
knowledgeable about the content they teach, but should also know and be committed to 
making decisions that involve the use of variety of instructional strategies and approaches 
appropriate to the students‘ diverse learning needs.  
 Travers, John and Garth (1971) stated that the geometry teacher of low-achieving 
students should systematically organise the instruction in such a way that it will be like a 
building block of linkage from known to unknown (cultural environment of the learners to the 
classroom situation). For example, the researcher used the teaching of the concept of area of 
cylinder to illustrate the Travers et al s‘ suggestion. This should involve: 
 Collection of real life solid shapes that is cylindrical in nature (for example, empty cans 
of milk) within the students‘ local environment. 
 Identification of the cylindrical shapes, 
 Observation, touching and feeling of cylindrical shapes,  
 Differentiation of cylindrical shapes from other shapes and other symbols,  
 Drawing of the cylindrical shapes on the chalkboard and on their paper. 
 Exploration of properties of a cylinder, 
 Formation of the formula of area of the cylinder; and  
 Calculation of the area of cylinder which culminates all the above concepts.  
 
By so doing, there will be a link between geometry and real life situations.  Kemeny 
(2006) explains that making the relationship between geometry and the real life experience of 
students is a way to reduce anxiety. When students gain confidence in Mathematics, they could 
become more successful in it (increase in Mathematics achievement and positive attitude 
towards the subject) and be better equipped to be successful in the world that is highly 
technologically and mathematically oriented.                 
     In addition to the above, research studies have shown the importance of counselling to 
the academic achievement of students (Graham, 2005; Kendall,1994). Stressing the importance 
of counselling in educational system, Fakunle (2007) acknowledges the influence of 
counselling on students‘ achievement, explaining that the poor achievement of students in 
Mathematics as well as students avoidance of its learning is attributed to unavailability of 
career counselling. Adeyoju (1989) argues that the roles of the school counsellors include 
provision of services for specific support for students with both academic and non-academic 
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problems.  According to Obanya (2000) and Atkinson (2004), counselling programme would 
be able to care for both the psychosocial and academic lives of the learners.  Fakunle (2007) 
stresses that failure of students in Mathematics, negative attitude towards it and hatred, are as a 
result of the inability of the students to receive proper counselling in Mathematics.  He noted 
that the roles of a good counsellor are to:  
 help students explore self;  
 help students make informed decision;  
 help students correct misconceptions especially in the area of Mathematics;  
 promote students‘ positive behavioural change; and  
 Promote students‘ healthy living.  
 
 Ford (1992, 1996) considered the characteristics of low-achieving students as follows: 
the students have negative attitude towards school; they have low self-concept; exerts little 
effort on school tasks, perform poorly academically and feel alienated both at home and in 
school. Therefore, having identified the characteristic of low-achieving students, (Paisley & 
Millson, 2007) reported that the problems of the low-achieving students could be addressed 
using group counselling strategy. Similarly, Gibson and Mitchel (1981) as cited by Oladele 
(2001) explain that humans are group-oriented. People are meant to complement, assist and 
enjoy each other.  Humans seek to meet most of their basic and personal–social needs through 
groups, including the need to know and grow mentally. Thus, group counselling serves both 
preventive and remedial purposes. Through group counselling, there might be some 
behavioural changes in terms of student attitude towards Mathematics, achievement among 
low-achieving students subsets can be promoted Mathematics performance and their personal 
characters (Gesinde, 1991; Paisley & Millson, 2007)).  
 In view of counselling, Sink (2005) suggests that school counsellors can directly impact 
student learning through small group counselling.  Sink (2005) emphasised that Cognitive 
Behavioural Therapy (CBT) interventions utilized within classroom small group meetings are 
the most logical and educationally applicable interventions school counsellors can use to 
impact academic achievement.  
 Ellis (2003) defined CBT as a learning-based approach that encourages students to 
modify their thinking and behaviour. Ellis described problems such as fear of mathematics, 
poor achievement, negative attitude and low self-efficacy by the low-achieving students as 
being triggered by how students analyse events in their lives.  When people develop irrational 
beliefs and unrealistic goals, it could lead them to unattainable expectations. Considering the 
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interrelationship between beliefs, values, thoughts and attitude underlining human behaviour 
and emotions, Ellis believed that the CBT could be used as a counselling technique to aid the 
low–achieving students in enhancing their academic performance. Cognitive behavioural 
therapies can as well be defined as those interventions with the core assumptions that what 
individuals think directly impacts how they feel and what they do (Graham, 2005).  Graham 
further suggests that if a school counsellor can re-educate students to confront their 
dysfunctional thoughts, then consequently symptoms of emotional distress and dysfunctional 
behaviours can be reduced. School counsellors utilizing CBT give strong significance to the 
conscious thought processes of their students, place emphasis on the present, give homework 
for the students to work on between sessions or groups, and assess the efficacy of the 
intervention to make changes as the relationship progresses (Graham, 2005).      
  The CBT holds that most of our emotions and behaviours are the results of what we 
think or believe about ourselves, other people and the world (Binggeli, 2010). These cognitions 
shape the interpretation and evaluation of what an individual experienced, influence how he 
feels about it and provide a guide to how he should respond.  
 Unfortunately, sometimes these interpretations, evaluations and underlying beliefs, and 
thoughts contain distortions, errors or biases that are not very useful or helpful. This results in 
unnecessary suffering and causes one to react in ways that are not in one‘s best interest.  
Among the reasons students identified for not performing well in Mathematics is that the 
subject is difficult (Udousoro, 2000). According to Ellis (2003), such thought is an irrational 
one or wrong conception which can be modified by the use of Cognitive Behavioural Therapy. 
For example, a low-achieving student who says ―I hate Mathematics‖, I don‘t think I will ever 
know Mathematics in my life‖ has internalized such a thought. The CBT counsellor would 
model more healthy and productive thoughts for the learners, such as ―Mathematics is for all‖, 
―you can love Mathematics as your best subject if more time is devoted for it.‖ The CBT 
counsellor can help learners to internalize a rational philosophy of life, just as he or she 
originally learned and internalized the irrational ones through a manner of ways and 
methodologies to replace the rational thoughts.  
    Research reports indicated that many reasons accounted for students‘ poor achievement 
in geometry. Among this is lack of confidence in the subject (Basturk & Yavuz, 2010).  With 
the trend of poor performance in Mathematics, educators (Campbell & Hackett, 1986; Pajares 
& Kronzler, 1995; Pintrich & De Groot, 2000) have advocated that perceived abilities are key 
elements for success in Mathematics.  According to Bandura (1986), self -efficacy is defined as 
people‘s judgment of their capabilities to organize and execute the course of action required to 
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attain designated type of performance and task. Yinyinola (2008) opines that self-efficacy 
beliefs act as a determinant of behaviour by, influencing the choice that students make, the 
effort they expend, the perseverance they exert in the face of adversities, the thought patterns 
as well as mental and emotional reactions they experience. A high sense of efficacy may serve 
students well when solving mathematical problems not because it ―makes‖ them to be better 
problem solvers, but because it engenders great interest in and attention to work the problems. 
With increased effort and greater perseverance in the face of adversity, such students are also 
likely to feel less apprehensive about mathematical capabilities. Self-efficacy encourages 
perseverance and provides the confidence to try different strategies. Students who doubt their 
ability to succeed may tend to give up a learning process if the early efforts do not result in 
perceived success (Brown & Inouye, 1978; Schunk, 1984). This is probably why people 
achieve readily even in the face of adversity.  When they believe they will be successful, they 
work harder towards achieving their goals.  Those who are confident about their abilities tend 
to succeed, while those who doubt their abilities to succeed tend to fail. In a similar view, 
Pajares (2001) asserts that the higher the students‘ mathematics self-efficacy, the more 
confidence they have. 
   Researchers (Young, 1997; Roeser, Strobel & Quihuis, 2002) have linked cognitive 
processes with motivation, a major building block for student academic achievement as well as 
the level of anxiety (Barabasz & Barabasz, 1981; Ergene, 2003; Fisher, Masia-Warner & 
Klein, 2004; Keogh, Bond, French, Richards, & Davis, 2004) students‘ experience at school.  
Zyromski and Joseph (2012) noted that using Cognitive Behavioral Intervention to intervene 
and help students control cognitive thought processes would directly impact these 
metacognitive influences on student learning; therefore, positively imparting academic 
achievement.  Ausubel (1973) stated that young children are capable of understanding abstract 
ideas if they are provided with sufficient materials and concrete experiences with phenomenon 
that they are to understand.  Kumar et al (2004) as cited by Bashir (2012) remarks that co-
curricular activities hold a place of great importance in the field of education for the all round 
development of children. Furthermore, some researchers examined the effects of computer 
instruction on geometry achievement (Arcavi & Hadas, 2000; Baharvand, 2001; Choi-Kok, 
1999), however, the previous studies on students‘ learning of geometry mainly focused on all 
the students generally and not specifically on the low-achieving students. It is against this 
background, that this study investigated the effect of Out-of-Class-Activities (OCA) and 
Cognitive Behaviour Therapy (CBT) a mode of Group Counselling Strategy (GCS) on 
achievement in and attitude towards geometry among low-achieving junior secondary school 
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students in Ibadan. 
 
1.2 Statement of the Problem  
Geometry plays an important role in human activities. Secondary school students dread 
Mathematics, especially in the area of geometry. Many students who are low-achieving face a 
lot of challenges in the learning of Mathematics in general, and geometry, in particular.  The 
problem of poor performance is of great concern to parents, teachers and school administrators.  
The result of poor performance has often resulted in low-achieving students developing 
negative attitudes towards Mathematics and having low performance.  The bodies of research 
on geometry instruction for secondary school students have focused on experimental studies 
that engage students only in academic activities inside the classroom which could improve the 
students‘ academic performance and enhance their mathematics concepts. However, these 
methods, as laudable as they might be, do not create situations in which students examine the 
connections between Geometry and life outside the classroom and apply what they are 
learning. 
Secondly, most of these studies have not considered the needs of low-achieving 
students who are performing below the academic standard. Therefore, in order to improve 
academic performance of low-achieving students in geometry, the present study investigated 
the effects of out of class activity and counselling strategies on learning outcomes in geometry 
among low-achieving secondary school students in Ibadan.   
 
1.3  Hypotheses 
The following hypotheses were tested in this study at.05 level of significance. 
Hypothesis 1: There is no significant main effect of treatment    
on participants‘          
(a) Achievement in geometry         
       (b) Attitude towards geometry       
Hypothesis 2: There is no significant main effect of self-efficacy    
on participants‘ 
(a) Achievement in geometry        
        (b)  Attitude towards geometry       
Hypothesis 3: There is no significant main effect of gender    
On participants‘ 
  (a) Achievement in geometry        
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(b) Attitude towards geometry         
 
Hypothesis 4: There is no significant 2-way interaction effect of treatment  
 by self-efficacy          
on participants‘ 
(a) Achievement in geometry         
 (b) Attitude towards geometry.          
Hypothesis 5: There is no significant 2-way interaction effect of treatment   
 by gender           
 on participants‘ 
  (a) Achievement in geometry           
(b) Attitude towards geometry.        
Hypothesis 6: There is no significant 2-way interaction effect of  
 Self-efficacy by gender         
On participants‘ 
(a) Achievement in geometry         
(b) Attitude towards Geometry        
Hypothesis 7: There is no significant 3-way interaction effect of    
 Treatment, self-efficacy and gender       
  On participants‘ 
(a) Achievement in Geometry       
 (b) Attitude towards geometry.   
 
1.4 Scope of the Study  
 The study involved Junior Secondary two (JS2) students. It was designed to provide 
information on the effectiveness or otherwise of out-of-class-activity and counselling strategies 
in enhancing learning outcomes of secondary school students in geometry. The study 
incorporates student‘s self-efficacy and gender as moderator variables. It involved achievement 
in geometry and attitude as dependent variables. The study was carried out in Ibadan, Oyo 
State, Nigeria. The participants were selected from Junior Secondary two (JS 2) students 
within Ibadan metropolis.  
 
1.5 Significance of the Study  
 The results of the study will provide students with a strategy for developing positive 
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attitude towards geometry which can enhance their performance in mathematics generally. 
Findings can be significant in validating the use of Out-of-class-activity based instruction in 
geometry. A growing body of evidence indicates that in helping students to acquire proper 
geometric concepts, activity based approach to teaching geometry are more effective than 
conventional methods in producing a wide range of desirable student outcomes.  
Furthermore, the significance of this study would be the development of a therapeutic 
programme for readjusting the negative effects of poor performance in Geometry. The 
response of the participants to therapy would enable the researcher to determine the suitability 
of the treatment. 
It is equally hoped that the study will generate problems for further research.  It will be 
useful to researchers who may intend to replicate the study or work in related fields of study. 
    
1.6 Operational Definition of Terms         
Low–achieving students: In this study, low-achieving students refer to the participants in the 
study who scored below the first quartile in students‘ selection test (SST) which was 
constructed by the researcher and was administered to the participants in the selected schools.    
Out-of-Class-Activity Strategy: This refers to activity delivered outside   the classroom 
whereby the participants were taken outside the classroom to carry out some mathematical 
operations after which geometry instruction was taught in the classroom. 
Attitude:  This refers to the students‘ scores on the Geometry Attitude scale (GAS). 
Counselling strategy: (Cognitive Behaviour Therapy). Counselling strategy refers to the 
intervention programme designed by the researcher through which participants acquired 
appropriate information to enable them develop positive attitude towards Geometry so as to 
enhance their performance   
Learning outcomes: Learning outcomes refer to the participants‘ scores obtained from 
Achievement Test in Geometry (ATG) and Geometry Attitude Scale (GAS).  
Mathematics self-efficacy: This refers to the belief, which the participants hold about their 
abilities to solve mathematics or mathematics related tasks.         
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CHAPTER TWO 
LITERATURE REVIEW 
 
2.1 Introduction  
 This chapter presents a synthesis of related literature on all the variables involved in the 
study. The chapter also contains the conceptual framework for the study. 
  
2.2 Theoretical framework   
2.2.1 Constructivist theory  
2.2.2 Ausubel‘s Theory of Organization of Knowledge  
2.2.3 Theory of Causation  
2.2.4 Theories of counselling  
2.2.5 Operant Conditioning  
2.2.6 Social Learning theory 
2.2.7. Cognitive behaviour Therapy 
2.3 Low-Achieving Students  
2.4 Teaching and Learning of Geometry in Secondary School 
2.5 Out –of- Class- Activity Strategy  
2.5.1 Strategy for Linking School Mathematics and Out of Class Activity                   
2.5.2    Out- of -Class -Activity Strategy and Achievement 
2.5.3 Out –of- Class- Activity strategy and Attitude  
2.6 Group Counseling Strategy   
2.6.1 Counselling Strategy and Achievement  
2.7 Mathematics Self-Efficacy        
2.7.1    Mathematics Self-Efficacy and Achievement  
2.7.2 Mathematics Self-Efficacy and Attitude towards geometry  
2.8 Theory of Gender     
2.8.1 Gender and Mathematics Achievement                     
2.8.2 Gender and Attitude towards Geometry   
2.9 The Concept of Attitude  
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2.10  Appraisal of the literature.  
 
2.2 Theoretical Framework  
 The theoretical framework for this study was built on :(1) Constructivist theory; (2) 
Ausubel‘s theory of Organization of Knowledge; (3) Ellis Theory of Causation  (4) Theories of 
Counselling (5)Operant Conditioning (6) Social Learning Theory (7) Cognitive Behaviour 
Therapy. 
 
2.2.1 Constructivists’ Theory  
 The constructivist believes that learners can help construct their knowledge based on 
their previous experiences and that they understand and learn better through interaction with 
their industral world (environment). The theory also predicts that knowledge encoded from 
data by learner themselves will be more motivating, flexible, transferable and useful than the 
one  encoded  and transmitted to them by the delivery agents like teachers (Cobb,  Wood,  
Yackel,  Nicholls,  Wheatley, Trigatti & Pertwitz, 1991). The theory postulates that knowledge 
is active rather than passive. That is to say that learning mathematics must be an active process. 
Learning of mathematics requires a change in the learner, which can only be brought about by 
what the learner does and what activities he or she engages in. Constructivists focus on 
learners‘ abilities to mentally construct meaning on their own environment and create their 
own learning. According to Bybee, Buakwalat, Luero, Matsu and Mclinery (1989), the 
constructivists‘ view of learning is linked to three (3) related ideas. These include prior 
knowledge, student learning styles and concentration of teaching on depth and understanding 
rather than on breadth of coverage and knowledge of vocabulary. To constructivists, all 
humans have the ability to construct knowledge in their own minds through the process of 
discovery and problem solving. They argued that as far as learning is concerned, the teacher 
who is the instructor should try to encourage students to discover principles by themselves. 
This involves collaborative learning where groups of students interact and help each other to 
learn.  
 Piaget (1965) as cited by Yinyinola (2008) offered a constructivist view of 
mathematical learning saying that children have a natural curiosity. According to him, children 
have an inherent desire to find patterns and resolve problems which according to Piaget (1965) 
is the essence of mathematics. Piaget further explained that the construction of mathematics 
understanding was the heart of real development of mathematical knowledge by interacting 
with their physical and social world.  
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 As an example of this, (Cobb, Wood, Yackel, Nicholls, Wheatley, Trigatti & Pertwitz, 
1991) describe an effort to teach second graders to count by tens. Rather than telling the 
students the principle directly, the task of counting objects bundled in sets of ten was assigned 
to the groups of students.  The groups discovered that counting by tens is more efficient than 
counting by ones.  Building mathematical curriculum around such techniques could help 
students transfer knowledge and express better attitudes about mathematics. The Vygotsky 
(1978) states that learning occurs during actual problem solving, joint activity or shared task 
definition with others.  When adult or well experienced teacher enhances learning, scaffolding 
occurs. This has been found not only to produce immediate knowledge of results, but also to 
instill the skill necessary for independent problem solving in the future.                    
 
2.2.2 Ausubel’s Theory of Organisation of Knowledge 
 Theories about how students learn are concerned with the justification of the way a 
teacher develops, selects materials, chooses instructional techniques and presents the given 
task (Emeke, 2002). The study was on Ausubel theory of organization of knowledge. Ausubel 
(1978) states that knowledge is hierarchically organized that new information is meaningful to 
the extent it can be related (attached, anchored) to what is already known. The theories of 
constructivist and Ausubel were employed by the researcher of this study since the 
instructional strategy used in the study is in line with constructivists‘ theories. It is in 
systematic stage and one stage links or relates and anchors to the other as advocated by the 
Ausubel‘s theory. A flow chart in chapter three illustrates the relationship between Ausubel‘s 
theory of organization and researchers‘ instructional strategy. In the study, the learner‘s prior 
knowledge is the knowledge acquired within the learner‘s real world experience, gathered 
through collection of instructional materials within school environment, home and community. 
In teaching, the prior knowledge experience is linked up with the teaching process and then the 
outcome, which is the achievement or the result of prior-knowledge and instruction.  The 
instruction is organized in a spiral connection, spanning from one level to another. Ausubel 
(1973) distinguishes between meaningful learning and rote learning and how the previous 
knowledge or experiences of the learner affect the retention of the learned mathematics 
concepts (Ausubel, 1960). To Ausubel, the learner‘s prior knowledge serves as an 
organizational framework within which new ideas and facts are situated. He explains that the 
new knowledge to be learnt can only be meaningful to the learner if there are relevant concepts 
in his memory to which the new material can relate. He refers to knowledge as what the learner  
knows or should know and advocates that this should be systematically arranged in an 
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hierarchical order in such a way that it will be presented from known to unknown.  
 On structural presentation of knowledge, Ausubel (1963) identified two types of 
concepts called Superordinate and Subordinate. Superordinate concept refers to building block 
of ideas to which subordinate ideas are closely linked. The implication of Ausubel‘s theory in 
this study is that Mathematics teacher should organize and present mathematics instruction in a 
systematic and hierarchical manner bearing in mind the individual differences among learners 
in the classroom situation.  
It is believed that mathematics is one of the hierarchically structured subjects which range from 
the most elementary level to the highest one and it is in a vertical spiral connections. Therefore, 
a well organized mathematics instruction may lead to positive attitude and which in turn 
increased performance. It is necessary for the teacher of mathematics to employ this theory in 
the classroom situation for benefits of our students.    
 
2.2.3 Theory of Causation (REBT)   
 In the early 1950s, Ellis, a clinical psychologist, became disillusioned with the slow 
progress of his students. He observed that his students tend to get better when they change their 
ways of thinking about themselves, their problems and the world. To him, an instruction   that 
focuses directly on the students‘ beliefs would facilitate learning. On the process of thought, 
Ellis describes Rational Emotive Behavioural Therapy (REBT) as the theory of causation 
which he refers to as a comprehensive theory of human behaviour. It is a combination of 
biological, psychological and social factors that are involved in the way human beings feel and 
behave. Ellis believes that almost all human emotions and behaviours are as a result of what 
people think, assume or believe about themselves, other people and the world in general. To 
Ellis, it is what the students believe about situations they face not the situations themselves that 
determine how they feel and behave.  
Ellis advocates that the students‘ belief system is seen to be a product of both biological 
inheritance and learning throughout life. A useful way to illustrate the role of cognition in this 
theory is by using Ellis ‗ABC model. In this framework, ‗A‘ represents an actual event or 
experience, and the student‘s inferences or interpretations as to what is happening. ‗B‘ 
represents the ‗evaluative‘ beliefs that follow from these inferences. ‗C‘ represents the 
emotions and behaviours that follow from those evaluative beliefs. Here is an example of an 
emotional episode experienced by a low-achieving student who tends to misinterpret the 
actions of his/her teacher. (This example is from the researcher‘s previous school.  It was an 
incidence that happened between a student and the mathematics teacher)  
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1
A   activating event-what happened? 
Teacher passed me at the school premises without responding to my greetings.  
2
A   Inferences about what happened: 
He does not respond to my greetings because I fail his mathematics test.  
B:  Beliefs about A: 
I am a failure as a student-so I must be worthless.  
C:  Reaction  
Emotions: depressed 
Behaviours: avoiding mathematics class- resulting to poor performance. 
It is noted that ‗A‘ alone does not cause ‗C‘, ‗A‘ triggers off ‗B‘, and ‗B‘ then causes ‗C‘. 
The implication of Ellis to mathematics teachers is that students should be counselled 
on the consequences of negative thoughts about mathematics instruction letting them know that 
the way each individual thinks concerning any issue affects the way he/she responds to the 
issue. The mathematics teacher ought to know that students could interpret the same life event 
differently, leading to many and varied emotional and behavioural consequences. Such 
consequences could lead either to positive or negative attitude, which invariably can either lead 
to enhanced mathematics performance or poor performance. 
Furthermore, the implication of Ellis‘ theory in this study is that the mathematics 
teachers should make instruction delivery eclectic by bearing in mind individual differences 
among the students in the classroom situation. Ellis viewed knowledge as a consequence of 
thinking patterns which he advocated should be improved through a well structured 
counselling training skills (Ellis, 2003).  In view of the objective of this study, the researcher 
employed the Ellis‘ theory as a theoretical framework for this study to counsel the low-
achieving students on the importance of mathematics and its related discipline using Cognitive 
Behavioural Therapy (CBT).  Counselling is a comprehensive system for ensuring that all 
students receive academic and psychological support needed for their intellectual development, 
success in school and capacity to move onto postsecondary education or a career path Asuru 
(2006).  Research on counselling, reports that both components (academic and psychological 
needs of students) are necessary to achieve high–level academic achievement as stipulated by 
Ellis‘ (2003) theory- biopsychosis. Students who often believe that mathematics is bored and 
unimportant need to be motivated through appropriate counselling training, which can lead to 
academic performance, especially in the area of mathematics. Therefore, adequate counselling 
skill is a necessary focus in developing positive attitude in students towards mathematics. This 
is necessary because mathematics is the gateway to all scientific and technological 
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development of any nation (Awofala, 2002).                                     
 
2.2.4  Operant Conditioning 
 Operant conditioning theory is based upon the idea that learning is a function of change 
in overt behaviour. Changes in behaviour are the result of an individual‘s response to events 
(stimuli) that follow the emission of the behaviour. This, in turn, will determine the 
reoccurrence or otherwise of such behaviour. Skinner (1938) and Thorndike (1932) as cited by 
Yinyinola (2008) are at the forefront of this proposition.  Woolfolk (1998) in Yinyinola (2008) 
reports that Thorndike established the basis for operant conditioning while Skinner developed 
the concept. A response produces a consequence such as defining a word or solving a 
mathematics problem. When a particular Stimulus-Response (S-R) pattern is reinforced 
(rewarded), the individual is conditioned to respond. The learner will repeat the desired 
behaviour, if the behaviour is followed by positive reinforcement. A positive reinforcer is 
anything that strengthens the desired response. Positive reinforcement or reward could be 
verbal praise such as ‗very good‘, ‗a good grade‘ or a feeling of increased accomplishment or 
satisfaction. 
 A behaviour that is followed by pleasant consequence (reinforcement) tends to be 
repeated, while a behaviour that is followed by an unpleasant experience (punishment) tends to 
be discarded. The poor performance of students in a learning task from the operant point of 
view therefore might be as a result of the fact that students‘ response to classroom activities are 
not followed by pleasant consequences (reinforcement) but rather by unpleasant consequences. 
For example, when a student does not respond to teacher‘s mathematics questions correctly, 
the teacher calls him ‗olodo‘ (giving a negative label to the student).  In a situation, where 
good performance of students in class activities is not rewarded or punishment is meted out for 
making a trial, the rate of participation in the classroom activities can be diminished.       
 
2.2.5  Modelling or Social Learning Theory  
 Social observational learning refers to changes in behaviour, thinking, or emotions that 
occur through observing another person (Woolfolk, 1998). Bandura (1975) as cited by 
Yinyinola (2008) who developed the theory and viewed modelling in learning as being made 
up of both initiating and identifying with the stimulus figure being modelled. This means that a 
change in behaviour or thinking is brought about through the process of observing the way and 
manner a model exhibits it. The observation of such would lead to later performance by the 
observer. The observer behaviour in this context may be desirable or undesirable.   
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 The poor performance of students in Mathematics from the observational learning 
theory point of view is as a result of student‘s exposure to undesirable role models. That is, 
students who perform poorly in mathematics have observed the performance from others. 
Hence, the multiplying effects. Oden (1999) sees mothers as resource persons in language 
learning for girls who are always at home with their mothers. If the mother does not develop 
positive attitude towards mathematics and has been failing the subject while in the school, the 
child may do the same. This evidently shows that exposure to undesirable role model is 
responsible for poor performance.  
 Exposure to a role model can affect the behaviour of observer in at least three ways 
(Gage & Berliner, 1979) as cited by Gesinde (2004). These include learning new behaviour, 
having already learned behaviour facilitated, and having already learned behaviour inhibited or 
disinhibited. This therefore, implies that exposure to wrong role model may influence poor 
performance of students in Mathematics.     
 
2.2.6  Cognitive Behaviour Therapy (CBT) 
 Cognitive Behaviour Therapy is a psychotherapy based on modifying cognitions, 
assumptions, beliefs and behaviours, with the aim of influencing disturbed emotions. The 
general approach developed out of behaviour modification, cognitive therapy and Rational 
emotive Behaviour Therapy, and has become widely used to treat various kinds of neurosis and 
psychopathology, including mood disorders and anxiety disorders. Cognitive Behaviour 
Therapy was developed from the ideas of Albert Ellis, the founder of Rational Emotive 
Behaviour Therapy, and Aaron Beck, the founder of Cognitive Therapy. The techniques and 
ideas it uses involve identifying distorted or erroneous thinking patterns and learning new ways 
of  thinking which correct the distortions and  lead to a more balanced life. The Words of a 
Greek Philosopher, Epictetus further states that: ―Men are disturbed not by things, but by the 
view which they take of them‖ (Carter, 2012). Despite the male-dominated language, this is 
one aspect in which women and men seem to be similar. Whatever one‘s gender, one may 
discover that if one draws negative conclusions from situations, about oneself, the world in 
general or one‘s future, one feels bad and finds it hard to take constructive positive steps to 
resolve the problems.  
 Cognitive BehaviouralTherapists opined that maladaptive behaviours such as anxiety, 
fears, stress, depression, worry, anger, complexies, cognitive distortions, negative thought 
patterns and dysfunctional attitude can be eliminated in individuals and rational thinking, 
positive thoughts patterns, effective living and learning new ways of thinking which correct the 
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distortions and lead to a more balanced life can be employed. Cogntive Behaviour Therapy 
(CBT) is a way of talking about: how you think about yourself, the world and other people, 
how what you do affects your thoughts and feelings, is a technique that relies on the use of 
logic and reason. Carter (2012) pointed out that negative and distorted thinking patterns are 
some other peculiar problems identified in individuals. One of the notable characteristics of the 
client (low-achieving students) is distorted Cognition.  Examples of such distortions include: 
self–defeating verbalization, irrational thinking, wrong interpretation, misconceptions, wrong 
attributions, overgeneralization and catastrophization (Carter, 2012)  
 CBT is described as a form of intervention that people have demonstrated to produce 
positive effects on individuals by effectively addressing the distortions. Psychologists refer to 
CBT as the way in which people interpret events, perceive themselves and judge their abilities 
(Ellis, 2003). Ellis argues that thousands of people live unhappy life because of irrational 
beliefs that ‗cloud‘ their interpretation of events.  Cognitive Behaviour Therapy interventions 
would be concerned with helping students realize three things: how the students‘ thought 
patterns affect behaviour, how they can take control of these thought patterns and how they can 
apply interventions to effect behaviour change (Brigman & Campbell, 2003).  Another 
approach that comes under CBT by Miechenbaum is self-instructional training. He teaches 
individuals how to think logical and positive thoughts in stressful situations, instead of 
plunging themselves into self-defeating verbalization monologues (Worthman, Loftus & 
Weaver, 1999) in Faloye (2009). The elements of this approach to treatment include:  
 Cognitive rehearsal and validity testing 
 Writing in a journal and Guided discovery 
 Modelling of appropriate behaviour and Homework therapy. 
  Systematic positive reinforcement (Nakate, 2011)  
 
 In addition, cognitive skills –based therapies seek to help individuals understand that 
they can control their behaviour- and their lives-by learning more effective, less antisocial 
ways of thinking in a process known as ―cognitive behavioural therapy‖. Knowledge about 
social skills, problem-solving and other behavioural control may teach individuals to control 
their anger, adjust their negative attitudes to difficult situations and understand how some of 
their thinking patterns may be distorted.    
Cognitive Behaviour Therapy can either be short-term or long-term depending on the 
intensibility of the problem. The session can also be run between 6 to 18 sessions.  The CBT 
process begins with identification of self-defeating verbalization and irrational thought patterns 
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and cognitions that remain problematic for the clients through record keeping by the clients, 
therapist or both. CBT identified some illogical ways of thinking which include: mind reading, 
overgeneralization, wrong attribution, name-calling (Carter, 2012).  The CBT therapist uses 
several approaches such as  Cognitive rehearsal and validity testing, Writing in a journal and 
Guided discovery, Modelling of appropriate behaviour and Homework techniques, Systematic 
positive reinforcement to modify behaviour (Nakate,2011).  
 The particular therapeutic techniques vary within the different approaches of CBT 
according to the particular kind of problem issues, but the common ones may include keeping a 
diary of significant events and associated feelings, thoughts and behaviours; questioning and 
testing cognitions (validity testing), assumptions, evaluations and beliefs that might be 
unhelpful and unrealistic, gradually facing activities which may have been avoided; and trying 
out new ways of behaving and reacting.  CBT concentrates on clients‘ present problems in 
contrast to the emphasis on past history that is a prominent feature of psychoanalyst Freud 
oriented therapies.  Reinecke, Dattilio and Freeman(2003) averse that Cognitive Behaviour 
Therapy has been successfully applied in the treatment of obsessive compulsive Disorder using 
classical conditioning through extinction  (a type of conditioning) and habituation. The use of 
CBT has also extended to children and adolescents with positive results. It has been applied to 
the treatment of major depressive disorder, anxiety disorder and symptoms related to trauma 
and posttraumatic, stress disorder and social phobia. Effectiveness of CBT has been validated 
in a group setting for the treatment of youth and child anxiety. The CBT has been used with 
children and adolescents to treat a variety of conditions with good success (Reinecke, Dattilio 
& Freeman, 2003). CBT has a good evidence base in terms of it‘s effectiveness to the 
treatment of variety of conditions, complex posttraumatic stress disorder and chronic 
maltreatment in children and adolescents.  
 The CBT is applicable to the present study in the sense that maladjustment /anxiety is 
seen as resultant from wrong perceptions/misconceptions, feelings, beliefs and poor 
performance in mathematics which the clients (low-achieving students) have registered in their 
cognition about mathematics(geometry included) through interactive experiences within their 
social environment. To bring about adjustment, it is required that the client would need a 
reorientation, re-ordered perceptions and views about self, others and the society (Graham, 
2005). It is pertinent to note therefore that for students to be fully internalized, positive self-
verbalization, develop positive attitude and enhance performance in mathematics, there is the 
need for restructuring of distorted cognitive perception and views of the clients (Reinecke, 
Dattilio & Freeman, 2003) about mathematics generally and geometry in particular. Hence, 
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this theory (Cognitive Behavioural Theory) is pertinent to the present study.                     
 
2.3     Low-Achieving Secondary Students (LASS) 
 The students who are performing below academic standard are described as low-
achieving students (Ford, 1996). They are students whose achievement lagged behind their 
intellectual potential, present a serious problem to the parents, society and finally to the nation.  
Instead of being the contributing members they turn out to be social problem and get involved 
in the most common social malaise-students unrest ((Riley, 2000). Low-achieving students 
tend to have poor basic skills, low academic self-concepts, poor auditory and less than average 
school attendance rates (Delisle & Berger, 1990).  
 In schools, low-achieving students may be isolated. They usually receive much 
criticism from teachers, peer mates and parents at home.  They feel that their academic 
freedom is restricted and that they cannot cope with the academic environment.  For such 
children, active emotional education in addition to teaching may be necessary and teachers 
need to seek the service of counsellors.  Delisle and Berger (1990) averse that low-achieving 
students could perform significantly better if they receive instruction that capitalizes on their 
learning style preferences.  
 
2.4 Teaching and Learning of Geometry in Secondary School using Out-of-Class-
Activity (OCA) Strategy        
Geometry is a branch of mathematics that deals with the measure and properties of 
points, lines, curves and surfaces. Students can solve problems from other fields easily when 
they represent the problems geometrically. In our daily life, we indulge in thinking, reasoning, 
debating, convincing and analyzing. Geometry teaches us the basic skill of logical thinking and 
reasons. It is true that the concept such as point, line, bisect, angle, parallel lines can not be 
encountered in everyday living, but through these concepts, the power of reasoning and logical 
thinking is presented. By going through the process of reasoning and proving, we could tackle 
numerous everyday activities that require us to be critical person that could not be swayed by 
opinions of men no matter how many hold such opinions. Geometry still seems to be a dreaded 
subject among the students because the students have the impression that geometry does not 
become real but it is an abstract subject (NCTM, 2000). This dreading of the subject probably 
leads to poor performance in geometry.   
Some of the causes of problems encountered by students in geometry can be attributed 
to the teaching methods employed by the teacher (Almeida, 2000; Baynes, 1998; Gfeller, 
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2005). Most teachers prefer the traditional method because it gives them opportunity of 
completing the prescribed syllabus at the end of the session. In traditional educational systems, 
the students are assigned a passive role. They listen to the teacher, absorb what the teacher 
says, and regurgitate what the teacher has said at a later time. Teacher is the presenter of 
information and he/she is in the centre of the classroom. There is a clear boundary between the 
teacher and students and the interaction between them is highly limited. Geometry is a branch 
of mathematics that deals with the measure and properties of points, lines, curves and surfaces. 
Geometry forms the building blocks of engineering and technical graphs. It affords students 
opportunity of developing their deductive thinking through formal axiomatic systems, which is 
applied in other fields of learning. Geometrical skills are important requisites for 
technologically inclined careers that a developing country like Nigeria needs. For students to 
acquire a sound reasoning, logical thinking capacity, the teacher has to employ acceptable and 
appropriate teaching methods, which according to Constructivist theory of learning will make 
students active, creative and critical in problem- solving. This method should empower the 
students by ensuring that there is proper acquisition of appropriate knowledge and skills. That 
is to say, that the teacher should refrain from the type of method that makes the students 
passive listeners. Instead, the geometry teacher should resort to more constructive approach.   
Previous research findings have shown that teachers affect students‘ learning and that 
the classroom learning environment and teacher differences also affect students‘ achievement 
(Fraser, 1994; Rawnsley, 1998). It has also been established that effectiveness in learning 
geometry is the result of the classroom learning environment, teacher influence on students‘ 
learning, and the quality of the teacher (Wetzel, 2009). Effectiveness in the teaching of 
geometry has been the subject of considerable theorizing. Many studies attempted to make 
connection between mathematics and the real world using several methods and several 
treatments. For example, Duatepe-Paksu (2009) as cited by Abdelfatah (2010) carried out a 
research to investigate the effects of drama-based instruction on students‘ geometry. The 
results showed, in comparison to the traditional teaching, that drama-based instruction on 
students‘ geometry, geometry thinking levels and attitudes toward mathematics and geometry 
made learning easier and provided students with more opportunities to experience geometric 
concepts and problems in a social contex, collaborative learning environment and motivations 
to learn the included new geometric knowledge. Duatepe-Paksu stated that in terms of 
Vygotsky‘s ideas, learning is shaped both by internal processes and social interaction. Drama 
method provides active communication among students and between students and teachers.  
 
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Yet, it seems that it is not enough to use everyday mathematics simply as a source of 
motivation in the beginning of geometry class. Civil (2002) argued that by going deeper into 
mathematizing everyday situations, students may be losing  what made them motivated in the 
first place. That was one of the motives of the present study. The study was aimed at 
examining the effectiveness of out-of-class-activity plus instruction in enabling students to 
gain a better understanding of geometrical concepts, enhance performance and develop 
positive attitude towards geometry. The goals of geometry, according to Kerr (1979), should be 
to have students develop useful intuition and knowledge about shapes and their relationships. 
And for this intuition and knowledge to be useful, it should be strongly tied to the real world. 
This is why the subject should be taught in a way that stresses its relationship with the real 
world. This could be done through the use of various materials like Akpan (1987) suggests the 
use of visual representation of concepts and relations. This he says seems to have a stronger 
and more enduring impact than mere verbal explanation. Various methods could also be used 
to achieve this objective of geometry, that is, it is being taught to stress its relationship with the 
real world.   
 
2.4.1 The Concept of Out-of-Class-Activity (OCA) Strategy:  
One of the main objectives of teaching and learning geometry is to prepare students for 
practical life. Students could develop their logical and analytical reasoning while learning 
geometry. And all these could help them to develop ability to solve problems in other fields of 
life. It is believed that elementary geometry should be the study of objects, motions and 
relationships in a spatial environment (Clements & Battista, 1986). Therefore, the students‘ 
first experiences with geometry should emphasize informational study of physical shapes and 
their properties and have as their primary goal the development of students‘ intuition and 
knowledge about their spatial environment. Subsequent experiences should involve analyzing 
and abstracting geometric concepts and relationships in increasing formal settings. This is 
necessary to equip them adequately with prior experience of the students which is needed in 
the learning of geometrical concepts in order to achieve a holistic and meaningful learning in 
mathematics generally.  
Therefore, Out-of-Class-Activity (the model of Outdoor Educational Activities (OEA) 
has been defined by different researchers based on their individual perspectives. Brookes and 
Richard (2004) as cited by Olatundun (2008) proposed that the measuring of outdoor 
educational activities is relative to time and place. Hattie, Marsh, Neil and Richards (1997) 
posited that Outdoor Educational Activities(OEA) (model of out of class Activity) is when 
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small groups of people participate in organized adventurous activities in natural settings and 
primarily use  themselves as the resource for solving problems. Edward (2002) as cited by Ford 
(2003) defines OEA as means of curriculum enrichment whereby the process of learning takes 
place out of doors.  Kuh (2003) defines students‘ engagement as the time and energy students 
devote to educationally sound activities inside and outside the classroom, the policies and 
practices that institutions use to induce students to take a part in these activities.   
Out -of -Class -Activity Strategy is therefore an experiential method of teaching and 
learning geometry with the use of hierarchical levels (recognition, analysis, ordering, deduction 
and rigor).  According to van Hiele (1984) in Abdelfatah (2010), he claims that when students 
learn geometry, they face difficulties in progressing from one of the five sequential and 
hierarchical levels (recognition, analysis, ordering, deduction and rigor) of geometrical 
thinking to a higher one if they do not have appropriate experience at the lower level. The 
relevance of this OCA to the present study can be summarized in the assumption that skipping 
one level in the teaching and learning processes might lead the students to enter a vicious circle 
of negative attitudes and difficulties in geometry class. The Strategy is student-centered 
instructional approach which is based on the assumption that learning is a process of 
knowledge construction that occurs through interaction with the social world, which situates 
the child (Van Glassenfeld, 1986) as cited by Erinosho (2004). The present study used OCA 
strategy to teach low-achieving students geometry concepts in order to keep the students at or 
above performance. The strategy employed makes the students very active because they learn 
by doing whereby the students were actively engaged in searching for knowledge.  The value 
of the strategy is its potential to appeal to students‘ instinctive interest and curiosity through 
the use of activities that involved measuring real life geometrical concrete objects, construction 
of geometrical shapes, solving problems and asking questions. The activity calls for 
cooperation of various kinds, the strategy (OCA) appeals to the students‘ self assertion.  
Creative work was encouraged which fostered self-expression and friendly environment. The 
experiences gained through these activities form the basis of sound reasoning at all stages in 
development.  
Each situation provides opportunities for dialogue, discussion and the expression of 
ideas in both practical and written form. At all levels of education, the range of intelligence is 
wide.  It therefore means that methods used should be varied enough to give scope to both low-
achieving as well as high achieving students. They must be varied to provide for academically 
as well as practically minded students. Out-of-Class-Activity gives opportunities to the low-
achieving students and can also be used by the high achieving ones. OCA allows for more 
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teacher student contact and interaction which provides a base for social contact. Low-achieving 
students developed self-confidence and improved attitudes through their own participation. It 
engages the students through participation, social interaction and enrichment; allowing 
students to experience geometry in the real world environment, enriches students‘ experiences, 
promotes experiential learning that facilitates understanding of some complex ideas in 
mathematics generally, and introduces excitement into geometry learning. Because all the 
students experimented, experienced and carried out activities during the out- of- class- activity, 
they built up lasting body of knowledge and develop powers of reasoning and acquiring 
attitude.  
In out-of-class-activity, students developed their ability to respond effectively to 
mathematical problems and physical challenges both individually and in cooperation with 
others. For effectiveness in geometry learning, students must be provided with opportunities 
for active interaction with their real world and engaging in meaningful activities within this 
context that stimulate their senses of excitement. More often than not, geometry teachers 
neither have the vocabulary nor the breadth and depth of experience to offer their students 
entry into the community of geometrical thinking outside of the school classroom (Gfeller, 
2005; Refaat2001). Nevertheless, the bottom line for efficiency in geometry learning is that 
activities in the in-and-out-of-class activity strategy should go hand-in-hand. As information is 
passed along or transmitted in class, strategies for helping students to make sense out of new 
information should concurrently be designed in-and- out of class, providing students the 
opportunity to use information in in-class knowledge and out- of class investigation can 
improve achievement, attitude and understanding of students (Olagunju, 2006).  
 
2.4.2 Summary of the related principles of the social and cognitive strategy in the 
teaching and learning of geometry in the present study                   
 In summary, as cited by Simon (2004) and Refaat (2005) in Abdelfatah (2010), the 
following points summarize the related principles of both social and cognitive constructivism 
in the present study context. 
 Knowledge should be actively constructed by students, 
 Learning is both an individual and social process. 
 Learning is a process in which sense-making of the real world takes a part. 
 Language plays an important part in learning and sharing thoughts.  
 Learning should occur and be enhanced with situated meaningful activities. 
 Students‘ interpretations should address the process of constructing knowledge and 
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beliefs. 
 Students should be motivated and purposely participate in order to achieve new 
knowledge. 
 Learning situations should recognize the cognitive structure to assimilate the new 
knowledge with the previous knowledge (Simon, S Refaat,2005) as cited by Abdelfatah 
(2010).    
 
2.5 Out –of- Class- Activity Strategy and Academic Achievement   
 Olatundun (2008) investigated the impact of outdoor educational activities on primary 
school pupils‘ environmental knowledge and attitude, interaction effects of location of pupils‘ 
residence and gender on pupils‘ knowledge of and attitude to selected environmental issues 
and problems. A 2x2x2 pretest, posttest, control group quasi-experimental factorial design was 
employed for the study. The participants were four hundred and eighty (480) primary five 
pupils drawn from twelve (12) schools selected through simple random sampling technique 
from three Local Government Areas of Ibadan in Oyo State.  The results of the study indicated 
that there was a significant main effect of treatment on pupils‘ environmental knowledge and 
attitude to environmental issues and problems. These findings lend credence to the findings of 
Brookes (2004), Smith (2002), Stine (1997) and Knapp (1996) on significance of outdoor 
educational Activities above the conventional teaching method.           
 Duffy (2001) conducted an evaluative study on a summer school programme that used 
a balance, accelerated and responsive approach to literacy in situation. Ten under-achieving, 
second-grade students participated in word study, guided reading, book talks, and aloud with 
the teacher, and wrote and read their stories. Analysis of the results revealed that students 
improved their word identification abilities, became more fluent in oral reading and writing, 
increased their instructional reading levels, and became more strategic in reading 
comprehension. The study reported that students also developed more positive attitudes 
towards reading and had more positive perceptions of themselves as readers. 
Harlow and Baenen (2001) conducted an evaluation of the Wake Country, North 
Carolina, and Out- of- School Time (OST) strategy. The study had an academic summer school 
component followed by school year programming with academic counselling, mentoring, and 
Saturday school and community service. The seventh graders involved in the study 
demonstrated performance gains (d=.16) and reduced drop out when compared to a group of 
similar students who had not attended summer school. Another similar study, the Pride 
Programme in Newport News, Virginia, was studied by Grimim (1997). The Pride study has a 
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residential summer school and school year component. During the school the participating 
middle school students attended academic classes and the field trips and were mentored by 
public school staff as well as Newport News shipbuilding, a partnership business. However, 
the standardized test results for the participants showed no gain in mathematics performance. 
Malaty (1994) established Mathematics clubs for primary school pupils and designed 
activities that could help them learn geometric concepts.  He found that geometric activities in 
Mathematical clubs tended to offer pupils an opportunity to think and develop their geometric 
thinking.  Furthermore; they guided these children to discover new concepts, new terms and 
new symbols. They learnt to solve problems and to reflect on their solutions. In other words, 
they learnt to analyze and reason. Through these clubs, the pupils thus participated in the 
activities and had a lot of time to explore various dimensions to many problems. This can be 
seen that for meaningful learning of geometric concepts, teachers must use activity centered 
methods, which involve a lot of 2-D and 3-D instructional materials. 
Duatepe (2004) investigated the effects of Drama Based instruction on seventh grade 
students‘ achievement on geometry, retention of achievements, Van Hiele geometric thinking 
level, attitude toward mathematics and attitudes toward geometry compared to the traditional 
teaching. The study was conducted on three seventh grade classes from a public school in the 
2002-2003 academic year, lasting 30 lesson hours (seven and a half weeks). 
The data were collected using geometry achievement test (angles, polygons, circle, 
cylinder), the Van Hiele geometric thinking level test, mathematics and geometry attitude scale 
and interviews. The quantitative analyses were used with two multivariate covariance analyses. 
The results showed that drama based instruction had a significant effect on students‘ geometry 
achievement, retention of these achievements, Van Hiele geometry thinking level, mathematics 
attitude and geometry compared to the traditional teaching.    
Hanna (1986) conducted a study on gender-related differences in mathematics 
achievement of the middle school students. Eight-grade students in Ontario, Canada, in one of 
her articles were used. The results of the study revealed that the mean percent of correct 
responses in geometry and measurement was slightly higher for boys than for girls, though the 
difference was minimal. Hanna explained that boys had some previous informal training 
through out-of-class activities that are not normally pursued by girls.  Examples of such 
activities are: following instructions for building models, reading charts and graphs. Hence, the 
differences in informal training could explain the differences in geometry achievement, 
especially in measurement. Similarly, McLean, Raphael and Wahlston (1983) who studied all 
geometry topics taught at, throughout the school years, support the idea that out-of-class 
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activities contributed to the differences in achievement between the sexes.      
2.6 The Concept of Group Counseling (CBT)  
 Group counselling is intended to help people (for example, the low-achieving students) 
who would like to improve their abilities to cope with difficulties and problems ( example, 
problem like mathematics) in their lives. In group counselling, the meeting is with a whole 
group and one or two counsellors can attend to the group. Group therapy focuses on 
interpersonal interactions, so relationship problems are addressed well in groups. The aim of a 
group counselling is to help with solving the emotional difficulties and to encourage the 
personal development of the clients (low-achieving students) in the group (Oladele, 2007) 
Group counselling is suitable for a large variety of problems and difficulties; beginning with 
clients who would like to develop their interpersonal skills and ending with clients with 
emotional problems like anxiety, depression. Group counselling expands the services of a 
counsellor since systematic counselling can be offered to more students. More insights, ideas, 
confirming messages and information may be shared in the group setting (Oladele, 2007). The 
group setting offers an opportunity for supportive environment. Anxiety, poor academic 
performance and hatred for mathematics can be reduced when students realize they are not 
alone with their concerns. Feelings of failure, anxiety, loss of confidence, and helplessness 
may be replaced by a sense of enhanced performance, positive attitude, self efficacy and sense 
of belonging. Achievement and hope can be a definite benefit of groups.  
 Counselling attempts to make students realize that their maladaptive behaviour and 
emotional disturbances are possibly related to or determined by what they say to themselves. 
For example, ―I can never pass mathematics‖. Ellis (2003) notes that human beings are both 
rational and irrational individuals. Emotional problems, Ellis emphasized, lie in illogical 
thinking. The thinking faculty of an individual plays significant role in the cognitive theory. 
For instance, a student‘s thinking influences what he or she observes or watches, which in turn 
influences his/her behaviour. According to Hall and Hughes (1989), Cognitive Behavioural 
Therapy (CBT) interventions in middle school were concerned with helping students realize 
three things: how their thought patterns affect behaviours; how they can take control of these 
thought patterns and how they apply interventions to effect behaviour change.  In view of this, 
the role of a counsellor is to find out why the students are not performing well academically or 
not being effective in their live activities /goals and render a therapy which would assist the 
students concerned to be more effective in coping with life challenges.    
 
 
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2.6.1 Counselling (CBT) and Academic Achievement  
Empirical studies have reported correlations between Cognitive Behavioural Therapy 
(CBT) intervention and increased academic achievement (Miranda, Webb, Brigman & Peluso, 
2007). They reported that achievement and behaviour are positively impacted by group 
counselling interventions that focused not only on these desired outcomes but also address the 
social and emotional dimensions of the participants. The Students Success Skill (SSS) is a 
cognitive Behavioural Therapy (CBT) based intervention that has been effective in closing the 
achievement gap in the mid to low-achieving students (Brigman & Campbell, 2003; Brigman, 
Webb, & Campbell, 2007; Campbell & Brigman, 2005; Webb& Brigman, 2006; Webb, 
Brigman& Campbell, 2005).  The SSS intervention is the one that has used CBT strategy to 
train small groups of low-achieving students in mathematics that meet once a week for 45 
minutes over an eight week period. The literature review was limited by the number of students 
nd
using CBT intervention solely with middle school students but in the present study, 2  grader 
low-achieving students were employed. Guidance programmes foster positive attitude towards 
school learning and work and hence, improve academic achievement. 
Venkatesh and Lissamma (2011) investigated the impact of Cognitive Behaviour 
Therapy on academic achievement in adolescent students. The sample for the study consisted 
of two hundred (200) adolescent, consisting of 100 males and 100 females.  The participants 
were equally assigned to treatment (50 males & 50 females) and control (50males & 50 
females) groups. The result indicated that there was a significant difference in the academic 
achievement between the experimental and the control groups. No significant gender 
difference was found.  
Fajonyomi (2001) investigated the effectiveness of the study skill counselling (SSC), 
Rational Emotive therapy (RET), and a combined treatment of SSC & RET in improving the 
performance of students in English language. The participants for the study who were 
randomly selected and assigned to the three experimental and control groups, were forty senior 
secondary school (SSII) students. The research design was pretest and posttest control group 
quasi-experimental design. The experimental groups were subjected to ten weeks training. The 
result of the finding revealed that there was a significant main effect of treatment.  The study 
further revealed that the three treatment modes have equivalent effect on student performance.  
Ch (2006) conducted an experimental study to examine the effect of guidance services 
on students‘ study attitudes, study habits and academic achievement. The sample of the study 
th
was drawn from the 9  grader of Government High School Karim Block, Allama Igbal Town, 
Lahore. Ten null hypotheses were tested in five subjects at 0.05 level of significance. The 
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results of the study indicated that the guidance services have significant effect on the students‘ 
study attitude, study habits and academic achievement.  Another study was conducted by 
Hudesman et al., (1986)  as cited by Ch (2006) to compare the impact of structured and non-
directive counseling studies on academic performance of Low-achieving students. Results 
indicated that students in structured counselling condition had higher GPAs (grade Point 
Averages) than those in non-directive counselling condition at the end of semester. 
 Turner and Berry (2000) conducted a large-scale study of the impact of psychological 
counselling on academic progress and retention. They compared retention and graduation rates 
for counselling center clients with rates for general student population both annually and across 
a 6-year period (academic years 1991-1992 through 1995-1996). The researchers examined  
five cohorts  of  students during this 6-year period, with the first cohort being followed over the 
course of the entire study. Using both objective and self-report measures, Turner and Berry 
provided strong support for the value of psychological counselling  in helping students in their 
decision to remain in school. Turner and Berry (2000) also reported that over the course of the 
entire study an average of 70% of the students reported that their personal problems were 
affecting their academic performance, and about 20% were considering withdrawing from 
school because of their personal problems. More than 60% of the students, who received, 
counselling, on average, reported that counselling was helpful in maintaining or improving 
their academic performance. It was found in addition that nearly half of the students reported 
that counselling helped them in deciding to continue being enrolled. 
 
2.7 Cognitive Behaviour Therapy (CBT) and Self-Efficacy        
 Earlier studies show that self-efficacy beliefs have varied influence on the overall 
functioning of the individuals, particularly their performance in the academic level.  According 
to Ormrod (2008), self-efficacy beliefs affect academic achievement through psychosocial 
influences. Students‘ achievement in arithmetic and in reading comprehension is predicted by 
one‘s perception of self efficacy (Ghosh, 2007). The findings of the study revealed that CBT 
was highly effective in enhancing the self esteem and Academic achievement in adolescent 
students.    
Hyun, Chun and Lee (2005) examined the effects of cognitive behaviour group therapy 
(CBT) on the self esteem, depression, and self-efficacy of runaway adolescents residing in a 
shelter in Seoul, South Korea. The results indicated that after the treatment, depression 
decreased and self-efficacy increased significantly.  Another study was carried out by Burleson 
and Kaminer (2005) on Youth substance abuse relapse prevention as a function of patients‘ 
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situational self-efficacy (SE), youth developed confidence to abstain from substance use in 
high risk situations. 
In the study conducted by Solomando, Kendall and Whittington (2008) on CBT, it was 
observed that CBT has a potentially important role in improving the mental health of children 
and adolescents.  McManus, Waite and Shafran (2009) in their study titled ―CBT for Low Self-
Esteem‖, described the assessment, formulation and treatment of a patient with low self-
esteem, depression and anxiety symptoms. The results of the treatment revealed large effect 
sizes on measures of depression, anxiety and self-esteem.  
Further studies were carried out on CBT by Suveg, Sood, Comer and Kendall (2009). 
They examined the changes in emotion regulation following CBT for anxious youth. The 
findings of their study showed that the treated youth exhibited a reduction in anxiety, increased 
self-efficacy and emotional awareness at post-treatment. Taylor and Montgomery (2007) 
evaluated the efficacy of CBT in improving self-esteem among depressed adolescents aged 13-
18 years. In their result they suggested that CBT might be an effective treatment for increasing 
global and academic self –esteem.           
 
2.7.1 Mathematics Self-Efficacy and Mathematics Achievement  
Research has been extensive on the relationship between self–efficacy and student 
achievement in academic settings (Marrat, 2005). Researchers have demonstrated that self-
efficacy beliefs are positively related to and influence mathematics achievement (Hodges, 
2003; Kabiri, 2003; Chanzadeth, 2001) and these beliefs mediate the effect of skills, previous 
experience, mental ability, or other self-beliefs on subsequent achievement (Pajares & Schunk 
2001). Furthermore, Bong and Skaalvik (2003) have indicated that higher self-efficacy is 
predictive of higher performance. That is, the role of self efficacy beliefs is more prominent 
than that of other factors in achievement.  
Collins (1982) as cited by Yinyinola (2008) identified children of high, middle and low 
mathematics ability who had, within each ability level, either high or low mathematics self-
efficacy. After the instruction, the children were given new problem to solve and an 
opportunity to rework those they missed. The result of the study indicated that within each 
level of ability, children who had the strongest belief in their efficacy were quicker to discard 
faulty strategies, solved more problems, chose to rework more of those they failed, held more 
positive attitudes towards the subjects and did so more accurately than children of equal ability 
who doubted their abilities.   
 
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 Pajares and Graham (1999) conducted a study to determine whether students‘ 
Mathematics self-efficacy beliefs make an independent contribution to the predictions of 
mathematics performance when other motivation variables shown to predict math-related 
outcomes are controlled. The participants for the study, who were two hundred and seventy 
th
three (273) 6  graders, were assessed both at the beginning and end of the school year across 
the following variables: Mathematics self-efficacy, mathematics anxiety, and Mathematics 
self-concept. The results of the study indicated that self–efficacy made a modest but 
independent contribution to the prediction of Mathematics performance. Mathematics self–
efficacy was the only motivation variable to predict Mathematics performance both at the 
beginning and end of the school year. The researcher concluded that there is strong evidence 
for a relationship between self-efficacy and Mathematics achievement. 
 In a study conducted by Kiamanesh, Hejazi and Esfahani (2004) to investigate  the 
predictive and mediational role of  self-efficacy beliefs and to identify the direct and indirect 
effects of mathematics self-efficacy, Mathematics self-concepts, perceived usefulness of 
mathematics, mathematics anxiety and gender on mathematics performance, the results of the 
path analysis revealed that mathematics self-efficacy was more predictive to mathematics 
performance than was mathematics self-concepts, perceived usefulness of mathematics or 
gender. Motivational beliefs, self-regulation strategies use and mathematics achievement. 
Similarly, Mousoulides and Philippou (2005), in their study to examine the relationship 
between motivational beliefs, self-regulatory strategies use and Mathematics achievement 
discovered that self-efficacy is a strong predictor of mathematics achievement.      
  Kabiri and Kiamanesh (2004) studied the role of self-efficacy, anxiety and previous 
Mathematics achievement in students‘ math performance. The participants were three hundred 
th
and sixty six 8  grade students (169 boys &197 girls).  They were randomly assigned to 
treatment and control groups, using multi-stage stratified technique. The obtained results 
revealed that prior math achievement had a stronger effect on mathematics performance than 
did any of the variables in the study. The results contradict the findings of Pajares (1996), 
Pajares and Kranzler (1995), since in these studies Mathematics self-concept had a stronger 
effect on Mathematics performance than did any other variables including prior math 
achievement.       
 
2.7.2 Mathematics Self-Efficacy and Attitude towards Mathematics 
Self-efficacy beliefs play an essential role in achievement motivation, interact with self-
regulated learning processes, and mediate academic achievement (Pintrich, 1999).  
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 Nicolaidou and Philippou (2003) conducted a study on relationships between students‘ 
attitudes towards mathematics, self-efficacy beliefs in problem-solving and achievement. The 
sample consisted of 238 fifth-grade students (99 boys and 139 girls) from eleven classes, from 
six primary schools in Cyprus, rural and urban. Three questionnaires were administered, 
measuring ATM, SE and achievement in problem solving. The analysis of the data indicated 
that attitudes and self-efficacy were correlated and both predicted achievement in problem-
solving. A stronger relationship was further indicated between efficacy and achievement. 
However, efficacy was a more powerful predictor than attitudes. No gender difference was 
found in any of the examined variables.  
 Bandura ( 1997) believes that when an individual works in a field, he develops a high 
self-efficacy towards it, becomes interested in it, and is willing to pursue his work in that 
particular field. Hence, he creates an internal motivation towards the task. It has also been 
reported that positive attitudes towards mathematics is mostly determined and predicted by 
their self-efficacy beliefs. Liu, Hsieh, Cho and Schallert (2006) conducted a study that 
implemented a computer-enhanced problem-based learning environment to investigate the 
relationships among students‘ self-efficacy attitude towards science and achievement. They 
found self-efficacy to be a statistically significant predictor of achievement as cited by Arizpe, 
Dwyers and Stevens (2006). 
 Randhana, Bearner and Landberg (1993) as cited by Tella (2009) reported that self-
efficacy is a mediator variable between mathematics attitude and mathematics achievement. 
Randhawa et al, (1993) adapted the Mathematics Self-efficacy scale for use with high school 
students and used NCES procedure to find that the composite self-efficacy score mediated the 
effect of a generalized mathematics attitude score on mathematics problem-solving. The 
criteria task used by the researchers- the solving of mathematics problems was conceptually 
related only to the problem subscale of the MSES. Many of the problems on the self-efficacy 
assessment also differed markedly from those on the achievement. Consequently, although 
generalized mathematics attitude had a strong direct effect on those of self-efficacy (beta =.64), 
they also had strong and direct effect on achievement (beta =.44) as did self-efficacy (beta = 
.32).  
 Pajares and Miller (1994), using path analysis, showed that efficacy in problem solving 
was more predictive of the achievement in mathematical problem solving than other variables-
mathematics anxiety, gender, mathematical background, mathematics perception and perceived 
usefulness of mathematics.      
 
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2.8  The Concept of Gender      
             Gender inequality in education has become a global phenomenon (Bordo,2001). The 
term gender has many overlapping meanings, and its meaning, still appears evolving. First, 
Achor, Imoko and Ajai (2010) described it as a socially ascribed attribute which differentiates 
feminine from masculine.  It is referred to as the social differentiation between maleness and 
femaleness or masculinity and femininity. This differentiation is socially constructed in social 
relations rather than on the basis of the biological characteristics of male and females.  The 
term gender is also sometimes used to refer to as an attribute of all human beings, that is, one is 
of the male or female gender.  In this second sense, gender is used interchangeably with sex as 
described thus. Sex refers to the physical or biological characteristics of males and females and 
as such, it is used as an attribute of all humans-one may be of the male or the female sex.     
 However, a number of studies have been conducted by various researchers (Adeyegbe, 
2000; Awofala, 2002; Osinubi, 2004; Bordo, 2001; United Nations Educational Scientific and 
Cultural Organization (UNESCO, 2003) on the influence of gender on mathematics 
achievement of students. This had led to series of divergent views on the influence of gender 
on the mathematics achievement of students. Many studies in Nigeria have shown that boys 
perform better than the girls in mathematics generally (geometry included) irrespective of the 
fact that they are taught under the same classroom condition (Etukudo, 2002; Ezeugo & 
Agwagay, 2000). Contrary to this, Agwagah (1993) had reported that female students perform 
significantly better than male counterparts. The findings of Agwagah (1993) were supported by 
Etukudo (2002). There are some researchers who reject the idea of sexual differentiation in 
ability. This group of researchers observed that there is no disparity in the performance of boys 
and girls (Gbodi & Laleye, 2006; Olagunju, 2001).  
Several explanations have been put forward for gender differences in mathematics. For 
example, The New Analysis of International Research (Science Daily,2001) opined that girls 
are not worse than boys in mathematics though boys are more confident in their mathematical 
abilities than girls. It further stated that girls are more likely to perform better than boys if they 
come from countries where gender equity is more prevalent.  According to Lee and Lockheed 
(1989),the gender difference borders on the maturation of female and marriage which leads to 
removal of girls from schooling, particularly in traditional cultures of Northerners that question 
the effect of education on subsequent role of female in family settings (Anderson and Bowman 
1982) as cited by Yinyinola (2008).  
 Benbow (1990, 1998) explains that biological differences are contributing factors to 
gender differences in mathematics. Republic (2001) believed that all students can perform 
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equally in a given task, irrespective of sex. Akinsola and Tijani (1999) assert that mathematics 
is not a male dominated subject as people assumed it to be, but for both sexes provided that 
both sexes are subjected to the same learning conditions.  It is not likely, therefore that if 
mathematics instructions are made relevant and interesting through appropriate access 
provoking strategies, females would perform as well as their male counterparts.  
 The absence of role models for the females, particularly in mathematics is a major 
reason for their inhibiting nature towards mathematics achievement, especially in geometry.  
The presence of role models, helps males feel that success in mathematics and science is both 
possible and legitimate. Girls are not given information about career possibilities requiring 
competence in advance mathematics, neither are they introduced to women role models with 
successful math careers. In general, role models can be an important factor in elevating a 
young person‘s aspirations.  At home, parents may unconsciously fail to provide support for 
their daughter‘s interest in mathematics, either by directing them elsewhere or by giving all 
their supports for the education of their sons.  Amelink (2009) suggests encouraging discussion 
of women mathematicians and scientists as this will provide girls with the opportunities to 
have female mathematicians as role models and lessen the male domain stereotype of 
mathematics. 
 Carr and Jessup (1997) aver that gender difference in the development of mathematics 
skills and knowledge are believed to emerge as a function of different experiences of both 
sexes in group setting, boys by their nature tend to dominate as a function of their interactions 
with classmates and teachers. It was explained that male demands more attention, complain 
more that they are not receiving enough and their teachers and female peers expect them to get 
it. Men dominate discussions even more as they get older, in some classes speaking as much as 
12 times longer than women (Krupnick, 1985). Even when females do participate in classroom 
talks, their approach may suggest to teachers they have less command over the subject matter 
than males (Wendy & Katherine, 1992). The dominance makes their approaches to 
mathematics become the preferred strategies in the classroom. The dominance as well as the 
preference for competition, (Carr & Jessup, 1997) remark, may push boys to acquire more 
complex strategies and meta-cognition. Girls are believed to be more concerned with pleasing 
and depending on teachers. The dependence leads to rote approach to mathematics. In addition, 
females believe that mathematics does not have any utility in their lives (Fennema & Sherman, 
1978). They see mathematics as unconnected to a relationship model of thinking. Even if they 
persist in taking mathematics courses, girls are apt to find that they do not like them, and liking 
a subject is a key to succeeding in it (Fennema, 2000). Another factor that has contributed to 
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gender difference in achievement is linked to the role of teachers in learning. In a classroom, 
teachers set the standard for discourse, their reliance on teaching methods that adhere to 
traditional norms and belief about gender differences that benefit only male students can create 
unfriendly environment for girls Amelink (2009). Teachers believing that participation is an 
indicator of learning are likely to ignore females because they participate less than males. 
Moreover, teachers are often unaware that they are concentrating more on teaching males 
because the process of classroom interaction is unconscious, and they respond automatically to 
student demands for attention. Amelink asserts that teachers should employ collaborative 
educational experiences that could utilize group work to impact math performance of females 
favourably; stating that teachers should be shaping the classroom experiences for both males 
and females so that both groups could respond to mathematics favourably.  
Yinyinola (2008) suggests that attributing Mathematics success to high ability is 
associated with expectations for future success and a willingness to approach new mathematics 
achievement situation. On the other hand, attributing failure to low ability is predicted to be 
associated with low expectation for future success and a desire to avoid future Mathematics 
achievement situation. Therefore, the implication of these for gender difference is that they 
affect future expectation and behaviour.   . 
 
2.8.1 Gender and Geometry Achievement                     
 The issue of gender differences in achievement has been the concern of many 
researchers across different domains (e.g., Halpern, 2000).  Most of the studies have reported 
the superior performance of boys over girls‘. Bessoondyal (2005) studied the gender difference 
in mathematics in Mauritius. The researcher administered a test consisting of multiple choice 
items and word problems from strands, number, algebra, geometry and probability to 
secondary level students. The findings indicated that boys performed significantly better than 
girls in overall test, also in separate strands of the test boys, outperformed girls in geometry.  
Battista (1990) conducted a study concerned with the spatial and geometrical thinking 
of students. The sample for the study consisted of 145 high school geometry students.  The 
participants were tested in four areas; spatial visualization, logical reasoning, geometrical 
knowledge, and geometrical problem solving. Battista (1990) found that males scored 
significantly higher than females on geometrical knowledge and geometrical problem solving.  
Similarly, El-Hassan (2001) in Lebanon found that, at the 13 grade in operation and geometry 
topics, males performed better than females. 
Ma (1995) conducted a study on a sample of 960 students from both senior and junior 
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classes in four countries namely: British Columbia, Ontario, Hong Kong,and  Japan. The aim 
of the study was to investigate gender differences across different education system in domain 
of algebra and geometry. The study utilised data from the second International Mathematics 
and Science Study (SIMSS). The findings indicated a significant gender difference among 
senior students.  It was further revealed that males outperformed females in the geometry 
subtest.  
However, some studies have found that girls are performing well in geometry than 
boys.  For example, Ma,moon (2005) found that females had significantly higher  scores  than 
males for subtest of Mathematical Proof in his test of mathematical thinking. TIMSS (2007) 
study which was undertaken in 59 countries for grade 4 and 8 students in  target content areas 
in mathematics for grade 4 were number, geometric shapes and measures ,data displayed and 
for grade 8 number, algebra ,geometry data and chance .  It is reported for both grades that 
girls had higher achievement on average in geometry. Girls had higher achievement in 15 
countries and boys in 6 countries.  
Healy and Hoyles (2000) conducted a study on Proof conceptions in Algebra by 
surveying high-attaining 14 and 15-year-old students and concluded that gender of the students 
was significantly associated with achievement where girls obtained higher scores than boys in 
construction of proofs.  In TIMSS (2003) Jordanian females had a significantly higher average 
score than males consistent with seven other countries in geometry.  
Senk and Usiskin (1983) conducted a study, using a large sample of 2699 in 99 
different classes to investigate any gender difference s in the understanding on geometrical 
proof for senior high students ranging from 7 grades to 12 grades. Three forms of a proof test 
were devised so that performance on a greater number of proofs could be analysed. The 
students were tested on their knowledge of geometry at the beginning of the year and their 
understanding of three types of standard geometry proofs at the end of the year. The 
researchers found that though boys had a slight higher score but no consistent pattern of 
statistically significant differences favoring either sex on any form of proof tests was found.   
Huntley (1990), studied the effect of diagram formats on performance on geometry.  
The researcher administered a 32 experimental, multiple-choice geometry items in two pretest 
versions: one version did and one version did not provide a relevant diagram. Log linear 
analysis of the data shows that there were no significant differences between males and 
females students performance on these items.   
 Adegoke (2002) investigated the Teacher influence as determinant dependent-prone 
students‘ learning outcomes in Senior Secondary School geometry in Ibadan South East local 
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government area of Oyo state. The research design employed for the study was A 2x2x3x3 
factorial design. The participants for the study were 864 secondary school students. They were 
randomly selected and assigned to treatments and control groups. The data generated for the 
study were subjected to analysis of covariance. The result indicated that there was no 
significant difference between male and female participants in their achievement in geometry.  
 There is no single direction regarding gender difference in the performance of students 
in geometry. Some studies support the superior performance of the male over female in 
geometry and mathematical proofs (Bessoondyal, 2005; Battista, 1990; El-Hassan, 2001; Ma,‘ 
1995) while some other report better performance in geometry by female students or no 
difference e.g. (Ma‘moon,2005; TIMSS,2007; TIMSS,2003; Senk and Usiskin, 1983; Huntely, 
1990). 
 
2.8.2 Gender and attitude towards Mathematics.   
 Research findings seem to pay limited attention to gender differences, with respect to 
attitude towards mathematics (ATM) and gender (Ma & Kishor, 1997). In addition, boys and 
girls report equal confidence in their math ability during elementary school, but by high school, 
boys are more confident than girls (Pajares and Graham, 1999).   
 Nicolaidou and Philippou (2003) conducted a study on relationships between gender, 
students ATM and their performance in problem-solving. The participants were 238 fifth-grade 
students (99 boys and 139 girls) drawn from eleven classes, from six primary schools in 
Cyprus, rural and urban. Three questionnaires were used, measuring gender, ATM, SE and 
achievement in problem-solving. The analysis of data indicated that no gender difference was 
found in any of the examined variables. That is, gender was not significantly correlated with 
any of the other variables-attitude or performance. The result of Shaw and Doan (1990) 
indicated no gender difference in achievement and attitudes of participants towards science.  
In a related study, Fadia and Menucha (2005) examined the structural model of 
th
Mathematics achievement of two culturally different groups of Jewish and Arab 8  graders in 
terms of 5 learners-related variables, namely, gender, epistemological beliefs, self-efficacy, 
attitudes, and Mathematics anxiety. Multi-group structural modeling analysis indicated that the 
goodness of fit of the hypothezised structural model and the total effects of Mathematics self-
efficacy and epistemological beliefs were comparable in both groups. The two groups differed 
in the effects that gender, attitudes toward Mathematics, and Mathematics anxiety exerted on 
Mathematics achievement. They also diverge in terms of the amount of variance in 
Mathematics achievement that the 5 learners-related variables accounted for.  
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Odunusi (1994) as cited by Yara (2009), in assessing the attitude of some science 
students towards modern orientation in science found that students‘ attitude to science is 
negative while gender and class level of the students did not significantly influence students‘ 
attitude towards science. Burstein (1992) as cited by Yara (2009), in a comparative study of 
factors influencing mathematics achievement found out that there is a direct link between 
students‘ attitudes towards mathematics and student outcomes. He also found that 25% in 
England and 26% in Norway accounted for the variation in students‘ attitude towards 
mathematics that were due to student gender.  
 Sungur and Telkaga (2004) investigated the effects of gender on attitude and 
th
achievement on reasoning ability and on the human circulatory system concept in biology. 47  
grade students participated in the study. Questionnaires were administered to the students. The 
results revealed that there was no statistically significant mean difference between boys and 
girls with respect to attitude and achievement in biology.  
Ojo (2003) investigated the relative effects of cooperative learning, self-regulatory, 
combined self-regulatory and cooperative strategies; and the conventional teaching on senior 
secondary school students‘ achievement and attitude towards Mathematics.  A 4x3x2x2 
pretest, posttest randomized control group quasi-experimental factorial design was employed 
for the study.  The participants were five hundred and eighty six (586) senior secondary school 
one (SS1) students drawn from 12 schools selected through simple stratified random sampling 
technique from twenty-two public schools located within Ibadan north local government area 
of Oyo state.  The findings of the study indicated that there were no effects of gender and self-
regulatory ability on students‘ achievement in Mathematics.   
            Mohamed and Waheed (2011) conducted a study to find out the students attitude and 
gender difference towards mathematics in a selected school of Maldives. 200 students were 
chosen from grade 9 and 10. Two questionnaire instruments were administered to the students 
regarding their personal confidence to mathematics and perceived usefulness of mathematics. 
The data were analyzed using statistical package for social Science (SPSS) and t-test to find 
significant difference between attitude and gender. The results show that the students‘ positive 
attitude towards mathematics is medium and there is no gender difference in their attitudes.  
Similarly, Nicolaidou and Philippou (2003) conducted a study on relationship between 
students‘ attitude and gender towards mathematics in problem-solving. 238 fifth (99 boys, 139 
girls) from eleven classes, from six primary schools; in Cyprus, rural and urban. The three 
questionnaires were administered to the subject measuring Attitude toward mathematics, self-
efficacy and achievement in problem-solving. The analysis of data indicated there was no 
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gender difference in the attitudes of students. Other studies that found no significant difference 
between attitude towards mathematics among male and female students are Mohd, Mahmood 
and Ismail (2011); Kogce, Yildiz, Aydin and Altindag( 2009).  
 
2.9  The Concept of Attitude  
  According to Yelland (2000), attitude towards a subject affects achievement.  Attitude 
is a learned pattern of manners that is developed through one‘s environment (Thompson, 1993) 
as cited by Duatepe (2004). Attitude is a central part of human identity. Everyday people tend 
to love, hate, like and dislike, agree and disagree etc. All these are evaluative responses to an 
object which bring the definition of attitude as a summary evaluation of an object of thought 
(Bohner & Wanke, 2002).  It represents one‘s feelings toward given circumstances and affect 
one‘s reaction to a particular situation. Aiken (2002) defined attitude as a learned 
predisposition or tendency on the part of an individual to respond positively or negatively to 
some objects, conditions, or concepts. Also, Akinsola and Olowojaiye (2008) believe that the 
students‘ attitudes toward a subject determine their success in that subject.  
Odubunmi (1998) sees attitude as a favourable or unfavourable reaction towards some 
experiences, situations or activities as a result of the way such an individual perceives and 
conceptualizes them. Attitude is synonymous to the opinion one holds about a thing. Attitudes 
related to mathematics include liking, enjoying, and interest in mathematics, or the opposite, 
and at worst math phobia (Ernest, 2004). Ma and Kishor (1997) offered the definition of 
attitudes toward mathematics as an aggregated measure of liking or disliking of mathematics, a 
tendency to engage in or avoid mathematical activities, a belief that one is good or bad at 
mathematics, and a belief that mathematics is useful or useless.  Attitude is often considered in 
educational research since the development of a positive attitude is desirable because of its 
association with achievement (Yelland, 2000). Ma and Kishor (1997) indicated there is a 
general belief that children learn more effectively when they are interested in what they learn 
and that they will achieve better in mathematics if they like mathematics.  
Attitudes are influenced by three components according to the Multicomponent model 
of attitude (Eagly & Chaiken, 1993). Several factors play a vital role in influencing the 
attitudes of students toward mathematics. These factors are categorized into three. The first 
factor is associated with the students themselves: these include students‘ mathematical 
activities, students‘ achievement scores, self-efficacy, self-concept and motivation (Kogce, 
Yildiz, Aydin, & Altundag, 2009). The second factors include teacher and school factor which 
include teachers‘ content knowledge, teaching topics in relation to real life examples, 
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personality of the teacher and classroom management. The third one is the factor relating to 
home background of the students which is associated with educational background of the 
parents, occupation and parental aspirations (Kogce et al, 2009).      
A number of researchers have demonstrated that there is a significant correlation between 
attitude towards mathematics and academic achievement of the students (Davis, 2002; Ma & 
Kishor, 1997; Duatepe, 2004).  However, it cannot be concluded that positive attitude always 
causes high achievement in mathematics. For example, Kiely (1990) showed that on average a 
small number of pupils who were not good enough in mathematics obtained high scores in the 
attitude test. Another study suggested that extremely positive or negative attitudes tend to 
predict mathematics achievement better than more neutral attitudes cited by Bergeson, Fitton, 
and Bylsma (2000) in Duatepe (2004).  
Ma and Kishor (1997) conducted a meta-analysis on 113 studies on relation between 
attitude and achievement of mathematics. They found that the overall mean effect size was 
statistically significant, relatively weak at the primary school and stronger at the secondary 
school level.  Ma and Kishor (1997) propose a wider definition; they conceive Attitude 
towards mathematics as an aggregated measure of a liking or disliking of mathematics, a 
tendency to engage in or avoid mathematical activities, as belief that one is good or bad at 
mathematics, and a belief that mathematics is useful or useless‖. Ma and Kishor (1997) also 
found that many children begin schooling with positive attitudes toward mathematics; these 
attitudes, however, tend to become less positive as children grow up, and frequently become 
negative at the high school. 
Bergeson, Fitton, and Bylsma (2000) opined that students develop positive attitudes 
toward mathematics when they see mathematics as useful and interesting. Similarly, students 
develop negative attitudes toward mathematics when they do not do well or view mathematics 
as uninteresting. Capraro (2000) found that attitude towards mathematics has a positive strong 
relation with the geometry content knowledge. 
 The development of positive mathematical attitudes is linked to the direct involvement 
of students in activities that involve both quality mathematics and communication with 
significant others within a clearly defined community such as a classroom. The middle grades 
are the most critical time period in the development of student attitudes toward mathematics. 
Students‘ attitudes toward mathematics are quite stable, especially in Grades 7–12 (Bergeson, 
Fitton, & Bylsma, 2000). Ezike (2007) gave age 10-12 years as the most significant for attitude 
formation. Marlon (1974) as cited by Ezike (2007) gave some recipe, which if adopted by the 
teacher could help to develop positive attitude among pupils towards themselves, other things 
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or people. These include:  
(a) Interesting learning activities  
(b) Individual differences should be adequately considered and  
(c) Providing meaningful learning activities.  
In conclusion, the previous studies have not provided consistent findings concerning 
the relationship between attitudes toward mathematics generally and mathematics 
achievement. 
 
2.10 Appraisal of Literature  
 Low-achieving students present special difficulties when considering any type of 
teaching approach. Apparently, the act of grouping students by ability level can have and by 
itself have an influence on attitudes, self efficacy and eventual achievement of students 
(Adeyoju, 1997). A child who is labeled as a low achiever may experience detrimental 
consequences that last throughout their entire school career. In support of this effect, research 
has indicated that low- achieving students tend to score lower and have lower self-efficacy in 
comparison to others on standardized tests (Reis & McCoach, 2000). Given the current level of 
their performance, it is unlikely that remedial work will be sufficient to close the gap between 
these students and their higher achieving peers, especially when that remediation is focused on 
mathematics learning (Civil, 2006).  Recent studies have suggested that out- of- school-Time 
activity (OST) strategy can improve the mathematics competence of low-achieving students 
(McREL, 2003). Educators see potential using OST strategies to keep their student at or above 
performance standards. In essence, OST is being used to provide low-achieving students with 
an opportunity to catch up to their peers and for improved performance. Silver and Lane (1995) 
were able to demonstrate that middle school students from low-income disadvantaged 
backgrounds were able to outperform their peers in a demographically similar school when 
they participated in the Quasar project, a programme that emphasized reasoning problem -
solving, and understanding.   
Research by (Bonotto & Basso, 2001; D‘Ambrosio, 2006) also showed  that instruction 
that emphasized  out-of-class-activity (OCA) strategy builds on students‘ understanding while 
increasing their desire to learn mathematics and provides more meaningful learning 
opportunity for students struggling with mathematics. Impact of out –of-class-activity has been 
shown to foster mathematics achievement and positive attitude towards mathematics for all 
rd th
students in the 3  and 6  grade student (Lauer et al, 2004).    
 
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 Most research efforts on instructional strategy have focused on experimental studies 
that engage students only on academic activities inside the classroom. Learning and personal 
development occur as a result of students engaging in both academic and non-academic 
activities, inside and outside the classroom (Astin, 1993; Lohr, 2004; Pascarella & Terenzini  
2005). Previous works done by researchers suggest some of the innovative methods of teaching 
Science and Mathematics. These include Cooperative Learning (Omosehin, 2004), problem 
solving (Iroegbu, 1998); Concept Mapping (Okebukola, 1990) which could improve the 
students‘ academic performance and enhance their mathematics concepts.  However, these 
methods, as laudable as they might be, have not considered the needs of students who are 
performing below the academic standard (low-achieving students). Further more, most of these 
studies do not create situations in which students examine the connections between their 
studies and life outside the classroom and to apply what they are learning. In many cases, the 
needs of these students are identified by the teachers who believe that the deficiencies of the 
students cannot be addressed using the traditional method of instruction.   
 One option being considered is the use of Out-of-Class-Activity (OCA) strategy. 
Educators see potential in using OCA strategy to help the low- achieving students improve 
mathematics performance. There is every possibility that out- of- class- activity strategy has 
not been used in Nigerian Mathematics classrooms at the time of this research work. For these, 
this study can fill the existing gap. 
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CHAPTER THREE 
METHODOLOGY 
 
 This chapter presents information on research design, population, sampling procedure 
and sample, instrumentation, procedure for carrying out the experiment, data collection and 
data analysis procedures.  
 
3.1 Research Design 
 A 3x2x2 quasi-experimental pre-test, posttest control group design was adopted for the 
study. The pretest, posttest control group design was adopted because the design has been 
recognized for its ability to establish cause and effect relationship. It is also known for its 
potential for controlling all threats to validity, so that a cause-and-effect relationship may be 
established (Ogunsanwo, 2003; Yinyinola, 2008).  The   treatment conditions are: A1 (Out-of-
Class-Activity + instruction), A2 (Group Counselling Strategy + instruction), and A3 (the 
Control group, which received instruction only). The moderating variables are: Mathematics 
Self-efficacy (MSE) and gender. MSE varies at two levels: low mathematics self-efficacy and 
high Mathematics self-efficacy. Gender also varies at two levels: that is male and female.  
 
3.2     Outline of Design  
A brief summary of the outline of the design is symbolically shown in figure 3.1  
 
Figure 3.1:Pre-test, Post-test, Control group, Experimental design. 
A1: O1  X1 O2 
A2: O1 X2 O2 
A3: O1 X3 O2 
Where:  
A1, 2   = represent experimental groups.  
A3   = represents control group. 
O1 = represents pre-test scores  
O2 = represents post-test scores  
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X1 = represents OCA with instruction  
X2 = represents GCS with instruction 
X3= represents Control Group with instruction only. 
 
Table 3.1:  3x2x 2 Factorial Designs  
 Mathematic self-efficacy(B) Total  
Low MSE (B1) High MSE (B2)  
Gender (C)   
 Male (C1) Female (C2) Male (C1) Female (C2)  
A1 A1 B1 C1  A1 B1 C2 A1 B2 C1 A1 B2 C2 40 
N= 11 N = 6 N = 13 n=10 
A2 A2 B1 C1 A2 B1 C2  A2 B2 C1 A2 B2 C2  30 
N = 5 N = 7 N = 10  n = 8 
A3 A3 B1 C1  A3 B1 C2  A3 B2 C1 A3 B2 C2  40 
N = 10 n =12 N = 8 n = 10 
       26       25       31       28 110 
 
3.3 Variables in the study  
 The following variables were involved in the study.  
 
3.3.1 Independent variable:  Instruction strategy operating at three levels: 
3.3.1.1 Out-of-Class-Activity Group (out- of- class -activity +instruction)   
3.3.1.2 Counselling Group (group counselling strategy +instruction) 
3.3.1.3 Control Group (which received instruction only) 
 
3.3.2 Dependent variables          
The two dependent variables are:  
3.3.2.1 Achievement in Geometry  
3.3.2.2 Attitude towards Geometry  
 
3.3.3 Moderator Variables:  
3.3.3.1 Mathematics Self-efficacy varying at two levels:   
(i) Low   
(ii) High  
3.3.3.2 Gender: Varying at two levels 
(i) Male  
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(ii) Female  
 
3.4 Population   
 All low-achieving Junior Secondary school students in Ibadan formed the population 
for this study. 
 
3.4.1 Participants   
The participants for this study consisted of one hundred and ten (110) low-achieving 
Junior Secondary Two (JS2) students (57males and 53females). The ages of the participants 
ranged between 12 and 18 years. The mean and standard deviation of their ages were 14.34 and 
1.60 years, respectively. The demographic information about the participants is presented in 
Table 3.2 
 
Table 3.2:  Information About the 110 Participants Involved in the study.  
Variable  Distribution  Number  Percentage (%) 
Age  12-14 63 57 
15-17 45 41 
18-20 2 2 
Gender   Male 57 52 
Female  53 48 
Self-efficacy Low 51 46 
High  59 54 
 
The choice of JS2 students was based on the following reasons. 
The second year of the Junior Secondary School is a crucial year in the life of Junior 
Secondary School students. This is because at this stage, the students have studied some 
Mathematics content enough to be able to respond to questions given to them by the 
researcher. The set of students are not preparing for immediate external examinations (BECE), 
unlike the JS3 students, they could participate effectively in the research.  Any positive effects 
that the treatment has, could be fed-back into the system since they still have sufficient time in 
the school to use whatever they gain to their own advantage. And if any group is negatively 
affected by the treatments, they still have about two years in secondary school for necessary 
remediation.  
The preclusion of JS3 students who were supposed to be beneficiaries to the 
programme was based on the fact that they were conscious of the prescribed Basic Education 
Certificate Examination (BECE). Teachers on their own side are equally anxious to complete 
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the prescribed syllabus, even at the expense of depth and comprehension.  
Again, most secondary school authorities do not allow their final year students to take part in 
research studies. 
 
3.5 Sample and sampling procedure 
  One hundred and ten (110) low-achieving secondary school students (LASSS) 
participated in the study. They were selected out of 247 students contained in the intact classes, 
113 were identified as low-achieving students based on their performance in the selection test. 
However, 110 students were finally selected to participate in the study having met the 
inclusion criteria of:  
(i) volunteerism  
(ii)  Parental consent.  
 Multi-stage random sampling procedure was adopted in the study. Three Local Government 
Areas (LGAs) were randomly selected out of the existing five LGAs in Ibadan metropolis. 
From the three LGAs thus selected, two schools were randomly selected from each LGA, 
thereby making a total of six (6) schools that were finally selected for the study. The researcher 
assigned the first LGA as experimental group I, the second LGA selected was labeled as 
experimental group II while the third LGA selected was tagged as control group III. This was 
done to avoid filtration of information thereby controlling for hawthorne effect.  
 
The distribution of the schools and the number of students selected for the experiment are 
presented in Table 3.3 below: 
 
Table 3.3: Distribution of schools and students used for the study 
Ibadan Total No. of Junior  No. of selected No of Selected 
secondary schools Junior Secondary junior secondary  
schools Two Low-achieving 
students  
Ibadan North  51 2 30 
Ibadan North West  37 2 40 
Ibadan South East  36 2 40 
Total  124 6 110 
 
3.6 Instrumentation  
  For the purpose of collecting relevant data for this study, the following instruments 
were employed: 
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i.  Students‘ Selection Test  (SST) 
ii.  Achievement Test in Geometry (ATG)  
iii.  Mathematics Self Efficacy Scale (MSES) 
iv.  Geometry Attitude Scale (GAS)   
 Each scale used was preceded by a section (section A) that required the participants to 
enter their demographic information.  
 
3.6.1 Students’ Selection Test (SST) 
The Students‘ Selection Test was a multiple-choice cognitive Mathematics 
achievement test developed by the researcher to identify low-achieving students. The items 
included the topics in Geometry which the participants had done on perimeter of plane shapes, 
properties and areas of planes. The initial number of test items was thirty-five. The test was 
given to mathematics teacher in the junior class to go through and make suggestion and 
modification. This was done to ensure the content validity of the instrument. The suggestion 
and modification as well as the result of the item analysed carried out on the instrument 
reduces the total items on the test to twenty (20). The test was given to Mathematics experts to 
go through and make corrections to make it possess content validity. Item analysis was further 
carried out which reduced the number of the test items to twenty. SST has two sections. 
Section A contained personal data while section B contained test options which ranged from A 
to D. The reliability of the instrument was carried out by administering the scale on a sample of 
30 students who did not take part in the study.  The test-retest reliability coefficient obtained 
after two weeks interval was .70.   
 
3.6.2  Achievement Test in Geometry (ATG)  
Achievement Test in Geometry (ATG) was constructed and validated by the researcher. 
It consists of thirty Multiple Choice Questions (MCQ) which were aimed at making decision 
on evaluation of treatment procedure. Initially, the researcher constructed sixty items. The test 
was given to five Mathematics experts who determined the degree to which the test served as 
an adequate sample of the area of measure.  The test was further subjected to item analysis to 
ascertain the suitability or otherwise of each item of the test. The necessary suggestions from 
the experts as well as the results of the item analyses helped in the deletion of some items on 
the scale thereby reducing the items on the test to the present 30 items.  The mean difficulty 
and discrimination indices obtained for the final test were 0.58 and 0.51 respectively.  The test 
items could be judged to be suitable for the class it was designed for. 
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The test was thereafter administered by the researcher on a sample of sixty (60) Junior 
Secondary two (JSII) low achieving students that did not take part in the study. The test retest 
reliability coefficient after two weeks was 0.81.  The items were generated across the three 
cognitive domains (knowledge, comprehension and application) using the scheme of work for 
JS2 Mathematics (from the section of geometry). The three levels of cognitive domains were 
employed because of the academic level of the participants. The result of how the items of the 
test were generated is displayed in Table 3.4. 
 
Table 3.4: Table of Specification for Geometry  
Content  Knowledge Comprehension Application Total No. of 
30% 40% 30%  questions 
Identification of 3-Dimentional 1,  25 4,  8  26    5 
objects  
Surface area of cubes & Cuboids  13  9,  12 19,  21 5 
Surface area of cylinder & cone   20,  28     6,  7 16    5 
Basic properties of pyramid & 24, 30 2,  5 29 5 
sphere 
Volume of cube and cuboids   3  14, 15 10,  11 5 
Volume of cylinder & cone 27 17,  18 22,  23 5 
Total 9 12 9 30 
 
3.6.3 Mathematics Self-efficacy Scale (MSES)  
Mathematics self-efficacy scale (MSES) was administered to the participants prior to 
the treatment. This was done to assess their level of Mathematics self-efficacy. The MSES 
developed and validated by Marat (2005) was adapted by the researcher. It comprised two 
parts:  
Part one dealt with demographic information of the participants.  
Part two included nine sections, each assessing self-efficacy in Mathematics on a range of 
specific dimensions.  The participants responded on a five-point Likert scale responses options 
of not well at all, not too well, satisfactory, pretty well and very well.   
The maximum score obtainable was 345, while the minimum score obtainable was 69. 
The higher the score, the more Mathematics efficacious the respondent is. The MSES was 
recently revalidated by Yinyinola (2008) on a sample of 50 Nigerian students. The test-re-test 
reliability coefficient obtained after two-week interval was 0.85.  
 
 
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3.6.4   Geometry Attitude Scale (GAS)  
Geometry Attitude Scale (GAS) developed and validated by Alvaro (1973) was adapted 
to obtain information about the attitude of students towards Geometry. GAS had sixty items, 
drawn on a five-point Likert scale response options of strongly agree (SA), Agree (A), 
Undecided (U), Disagree (D) and Strongly Disagree (SD). Positive statements were scored as 
5,4,3,2, and 1 and negative statements were scored as 1, 2, 3, 4 and 5. The items rated 3 
retained their positions.  Alvaro reported KR20 reliability coefficient of the scale as 0.96. The 
Alvaro‘s attitudinal scale was modified as follows: the scale was confined to geometry by 
replacing mathematics with geometry in all the statements of Alvaro. The double-barrel 
statements such as ―I prefer sets of mathematics problems that are all alike rather than sets 
having different kinds mixed‖. Now written as; I prefer sets of Geometry problems that are all 
alike rather than sets having different kinds mixed.  The items were made short because long 
statements can be boring and do not appeal to the respondents.  Another point was that the 
wordings of the statements of the scale were made explicit, hence, there were no reason for 
misinterpretation.  For example, ―I often forget how to do one kind of geometry problem after I 
have worked on other kinds‖.  The total score for all the items constituted the index of attitude.       
For the purpose of revalidating the instrument, the test-re-test reliability was carried out 
on a sample of 50 J.S.II low achieving students that were not taking part in the study. The 
reliability coefficient obtained after two weeks interval was 0.73. 
 
3.6.5  Researcher’s Instructional Guide in Geometry (RIGG)  
Researcher‘s Instructional Guide in Geometry (RIGG) was a note of lesson prepared by 
the researcher and which was used by the mathematics teachers in the selected schools to teach 
participants geometry in both the experimental and control groups. The RIGG was vetted by an 
experienced WAEC mathematics examiner before being used.  
 
3.7 Procedure for the experiment  
 The following steps were taken while carrying out this study. The concerned authorities 
of the selected schools were met and permission was sought by the researcher and it was 
granted. A two-day training programme was organised by the researcher for the teachers in 
different groups according to the treatment conditions. They were selected based on the 
following conditions:  
(i) They must be graduates of mathematics.  
(ii) (ii) They must have taught for 3 years  
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(iii) (iii) They must be professional counsellors with a B.ed in Counselling and 
Mathematics.  
(iv) They must have had the experience of counselling for 3years.   
 
Table 3.5: Shows Training Time-Table for the Teachers   
Day session Activity 
1 1 The researcher met with the teachers of experimental groups (1&2) for 
general discussion. This discussion centered on the problems of teaching 
and learning geometry in secondary schools as highlighted by WAEC 
Chief Examiners‘ Reports as well as research findings.   Hence the need 
for an intervention. The prepared manual was introduced.  
2 2 The teaching commenced with the researcher doing the demonstration 
teaching to the teachers. The teaching involved a topic each from the 
experimental groups 1 & 2 manuals. The experimental group 1 teachers 
were given the opportunity to carry out micro teaching as well, after which 
they were corrected. The counsellors in experimental group 2 were also 
given the hypothetical case to handle because counsellors do not teach but 
help students to solve problems.     
2 3   Discussions followed after the micro teaching. Teachers were allowed to 
comment about the problems they encountered and the researcher gave 
some suggestions about how to overcome their problems during the 
subsequent lessons. Questions were asked from the teachers and more 
clarifications were made by the researcher on the topics treated.     
 
The trained teachers were eight research assistants, consisting of 2 male teachers,4 
female ones and 2 female counselors.  The professional counsellors with the knowledge of 
Mathematics/ Guidance & Counselling were employed by the researcher due to the nature of 
the counselling training (Mathematics/ Counselling) that were involved in what they would 
deliver to the participants. Secondly, the professional counsellor therefore had the necessary 
skills and qualification required for the training which the school counsellor might not have. 
Most of the times, the school counsellors were classroom teachers picked up at random by the 
school principals simply because the teacher had the little knowledge of counselling or because 
he/she studied counselling in Nigeria College of Education.  Based on the above reasons the 
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researcher employed the services of the professional counsellors for the training of the 
experimental group two (II) participants in the study.  However, all the research assistants were 
trained on how to use the prepared treatment packages given to them.   
During the first week of the training programme, the following instruments were used 
to collect baseline data on all the participants in the three groups with the help of the research 
assistants. Students‘ Selection Test (SST),  Achievement Test in Geometry (ATG) 
Mathematics Self Efficacy Scale (MSES) and Geometry Attitude Scale (GAS)  
Students‘ Selection Test (SST) was administered to all the students in the selected JS2 
arms in the selected schools. Scores obtained on the selection test were used in grouping the 
participants into low and high achieving students based on the first quartile. Scores collected 
from MSES were only used to group the participants on the basis of their level of Mathematics 
self efficacy (low and high) based on the first quartile. Any participant who scored below the 
first quartile was regarded as having low mathematics self-efficacy and any one who scored 
above the first quartile was regarded as having high mathematics self-efficacy.  
          One hundred and ten participants out of two hundred and forty-seven were used for the 
study. Experimental Group II consisted of 30 participants instead of 40 like in the case of 
Experimental Group1 and Control Group.  This was done following the suggestion of 
researchers like Borg and Gall (1983) as cited by Oladele (2001) who claimed that in group 
counselling, it is desirable to have a maximum of 15 cases.  15 participants were selected from 
each of the two schools selected for counselling group and making a total of 30 participants for 
counselling group.  
Instruction commenced in all the groups in the second week of the training. During the 
next six weeks, the geometry content of Junior Secondary two (JSII) curriculum from which 
the concepts of geometry were chosen, was covered using a lesson per week period, each 
period lasting forty (40) minutes. The two treatment groups met once a week- Tuesday and 
Thursday respectively. The training took place during break period after which the participants 
went back to their classroom and received their normal lesson by the teacher (the research 
assistant) on the topic prepared by the researcher on the Teachers‘ manual for that particular 
week .The take-home assignment stated in the Teachers‘ manual were often done after the 
training period at home since the 40 minutes were not enough for the activities and learning. 
The take-home assignment was corrected by the teacher based on the answers provided by the 
researcher. This was not part of the assessment used for data collection for this study.          
All the geometry concept materials for the activities for the experimental groups were 
supplied to the teachers on weekly basis to ensure that no prior practicing took place before the 
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time for which they were necessary. While the training was going on, the researcher moved 
round the sampled schools for supervision, to ensure that the teachers followed the Teachers‘ 
manual judiciously. In the Control Group, the participants were taught geometry instruction 
only, using Conventional method.  The training was conducted on a period per week for each 
of the three groups, spanning over a period of eight weeks. 
The eighth week of the training was used for collection of the posttest data using ATG 
and GAS. Both pre and post tests were administered in all the groups by the teachers, assisting 
to collect the question papers and administer. The treatment packages for the three groups are 
presented below apart from the general procedures discussed above.  
 
3.7.1 Experimental Group 1 (OCA+ instruction) 
Out of class activity Strategy (OCA)           
The group underwent an activity that infused out- of- class- activity with instruction.  
Week I: Selection of weak students, General orientation about the training and 
administration of pretest measures. 
Week II: Explanation of the goal of the training and identification of 3-Dimensional (3-
D) objects.  
Week I II: Exploration of the surface area of cube and cuboid.   
Week IV: Exploration and discussion on the surface area of cylinder and cone using the 
real life experiences of the participants. 
Week V: Discussion on the properties of the pyramid and sphere with concrete 
experiences of the participants. 
Week VI: Discovering of the volume of cube cuboid of 3-D objects  
 In out-of-class-activity strategy, the teacher used the relevant experiences of the 
participants to teach them simple geometry. How? The participants were asked to gather 
geometrical objects from their community.  The participants were also taken out of the class to 
collect geometrical objects within the school community by the guidance of the teacher. Such 
geometrical objects as plastic funnel, milo tins, blocks, etc were used to improvise mathematics 
laboratory.  Participants were led to measure the length, breadth and height of the geometrical 
objects. For example,  
Volume: The volume of a cuboid which is often taught by mere definition and memorization 
of equation was illustrated and taught linking the concept to the experience of the participants. 
The participants were led to measure the length, breadth and height of the block they collected 
out of the class.  Thus: Length – 6cm, breadth-3cm and height-1½cm. By using the dimensions 
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of the blocks, the concept of the volume of cuboids was studied and taught. The dimensions 
were used to teach the concept of volume of cuboids in the in-class, connecting the fact in the 
out- of- class- activity with corresponding idea in the in-class geometry content.  This brings 
about geometry curriculum that incorporates ideas from the out-of-class-activity to in-class 
knowledge. Doing so might provide rich real life and relevant experiences for finding solutions 
to mathematics problems generally. 
Week VII: Exploration and discussion of volume of cylinder and cone using real life 
experiences of the participants.  
Week VIII: Administration of post test measures using Achievement Test in Geometry (ATG) 
and Geometry Attitude Scale (GAS).  For more detail, see Appendix V 
 
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Experimental Group I 
 
 1 Selection of weak students, General 
 orientation about the training and 
administration of pretest measures. 
  
 2 Explanation of the goal of the training  
and identification of 3-Dimensional  
 
(3-D) objects. 
 
 3 Exploration of the surface area 
of cube and cuboid.   
  
 
 Out of 
 Classroom 
Exploration and discussion on Activity + 
  
the surface area of cylinder and instruction 
 cone using the real life 
experiences of the participants. 
 4        
 
Discussion on the properties of 
        Administration of post test 
the pyramid and sphere with  
8 measures using Achievement 
 concrete experiences of the   Test in Geometry (ATG) and 
participants. 5   
 Geometry Attitude Scale 
(GAS).  For more detail, see 
 
Appendix  
Discovering of the volume of 
  
cube cuboid of 3-D objects.  6 
  
 
Exploration and discussion of 
 volume of cylinder and cone 
 using real life experiences of 
the participants.   7                
 
 
     Figure 2 
 
Schematic Representation of Experimental Procedure: Out-of-Class-Activity (OCA) Strategy + 
Instruction. Adapted from Falaye, 1995. 
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3.7.2 Experimental Group II (GCS + Instruction) 
This group was exposed to counselling training by the professional counsellor using the 
counselling guide prepared by the researcher which was based on Cognitive Behaviour 
Therapy (CBT).  
Week I Selection of low-achieving students, General orientation about the training and 
administration of pretest measures  
Week II: Explanation of the goal of going to school to the participants.    
Week III:  Explanation of the concept of Cognitive Behavioural Therapy (CBT) and 
Identification of cognitive distortions.  
Week IV: Discussion and explanation of the concept of CBT using the technique of 
Cognitive rehearsal and Validity testing.  
Week V: Further explanation on the concept of CBT using the technique of writing in a 
Journal and Guided discovery as an aid to memory.  
Week VI: Discussion on Modelling and Homework as CBT techniques to increase the 
probability of the emission of the desired behaviour.  
Week VII: Further explanation on CBT technique of Systematic positive reinforcement 
using the case study of Felicia.  
Week VIII: Administration of post test measures using Achievement Test in Geometry 
(ATG) and Geometry Attitude Scale (GAS).  For more detail see (appendix VI)  
 
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Experimental group II 
 
 
 Selection of low-achieving students, 
1 General orientation about the training and 
 administration of pretest measures  
  
 Explanation of the goal of going to 
 2 school to the participants.    
  
 Explanation of the concept of Cognitive 
 
3 Behavioural Therapy (CBT) and  Identification of cognitive distortions.  
 
  
 
Group 
 Discussion and explanation of Counselling 
the concept of CBT using the + 
 technique of Cognitive. 4 Instruction 
 rehearsal and Validity testing.  4 
 Further explanation on the 
 concept of CBT using the 
technique of writing in a Administration of post test 
  Journal and Guided discovery. 5 8 measures using Achievement 
 as an aid to memory.  Test in Geometry (ATG) and 
 Geometry Attitude Scale.  
 Discussion on Modelling and (GAS).  For more detail see 
 Homework as CBT techniques (appendix VI) 
to increase the probability of the 
 emission of the desired. 6 
 behaviour. 
 Further explanation on CBT 
technique of Systematic 
 
positive reinforcement using the 
 case study of Felicia.    7  
 
 
     Figure 3 
Schematic Representation of Experimental Procedure. Group Counseling Strategy (GCS) + 
instruction. Adapted from Falaye, 1995. 
 
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3.7.3 Control group: Conventional Method 
 Participants in this group received instruction on geometry using only the conventional 
method, with the instructional guide prepared by the researcher. The conventional teaching 
strategy is described as expository in nature, involving teacher-student interaction through 
chalk and talk. To accomplish this conventional model, the teacher needs to evolve a certain 
mode of behaviour. A conventional teacher strives to be in control of her class; he/she assumes 
the role of an authoritative figure. The participants are usually expected to get permission from 
the teacher to speak. All participants are expected to be silent when the teacher is talking, and 
try to understand her explanation. The teacher uses the first fifteen minutes to introduce a new 
concept. He/she provides all the necessary facts on geometry concepts in question to the 
participants. He/she teaches, gives facts and opinions, and overviews of materials about the 
subject matter being discussed. The concept is then illustrated on the chalkboard by the teacher 
working out some related examples for ten minutes or more. 
At this stage, the participants proceeded with 'Seat work‘.  This is the part of the lesson 
when participants usually work at their desks, independently trying to solve problems similar 
to the ones worked out on the board by the teacher. During seat work, the teacher supervises 
the participants‘ works by making sure that the participants are working quietly so they do not 
disturb others. Finally, the discussion of the assignment usually means that the teacher is 
willing to work out solutions on the chalk-board. He/she involves the participants in working 
these problems by asking those questions so that the problem is really being solved as 
collaboration between participants and the teacher. During this time, the teacher expects the 
whole class to pay attention to what is being done. At the expiration of the eight weeks 
duration, the Achievement Test in geometry (ATG) and the Geometry Attitude Scale (GAS) 
were given to the participants as post-test measures. 
 
3.8 Control of Extraneous Variable 
 In an experimental study of this nature that involves the manipulation of independent 
variables by researcher to determine the effect of independent variable on the participants, it 
becomes imperative for the researcher to determine whether the observed differences or effect 
noticed in the study as represented by measured outcomes is actually not due to other 
extraneous variables within and without, participants, researcher, environment and 
methodology. The fact is that in an experimental study of this kind, a lot of contamination, 
which can distort the result of an experiment if the researcher does not adequately control the 
extraneous variables, is possible.  The researcher, having all these in mind therefore, controlled 
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the extraneous variable through the use of experimental design. A 3x2x2 factorial design, 
which guided against the possible variations that could occur in participants. This was 
forestalled through randomization.   
The assignment of treatment and control groups to schools employed, creates the 
necessary distance between the participating schools such that there was no filtration of 
information of treatment from one school to another, thereby controlling Hawthorne (novelty) 
effect. To ensure that the research assistants followed the treatment manuals religiously, 
thorough supervision was carried out by the researcher. In addition, little or no explanation was 
given by the teachers during the pre and posttests.  Since the language of the items were simple 
and straight forward and coupled with the fact that the researcher has provided all the 
necessary instructions at the beginning of the test, there was little or no quest for explanation. 
  The use of ANCOVA reduces the effect of selection bias and other possible sources of 
threat to validity. Best (1981) as cited by Yinyinola (2008) describes ANCOVA as an 
important method of analyzing experiments carried out under a condition which otherwise 
could be unacceptable. Differences in the initial status of the groups being compared are 
removed statistically so that they can be compared as though their initial status had been 
equated. In this case, the pretest scores were used as covariates in the analyses. 
 
3.9 Data analysis 
The data collected for the study were subjected to Analysis of Covariance (ANCOVA) 
with the pretest scores as covariate to test for the main effect. ANCOVA was employed 
because it has the high tendency to adjust the initial mean differences that might exist between 
the experimental groups on pretest measure, and correlates the pretest and posttest measures as 
covariates (Kerlinger, 1973).  It was also used to determine the effects of the independent 
variables (treatment, Mathematics self-efficacy, gender) on the dependent variables 
(participants‘ achievement in geometry and attitude towards geometry).  To ascertain the 
relative effectiveness of the independent variables, Scheffe pair wise test was employed.  
 
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Table 3.6: The Hypotheses and the Method of Analysis  
S/N HYPOTHESES Method of Analysis 
  There is no significant main effect of  ANCOVA 
(1)  (a) treatment 
(2) (b) self-efficacy and 
(3) (c) gender on 
(i) (a)achievement in  geometry 
           (b) attitude towards geometry 
  There is no significant 2-way interaction effect of ANCOVA 
(4) (a) treatment by self efficacy 
(5)  (b) treatment by gender 
(6)  (c) self-efficacy by gender on 
(i)  (a) achievement in geometry 
(ii)  (b) attitude towards geometry 
 
(7) There is no significant 3-way interaction  effect  ANCOVA 
of treatment, self-efficacy and gender on 
(i) (a) achievement in geometry 
(ii) (b) attitude towards geometry 
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CHAPTER FOUR 
 
4.0 Results and Discussion  
 This chapter presents the results and discussion of the findings based on the hypotheses 
stated in chapter one of this study. The hypotheses were tested and the results were interpreted 
at the 0.05 level of significance.  
The results are hereby presented in the order in which the hypotheses were stated. 
 
4.1 Hypothesis 1a  
There is no significant main effect of treatment on participants‘ achievement in geometry.  
Table 4.1 shows the adjusted mean as well as the standard deviation of participants‘ score in 
geometry achievement test after the treatment.  
 
Table 4.1: Mean and Standard Deviation of Participants’ Score in Geometry 
Achievement Test.  
Treatment N Mean S.D Lower Bound     Upper Bound 
OCA 40 18.763 3.99 17.886                 19.639 
GCS 30 17.694 3.56 16.666                 18.722 
Control 40 13.650 3.75 12.773                 14.526 
 
From Table 4.1 the mean difference between OCA and control group is 5.11; between GCS 
and Control 4.04; between OCA and GCS (1.069). The results of ANCOVA in Table 4.2 
shows that the mean differences in scores among the group is statistically significant F (2, 97) = 
35.77, p< 0.05. Partial Eta Square =0.424.  The null hypothesis 1a was therefore rejected. The 
fact that the three groups were homogeneous before the training and were found to be 
significantly different after the training is an indication that the treatment was effective.  The 
result presented in Table 4.2 also indicated that the partial Eta square estimate was 0.424. This 
implies that the treatment accounted for 42.4% of the total variance observed in the 
achievement posttest scores in Geometry. 
 
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Table 4.2: ANCOVA of between subject effects 
 
Source of variation  Sum of Df  Mean F Sig of Eta  
square  square  F squared 
Covariates         
Corrected Model  1915.693  12 159.641   22.217  .000 .733  
Intercept 468.509  1 468.509   65.202  .000 .402  
Pre-Ach. Score  729.220 1 729.220  101.484  .000 .511  
Treatment  514.081  2 257.041    35.772  .000 .424 * 
Gender    12.261  1   12.261      1.706  .195  .017 Ns 
Self efficacy    29.233  1   29.233     4. 068  .046 .040 * 
TRS X Gender      2.499  2     1.249       .174  .841 .004 Ns 
TRS X Self efficacy    17.242  2   8. 621      1.200  .306 .024 Ns 
 
Gender X Self –   9.230 1   9. 230     1.284 .260 .013 Ns 
efficacy  
TRS X Gender X   5.754 2    2.877    . 400 .671  .008 Ns 
Self-Efficacy  
Error  696.998   97      7.186      
Total  33324. 000 110       
Corrected Total 2612.691  109      
2  2 
     R  = .733 (Adjusted R = .700)  
     *=sig. at p<.05  Ns=Not Significant 
 
In order to determine the actual source of the observed significant differences, Scheffe 
Post hoc analysis was carried out on the posttest mean scores of the three (OCA, GCS and 
Control) groups.  The summary of the Scheffe test is as presented in Tables 4.3 
 
Table 4.3: Scheffe Post Hoc Means for Groups in Homogeneous Subsets by Treatment. 
MEAN  Groups OCA GCS CONTROL 
18.763 OCA   * 
17.694 GCS   * 
13.650 CONTROL * *  
 
* Pairs of categories significantly different at 0.05 level 
 From the Scheffe Post hoc analysis presented in Table 4.3, the following observations were 
made: 
(i) There was a significant difference in the achievement test scores in geometry between 
the participants in OCA (18.763) and Control groups (13.650).  
(ii) GCS (17.694) group differs significantly from the control (13.650) group on measures 
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of achievement in Geometry. 
(iii) However, there exists no significant difference between the posttest mean scores of the 
participants in OCA (18.763) and GCS (17.694) groups. 
 
4.1.1 Hypothesis 1b: There is no significant main effect of treatment on participants‘ attitude 
towards geometry.  
 
Table 4.4: Shows the mean and standard deviation of treatment on participants’ attitude 
towards geometry   
Attitude  Number Mean Std. 95% confidence interval 
Deviation 
LowerBound UpperBound 
 
 
OCA 40 220.200 28.58 212.450 224.624 
                     
GCS   30 205.867 21.86 198.934 212.856 
Control  40 157.925 27.40 152.702 164.509 
               
 
From Table 4.4the mean difference between OCA and Control (62.275), between GCS and 
Control (47.942), between OCA and GCS (14.333). The mean difference among the group is 
statistically significant (F (2, 97) =108.214, p<0.05).  
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Table 4.5: ANCOVA of participants’ Attitude Scores by Treatment, Self-efficacy and 
Gender  
Source    Sum of Df  Mean square  F Sig of Eta 
squares  F squared  
Corrected model  125091.280 12 10424.273 30.078 .000 .788 
Intercept  32797.324 1 32797.324 94.632 .000 .494 
PREATS 36218.850 1 36218.850 104.505 .000 .519 
TRS 75008.901 2 37504.450 108.214 .000 .691 
Gender      103.300 1     108.300       .312  .577 .003 
SEL EFF     275.404  1     275.404       .795  .375 .008 
TRS x Gender      137.413 2       68.706         .198 .821 .004 
TRS x Self Efficacy        57.617 2       28.809        .083 .920 .002 
Gender x Self-Efficacy      114.960 1     114.960        .332 .566 .003 
TRS x Gender x Self- 344.453 2    172. 227        .497 .610 .010 
Efficacy 
Error 33617.893 97     346.576    
Total  4283551.000 110     
Corrected Total    158709.173 109     
   R squared =.788 Adjusted R =.762)  
*=Significant at p<.05     ns=Not Significant 
 
Table 4.5 revealed that the main effect of treatment on participants‘ attitude towards geometry 
was significant (F (2, 97) =108.214, p<.05). The hypothesis which stated that there is no 
significant main effect of treatment on participants‘ attitude towards Geometry was rejected.  
The result presented in Table 4.5 also indicated that the partial square estimate was 0.691. This 
implies that the treatment accounted for 69.1% of the total variance observed in the attitude 
post test score in Geometry. In order to determine the significant group difference, Scheffe 
Post-hoc analysis was done. The results are presented in Tables 4.6a and 4.6b.  
 
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Table 4.6(a): Scheffe Post Hoc Multiple Comparison of Participants’ Attitude by 
Treatment    
(I)Treatment (J)Treatment   Mean (I-J) Sig 
Difference    
*
OCA  GCS 14.333  .008 
*
Control 62.275  .000 
*
GCS OCA -14.333  .008 
*
Control 47.942  .000 
*
Control OCA  -62.275  .000 
GCS -47.942* .000 
   *=Mean difference is significant at p<.05 
   
Table 4.6(b): Scheffe Post Hoc Means for Groups in Homogeneous Subsets on Attitude 
by Treatment 
Mean Treatment  OCA  GCS  Control 
 220.200 OCA    *  * 
205.867 GCS *  * 
157.925 Control * *  
 
*=Pairs of categories are significantly different at p<.05 
 
From the results presented in Tables 4.6a and 4.6b, the following are observed: 
(i) There was significant difference in attitude towards Geometry between participants in 
OCA and GCS groups (14.333).  
(ii)  There was significant difference in attitude towards Geometry between participants in 
OCA and Control groups (62.275)  
(iii) There was significant difference in attitude towards Geometry between participants 
 in GCS and Control groups (47.942). 
 
4.2 Hypothesis 2a: There is no significant main effect of self-efficacy on participants‘ 
 achievement in geometry. 
 
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Table 4.7: Shows the mean and standard deviation of self-efficacy on participants’ 
achievement in geometry. 
 Self-efficacy Number Mean Std. Deviation LowerBound UpperBound 
  
OCA:     Low/SE, 17 18.824, 3.83 212.450 224.629 
               H/SE 23 19.304 4.18  
Total 19.100 3.99 
GCS:      Low/SE, 12 17.833 3.22 198.934 212.856 
               H/SE  18 19.833 3.65 
Total 19.033 3.57 
Control:  Low/SE,  22 12.955 3.91 152.702 164.509 
               H/SE 18 12.111 3.60 
Total: 12.575 3.75 
 
The result presented in Table 4.7 shows that the mean difference between high math 
self-efficacy (HMSE) and low math self-efficacy (LMSE) in achievement test scores in 
geometry were: OCA and control (6.525), between GCS and control (6.458), between OCA 
and GCS (0.067). The observed MSE difference was however statistically significant (F (1, 97) = 
4.068, p< .05). 
The result presented in Table 4.2 shows that there is significant main effect of self-
efficacy on participants‘ achievement in geometry (F (1, 97) =4.068, p< .05). The hypothesis 
was therefore rejected. The result also indicated that the partial Eta squared estimation was 
.040, this means that self-efficacy accounted for 4% of the variance in the observed post-test 
achievement scores in geometry. For the purpose of establishing where the significant 
difference lies, Tables 4.8a and 4.8b are presented below. 
 
Table 4.8 (a): Scheffe Post Hoc Multiple Comparison of Participants’ Achievement in Geometry  
(I)Self-Efficacy (J)Self-Efficacy Mean Difference (I-J) Sig. 
*
Low High -1.220  .046 
*
High Low 1.220  .046 
 *The mean difference is significant at P<.05 
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Table 4.8(b): Homogenous subsets by Self-Efficacy 
Mean Self-Efficacy Low High 
16.050 Low  * 
17.270 High *  
*=Pairs of categories significantly different at .05 level. 
 
It is revealed from Tables 4.8(a) and 4.8(b) that the difference between the means of low self- 
efficacy (x=16.050) and high self- efficacy (x=17.270) participants is significant. Therefore, 
level of self-efficacy contributed significantly to the participants‘ achievement in geometry. 
 
4.2.1 Hypothesis 2b: There is no significant main effect of self-efficacy on participants‘ 
attitude towards Geometry. Results on Table 4.5 revealed that self-efficacy did not have a 
significant main effect on participants‘ attitude towards Geometry (F (1, 97) =.795; p>.05). 
 
Table 4.9: Shows the mean and standard deviation of self-efficacy on participants’ 
attitude towards geometry.   
Self-efficacy Number Mean Std.Deviation LowerBound UpperBound 
  
OCA:      Low/SE, 17 212.118 23.78 212.450 224.629 
               H/SE  23 226.174 30.81 
               Total 40 220.200 28.58 
GCS:      Low/SE, 12 203.833 23.35 198.934 212.856 
               H/SE  18 207.222 21.38 
               Total 30 205.867 21.86 
Control:  Low/SE,  22 154.546 25.65 152.702 164.509 
               H/SE 18 162.056 29.61 
Total 40 157.927 27.40 
 
From Table 4.9, the mean difference between high and low mathematics self-efficacy on OCA 
(14.056); between high and low mathematics self-efficacy on GCS (3.389), between high and 
low mathematics self-efficacy on Control (7.510). The mean difference among the group is not 
statistically significant (F (1.97) =.795, p>0.05).  
Based on this finding, hypothesis 2b was not rejected. Though high self-efficacy participants‘ 
attitude mean score (196.01) was higher than that of low self-efficacy participants, with mean 
attitude score of (192.69), it was not statistically significant.  
 
4.3 Hypothesis 3a: There is no significant main effect of gender on participants‘ 
achievement in geometry.  
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Table 4.10: Shows the mean and standard deviation of gender on participants 
achievement in geometry   
Gender Number Mean Std. 95% confidence interval 
Deviation 
LowerBound UpperBound 
 
 
OCA:                  male 24 18.999 3.84 17.898 20.099 
                         female 16 18.527 4.15  17.145 19.908 
   
                             
GCS:                   male 15 17.940 3.13 16.453 19.427 
                         female   15 17.448 3.94 16.062 18.834 
  
                                          
Control Group:   male  18 14.213 3.63 12.925 15.501 
                          female    2  2                1  3  . 0  8  6         3  . 8  9              11.934 14.238 
                               
Total                   male  57 17.614 4.74   
Total                 female  53 15.736 4.92 
 
The result in table 4.10 shows that the gender differences in achievement test scores in 
geometry were OCA (0.472), GCS (0.492) and control (1.127).  The overall gender difference 
was 1.878. The observed gender difference was however not statistically significant (F (1, 
97=1.706, p>0.05).     
The result presented in Table 4.2 shows that there was no significant main effect of gender on 
participants‘ achievement in geometry (F (1, 97) = 1.706; p>.05). The hypothesis was therefore 
accepted. The partial Eta square estimate was .017. This implies that gender accounted for 
1.7% of the variance observed in the post-test scores of the participants in geometry.  
 
4.3.1  Hypothesis 3b: There is no significant main effect of gender on participants‘ attitude 
towards Geometry.  
 
 
 
 
 
 
 
 
 
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Table 4.11: Shows the mean and standard deviation of gender on participants’ attitude 
towards geometry   
Gender (Attitude) Number Mean Std. 95% confidence interval 
Deviation 
LowerBound UpperBound 
 
 
OCA:                    Boy 24 217.833 31.39 17.898 20.099 
                             Girl  16 223.750 24.31 17.145 19.908 
            
GCS:                    Boys  15 209.867 20.89 16.453 19.427 
                             Girls  15 201.867 22.78 16.062 18.834 
             
Control Group:    Boys  18 154.889 25.27 12.925 15.501 
                            Girls 22 160.409 29.37 11.934 14.238 
                        
   
The result presented in Table 4.11 shows that the gender difference in attitude test scores in 
geometry were OCA (5.917), GCS (8.000) and Control (5.520). The observed gender 
difference was however, not statistically significant (F (1, 97) =.312, p>0.05). 
The ANCOVA summary in Table 4.5 has shown that gender did not have a significant main 
effect on participants‘ attitude towards Geometry (F (1, 97) =.312, p>.05). Consequently, 
hypothesis 3b was accepted. The estimated Eta square reveals that gender contributed 31 
percent of the variance observed on the participants‘ attitude towards Geometry. Male 
participants had higher mean post-attitude score (195.38) while the female had a lower post 
attitude score of 193.32.  However, the difference in the posttest attitude scores between the 
two groups being compared was not statistically significant. 
 
  
4.4 Hypothesis 4a: There is no significant interaction effect of treatment by self-efficacy 
on participants‘ achievement in geometry. The data on Table 4.2 show that there was no 
significant interaction effect of  treatment by self-efficacy on participants‘ achievement in 
geometry (F(2,97) = 1.2000; P>.05). The conclusion was that the hypothesis 4a was not rejected.  
This implies that the self efficacy of participants had no effect on treatment (out-of-class-
activity and group counselling) strategies to produce joint effects on dependent variables. Each 
of the strategies could be effectively used by practicing Mathematics teachers, whether 
participants are of low or high self-efficacy group.  
 
4.4.1  Hypothesis 4b: There is no significant interaction effect of treatment and self-efficacy 
on students‘ attitude towards Geometry. The ANCOVA summary in Table 4.5 showed that 
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there was no significant interaction effect of treatment by self- efficacy on participants‘ attitude 
towards Geometry (F(2,97)= .083, p >.05).  As a result of this finding, hypothesis 4b was 
accepted.  
 
4.5 Hypothesis 5a: There is no significant interaction effect of treatment by gender on 
participants‘ achievement in geometry. Table 4.2 revealed that there was no significant 
interaction effect of treatment by gender on participants‘ achievement in Geometry (F (2, 97) = 
.174, p >.05). As a result of this finding, hypothesis 5a was therefore accepted.  It, thus, implies 
that the effect of treatment on the achievement of participants in geometry is not sensitive to 
gender. The treatment strategies used during the whole of this study could be used to improve 
participants‘ performance in geometry whether they are male or female. 
 
4.5.1 Hypothesis 5b: There is no significant interaction effect of treatment by gender on 
participants‘ attitude towards Geometry.  The results presented on Table 4.5 showed that there 
was no significant interaction effect of treatment and gender on participants‘ attitude towards 
Geometry (F(2, 97) =.198, p >.05). Therefore, hypothesis 5b was not rejected. 
 
4.6 Hypothesis 6a: There is no significant interaction effect of self efficacy by gender on 
participants‘ achievement in geometry. The two-way interaction on Table 4.2 showed that 
there was no significant interaction effect of self-efficacy by gender on participants‘ 
achievement in geometry (F(1,97)=1.284), p >.05).  Based on this result, hypothesis 6a was 
accepted.  It means that participants‘ performance in geometry was not significantly affected 
by the interaction of self efficacy by gender. 
 
4.6.1 Hypothesis 6b: There is no significant interaction effect of self- efficacy by gender on 
participants‘ attitude towards Geometry.  Table 4.5 showed that there was no significant 
interaction effect of  self-efficacy by gender on participants‘ attitude towards Geometry 
(F(1,97)=.332, P>.05). The hypothesis 6b was therefore accepted. 
 
4.7 Hypothesis 7a: states that there is no significant 3-way interaction effect of treatment, 
self-efficacy and gender on participants‘ achievement in geometry.  ANCOVA result presented 
on Table 4.2 showed that there was no significant interaction effect of treatment, self-efficacy 
and gender on participants‘ achievement in geometry (F(2,97) = .400, P>.05).  It then follows 
that the hypothesis 7a was not rejected. 
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4.7.1 Hypothesis 7b: There is no significant 3-way interaction effect of treatment, self- 
efficacy and gender on participants‘ attitude towards Geometry (F (2, 97) =.497, P>.05). 
The three-way interaction ANCOVA result for this hypothesis as shown on Table 4.5 
revealed that there was no significant interaction effect of treatment, self-efficacy and gender 
on participants‘ attitude towards Geometry. (F (2, 97) =.497, P>.05). Therefore, hypothesis 7b 
was not rejected. That is, participants‘ attitude towards Geometry was not significantly 
influenced by the interaction effects of treatment, gender and self-efficacy. It then suggests that 
practicing Mathematics teachers could use any of the teaching strategies (out-of-class activity 
or counselling) to support the instruction of Mathematics (geometry included), irrespective of 
the gender and self-efficacy of participants. 
 
4.8 Discussion 
 
4.9 Hypothesis 1: The hypothesis stated that there is no significant main effect of 
 treatment on participants‘:  
(a)  achievement in geometry; and  
(b)  attitude towards geometry.   
 The results of the finding revealed that there was a significant main effect of treatment 
on the participants‘ achievement in geometry. The hypothesis could not be upheld with the 
result of the findings; the hypothesis was therefore rejected. It is therefore concluded that there 
is a significant main effect of treatment on the participants‘ achievement in geometry. 
 The findings show that the two therapeutic techniques proved to be effective in 
enhancing the participants‘ achievement in geometry. The participants in the experimental 
groups (OCA&GCS) showed a significantly greater enhancement in the posttest scores on 
Achievement Test in Geometry (ATG) than the participants in the control group.  The fact that 
the participants in the experimental groups performed better in the posttest scores in ATG than 
the control group proved that the treatments employed were effective on one hand and that the 
utilization of the treatment gain by the participants on the other hand.      
The low scores of the participants in the control group as observed in the posttest scores on the 
ATG is not a surprise, since they did not have the opportunity of taking part in the treatment 
programmes.  It is obvious that they maintained their previous performance.  It was possible 
that while the participants in the experimental groups were participating actively in the various 
training programmes, the participants in the control group were engaged in various other 
activities that are not capable of enhancing their achievement in geometry. The findings tend to 
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confirm that students exposed to OCA & GCS excelled more than those who had the same 
ability but lacked the skills in the training programmes.  
 The results further indicated that there was no significant difference in the post test 
score on ATG between the participants in OCA & GCS. The techniques inherent in these two 
techniques produced equal amount of effectiveness in enhancing achievement in geometry 
among the participants.  
 One way of explaining this result is that the training prgorammes created the much 
needed self-awareness, independent will and the need of the participants to have their 
achievement in geometry improved. The results have therefore confirmed that achievement in 
geometry could be enhanced through OCA and GCS. This result also confirmed the 
observation of Olatundun (2008) that Outdoor Educational Activities were effective in 
enhancing academic achievement in his study.  The results of the findings also corroborate 
those of Brigman,Webb and Campbell (2007),   Ventakesh and Lissaman (2004), Fajonyomi 
(2001).     
 Another possible explanation for the significant improvement in the ATG scores of the 
participants in the experimental group may be found in the degree of motivation to acquire 
some basic skills in learning which they hitherto lacked. The participants in the experimental 
groups might have been experiencing some degree of moderate dosage of anxiety because of 
the importance of geometry to their daily lives. Some researchers such as (Burton, 1999, 
Adegoke, 2002, Duatepe, 2004) lent credence to the importance of geometry.  The result of 
this finding deviates from the view of Eysenk (1952; 1965) as cited by Yinyinola (2008) who 
held the opinion that researches on psychological, educational and behavioural treatment 
showed no convincing effect. However, the result is in line with the opinion of some 
researchers (Robbinson, Berman & Neinmeyer, 1990; Smith & Glass, 1977) as cited by 
Yinyinola (2008) who reported that in psychotherapies, differences are found, and when they 
are, they can often be attributed to the allegiance of the investigators involved.  
 The outcome of the result from hypothesis one also agrees with the findings of the 
previous researchers (Harlow & Baenen, 2001, Grimm, 1997, Brookes, 2004; Smiths, 2002) 
who found that OCA was effective in enhancing academic achievement of participants in their 
various studies.  
 The outcome of the result also supports the findings of the previous researchers 
(Brigman & Campbell, 2003; Webb & Brigman, 2006; Campbell & Brigman, 2005) Venkatesh 
& Lissaman, 2011) who found that cognitive behavioural Therapy was effective in enhancing 
academic performance. The findings also support the view of Fakunle, 2007 and Johnson 1984 
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who acknowledge the influence of counseling strategies on student academic performance. 
 
4.9.1 Hypothesis1b: The hypothesis stated that there is no significant main effect of 
treatment on participants‘ attitude towards geometry. The result of the findings revealed that 
there was significant main effect of treatment on participants‘ attitude towards geometry. The 
hypothesis was not supported with the result of this findings, the hypothesis was therefore 
rejected. It is therefore concluded that there is a significant main effect of treatment on 
participants‘ attitudes towards geometry. 
 The findings showed that the two training programmes proved to be effective in 
enhancing participants‘ attitude towards geometry. The participants in the experimental group 
showed a significantly greater enhancement in the posttest score on Geometry Attitude Scale 
(GAS) than the participants in the control group. The fact that the participants in the treatment 
group performed better in the posttest scores on GAS than the control group proved that the  
training programmes employed were effective  in enhancing attitude towards geometry on one 
hand and that the utilization of the treatment gain by the participants on the other hand.  
 The low scores of the participants in the control group as observed in the post test is  
not surprising since they did not have the opportunity of taking part in the treatment 
programmes. It is obvious that they maintained their previous position. It was possible that 
while the participants in the experimental groups were participating actively in the various 
training programmes, the control group participants were engaged in various other activities 
that are not capable of enhancing their attitude towards geometry. The findings tend to confirm 
that the participants with positive attitude excelled those who have the same abilities but had 
low attitude towards geometry. 
 The results of the finding indicate that the participants in the Out-of-class activity 
(OCA) group performed better than their counterparts in the GCS group. This can be explained 
in terms of the effectiveness of each of the training programmes. This is seen in the light of 
various techniques such as cognitive rehearsal and validity testing; writing in a journal and 
guided discovery; modelling of appropriate behaviour and homework; systematic positive 
reinforcement used in the delivery of the training programme, which are unique in the 
individual training; and which distinguished one training programme from the other. The 
techniques inherent in these training programmes are expected to produce varying degrees of 
effectiveness in enhancing attitude towards geometry among the participants.  One way of 
explaining this result is that the training progammes created the much needed self-awareness, 
independent will and the need of participants to have their attitude towards geometry 
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improved. The result has therefore confirmed that attitude towards geometry could be 
enhanced through out-of-class-activity and group counselling strategies. This result also 
confirmed the study of Duffy (2001) who observed that students‘ attitude can be enhanced 
through out-of-school-time and group counselling strategies. 
 The exposure of the GCS group to counselling skills which reduced mathematics 
anxiety, which the participants suffer during mathematics lesson might be accounted for  the 
development of positive attitude towards geometry.  This has been in line with findings of 
researchers (Duatepe, 2004; Duffy, 2001; Grimm,1997; Hanna, 1986; Malaty, 1994) who have 
observed that when participants are taught mathematics (geometry included) using activity 
based instructions, they have reduced anxieties, develop positive attitude towards mathematics 
(geometry included) and even have better performance than equally competent participants 
who are taught without using activity-based instructions.  
 Another possible explanation for the significant improvement in the attitude towards 
geometry of the participants in the experimental groups may be found in the degree of 
motivation to acquire some basic skills in learning which they hitherto lacked.  
The participants in the experimental groups might have been experiencing some degree of 
moderate dosage of anxiety because of the importance of geometry to their daily life. Some 
researchers such as Burton (1999); Adegoke (2002); Duatepe (2004) lend credence to the 
importance of geometry,  
 The results of this finding deviate from the view of Eysenk (1952, 1965) as cited by 
Yinyinola (2008) who held, the opinion that researches on psychological, educational and 
behavioural treatment showed no convincing effect. However, the results is in line with the 
opinion of some researchers (Robbinson, Berman & Neimeyer, 1990; Smith & Glass, 1977) as 
cited by Yinyinola (2008) who reported that in psychotherapies, differences are found and 
when they are, they can often be attributed to the allegiance of the investigators involved.  
 The outcome of the results from hypotheses one also agrees with the findings of 
previous researchers (Bergeson, Fitton & Bylsm 2000, Duatepe, 2004, Knap, 1997, Olosunde, 
2009) who observed that the development of positive attitudes of participants in their various 
studies can be linked to the direct involvement of students in activities.  
 The outcome of the result also corroborates the findings of previous researchers (Webb 
& Brigman, 2006; Brigman, Webb & Campbell, 2007; Tylor & Montgomery, 2007) who 
found in their studies that counselling could be an effective treatment for increasing global and 
academic self-esteem. The findings also support the views of Ch (2006) who reported that 
counselling services were found to be effective on the students‘ study attitude.     
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4.10 Hypothesis 2: There is no significant main effect of Self-efficacy on 
 participants’:  
(a) achievement in geometry and  
(b) attitude towards, Geometry  
 There was a significant main effect of Mathematics Self-Efficacy (MSE) on 
participants‘ achievement in geometry. The hypothesis 2a was rejected based on this finding.  
The results of ANCOVA analysis on Table 4.2 indicated a significant main effect of self-
efficacy on participants‘ achievement in geometry. This showed that participants with high 
mathematics self-efficacy can be associated with high achievement in geometry. In other 
wards, MSE was a positive predictor of achievement in geometry. This finding further revealed 
that participants who were confident of their performance in geometry tended to have better 
achievement in geometry.    
 One of the possible reasons of a significant main effect of MSE on participants‘ 
achievement in geometry can be attributed to the instructional strategies employed in the study. 
Research has indicated that self-efficacy could be increased through the use of appropriate 
instructional strategies (Siegle & McCoach,2007),which include, helping students to set a 
learning goal Bandura (1997), encouraging students to study harder and also the use of models 
(Siegle & McCoach,2007).  
 Another reason for a significant main effect of mathematics self-efficacy could stem 
from the observation made by Bandura (1997) that high self-efficacy and skills are the 
determinants of academic success. Skill without self-efficacy might not necessarily result in 
high personal accomplishment. Hence, the high MSE participants that performed better than 
the low MSE participants in geometry achievement could be interpreted to mean that the 
participants with high level of self-efficacy were confident that they could master the skills 
being taught in geometry lessons, they tend to approach challenges with the feeling of 
optimism which invariably afforded them good performance. The findings of this study 
corroborate the findings of Hodge (2005); Nicolaidou and Philippou (2003) ; Yinyinola (2008) 
whose findings revealed a significant relationship between mathematics self-efficacy and 
mathematics achievement.  The results of the study contradict the findings of Kabiri and 
Kiamanesh (2004) who observed that prior mathematics achievement predicts mathematics 
achievement better than mathematics self-efficacy.   
 
4.10.1 Hypothesis2b: However there was no significant main effect of MSE on participants‘ 
attitude towards geometry. Based on this finding, hypothesis 2b was accepted. This could be 
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explained by the fact that the type of instructional strategies employed by the researcher in the 
teaching of geometry gave both the high and the low MSE participants a non-threatening 
environment (that is, a democratic environment), which might have motivated the low MSE 
participants to develop positive attitude towards geometry. The finding has therefore implied 
that the classification of participants into high or low levels of MSE does not affect their 
attitude towards geometry. The finding supports the observation of (Liu, Hsieh, Cho & 
Schallert, 2006) who found no significant effect of MSE on participants‘ attitude to science 
 
4.11 Hypothesis 3: There is no significant main effect of gender on  
      participants’:  
(a)  achievement in geometry and  
      (b) attitude towards geometry     
 The results of the finding revealed that there was no significant main effect of gender 
on participants‘ achievement in geometry. Hypothesis3a was accepted. The existence of no 
difference in posttest scores on achievement in geometry between male and female participants 
can be said that both male and female participants benefited equally, in the same manner from 
the training programme they were exposed to. One way of giving possible explanation for no 
significant main effect of gender on participants‘ achievement in geometry could be attributed 
to the existence of role models for girls. The fact that women are seen holding different key 
positions in various fields of endeavour like their male counterparts was an inspiration for the 
girls. This is a factor that provides situations of success for both sexes. Consequently, this 
could improve females‘ sense of efficacy and their attitudes towards learning.  
Gender difference that had been observed before in students‘ learning outcomes could 
also be said to be diminishing due to the effort of science educators towards the formulation 
and design of policy statements and intervention strategies that can promote gender equality 
for educational advancement. The finding is in line with that of Akinsola and Tijani (1999)  
who assert that mathematics is not a male dominated subject as people assumed it to be, but for 
both sexes provided that both sexes are subjected to the same learning conditions. The results 
of this study lent credence to the findings of previous researchers such as Adegoke (2002); 
Akay (2011) and Seleshi (2001) in Adegoke (2002) who did not find main significant gender 
differences in their various studies. The result did not support the finding of Olatundun (2008) 
whose study reported a main significant difference in the environmental knowledge scores of 
male and female pupils. 
 
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Table 4.5 presents a summary of the results of the Analysis of covariance (ANCOVA) 
for the dependent variable: attitude as measured by the Geometry Attitude Scale (GAS), which 
tested the second part of this hypothesis. The results in Table 4.5 revealed that there was no 
significant main effect of gender on participants‘ attitude towards geometry. The reason could 
be that both male and female participants have the same opportunities in the classroom 
environment. That implies that female participants can express themselves in the classroom 
situation and also take part actively in the lessons as much as their male counterparts. The 
findings corroborate the observations of Adegoke (2002) who found no significant main effect 
of gender on dependent-prone students‘ posttest mean scores in Geometry Achievement Test 
and Mathematical Attitudinal Scale. The results of the study also lent credence to the findings 
of Akay (2011) who did not find any significant gender difference in transformational 
geometry and attitude towards mathematics. The results of the study contradict the 
observations of Olatundun (2008) whose study reported a main significant difference in the 
environmental knowledge and attitude scores of male and female pupils. 
 
4.12 Hypothesis 4: There is no significant 2-way interaction effect of Treatment by Self-
efficacy on participants’ Achievement in and Attitude towards Geometry    
There is no significant interaction effect of treatment by self-efficacy on participants‘ 
achievement in and attitude towards geometry. The two treatments can be generalized across 
the levels of self-efficacy (low and high).  This implies that any of the treatments could be 
applied either of low self-efficacy or high self-efficacy.  This indicates that the combination of 
treatment (OCA, GCS) does not have a great influence on the participants‘ achievement. High 
and low self-efficacy of participants in the treatment groups had post-test mean scores that 
were statistically insignificant. This observation supports the results of Bridgeman and 
Wendler (1991), who observed that the pattern of achievement of high and low Mathematics 
self-efficacy levels of participants in the study group were not significantly different from one 
another.  
 
4.13 Hypothesis 5: There is no significant 2-way interaction effect of Treatment by 
 Gender on participants’ Achievement in and Attitude towards Geometry    
 From the ANCOVA summary as shown in Tables 4.2 and 4.5, there was no significant 
2-way interaction effect of treatment by gender on participants‘ achievement in and attitude 
towards, geometry.  This implies that treatment (OCA, GCS) is not gender sensitive to 
participants‘ achievement in and attitude towards geometry.  In other words, the treatments can 
be generalized across the two levels of gender (male & gender). The findings of this study also 
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corroborate the results of other studies (Adegoke, 2002; Ajiboye,1996; Ishola, 1999) as cited 
by Adegoke (2002) who observed no statistical significant interaction effect of instructional 
strategies and students‘ gender on geometry, population concepts and physics achievement test 
in and attitude towards problem-solving. The result is in conflict with such study as that of 
Olatundun (2008) who found interaction effect of treatment by gender in his study.  
 
4.14 Hypothesis 6: There is no significant 2-way interaction effect of Self-efficacy  by 
 Gender on participants’ Achievement in and Attitude towards Geometry  
There is no significant 2-way interaction effect of self-efficacy by gender on 
achievement in and attitude towards, geometry. The results of this study indicate that the two-
way interaction effect of self-efficacy by gender was not significant on participants‘ 
achievement in and attitude towards geometry. This indicates that the effect of self-efficacy on 
achievement and attitude towards geometry can be generalized across the two levels of gender 
(male & female) The findings of this study agreed with the reports of Venkatesh and  
Lissammi (2011); Stage & Kloosterman (1995) and contradict the results of Skaalvik and 
Rankin (1994) who affirm that Mathematics self-efficacy of males was statistically superior to 
that of females. 
One way of explaining the result of the present study is the fact that both the male and 
female participants were exposed to the same treatment conditions which gave the two sexes 
equal opportunities to learn. The female participants now believe in their abilities that they can 
learn. This is different in the time past, when the culture of the participants exerted influence 
on male participants who were given free interaction while the females were expected to be 
engaged in domestic works. But with the present provision of equal learning opportunities, 
females could perform as well as their male counterparts.            
 
4.15 Hypothesis 7: There is no significant 3-way interaction effect of Treatment,  Self-
 efficacy and Gender on participants’ Achievement in and Attitude towards 
 Geometry 
 The three-way interaction effect of treatment, self-efficacy and gender was not 
significant on participants‘ achievement in and attitude towards geometry.  This implies that 
the combination of treatment, self-efficacy and gender does not associate with participants‘ 
learning outcomes (achievement and attitude). That is, the interaction effect involving the three 
variables is not mutually influenced by achievement and attitude to produce a joint effect. The 
effect of the treatment can be generalized across the two levels of self-efficacy (low & high) 
and two levels of gender (male & female).    
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CHAPTER FIVE 
SUMMARY AND CONCLUSIONS 
 
5.1      Introduction 
The major findings of this study as well as their educational implications and 
recommendations are summarized. Also, the limitations of this study as well as suggestions for 
further research are presented.  
 
5.2. Summary of findings 
The findings of this study are summarized below: 
1. There was significant main effect of out-of-class- activity, counselling and 
conventional teaching strategies on participants‘ achievement in and attitudes towards 
Geometry. 
2. Out-of-class and counselling strategies produced better participants‘ performance in 
geometry than conventional strategies. 
3. Attitude of participants was better under out-of-class-activity and counselling than the 
conventional strategy. 
4. There was significant main effect of self-efficacy of participants on achievement in 
Geometry.  
5. There was no significant main effect of self-efficacy on participants‘ attitudes toward 
Geometry  
6. There was no significant main effect of gender on participants‘ achievement in 
Geometry.  
7. There was no significant main effect of gender on participants‘ attitudes towards 
Geometry.  
8. There was no significant two-way interaction effect of treatment by self-efficacy on 
participants‘ achievement in and attitude towards Geometry.   
9. There was no significant two-way interaction effect of treatment by gender on 
participants‘ achievement in and attitude towards Geometry.   
10. There was no significant two-way interaction effect of self-efficacy by gender on 
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participants‘ achievement and attitude towards Geometry.   
11. There was no significant three-way interaction effect of treatment, self- efficacy and 
gender on participants‘ achievement in and attitude towards Geometry. 
 
5.3 Implications of the findings  
The findings of the study have many implications for Mathematics education. The 
instructional strategies of Out-of-Class-Activity (OCA) and Group Counselling Strategy (GCS) 
employed in this study showed superiority over the Conventional Teaching Strategy (CTS) 
throughout the study. That the treatment had significant main effect on achievement and 
attitude implies that the two strategies are viable alternatives to the Conventional Teaching 
Strategy and, as such, should be encouraged for use in our schools alongside the Conventional 
Teaching Strategy. Moreover, the strategies have been found to be effective in the teaching of 
geometry, especially to low-achieving students. This is a pointer to the fact that there is a need 
to shift from the traditional way of Mathematics instruction to some other instructional 
strategies that are more provocative, facilitative and have empowering effects on the students. 
Hence, the results of the study have exposed the effectiveness of Out-of-Class-Activity and 
Group Counselling Strategy in the teaching of geometry and therefore suggest that 
Mathematics teachers should adopt the Out-of-Class-Activity and Group Counselling 
Strategies in the teaching of Mathematics generally at the Junior Secondary School level. The 
present study has proved that OCA and GCS are effective strategies in enhancing learning 
outcomes among low-achieving secondary school students, especially in the area of geometry.   
The study has also exposed the participants to the importance of rational thinking 
through counselling strategy, which affected their performance in Mathematics positively. The 
two therapeutic strategies applied were effective in improving achievement in and attitude 
towards Mathematics. A significant relationship has been found to exist between attitude and 
achievement. As participants‘ mathematics achievement improves, they tend to develop 
positive attitude towards Mathematics. Low-achieving students are bound to achieve better in 
Mathematics when taught with appropriate teaching strategies. It is envisaged that the 
introduction and implementation of these strategies in our schools could further enhance the 
much needed positive attitude not only to Mathematics, but also to other related disciplines. 
Another implication is that Mathematics students should not be taken as a homogenous group 
without due cognizance to individual inherent innate learning characteristics which are 
embodiments of learning styles in the classroom situation. In other words, Mathematics 
educators should put into consideration individual differences among students. If this is not 
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done, Mathematics educators will be teaching a fraction of the class with a resultant effect of 
poor academic performance and negative attitude to Mathematics from students whose 
learning styles and needs may not be met in the normal regular classroom. A large number of 
studies discussed in this study stress that it is desirable to improve the instructional strategy of 
students. Therefore, it is very necessary to include out-of-class-activity and group counselling 
strategies as part of the instructional strategies in the mathematics curriculum. This might help 
the classroom teachers in working with students who are low-achieving in Mathematics. The 
results of this study also show that concerted efforts are needed to help students to maximize 
their potential and improve their area of academic weaknesses. The findings of this study have 
educational implications for Mathematics classroom teachers, counsellors, policy makers and 
curriculum planners.  
 
5.4 Recommendations                   
The following recommendations are made based on the findings of the study:  
Secondary school mathematics teachers should be encouraged to explore the 
application of Out-of Class-Activity Strategy in their classroom instruction 
Teachers can sequence their instructional content to include OCA strategy for learning 
new topics. This is because changing the instructional method from traditional to modern has a 
positive effect on the academic performance of the low-achieving students.  
Students should be given a chance to be involved in the teaching and learning process 
to learn meaningfully. School counsellors should implement a comprehensive school 
counselling programme that would focus on increasing students‘ academic achievement using 
rich empirically based intervention strategies, such as group counselling strategy.  
Government should organize workshops, seminars, symposia, and conferences for 
teachers whereby they will be exposed to various enhancement strategies that will assist them 
in taking care of individual differences among students in the classroom environment. This will 
help students develop positive attitude towards Mathematics, have confidence in themselves, 
and be more positively disposed towards obtaining good scores in Mathematics and even in 
other related subjects. 
The Mathematics educators should utilize the findings of this study to encourage the 
school counsellors to be organizing school intervention strategies that will assist not only the 
low-achieving students but also all the students generally on the need for the learning of 
Mathematics, for their future careers. Utilizing the findings of this study would help the 
students control cognitive thought processes and positively impact on academic achievements. 
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5.5 Limitations of the study 
 There are limitations to this study that should be considered before the results are 
applied. The sample selected was restricted to only six junior secondary schools in three local 
government areas out of the existing eleven local government areas in Ibadan.  This     reduces 
the degree of generazability of the results. Only students in Junior Secondary Two (JS2) were 
included in the study as samples.  Further research with inclusion of all categories of secondary 
school students is needed to understand more the effect of the interventions on the dependent 
variables. 
Another possible limitation to the study is the sample size; the number of participants in 
the study (110) seems small compared to the large number of secondary school students.    
Despite the experimental method that has been adopted to control the present study, 
differences of such factors as personality, socio-economic background and gender cannot be 
controlled.  Randomization does not take care of these differences.  Therefore, statistical 
control was used to equate factors like mental ability and other forms of individual differences. 
Another area of possible limitation is the fact that it is not possible to conduct the 
experiment in an entirely stimulus controlled experimental environment.  There is a possibility 
that routine school procedures would have been a source of distraction to experimental groups.  
Should such distractions have effect, only the treated groups would be affected. 
The use of intact class could not permit randomization of the participants used for the 
study. Although any error in sampling should have been taken care of, through the use of 
ANCOVA. 
 
5.6 Suggestions for further study 
Replication of the study is needed with longer period of treatment; say 12 weeks, as 
well as with students from varied abilities (high, moderate and low) to see if the same results 
would be obtained.  
Furthermore, it is necessary to vary the experimental conditions to see their effects on 
the participants. For example, a different design, like 4x3x2 which will combine the two 
experimental groups (OCA and GCS) as well as three levels of Mathematics self-efficacy 
(high, moderate and low) could be employed. 
The study could be carried out in such a way that one would avoid the use of intact 
class which would permit randomization of participants to treatment and control groups   
Other aspects of Mathematics could be looked into to see what effect OCA would have on 
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them.  
5.7 Contribution to knowledge   
The main contribution of this study is the attempt to improve Geometry achievement by using 
Out-of-Class-Activity (OCA) strategy.  This approach will hopefully make Geometrical 
concept more real than abstract since the activities are those they engage in on a day to day 
basis outside their classroom.   
The findings of the study have shown the effectiveness of Out-of-Class -Activity and 
Group Counselling Strategies (OCA and GCS) as means of enhancing achievement in 
Geometry and attitude of low-achieving students towards Geometry.  
The strategies employed have exposed the fact that the teaching learning process should 
not be restricted to the four walls of the classroom alone.  
The study proves to the educators that when low-achieving students are equipped with 
appropriate teaching strategies, their academic achievement could be improved.  It also assures 
stakeholders in education that when classroom instruction is supported with OCA, performance 
could be enhanced. In sum, the result of the study provides a basis for curriculum innovation in 
the preparation of Mathematics teachers. 
The study has demonstrated that the combination of classroom and out-of classroom 
activities have positive effect on achievement as well as attitude.   
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REFERENCES 
 
Abdelfatah,H., 2010. Improving attitudes towards geometric proof through a suggested Story-
Based Dynamic Geometry approach. A Dissertation for the Doctor of Philosophy. 
Institute of Mathematics and Computer Science, University of Education Karlsruhe, 
Germany.    
 
Abdullah, F.E. 1984. Programmed learning: A study in literary. Programmed learning and 
educational technology. Journal of APPLET. 15.1:69-78.   
 
Abiam, P.O. and Odok, J.K. 2006. Factors in students‘ achievement in different branches of 
secondary school mathematics. Journal of Education and Technology 1.1:161-168. 
 
Abimbade, A. 1990. Programmed instruction in the Nigerian school system: an investigation of 
effectiveness and efficiency. Journal of Nigeria Association for Educational Media and 
Technology. 4.1: 73-85. 
 
Abimbade, A. 1996. Computer Assisted Instruction (CA1) and the teacher. The Nigeria 
Journal of Computer Literacy, 1.1:74-81. 
 
Abimbade, A. 1997. Principles and practice of educational technology. Ibadan International 
Publishers Limited, Ibadan. 
 
Achor, E.E; Imoko, B.I and  Uloko, S.E., 2009. Effect of ethnomathematics teaching approach, 
on senior secondary students‘ achievement and retention in Locus. Educational 
Research and review. 4.: 8 385-390.  
 
Ackerman, Philip L. and Woltz, Dan J. 1994. Determinants of learning and performance in an 
associative memory/substitution task: task constraints individual differences, volition, 
and motivation. Journal of Educational Psychology. 86.4: 487-515.      
 
Adebayo, F.O. 2005. Brain-based Instructional Strategy and Students Learning  Outcomes 
 in Chemistry in Ibadan, Nigeria. An Unpublished M.Ed Project  University of 
 Ibadan, Nigeria.  
 
Adebowale, D.A. 2000. The relationship between changes in attitude towards a course and 
 final achievement. An International Journal of Applied Psychology, 46:15-28. 
 
Adegbile, J.A. 2002. Advance organizer and secondary school teacher. In S.O. Ayodele. 
 (Eds.)  Teaching strategies for Nigerian secondary schools, Ibadan: Powerhouse  Press 
 and  Publishers. Chapter 4:45-56. 
 
Adegoke, A. B. (2002). Teacher influence as a determinant of dependent prone students‘ 
learning outcomes in senior secondary school geometry. PhD. Thesis. Institute of 
Education. University of Ibadan. ixviii+243pp 
 
Adegoke, A.B. 1999. School enrolment and the girl: and overview of the Nigerian 
 situation. Counsellor 17.1:58-65. 
 
 
 85 
UNIVERSITY OF IBADAN LIBRARY
Adeleke, J.O. 2007. Gender role on topic preference of senior secondary school students in 
th
 mathematics. A paper presented at WAEC monthly seminar held in Lagos on 27  
 April,  2007  
 
Adepoju, A.A. 2002. Mastery Learning Strategy and secondary School Teaching. In S.O. 
 Ayodele. (Eds). Teaching strategies for Nigerian secondary schools. Ibadan, 
 Nigeria. Powerhouse Press and Publishers. Chapter 5:57-67.  
 
Adesoji, F.A. 1991. A comparative Analysis of problem-solving and self-Learning 
 Technique in Teaching Electrolysis. Ph.D. Thesis. Obafemi Awolowo University,  
 Ile-Ife.  
 
Adesoji, F.A. 2008. Students‘ ability levels and effectiveness problem-solving instructional 
strategy. Kanla-Raki Journal of Social Science, 17.1:5-8. 
 
Adetunji, F.O. 2000. A study of some Nigerian Primary school teachers‘ attitude to 
mathematics. African Journal of  Educational Research, 6.1& 2: 93-99.  
 
Adeyegbe, S.O. 2000. Innovation in assessment procedures as an interventionist strategy for 
equity in gender performance in science.  Technology and mathematics(STM) 
th
proceedings of Ajumogba Memorial conference in commemoration of the 40  
anniversary of science teachers‘ association of Nigeria. 
 
Adeyegbe, S.O. 2000. Packing Science, technology and mathematics education. To maximize 
st
 standards progression and continuity; Challenges of the 21  century. Keynote address 
th
 at the 4  International conference of Science Teachers Association of Nigeria (Lagos 
 Brand). 
 
Adeyoju, C.A. 1989.  The relative effectiveness of cognitive restructuring and study skills 
training on the adjustment to academic failure among a group of Nigerian students. 
Ph.D Thesis, Department of Guidance and Counselling.  University of  Ibadan  
vi+192pp .  
 
Adler, Irving. 1965. ―Mathematics for the Low Achievers,‖ N.E.A. Journal (now Today‘s 
Education), 54: 29-30. 
 
Agomoh, C.C. 2006. An evaluation of child-friendly environmental status of primary schools 
in Abia State.  Ph.D Thesis. Institute of Education.  University of Ibadan, Ibadan.  
 
Agwagah, U.N.V. 1993. Instruction in mathematics reading  as a factor in  students‘ 
 achievement and interest in word problem-solving. Unpublished  doctoral Thesis, 
 niversity of Nigeria, Nsukka. 
 
Aiken, L. R.  1976.  Update on attitude and other affective variables in learning 
 Mathematics.  Review of Educational Research. 46 .2: 290-310. 
 
th
Aiken, J.R. 2002a. Psychological testing and assessment (10  ed.) Boston, MA: Allyn and 
Bacon. 
 
 
 86 
UNIVERSITY OF IBADAN LIBRARY
__________2002b. Attitude and related psychosocial construct: Theories  and Assessment, 
 18.  
 
Ajewole, G.A. and Adewoyin, J.A. 1996. Use of micro-computer vis-à-vis traditional 
 methods in Sscondary School Integrated Science Classroom: Nigeria Journal of 
 Computer Literacy. 4.1:49-54. 
 
Ajiboye, J.O. 1996. A Self-Learning Programme, the Modified Lecturer Method and Students‘ 
Cognitive and Affective Outcome in Some population Education Concepts. PhD. Thesis 
Dept. Of Teacher Education, University of Ibadan Tr Edu. XIV+Pp 280.  
 
Ajitoni, S.O. 2005. Effects of full and quasi participatory learning strategies on senior 
secondary pupils‘ environmental knowledge and attitude in Kwara State Nigeria. Ph.D 
Thesis. Dept of Teacher Education, Faculty of Education, University of Ibadan.  
xxii+274pp.  
 
Akande, J. 2002. Engendering University Curriculum and Administration. Paper presented 
 at workshop on gendering curriculum and administration in the University, Olabisi 
 Onabanjo University, Ago-Iwoye, Nigeria. 
 
th
Akay, G. 2011. Effect of Peer instructional method on the 8  grade students‘ mathematics 
achievement in Transformation Geometry and Attitudes toward mathematics.   
 
th
Akay, G. 2011. The effect of peer instruction method on the 8  grade students‘ mathematics 
achievement in transformation geometry and attitude towards mathematics. M.Sc 
Thesis, Dept of Elementary Education, Middle East Technical University. Retrieved on 
th
6  September, 2012 from htt://etd.lib.metu.edu.tr/upload/12612931/index.pdf.   
 
Akinbote, R.O. 1993. Instructional Sequencing Modes and Feedback Mechanism 
 administration in primary and secondary schools: Determinants of Achievement  in 
 Primary School Social Studies.  Ph.D Thesis, Dept of Teacher Education,  University 
 of Ibadan,  xxii+288 Pp. 
 
Akinola, E.M. 2003. The Impact of Se lf-assessment on achievement. Journal of Educational 
Research, 87:60-75. 
 
Akinsola, H.Y. 2005. A problem-based learning curriculum. Curriculum development in 
Nursing. Process and Innovation. U.Is, L.R. and Gewele, N.S. New York. Routledge 
Taylor & Francis Group Chapter 8: 127-141. 
 
Akinsola, M.K. 1995. Comparative effects of mastery learning and enhanced mastery learning 
strategies on students achievement and self-concept in mathematics Ph.D Thesis. 
Department of Teacher Education. University of Ibadan, Ibadan, xiv+ 234. 
 
__________1999. Factors inhibiting the learning of Mathematics. in Obemeata, J.O; 
 Ayodele,S.O; Araromi, M. A. (Eds). Evaluation in Africa in Honour of E.A. 
 Yoloye. Ibadan Stirling Horden Publishers. 
 
 
 
 87 
UNIVERSITY OF IBADAN LIBRARY
Akinsola, M.K. and Tella, A. 2001. Diagnosis of public difficulties and errors in learning 
 mathematics in primary school in Ibadan. Ibadan Journal of Educational Studies 
 1.1:118-127.  
 
__________2002. New Direction in School Mathematics.  In J,A,Ajala (Eds) Designing 
content of the curriculum. A guide to practice.  Published by MayBest Publication. 
16Ayoola Drive New Bodija  Extension Ibadan, Nigeria. 
 
__________ & Tella, A. A. 2007. Correlates of academic procrastination & mathematics 
achievement of university undergraduate students. Eurasia Journal of Mathematics, 
Science & Technology Education, 2007. 3.4: 363-370.  
 
__________ and Olowojaiye, F.B. 2008. Teacher Instructional Methods and Students attitudes 
toward Mathematics International Electronic, Journal of Mathematics Education, 
3.1:60-73. 
 
Akpan, A.A. 1987. Correlates of mathematical problem solving ability among secondary 
school students.  Ph.D Thesis. University of Ibadan, Ibadan. Department of Teacher 
Education xxi+378pp. 
 
Alao, K. 2000. The impact of counselling services and tenure satisfaction of junior staff in 
Nigerian university. Department of Educational Foundations and Counselling, Faculty 
of Education, Obafemi Awolowo University, Ile-Ife.  
 
Alderman, R. V. 2008. Faculty and students out-of-classroom interaction: Student perceptions 
of quality of interactions doctoral dissertation. Texas A&M University. 
 
Alemni, S.O. 2008. Teaching Modules for Junior Secondary Mathematics 1. Published by 
National Mathematical Centre, Abuja Lokoja Highway Kwali, Abuja. 
 
Alexandria, V.A. 2005. American School Counselling and Association 2005. The ASCA 
nd 
National model. A framework for School Counselling programmes (2 ed). 
 
Almeida, D. 2000. A Survey of mathematics undergraduates interaction with proofs some 
 implications for mathematics education. International journal of mathematical 
 education in science and technology, 31. 6:869-890. 
 
Alrwas, A.M. 2000. The Relationship among eighth-grade students‘ creativity, attitudes, 
school grade and their achievement in Mathematics in Saudi Arabia. Ph.D. 
Dissertation, Ohio University, Retrieved from wwwlib.vmi.com/dissertation/results. 
 
Alvaro, D.A.1973. A comparison of Scientific Heuristic and Traditional Method of Teaching 
Mathematics.  Master of Science thesis, Faculty of Education, Simon Fraser University.  
 
Amelink, C.T.  2009. Information Sheet: Gender Differences in math performance. Ph.D 
st
Virginia Tech. Retrieved on 21  October, 2012 from http://www.AWEonline.org. 
 
Arcavi, A. & Hadas, N. 2000. Computer Mediated Learning: An Example of an Approach. 
International Journal of Computers for Mathematical Learning, 5.1: 25-45. 
 
 88 
UNIVERSITY OF IBADAN LIBRARY
Aremu, A. 1998.  Effects of card and Geoboard Game-based instructional strategies on primary 
school pupils‘ achievement in practical Geometry. Ph D.Thesis. Department of Teacher 
Education,  University of Ibadan, xvii+188pp. 
 
__________1998. Strategies for improving the performance of female pupils in Mathematics. 
African Journal of Education Research 5.1:77-85. 
 
__________2001. Effects of games on Mathematics achievements on Pupils ability in Nigeria 
Primary School Ibadan. Journal of Education Studies. 96-105. 
 
Aremu, S. 2001. Techniques of achievement analysis. In S.O. Ladipo. (Eds). Fundamentals of 
Guidance and counseling II.  Oyo, Nigeria, OYSCE Publication Series. Chapter 2:30-
49.  
 
Aremu, A.O. 2002. Application of psychology to secondary school teaching in S.O. Ayodele 
(Eds). Teaching strategies for Nigerians secondary schools Ibadan: Powerhouse Press 
and Publishers, Ibadan. Chapter 1:3-14. 
 
Arizpe, O.; Dwyer, J. and Stevens, T., 2006.  Mathematics self-efficacy of Middle school 
students solving the Rubik Cube. Department of Mathematics & Statistics, MS 1042 
Texas Tech University.  
 
Asim, A. E. 1998.  An evaluation of the relative effectiveness of two teaching approaches 
based on the constructive perfective for teaching primary science. Ph.D Thesis. Institute 
of Education. University of Ibadan. x+ 220pp.  
 
Astin, A.W. 1993. What matters in college: Four critical years revisited. San Francisco, CA: 
Jossey Bass. 
 
Asuru, V. A. 2006.  An Evaluation of implementation of the Universal Basic education 
programme in River State. Ph.D.Thesis, Institute of  education University of Ibadan.59-
63,97pp.  
 
th
Atkinson, D.R. 2004. Counselling American minorities (6  ed.) New York. Mc Graw Hill: 
th
 Retrieved in 30  December, 2009 from 
 http://www.thefreelibrary.com/closing+gap:a+group+counselling.    
Ausubel, D.P 1960. Use of advancer organizers in the learning and retention of meaningful 
material. Journal of Educational Psychology 51. 267-272.  
 
__________1963. The Psychology of meaningful verbal learning. New York. Gruine and 
Striation. 
 
__________1968. Educational psychology: A cognitive view. New York: Holt, Rinehart and 
Winston.  
 
__________1973.The psychology of meaningful verbal learning.  New York, NY: Harvard 
University Press. 
 
 
 89 
UNIVERSITY OF IBADAN LIBRARY
_________1978. Educational psychology: a cognitive view (2nd .ed). New York: Werbel and 
Peck.  
 
Awofala, A. O. 2002. Cognitive style, concept mapping paradigms and achievement in 
secondary school mathematics. Med Thesis. Dept of Teacher Education. University of 
Ibadan. x+150pp.  
 
_________2007. The impact of personalized instructional context in word problem type on 
SSS learning outcomes in mathematics. Seminar presented at the joint staff/higher 
degrees students seminar series. Dept. of Teacher Education, University of Ibadan, 
Ibadan.  xi+56. 
 
Ayedun, J.O. 2000. Influence of Sex difference of students on their achievement in secondary 
 school mathematic Abacus. The Journal of Mathematical Association of Nigeria.  
 
Ayodele, S.O. 2002. Teaching strategies for Nigerian Secondary Schools (Eds). Ibadan, 
Nigeria. Powerhouse Press and Publishers.  
 
_________and Adegbile, J.A. 2003. Methods and strategies for effective teaching. Ibadan: The 
Powerhouse Press and Publishers, Ibadan.       
 
Ayoola, E.B. 2002. Teaching strategies for an improved teaching of government in the 
secondary schools. In S.O. Ayodele. (Eds). Teaching strategies for Nigerian secondary 
schools. Ibadan, Nigeria. The Powerhouse Press and Publishers, Ibadan. Chapter 
13:149-157.  
 
Baharvand, M. 2001. A Comparison of the Effectiveness of Computer-Assisted  Instruction 
 versus Traditional Approach to Teaching Geometry.Unpublished Master Thesis, 
 California State University, USA. 
 
Baker, D., With, P.A. 1996. Evaluation of the impact of two after-school programs. Journal of 
Park and Recreation Administration, 14. 3: 23-44.  
 
Baker, S. Gersten, R. and Lee, D. 2002.  A synthesis of Empirical Research on Teaching 
Mathematics to low Achieving Students. Elementary School Journal, 103:45-74. 
Retrieved in March 18, 2010 from http://www.nichy.org/Research/Summaries/ 
pages/Abstractlb.aspy.  
 
Bandura, A. 1986. Social foundation of thoughts and actions. A social cognitive theory. 
Englwood cliffs: N.J: Prentice –Hall.  
 
__________1996. ―Multifaceted Impact of Self-Efficacy Beliefs on Academic Functioning‖. 
Child Development.  67.3:1206-1222. 
 
__________1997. Self-efficacy. The exercise of control. New York W.H. Freeman and 
Company. 
 
__________2000.Exercise of human agency through collective efficacy. Current Diretions in 
Psychological Sciences,9.3: 75-78 
 
 90 
UNIVERSITY OF IBADAN LIBRARY
__________and Barbaranelli, C. Caprara, G.V. & Pastorelli, C. 2001. ―Self-Efficacy Beliefs as 
Sharpers of children‘s Aspiration and Career Trajectories Child Development. 
72.1:187-206. 
 
Barabasz, A.F and Barabasz, M. 1981.  Effects of rational-emotive therapy on psychological 
and reported measueres of test anxiety arousal.  Journal of Clinical Psychology,37.3: 
511- 514. 
 
Battista, M. (1990). Spatial Visualization and gender difference in high school geometry. 
Journal for research in Mathematics Education,21.1:47-60. 
 
Battista, M. T. 1994. Greeno‘s Environmental/model View of Conceptual Domains: A 
Spatial/geometric Perspective. Journal for Research in Mathematics Education, 25.1: 
87-94. 
 
__________and Clement, D. H. 1999. Research into Practice: Using Spatial imaginary in 
 Geometric reasoning. Arithmetic Teacher, 39. 3: 18-21. 
 
Baynes, J. F. 1998. The Development of a van Hiele-based SummerGeo metry Program and its 
Impact on Student van Hiele Level and Achievement in High School Geometry. 
Unpublished EdD Dissertation, Columbia University Teachers College, USA. 
 
Beck, A.T. 1997. The past and future of cognitive therapy. Journal of psychotherapy practice, 
6:276-284.  
 
Bendow, C.P. 1990. Sex differences in mathematics reasoning ability among intellectual 
talented. Further thoughts. Behavioural and Brain Sciences. 13. 196-198. 
 
Bergeson, T., Fitton, R., & Bylsma, P. 2000.  Teaching and Learning Mathematics Using 
Research to Shift From the ―Yesterday‖ Mind to the ―Tomorrow‖ Mind. Washington 
State, State Superintendent of Public Instruction. 
 
Bergman, G. And Earley, B. 1991. Group Counselling for school counsellor: A practical guide. 
Maine: Jweston Walch.  
 
Bessoondyal, 2005. Gender and other Variables in Mathematics Achievement in Mauritius.  
Unpublished PhD Thesis, Curtin University library. 
 
th
Best, J.W., 1981. Research in Education (4  edition) New Jersey: Prentice-hall Inc.  
 
rd
Biehler, R.F. 1978.  Psychology applied to teaching (3  .ed).  Houghton Mifflin Company 
Boston Dan.  Geneva, Illinois Hopewell, New jersey Palo Alto London. 
 
Bindak,R.2004.  Geometri tutum Olcegi guvenirlik calismasi ve bir uygulama. Unpublished 
doctoral dissertation, Diele University , Diyarbakir. 
 
Binggeli, N. 2010.Cognitive Behavioural Therapy techniques part I: Cognitive restructuring.  
 
Bishop and Walker 1990. College Counselling and student retention: research findings and 
implication for counseling centres. Journal of colleges counseling.  
 91 
UNIVERSITY OF IBADAN LIBRARY
Boaler,cited by Riddon, C. L., 2004. Article: The effect of a problem centered approach to 
th
mathematics on low-achieving six graders. Retrieved on 18  march, 2010 from  
http;//www.highbeam.com/doc/IGI-120635860.htm. 
 
Bohner, G.,& Wanke,M.,2002.Attitudes and attitude change. Psychology Press.  
 
Bong, M. and Skaalvik, E.M. 2003. Academic self-concept and self-efficacy: How different 
are they really? Educational Psychology Review,15:1-14. 
 
Bonotto, C. and Basso, M. 2001. Is it possible to change the classroom activities in which we 
delegate the process of connecting mathematics with reality? International Journal of 
Mathematical Education in Science and Technology, 32. 3: 385-399.  
 
Bordo, S. 2001. Selection from the flight to objective in Leadernman, M. and Rarrtsg. Ids. The 
Gender and Science Readers London. Routledge.  
 
Borrow, C. V. A. (2000). An Investigation of the Development of 6th Grade Students' 
Geometric Reasoning and Conceptualizations of Geometric Polygons in A Computer 
Microworld. Unpublished PhD Dissertation, Kent State University. 
 
Brief Relational Mathematics Counseling Approach to Support Students Taking introductory  
College Mathematics. Jihan M. Knowles Endicott College jiknowles@endicott.edu. 
 
Brigman, G and Campbell, C. 2003. Helping students improve academic achievement and 
school success behaviour, Professional School Counselling. 7.2: 91-98.  
 
Brigman, G.A., Webb, L.D., and Campbell, C. 2007. Building skills for schools success: 
 Improving the academic and social competence of students, Professional School 
 Counselling. 10:279-288.  
Brookes, O.K. and Richard, O. 2004. The Wilderness as therapy. Journal of Experimental 
Education 6:6-9.  
 
Brown I. Jr. and Inouye, D.K. 1978. Learning helplessness  through modeling: The role 
perceived similarity in competence. Journal of Personality and social Psychology 36: 
900-908.     
 
Bruning, R.H., Schraw, G.J. Roming, R.R. 1995. Cognitive Psychology and Instruction. 
Englewood Cliffs, NJ: Merrill. 
 
Burieson, J.A and Kaminer, Y. 2005. Self-efficacy as a predictor of treatment outcome in 
adolescent substance use disorders.  Addictive Behaviour, 30. 17: 51-64.  
 
Burton, D. M., 1999. The History of Mathematics: An Introduction, 4th ed. Boston, WCB 
 McGraw-Hill. p.79. 
 
Bybee, R.W.; Buakwalat, T; Luero P. T; Matsu, M & Mclinery I.D, 1989.  Science and 
technology education for the elementary years framework for curriculum and 
instruction Washington D.C. National Census for improving science education. 
Retrieved June,26,2003,fromhttp://www.Ericdgests.org/1997-2/selfhtm. 
 92 
UNIVERSITY OF IBADAN LIBRARY
Callahan, W.J. 1971. Adolescent attitude towards math.  Mathematics Teacher. 64:751-755. 
 
Campbell, N.K. and Hackett, G. 1986. The effects of mathematics task performance on math 
 self-efficacy and task interest. Journal of Vocational Behaviour, 28:149-162. 
 
Campbell,C.A. and Brigman,G, 2005. Closing the achievement gap: A structured approach to 
group counselling, The Journal for Speciallist in Group Work,30: 67-82. 
 
Canadian council on learning 2006. Lesson on learning. The Rural-Urban Gap in Education. 
Downloaded [23.06:09] from http://www.ccl-cca.ca/pdfs/LessonsInLearning/10-0301 
06E.pdf.  
 
Capraro, R. M. 2000. Exploring the effects of Attitude toward mathematics, Gender and 
ethnicity on the acquisition of Geometry content knowledge And Geometric spatial 
visualization. Unpublished PhD Dissertation. The University Of Southern Mississippi, 
USA. 
 
Carter,D.B. 2012. Life Coaching.Bristol, London, UK& International. Retrieved on 
August17,2007,fromhttp://www.noanxiety.com/psychotherapies/cognitive-behavioural-
therapy.html.  
 
Cavanagh,S. 2009.  Parents schooled in learning How to Help with Math Education Week. 
 
Ch, A.H. 2006. Effect of guidance services on study attitudes, study habits and academic 
achievement of secondary school students. Bulletin of Educational & Research 28. 
1:35-45.  
 
Chanbarzdeh, N. 2001. An investigation of the relationship between mathematics attitudes, 
self-efficacy beliefs ad mathematics performance expectation and mathematics 
th
performance of the 19  grace girls and by students in Tehran. M.A. Thesis, University 
of Tehra.  
 
Change, J.C. 2005. Faculty-student interaction at the community college: A focus on students 
of color. Research in Higher Education, 46.7:769-802.   
 
Chazan, D. 1998. Similarity: Exploring the Understanding of a Geometric Concept. 
 (Technical report no:88- 15). Cambridge, MA. Educational Technology Center. 
 
Chemers, M.M. Hu, Land Gracia, B. F. 2001. Academic self-efficacy and first-year college 
student achievement and adjustment. Journal of Educational psychology.93.1:55-64.  
 
Chibuogwu, V.N. 2006. Enhancing female students‘ participation in Science, Technology and 
Mathematics Education (STME) through gender-fair instructional behaviour. In 
E.Okeke; M .Opara STAN (Eds). Gender and STM Education series 1.  
 
Chickering, A.W; & Gamson, Z.F.1987. Seven practices for good practice in undergraduate 
education. AAHE Bulletin, 39.7:3-7. 
 
Chief Examiners‘ Reports, 2005 & 2007.  West Africa Examinations Council. 
 
 93 
UNIVERSITY OF IBADAN LIBRARY
Choi-Koh, S. S. 1999. A Student‘s learning of Geometry Using the Computer. Journal of 
 Educational Research, 92. 5: 301-331. 
 
Civil, M. & Bernier, E. 2006. Exploring images of parental participation in mathematics 
education: challenge and possibilities. Mathematics Thinking and Learning, 8. 3: 309-
330. 
 
Civil, M. 2002. Everyday mathematics, mathematicians‘ mathematics and school mathematics; 
 can we bring them together? In Brenner, M. and classroom, Journal of Research in 
 Mathematics Education Monograph II, Reston, V.A. MCTM, Pp 40-62.  
 
Clement, J.J. 1982. Students‘ preconceptions in introductory mechanics. American Journal of 
physics. 50:66-71.      
 
Clements J.J. & Anderson, B. 1991. Women of colour in Mathematics, Science and 
Engineering: a review of literature. Washington DC: Center for Women Policy Studies. 
 
Clements, D. H. & Battista, M. T. 1992. Geometry and Spatial Understanding. In Dougles A. 
Grouws (Ed.,), Handbook of Research in Mathematics Teaching and Learning. New 
York. McMillan Publishing Company. 
 
Cobb, P., Wood, T., Yackel, E., Nicholls, J., Wheatley, G.,Trigatti, B.,and Pertwitz, M 1991. 
Assessment of  a problem-centered second grade mathematics project. Journal for 
research in Mathematics Education. 473:15-31.  
 
Colley A. and Comber C. 2003. Age and gender difference in computer use and attitudes 
among secondary schools students: What has changed? Educational Research 5: 2-7. 
 
Collins, J.L. 1982. Self-efficacy and ability in achievement behaviour. Paper presented at the 
Annual meeting of the American Educational Research Association, New York.  
 
Cotton, S.R. and Wilson, B. 2006. Student –faculty interactions: Dynamics and determinants. 
Higher Education, 51:487-519.    
 
Crowley, M. 1987. The van Hiele Model of Development of Geometric Thought. In Learning 
and Teaching Geometry K-12. In Mary M. Lindquist & Albert P. Shulte (Eds.), 1987 
Yearbook of the National Council of Teacher of Mathematics, 1-16. Reston, Va. 
NCTM. 
 
Curren, Mary T. and Harich, Kabiri R 1993. Performance attributions: effects of mood and 
involvement. Journal of Educational Psychology. 85.4: 605-609. 
 
D‘Ambrosio, U. 2006a. Ethnomathematics. Rotterdam: Sense Publishers. 
 
D‘Ambrosio, U. 2006b. The program ethnomathematics: a theoretical basis of the dynamics of 
intra-cultural encounters. The journal of Mathematics and culture, 1.1: 1-7.  
 
Davis, B. 2002. Motivating Students. Tools for teaching, Retrieved September 14, 2003, from 
http://teaching.berkley.edu/bgd/motivate.html.   
 
 94 
UNIVERSITY OF IBADAN LIBRARY
Davis, R. Braun, E. 2003. The gift of learning: Proven new method for correcting ADD math 
and hand writing problems. New York, Berkley Publishing Group.   
 
Delisle, J.R. and Berger, S.L. 1990. Underachieving gifted students. ERIC EC Digest II E 478. 
 
Dewey, T. 1975. Experience in Education. New York, Coker books.   
 
Din, F. S. & Whitson, J. M. 2001. The Effects of Using the TI92+ Calculator as a 
Demonstration Device in Geometry Instructions. Eric Digest, ED458114. 
 
Dixon, J. K. (1997). Computer Use and Visualization in Students‘ Construction of Reflection 
and Rotation Concepts. School, Science and Mathematics, 97. 7: 352-358. 
 
Douville, P. 2004. Use mental Imagery Across the curriculum: Preventing school failure 
49.1:36-39. 
 
_________and Pugalee, D. K. 2003.  Investigating the relationship between mental imaging 
 and mathematical problem solving.  Proceedings of the international conference of 
st
 Mathematics Education into the 21  century project September 2003.Ed.Bmo Czech 
 Republic 62-67. 
_________and Ersoy, Y. 2002. The Effects of Using Advanced Calculator (TI92/CABRI) on 
nd
Learning Transformational Geometry. Proceeding of 2  International Conference on 
the Teaching of Mathematics at the Undergraduate Level, University of Crete. Greece. 
 
_________Paksu,,A;  Ubuz, B.,2009. Effects of drama-based geometry instruction on student 
achievement, attitudes,and thinking levels. The journal of Educational Research, 102: 
272-286. 
 
Duatepe, A., 2004. The effects of drama based instruction on seventh grade students‘ 
Geometry achievement, Van Hiele geometric thinking levels, attitude toward 
mathematics and geometry. A Thesis submitted to the Graduate school of Natural and 
Applied Sciences of Middle East Technical University xix+310 pp. 
 
Duatepe-Paksu, A., Ubuz, B. 2009. Effects of drama-based geometry instruction on student 
 achievement, attitudes, and thinking levels. The Journal of Educational Research, 102: 
 272-286.  
 
Duffy, A.M. 2001. Balance, literacy in acceleration, and responsive teaching in a summer 
school literacy programme for elementary school struggling readers. Reading research 
and instruction. 40.2:67-100. Eric document reproduction service No. EJ. 624-633.        
 
Dynarski, M. & Gleason, P. 1999. How can we help? Lessons from Federal dropout Prevention 
programmes. Princeton, NJ: Mathematics Policy Research Inc. 
 
Eagly and Chaiken, 1993. The Psychology of Attitudes, Fort Worth, NY: Harcourt Brace 
Javanovich.  
 
 95 
UNIVERSITY OF IBADAN LIBRARY
Ebenezer, J.V. & Zoller, U. 1993. Grade 10 students‘ perceptions of and attitude toward 
science teaching and School Science. Journal of Research in Science Technology 30. 
2:175-186. 
 
Education Matters, 2009: Student achievement in Mathematics- the roles of attitudes, 
perception and family background. Retrieve on2/17/2009from 
http://www.stateen.gc.ca/pub/81-004-x/200 5001/7836-eng.htm. 
 
El Hassan, K. 2001. Gender issues in achievement in Lebanon. Social Bebaviour and 
Personality, 29.2:113-124. 
 
Ellis, A & Dryden, W. 2003. The practice of rational emotive therapy (2.ed). 
http://en.wikipedia.org/wiki Rational_Emotive_Behavior_Therapy. 
 
Emeke, E. A. 2002. The role of intelligence in mastery learning.  In Abdul Mansaray and Israel 
 Olu Osokoya (eds).  Curriculum development at the turn of the century, the Nigerian 
 experience. 
Emunemu, B.O. (1999). The Gender Gap in base Education: Evolving Strategies to increase 
girls‘ access. In Jobeme ata J.O., Ayodele S. and Araromi, M.A. (eds.) Evaluation in 
Africa in honour of Professor E.A. Yoloye. Institute of Education. 
 
Ergene, T.2003.  Effective interventions on test anxiety reduction: A meta-analysis. School 
Psychology International, 24.3: 313-328.  
 
Eric document 1987. A comparative effectiveness of four test preparation programmes. Final 
Evaluation report.  European Journal of Scientific Research 36. 3:336-341 “Retrieved 
from htt://www.eurojournals.com/ejsr.htm‖. 
 
Erinosho, S.Y. 1997. Female participation in Science: an analysis of secondary school 
curriculum materials in Nigeria. A bridged Research Report. No 29, Nairobi Academy 
science publisher.  
 
Erinosho, S.Y. 2002. Linking school science and indigenous science: A Science performance 
improvement programme. A research report submitted to AFCLIST.  
 
Erinosho, S.Y. 2004. Teaching science beyond the classroom four-walls. Issues in educational 
measurement and evaluation in Nigeria In honour of Wole Falayajo Institute of 
Education, University of Ibadan.   
 
Ernest, P. 1989. The Knowledge, beliefs and attitudes of the mathematics Teacher:   A Model. 
Journal of Education for Teaching, 15 .1: 13-33. 
 
Ernest, P. 2004. Images of mathematics, values and gender. In S. Johnston-Wilder and B. 
Allen (Eds.),  Mathematics Education: exploring the culture of learning. Routledge.     
 
Etukudo, U.E.,2002. The effect of computer-assisted instruction on gender and performance of 
junior secondary school students in mathematics. ABACUS, Journal of mathematical 
Association of Nigeria, 27.1:1-8. 
 
 96 
UNIVERSITY OF IBADAN LIBRARY
Ezeugo,N.C and Agwagah, NU.N.V.,2000. Effects of concepts mapping  onstudents‘ 
st
achievement in algebra, implications for secondary mathematics education in the 21   
century.ABACUS, Journal of Mathematical Association Nigeria, 25. 1:1-12. 
 
Ezike, B.U., 2007. Effects of self-learning and learning –together instructional strategies on 
senior secondary school students‘ achievement in and Attitude towards Chemistry.  
 
 
Fadia, N. and Menucha, B. 2005. Modelling Mathematics achievement of Jewish and Arab 
Eight graders in Israel. The effects of learners-related Variables. Educational Research 
and Evaluation. 11.3:277-302. 
 
Fair child, 1994.  Helping students improve academic achievement and school success 
behaviour. 
 
Fajemidagba, D. 1996. School Mathematics and mass education in Nigeria.. In S. Ayodele 
(Ed). Results of an exploratory study. Education in the service of humanities. Ibadan: 
Educational Research and Study Group. 
 
Fajonyomi, M.G. 2001. Relative Effectiveness of three models treatments on English 
Language performance among secondary school students in Maiduguri, Ife pscyhologia 
9.1:11-104. 
 
Fakolade, O.A. 2008. Career Development and personality construct.  Challenges for school 
counselors.  A paper presented at a three day training workshop on social structure  and 
behavioural modification. Challenges of Guidance counselors in public secondary 
schools 81-87. 
 
Fakunle, O. 2007. Building in peaceable school. A lecture delivered at one-day workshop 
organized for guidance counsellors in Oyo State Secondary Schools by the Oyo State 
Ministry of Education at Largelu Grammar School, Ibadan. 
 
Falade, 2001. Questions and answers on concepts, methods, issues and problems in social 
studies Pumak Nigerian Ltd. 
 
Falaye, F.V. 1995. Comparative Effectiveness of Delayed and Immediate Feedback on senior 
 secondary school students‘ performance in Geography. A Thesis in the Institute of 
 Education, University of Ibadan, Ibadan xviii+222Pp. 
 
Falk, J.H, Dierking L.D, 1992. The Museum experience. Washington D.C: Whale Sback 
Books. 
 
Faloye, J.O. 2009. Measured Effects of Cognitive restructuring and Self-regulatory Training on 
attributional Behaviour and Academic Self-Efficacy of Low-Achieving Students in 
Ondo State.Ph.D Thesis.  Department of Guidance and Counselling, University of 
Ibadan,  Ibadan. xi+135pp. 
 
Fennema, E. H. 1974. Sex differences in mathematics achievement: A review Journal of 
Research in mathematics Education 5: 126-139.  
 
 97 
UNIVERSITY OF IBADAN LIBRARY
__________and Sherma, J. 1978. Sex related differences in mathematics achievement. Journal 
for research  in mathematics education 9:189:203.  
 
__________and Peterson, P. L. 1986. Teacher –student interaction and sex related differences 
in learning mathematics.  Teaching and Teacher Education 2:19-42.     
 
__________2000. Gender and Mathematics: What is known and what do I wish was known?. 
 A  paper prepared for the 5th Annual Forum of the National Institute for Science 
 Education by Wilcosin Centre for Educational Research, Michigan. 
 Retrieved12/3/09fromhttp://www.wceruw.org/archive/nise/NewsActivities/Forums/Fen
 n. 
Fisher,P.H. , Masia- Warner, C.,& Klein, R.G.2004.  Skills for social and academic success: A 
school-based intervention for social anxiety disorder in adolescents.  Clinical Child and 
Family Psychology Review, 7. 4 :241-249. 
 
Flanagan, K. A. 2001. High School Students' Understandings of Geometric Transformations in 
the Context of a Technological Environment. Unpublished PhD Dissertation, The 
Pennsylvania State University, USA. 
 
Ford, D.Y. 1992. Determinants of underachievement as perceived by gifted, above-average, 
and average Black students. Paper review, 14.3: 130-136. 
 
_________1995. A study of achievement and underachievement among gifted potentially and 
regular education black students. Storrs, CT: The University of Connecticut, National 
Research Centre on the Gifted and talented. 
 
_________1996. Reversing underachievement among gifted black students: promising 
practices and  programmes. New York: Teacher College Press.    
 
_________and Thomas, A. 1997. Underachievement among gifted minority students: 
Problems and promises. ERIC digest E544. Reston, VA: Eric clearinghouse on 
disabilities and Gifted Education. 
 
Ford, P. 2003. Outdoor Education: definition and philosophy. ERIC Clearing house on Rural 
Education and small school, (ED 267941).  
 
Fouad, N.A.  1995. Career linking: An intervention to promote math and science career 
awareness. Journal of Counselling and Development, 73.527-534.  
 
Fraenkel, J.R. & Wallen, N.E, 2006. How to design and Evaluate Research in Education. 
McGrew Hill, London.  
 
Fransen, W.F. 2003. process Dramo and Integrated problem Solving: An Integrated Approach. 
Unpublished Ph.h Dissertation Texas, Tech. University, USA.   
 
Fraser, B.J. 1994. Research on Classroom and School Climate. In D. Gabriel (Ed.), Handbook 
of research science teaching and learning (pp 493-541), New York: Macmillan.  
 
 98 
UNIVERSITY OF IBADAN LIBRARY
FRN, 2004.  National Policy on Education 4th Edition. 
 
Froggatt,Wagne, 2005. A Brief Introduction to Rational Emotive Behaviour Therapy. Third ed. 
Retrieved 24/01/2008. 
 
Fullilove, R. E. 1987. Images of science: factors affecting the choice of Science as a career.  
The Journal of Negro Education.  59. 3: 463-478. http://www.jstor.org/FriFeb 4:20: 
2005. 
 
Furinghetti, F. & Paola, D. 2002. Defining Within a Dynamic Geometry Environment: Notes 
th
from the Classroom. In Proceeding of the 26  conference of the International Group 
for the Psyhology of mathematics education. Norwich, UK. 2: 392 – 399. 
 
Garii; Silverman, F.I. ‗Risk‘ J. 2008. Crossing Borders Visualizing School Mathematics. In 
Banta Babara Outside the Classroom Walls. International Congress on Mathematics 
Education Monterey, Mexico. 
 
Garrity, C. 1998. Does the Use of Hands-on Learning, with Manipulatives, Improve the Test 
Scores of Secondary Education Geometry Students? Eric Digest, ED-422-179. 
 
Gbodi, B. E and Laleye, A.M.2006.Effects of videotaped instruction on learning of integrated 
science. Journal of Research in curriculum and Teaching 1.1: 10-19. 
 
Gensinde, A.M. 2004. Multi-Aetilological predictors of non-school attendance behaviour 
among secondary school students in Oyo State, Nigeria. Ph.D Thesis Dept. of Guidance 
and Counselling, University of Ibadan. xii+240pp.  
 
George, D.K., Katie B.D, Jon P.L. and Jackie R.G., 1991. Students Learning Outside the 
Classroom: Transcending Artificial Boundaries.  
 
Georgewill, J.W. 1990 ―Causes of poor achievement of West African School Certificate 
mathematics examination in Rivers State Secondary Schools, Nigeria‖. International 
Journal of Mathematics Education in Science and Technology 21.3:379-385.  
 
Gesinde, S.A. 1991. Guidance and Counselling. Readings in Counselling  Practicum,  
S.A.Gesinde Ed. Ibadan. Vantage.11-16.  
 
Gfeller, M; Niss, M. 2005.An Investigation of tenth grade students‘views of the purposes of 
geometric proof. In the annual meeting of the American Educational Research 
Association, Montreal, QC, April,2005. 
 
Ghosh, A. 2007. Academic self-efficacy and achievement in a group of siblings of primary 
 schools, Psychological studies, 52: 364-366.  
 
Glasserfield, E. Von, 1986. The construction of knowledge seaside, intersystem publications. 
The system inquiry services.   
 
Gober, D and Mewborn, D. 2001. Promoting equity in Mathematics classrooms. Middle School 
Journal 32. 3:291-310.  
 
 99 
UNIVERSITY OF IBADAN LIBRARY
Goldstein, F.C., & Levin H.S. 1987. Disorders of reasoning and problem-solving ability. In M. 
Meier, A. Benton, & L. Diller (Eds.), Neuropsychological rehabilitation. London: 
Taylor & Francis Group. P327-354.  
 
Gonzales, P., Guzman, G.C., Partelow L. Pahlke, E. and Kastberg D., 2004. Highlights from 
the Trends in International Mathematics and Science Study (TIMSS) 2003. U.S. 
Department of Education Institute of Education Sciences NCES 2005-005. 
 
Graham, P. 2005. Jack Tizard lecture: Cognitive behaviour therapies for children: Passing 
fashion or here to say?.Child and Adolescent Mental Health, 10,57-62. Retrieved on 
st
21  September,2011 from jsc.montana.edu/articles/v6n15.pdf. 
 
Gray, A. 1999. Wikipedia, the Free Encyclopedia. Retrieved from 
http://en.wikipedia.org/wiki/Constuctivist.-teaching-methods last modified 24th May 
2010. 
 
Greer, B. 1989: Cognitive psychology and Mathematics challenges. New Directions in 
Mathematics Education.  
 
Grimm, M.T.A. 1997. A study of the ‗pride‘ programme: A residential, summer–school 
 program for at-risk middle-school students in an urban community (Intervention, 
 mentorship, school business partnerships). Doctoral dissertation, Old Dominion 
 University, 1997. Dissertation Abstracts International, 58, 09A.  
 
Gysbers, N.C.2004. Comprehensive Guidance and Counselling programes: the evolution of 
accountability, Professional school couselling 8.1:1-14. 
 
Hagerdon, L.S., Maxwell, W., Rodriguez, P., Hocrevar, D, and Fillpot, J. 2000. Peer and 
student-faculty relations in community colleges community College Journal of 
Research and Practice, 24. 5:87-598.  
 
Hall, R.J.and Hughes,J.N., 1989. Cognitive- behavoural approaches in the schools: An 
overview. In J.N Hughes, & R.J. Hall (Eds.), Cognitive Behavioural psychology in the 
schools: A Comprehensive Handbook (pp.1-11) New York: The Guilford Press.  
 
rd
Halpern, D.F. 2000. Sex differences in cognitive abilities (3  ed.) Mahawah, NJ: Erlbau.  
 
Hanlon, E.H. & Schneider, Y. 1999. Improving Math Proficiency through Self-Efficacy 
Training. U.S, New York: Annual Meeting of the American Educational Research 
Association, ERIC Document Reproduction Service ED433236. 
 
th
Hanna, G. 1986. Sex differences in the mathematics achievement of 8  graders in Ontario. 
Journal of Research in Mathematics Education, 17; 231-237.  
 
Harlow, K. And Baenen, N. 2001. The effectiveness of the Wake Summer bridge, Summer 
Enrichment programm. Eye on evaluation. E&R Report. Raleigh, NC: Wake Country 
Public school System and the Department of Evaluation & Research. (ERIC Document 
Reproduction Service No. ED 466 489).  
 
Harton, M.S. and Brosan, P.A. 1994. Doing mathematics with your child. ERIC DIGEST, 3. 
 
 100 
UNIVERSITY OF IBADAN LIBRARY
Hattie J, Marsh H, Neil J, and Richards G, 1997. Adventure education and outward bound: 
Out-of-class experiences that make a lasting difference. Review of educational 
research, 67. 1: 43-87.  
 
Healy L, and Hoyles C. 2000. A Study of Proof Conceptions in Algebra. Journal for Research 
in Mathematics Education, 31.4:396-428.  
 
Healy, L. 2000. Identifying and Explaining Geometrical Relationship: Interactions With 
Robust And Soft Cabri Constructions. In the Proceeding of the 24th Conference of the 
International Group for the Psychology of mathematics Education. Japan. 1: 103 – 117. 
 
Henry, I.O. 2008. Efficacy of Motivational Counselling and Cognitive Behavioural Therapy in 
Reducing Adolescent Nicotine Dependence Risk in Benin City, Nigeria.  
 
Hodanbosi, C. L. 2001. A Comparison of the Effects of Using a Dynamic Geometry Software 
Program and Construction Tools on Learner Achievement. Unpublished PhD 
Dissertation, Kent State University, USA. 
 
Hodges, C. B. 2005. Self-efficacy, motivational Email, and achievement in an asynchronous 
mathematics course. Ph.D Thesis. Faculty of the Virginian Polytechnic. Institute and 
State University. 
 
Hölzl, R. 2001. Using Dynamic Geometry Software to Add Contrast to Geometric Situations. 
International Journal of Computers for Mathematics Learning, 6. 1: 63-86. 
 
Hyun, M. S, Chung, H. I and Lee, Y. J. 2005.  The effect of cognitive behavioural group 
therapy on the self-esteem, depression, and self-efficacy of runaway adolescents in a 
shelter in South Korea. Applied nursing Research, 18:160-166.  
 
Ifamuyiwa, A. 2006. Effects of Self and Cooperative Instructional Strategies on Senior 
Secondary School Students‘ Learning Outcomes in Mathematics Ph.D Post-field 
Seminar Paper. The Department of Teacher Education University of 
Ibadan.Xiv+264pp.   
 
Iji, C. O. 2005.  Effects of Logo and Basic Programming on the achievement and retention in 
Geometry of Junior Secondary School Students.  Journal of Mathematical Association 
of Nigerian 
 
Ireogbu, T.O. 1998. Problem–Based Learning Numerical Ability and Gender as Determinants 
of Achievement, Problem Solving and Line Graphing Skills in Senior Secondary 
Physics of Ibadan. Ph.D Thesis, Dept of Teacher Education. University of Ibadan, 
Ibadan. xv+177pp.    
 
Ives, D. L. 2003. The Development of Seventh Graders' Conceptual Understanding of 
Geometry and Spatial Visualization Abilities Using Mathematical Representations with 
Dynamic Models. Unpublished EdD Dissertation, Montclair State University, USA. 
 
Jacquess, I. 1994. Mathematics Teaching: The Issue of Quality. International Journal of 
Mathematics Education in Science and Technology 256:823-830.  
 
 101 
UNIVERSITY OF IBADAN LIBRARY
Jeffreys, M.R. 1998. Predicting non-traditional students retention and academic achievement. 
Nurse Educator, 23. 1: 42-48.   
 
Jegede, O. 1998. The knowledge base for learning in science and technology education (151). 
In Naidoo et al. (Eds.) African Science and technology education into the new 
millennium: Practice, Policy and priorities, Kennyl: Juta & Co Ltd.  
 
th
Johnson D.W. & Johnson F.P. 2000. Joining together: group theory and group skills (7  ed). 
Boston: Allya and Bacon. 
 
Johnson, C. D. 2002. The Effects of the Geometer's Sketchpad on the van Hiele Levels and 
Academic Achievement of High School Students. Unpublished PhD Dissertation, 
Wayne State University, USA. 
 
Johnson, M. L. 1984. Blacks in mathematics: A Status report. Journal for research in 
Mathematics Education 15.22:145-153.  
 
Jokthan, E.T. 1996. Self Concept and its Implications for Counsellors. Nigerian Journal of 
Clinical and Counselling Psychology 2:1-2. 
 
Jones, K. 1998. The Mediation of Learning within a Dynamic Geometry Environment. In the 
Proceeding of the 22nd Conference of the International Group for the Psychology of 
Mathematics Education. Stellenbosch, South Africa. 3: 96-103. 
 
July, R. A. 2001. Thinking in Three Dimensions: Exploring Students' Geometric Thinking and 
Spatial Ability with the Geometer's Sketchpad. Unpublished EdD Dissertation, Florida 
International University, USA. 
 
Kabiri, M. 2003. The role of maths self-efficacy in mathematics achievement with regard to 
personal variables. MA. Thesis. Teacher Training University.  
 
Kabiri, M. and Kaimane sch, R.A. 2004. The role of self-efficacy, Anxiety, attitude and 
previous mathematics achievement in students‘ math performance. Retrieved June 5, 
2007. from http://www.uws.ed.au/conferences/2004 kabiri kiamanesh.pdf.  
 
Keiser, J. M. 1997. The Development of Students‘ Understanding of Angle in a Non-directive 
Learning Environment. Unpublished PhD Dissertation, Indiana University, USA. 
 
th
Kemeny, V. 2006. Mathematics learning: Geometry. Retrieved May 18 , 2008 from 
http://www.education.com/reference/article/mathematics-learning-geometry. 
 
Kendall, P.C. 2005. (ed): Child and Adolescent Therapies: Cognitive Behavioural Procedures, 
rd 
(3 ed). Guilford) Press ISBN 1-59385-113-8. 
 
Keogh, E., Bond, F. W.,French, C.C., Richards, A. & Davis, R. E.2004.  Test anxiety, 
susceptibility to distraction and examination performance. Anxiety, stress coping, 17. 
3:241-252.  
 
Kerlinger, F.N. 1973. Foundation of behavioural research. ondon: Holt Rinchert and Winston.   
 
 102 
UNIVERSITY OF IBADAN LIBRARY
th
Kerlinger, F.N. and Lee, H.B. 2000. Foundations of Behavioural Research, 4  edition. USA 
Wadsworth Thompson Learning, 662-3. 
 
Kiamanesh, A.R., Hejazi, E.  Ebfahani, Z.N. 2004. The role of math self-efficacy, self-concept, 
 perceived usefulness of math and math anxiety in math achievement. ―retrieved March 
 8, 2007 from http://20.85.129.104/Search?q =Ca che: u-6TrorpkhYsj:self.UWS 
 ed.au/.conferences/2004 Kaimanesh Hejazi 
 Esfahani.pdftself+efficacy+and+mathematics+achievement&ht=en&ct= 
 clinic&ed=178= ng‖.  
Kiely, J. H. 1990.  Success and failure in mathematics among standard sevens in the Bafokeng 
region. Unpublished PhD Dissertation, University of Witwatersrand, Johannesburg, 
South Africa. 
 
Kiely, J.H. 1990. Success and failure in mathematics among standard sevens in the Bafokeng 
region. Unpublished PhD Thesis, University of Witwatersrand, Johannesburg.  
 
Knapp, C.L. 1996. Just beyond the classroom community adventures for inter-disciplinary 
learning, Charleston, WV: ERIC clearing house on rural education and small schools. 
(ED 388 485).  
 
Kogce, D.,Yildiz, C., Aydin, M. & Altindag, R. 2009. Examining Elementary School Students‘ 
Attitudes towards Mathematics in Terms of Some Variables, Procedia Social and 
Behavioural Sciences, 1: 291-295.  
 
Koscinki, S.T. and Gast, D.L. 1993. Computer Assisted Instruction with Constant Time  Delay: 
Teach multiplication Facts to students with learning disabilities. Journal of Learning 
Disabilities. Research and Practice. 8.3:157-158.   
 
Krammaerae, C. and Trei Cler, P.A. 1990. Power relationships in the Classroom. In S.L. 
Gabriel and I. Smithson (Eds.), Gender in the Classroom: Power and Pedogy (Pp.41-
59). Urbana and Chicago: University of IIlinois Press. 
 
Krupnick, D. 1985. Spring Women and Men in the Classroom. Inequality and the Remedies on 
teaching and learning. Journal of the Harvard Danforth Centre. 
 
Kuh, G.D. 2003. What we‘re learning about student engagement from NSSE: Benchmarks for 
effective educational practice. Change, 24-32. 
 
Kuh, G.D., Kinzie, J., Schuh, J.H., Whitt, E.J. & Associates 2005. Student success in college: 
Creating conditions that matter. San Francisco, CA: Jossey-Bass.    
 
Kurumeh M. S. 2006. Effect of Ethno-mathematics approach on students‘ achievement in 
geometry and mensuration. ABACUS: The Journal of the Mathematical Association of 
Nigeria 31.1:35-44. 
 
 103 
UNIVERSITY OF IBADAN LIBRARY
Laborde, C. 2002. The Process of Introducing New Tasks Using Dynamic Geometry into the 
Teaching of Mathematics. In the Proceedings of the 25th Annual Conference of the 
Mathematics Education Research Group of Australia Incorporated, Auckland, New 
Zeland, July 7 – 10. 
 
Lauer, P.A., Akiba, M., Wilkerson, S.B., Apthorp, H.S., Snow, D., & Martin-Glenn M. 2004. 
The effectiveness of out-of-school-time strategies in assisting low-achieving students in 
reading and mathematics: A research synthesis. Aurora, CO: Continent Research for 
Education and Learning.  
 
Leder, G.C. 1992. Mathematics and gender: changing perspectives. Handbook of research on 
mathematics teaching and learning New York: Macmillan. pp 597-622. 
 
Liu, M., Hsieh, P., Cho, Y., & Schallert, D. 2006. Middle School Students‘ Self-Efficacy, 
Attitude and Achievement in a Computer-Enhanced Problem-Based Learning 
Environment. Journal of Interactive Learning Research, 17.3:225-242.  
 
Lohr, S.C., 2004. Student faculty connections: Grasping the essence of informal interaction. 
Unpublished doctoral dissertation, University of Southern California. 
 
Low, R. and Over, R. 1990. Text editing of algebraic word problems. Australian Journal of  
Psychology. 43. 63-70. 
 
_________1992. Hierarchical ordering of schematic knowledge relating to area of rectangle 
problems. Journal of Educational Psychology 84.1:62-69. 
 
_________1993. ―Gender differences in solution of algebraic word problems containing 
irrelevant information‖ Journal of educational Psychology. 85.2:231-239. 
 
Ma, X. and Kishor, N. 1997. Assessing the relationship between attitude towards mathematics 
and achievement in mathematics: A metal-analysis. Journal for research in mathematics 
education, 28.1:26-47.     
 
Ma‘moon M. 2005. Mathematical Thinking and Mathematics Achievement in year 11 Student 
Jordon. Unpublished thesis. University of New Castle, Australia. 
 
Malaty, G. 1994. Can young children learn abstract ideas in geometry. International Journal of 
Mathematics Education in Science and Technology 25. 5:751-758. 
 
Malkevitch, J. 1998. Finding room in the curriculum for recent Geometry. In Carmelo 
 Mammana & Vinicio Villani (Eds.,), Perspectives on the teaching Of Geometry  for 
 the 21st century. An ICMI study. Netherlands. Kluwer Academic  Publishers. 
 
Malloy, C. E. & Friel, S. N. 1999. Perimeter and Area Through the Van Hiele Model. 
Mathematics Teaching in the Middle School, 5. 2: 87–90. 
 
Mansary, A. and Ajiboye, J.O. 1994. Topic difficulties in senior secondary school geography 
among Nigerian students Abraka. Journal of Curriculum students 2.1:80-92.   
 
 104 
UNIVERSITY OF IBADAN LIBRARY
Marat, D. 2005. Secondary School Students‘ Self-efficacy in mathematics and achievement in 
diverse schools. ‗Retrieved May 10, 2007. from  
http://repositoryaut./conz.ac.nz/theses/40. 
 
Marland, P.W. 1994. Teaching implicit theories. In T. Husen & T.N Postlewaite (Eds), The 
International encyclopedia of education pp. 6178-6183. New York Pergamon. 
 
Marrades, R. & Gutierrez, A. 2000. Proofs Produced by Secondary School Students Learning 
Geometry in a Dynamic Computer Environment. Educational Studies in Mathematics, 
44: 87-125. 
 
Maxwell, J.A. 1996. A Model of qualitative research design. USA: Sage Publication. 
 
Mayberry, J. W. 1983. The van Hiele Levels of Geometric Thought in Undergraduate 
Preservice Teachers. Journal for Research in Mathematics Education, 14. 1: 58– 69. 
 
McCormick, J. and McPherson, G.E. 2003. The role of self-efficacy in a musical achievement 
in examination: An exploratory Structural equation analysis. Psychology of Music 
31.1:37-51. 
 
Mcgrannon, W. Carey, J & Dimmitt 2005. The current status of School counselling outcome 
st
Research. Research Monograph, Number 2. Retrieved 21  January, 2012.     
 
McLearn L, Raphael, D. and W. Hlstron, M. 1983. The Second International study of 
Mathematics: An overview of the Ontario grade 8 study. Orbit 67,14 (3). In Hanna, G. 
th
(1986). Sex differences in the mathematics achievement of 8  graders in Ontario. 
Journal of Research in Mathematics Education, 17:231-237.  
 
McLeod, D. B. 1992.   Research on affect in mathematics education: A reconceptualization. In 
Douglas A. Grouws (Ed.), Handbook of Research on mathematics teaching and 
learning. 575–596. New York. Macmillan. 
 
McManus, F., Waite, P. & Shafran, R. 2009. Cognitive Behaviour Therapy for low self-
esteem: A case example, cognitive and behavioural practice 16, 266-275.  
 
th
McREL, 2002.  List of benchmarks for language arts (4  ed.) Retrieved August 15, 2003, 
fromhttp://www.mcrel.org/compendium/standardDetails.asp?subjectID 
=7&standardID=5. 
 
McREL, 2003. The effectiveness of Out-of-School-Time Strategies in assisting low-achieving 
rd
students in Reading and Mathematics: A Research Synthesis. Retrieved on  3  
May,2010 from www.mcrel.org.     
 
Meece, J. Wigfield, A. & Eccles, J. S. 1990. Predictors of math anxiety and its influence on 
 young adolescents‘ course enrolment intentions and performance in mathematics. 
 Journal of Educational Psychology. 82. 60-70.  
 105 
UNIVERSITY OF IBADAN LIBRARY
Melihan, U., Seher, A., Ramazan, A. 2010. The relationship between geometry attitudes and 
self-efficacy beliefs towards geometry. Dept. of Elementary Mathematics Education, 
Faculty of Education, Aksaray University. Retrieved from www.sciencedirect.com on 
29/03/2013.    
  
Miller, P. 2001. Learning styles the multimedia of the mind. Educational Resources inform 
center 451-140. 
 
Miranda, A., Webb, L., Brigman, G.and Peloso, P. 2007. Student Success Skills: A promising 
programme to close the academic achievement gap for African American and Latino 
students. Professional School Counselling, 10: 490-497. 
 
Mitcell, K. and Ng. K. 1972. Effects of group counselling and behaviour therapy on the 
academic achievement of tests-anxious students. Journal of counselling psychology 19, 
491- 497. 
 
Mitchelmore, M.C. 1997. Children‘s informal knowledge of physical angle situations. 
Cognitive and Instructions, 7.1:1-19. 
 
Mohamed, L. Waheed, H, 2011. Secondary Students‘ Attitude towards Mathematics in a 
Selected School of Maldives. Institutes of Education International Islamic University 
Malaysia. International Journal of Humanities and Social Science. 1.15:277-281. 
 
Mohd, N., Mahmood, T.F.P.T. & Ismail, M.N. 2011. Factors that influences students in 
mathematics achievement. International Journal of Academic Research, 3. 3:49-54.  
 
Morge, S . 2005. Fall High school students‘ mathematics beliefs and society. Academic 
Exchange Quality, 9:182-187.  
 
Moss, L. J. 2000. The Use of Dynamic Geometry Software as a Cognitive Tool, Unpublished 
PhD Dissertation, The University of Texas at Austin, USA. 
 
Mousoulides, N. Philipous. G. 2005. Students motivational beliefs, self-regulations strategies 
and Mathematics achievement. ―Retrieved August, 31, 2007 from 
http://www.emis.de/proceeding/PM29/PME 29 RRpapers Vol. 3 Mousoulides 
Philippous.pdf. 
 
Mullis, I.V.S. Martin, M.O. Gonzales, E.J., Gregory, K.D., Garden, R.A.O‘Conor, K.M., 
Chrostowski, S.J., & Smith, T.A. 2000. TIMSS 1999 international mathematics report: 
Findings from IEA‘s repeat of the Third International Mathematics and Science Study 
at the eight grade. Chestnut Hill, MA: Boston College.   
 
Nakata,S.,2011.CognitiveBehaviouralTherapy(CBT)Techniques.Retrieved May5,2012,from 
http://www.buzzle.com/articles/cognitive-behavioral-therapy-cbt-techniques.html. 
 
National Education Association 1998. ―Reconstituting low-performing school and the role of 
the union in school in school improvement trends, Issues in urban Education. Volume 
No. 7. November. 
 
 106 
UNIVERSITY OF IBADAN LIBRARY
NCTM 1989. Curriculum and Evaluation Standards for School Mathematics. Reston, VA. 
NCTM publication. 
 
NCTM 2000. Principles and Standards for School Mathematics. Reston, VA. NCTM 
publication. 
 
Nichols, J.D.and Hall, H. 1995. The Effects of Cooperative learning on Student achievement 
 and motivation in a High School Geometry class. Eric Digest ED387341. 
 
Nicolaidou, M. and Philippou, G. 2003. Attitudes towards mathematics, self-efficacy and 
achievement in problem solving. European research in Mathematics Education III. 
 
No Child Left Behind Act of 2001. No. 107-110. 
 
Notting, 1990. The effects of Counselling and Study skills training on mathematics academic 
achievement. http://www.academicsuccess.com/research/mss-acbieve.  
 
Nwangwe I.P.  West African Journal of Counseling and Psychotherap. 
 
Obanya, P.2002. Channeling the energies of students to more purposeful 
endeavours.Revitalizing Education in African,Ibadan. 
 
Obanya,P.2009.  Dreaming,living and doing education.  Published by educational research and 
study group.  Institute of Education University of Ibadan. 
 
Oden, S.N. 1999. The process writing approach as a facilitator of university undergraduates 
competence in English Composition. Ph.D, Thesis. Department of Teacher Education, 
University of Ibadan. xiii + 188pp. 
 
Odeyemi J. O. 2004. Nature of Mathematics and its instructional problems. A valedictory 
Lecture by Institute of Education, University of Ibadan, Nigeria.  
 
Odogwu, H.N. 2002. Female students‘ perception and attitude to mathematics Association of 
Nigeria. 27.1:19-29. 
 
Odubunmi, E.O. 1998. The nature of attitude and its pedagogical implications with reference to 
science. Issues in Teacher Education and Science Curriculum in Nigeria. Curriculum 
Organization of Nigeria Monograph Series 288-299. 
 
Ogunleye, 2003. Evaluation of environmental aspect of the senior secondary school. 
Chemistry, Curriculum in Ibadan, Nigeria. Ph.D. Thesis Department of Teacher 
Education, U.I. xviii+230pp.  
 
Ohanaka, B.I. 2010. P-R-R Study Technique Group Counselling and Gender influence on 
Academic performance of Secondary School students. Retrieved February 19, 2007 
from http://groupcounselling.htm.  
 
 107 
UNIVERSITY OF IBADAN LIBRARY
Ojo, O. J. 2003. Relative Effectiveness of self-regulatory and cooperative learning strategies on 
 learning outcomes in senior secondary school mathematics. Ph.D Thesis, University of 
 Ibadan.  
Okebukola, P.A. 1984. Effects of cooperative, competitive and individualistic laboratory 
interaction patterns on students performance in Biology. Ph.D Thesis, Dept of Teacher 
Education.  University of Ibadan. 
 
Okebukola, P.A. et al. 1992. Women in Science Technology and Mathematics in Nigeria: 
STAN –Position Paper No. 2.  
 
Okebukola, P.A.O. 1990. Attaining meaningful learning of concepts in genetics and Ecology. 
 An Examination of the Potency of Concept Mapping. Technological Journal of 
 Education, 69.501- 509. 
 
Okpala, P. 2008. Evaluation –Driven  Educational  programmes for sustainable national 
development. The roles of institutes of Education in Nigeria. A guest lecture delivered 
th
at the 60  anniversary celebration of the University of  Ibadan. 
 
Okwilagwe, E.A 2001. Patterns of Undergraduates‘ attitude to academic work. In Awosika, Y. 
Babalola, J.F. Fabunmi, M. Osiki, J.O. and Emunemu, B.O. (eds) Topical Issues in 
Education-papers in honour of Professor C.O. Udoh. Ibadan: Faculty of Education, 
University of Ibadan, Nigeria. 
 
Oladele,2007.Guidance & Counselling. A functional approach. Focus on the 6-3-3-4 
educational system. Johns-Lad Publishers Ltd, Lagos. 
 
Olagunju, A. M. 2006. The effects of environmental education module, gender and subjects 
specialization on students problems solving and cognitive achievement in Biology. 
th th
Proceeding of international conference on education, 6  - 9 . December, 2005, 
National University of Singapore, 2005, Francis, E.H.J. Tay, S.C. and Schen, H. 
 
Singapore: National University of SINGAPORE, 314-319.    
 
Olagunju, S.O. 2001. Sex, age and performance in mathematics. ABACUS of Mathematical 
Association of Nigeria 26. 1: 8-16. 
 
Olatundun, S.A. 2008. Impact of Outdoor Educational Activities on Pupils Environmental 
knowledge Attitude in Selected Primary Schools in Ibadan, Nigeria. Ph.D Thesis. 
Department  of Teacher Education, University of Ibadan. xix+ 202. 
 
Olowojaiye, F. B. 1999. Attitude of Senior Secondary School Students as it relates to 
achievement in mathematics. Lagos Journal of Science Education 4. 51-56.   
 
___________2001. Instructional materials as channels for effective teaching and learning of 
Mathematics. African Journal of Information Technology and Educational Media 
(AJITEM) 1.1: 90-95. 
 
Olunloye,  O. 2010.  Mass failure in mathematics: a national disaster, Tribune of 07/02/2010 
 retrieved from http/www.tribune.com.nig on 08/05/2011. 
 
 108 
UNIVERSITY OF IBADAN LIBRARY
Omosehin, F.M. 2004. Effects of a training programme in cooperative learning on preservice 
 teachers, classroom practice and pupils‘ learning outcomes in social studies PhD Thesis 
 University of Ibadan.  
 
Onabamiro, A.T. 2005. Teachers‘ Factors as determinants of students‘ achievement in senior 
secondary mathematics. M.Ed. project at the Institute of Education, University of 
Ibadan, Nigeria. 
 
Onabanjo, I.O. 2000. Peer tutoring assisted instruction. Parent supportiveness and students 
focus of control as determinants of learning outcomes in senior secondary school 
mathematics Ph.D. Thesis.  Institute of  Education, University of Ibadan. xv + 190pp.  
Onasanya, S.A and Omosewo, E.O (2011).  Effect of improvised and standard instructional 
materials on secondary school students‘ academic performance in physics in Ilorin, 
Nigeria. Singaore Journal of Scientic research 1: 68-76. 
 
Onosode, T.T. 2004. Effect of instructional strategy, focus of control and gender on 
achievement in English language written comprehension among primary five pupils in 
Benin city. Ph.D Thesis Dept of International Centre for Educational evaluation. 
University of Ibadan xvii+217pp.   
 
Onuka, A.O.U. 2004. Planning Distance Learning programme. In Fagbamiye, E.O.; Babalola, 
J.B. ;Fabunmi, A. and Ayeni, A.O. (Eds). Management of primary and secondary 
Education in Nigeria. National Association for Educational Administration and 
Planning publication. 227-242.  
 
Onuka, A.O.U. 2006. Total Quality Management and Students Attitude as Predictors of 
Students Choice of a Distance Learning Programme in Nigeria. A Pre-conference 
Seminar. Institute of Education, University of Ibadan, Nigeria. 
 
Opolot-Okurot, 2005. Students attitudes toward Mathematics in Uganda Secondary Schools. 
African Journal of Research in Mathematics Science and Technology Education. 9.2: 
167-174. 
 
Organization for Economic Co-operation and Development 2000. Knowledge and skills for 
life: First results from PISA 2000. Paris: Author.  
 
th
Ormrod, J E. 2008. Human learning (5  ed.). Upper saddle River,NJ: Pearson. 
 
Osborne, J., S 2003. A review of the literature and its implication. International Journal of 
science Education 25. 9:1049-1079. 
 
Osborne, J.; Simon, S. and Collins, S 2003. Attitudes toward Science: A review of the 
literature and its implication. International Journal of science Education 25. 9: 1049-
1079. 
 
Osibodu, B.M. 1981. Teaching and learning Secondary school Mathematics in the 80s. Journal 
of Nigerian Educational Research Association Vol. 2. 
 
 109 
UNIVERSITY OF IBADAN LIBRARY
Osinubi, E. O. 2004. Constructivist Methods of Teaching and Meta Cognitive Strategy as 
determinants of learning Outcomes in Integrated Science.  Ph.D Thesis. Institute of 
Education. University of Ibadan. x+ 237pp. 
 
Otwell & Mullis, 1997: Helping students improve academic achievement and school success 
behaviour. Retrieved 12/27/2007. 
 
Oyebade, S.A. 2003. Education and unemployment of youths in Nigeria: courses, impact and 
suggestions.  In Babalola, J.B. and Adedeji, S.O. (eds) Contemporary issues in 
educational management. A book of honour, Ibadan: Department of Educational 
Management, University of Ibadan, Nigeria.  
 
Oyedeji, O. 1998. Learn Science by Doing: Prospects and problems of Implementation in 
Nigerian Environment.  In Erinosho, S.Y. 2002. Learn Science by Doing A manual for 
Teaching Integrated Science for Secondary Schools NIGLS Project Secretariat.  
 
Oyeniran, J.O. 2008. Setting up mathematics laboratory in schools. A paper presented at the 
one-day Conference of the Mathematical Association of Nigeria, Oyo State branch.  
 
OYSG, 2005. Blue Print on Guidance and Counselling programme for Secondary Schools in 
Oyo State (unpublished paper).  
 
Pajares, F. 1996. Self-efficacy beliefs in academic settings. Review of Educational Research 
 66: 543-578. 
 
Pajares, F. and Miller, M.D. 1994. Role of self-efficacy and self-concept beliefs in 
 mathematics problem-solving. A path analysis. Journal of Educational Psychology 
 86:193-203. 
 
___________and Kransler, J. H 1995.  Self- efficacy beliefs and general mental ability in 
 mathematical problem solving.  Contemporary Educational Psychology 20: 426-443.                       
 
___________and Kransler J.H. 1995a.  Mathematics self-efficacy and Mathematics outcomes: 
The need for specificity of assessment.  Journal of Counselling Psychology 42: 190-
198. 
 
__________and Miller 1995b, August.  Mathematics self-efficacy and mathematics problem 
solving: Implication for using varying forms of assessment.  Paper presented at the 
meeting of the American Psychological Association New York City. 
 
__________S. and Miller M.D 1995.  Specificity of self-efficacy assessment.  Journal of  
counseling psychology, 42. 190 – 198. 
 
__________and Johnson, M.J. 1996. Self-efficacy beliefs in the writing of high school 
students:  A path analysis psychology in the schools, 33. 163-175.  
 
__________and Miller M.D.  1996.  Self-efficacy beliefs in academic settings.  Review of 
Educational Research 66.4: 543 – 578. 
 
 110 
UNIVERSITY OF IBADAN LIBRARY
__________and Graham, L. 1999. Self-efficacy, motivation constructs and mathematics 
performance of entering middle school students. Contemporary Educational 
Psychology 24: 124-139. 
 
__________and Schunk, D.H 2001. Overview of self-efficacy. ―Retrieved August 31, 2006.  
from  www.emory.edu/ EDUCATION/mfp/eff.html”. 
 
__________and Shunk, D.H. 2001a. Self-beliefs and school success: self-efficacy, self-concept 
and school achievement.  In R.Riding and S.Rayner (Eds) Self-perception Pp 239–266. 
London: Alex Publishing. 
 
__________and Schunk, D. H. 2001b. Self-efficacy, Self-concept, and academic achievement. 
In J. Aronson & D. Cordova (Eds), Psychology of education: Personal and 
Interpersonal forces. San Diego: Academic Press.   
 
__________and Schunk, D.H 2003.  Self-efficacy beliefs, motivation and achievement in 
writing. Reading and Writing Quarterly 19.2: 139 – 158. 
 
Papanastasiou, E.C., 2001. Willingness to follow mathematics related career among seniors in 
advanced math classes: The case of Cyprus manuscript submitted for publication.   
Science  Education. International 13.2:20-21.  
 
Pascarella, E, T. and Terenzini P.T. 2005. How college affects students: A third decade of 
research. Vol.2. San Francisco, CA: Jossey-Bass. 
 
Pauk, W. 1984.  How to study in college. Boston.  In M.A. Houghton Mifflin. 
 
Payne, O. 1992.  The Effects of Learning  strategies on a group black secondary student‘s 
verbal and mathematics SAT Scores: Paper presented at the annual meeting of the 
American Educational Research-in-Mathematics Education 26. 2:163-181. 
 
Pehkonen, E. 2003. Laereres og elevens oppfatninger som en skjult factor I matematikk-
underv/sningen, in B: Grevholm (ed.), Matematikk for skolen (154-181). Bergen: 
Fagbokforlaget. 
 
Pehkonen, E. and Torner, G. 2004. Methodological considerations on Investigating Teachers‘ 
Beliefs on Mathematics Teaching and Learning. Nordic Studies in Mathematics 
Education. 9.1:21-49. 
 
Peterson, G.W., Long, K.L. & Billups, A. 1999.  The effect of three career interventions on the 
educational choices of 8th grade students. Professional school Counselling. 3.1:34-42.  
 
Piaget, J. 1970. Science of education and psychology of the child. New York: Orlon Press. 
 
Pietsch, J., Walker, R., and Chapman, E. 2003.  The relationship among self-concept, self-
 efficacy and performance in mathematics during secondary school (Electronics 
 version). Journal of Educational Psychology 95.3: 589-603. 
 111 
UNIVERSITY OF IBADAN LIBRARY
Pintrich, P.R. and De Groot, E.1990. Motivational and self-regulated learning components of 
classroom academic performance. Journal of Educational Psychology,82,33. 
 
Pintrich, P.R and Garas T. 1991.  Student goal orientation and self-regulation in the college 
classroom.  In: M.L. Macher and P. R. and achievement.  7, Greenwich: CT. JAI Press. 
 
__________and Schunk, D.H 1995 Motivation in Education:  Theory research, and 
applications. Englewood Cliffs, NJ: Prentice-Hall. 
 
__________and Garas T. 2000.  The role of goal orientation in self-regulated learning. In 
M.Baekaerts; P.R. Pintrich and M. Zeidner (eds).  The handbook of self-regulation. Pp 
451 – 502  San Diego, CA.  Academic Press. 
 
Pisa 2003. OECD programme for International Students Assessment (PISA). Retrieved 29 
June 2011 from http://www.pisa.oecd.org/. 
 
Pollitt, A.B, Searl, J.W. and Sheikh, A. S. El. Factors Affecting Girls Learning of mathematics 
in Sudan.  Evaluational studies in Mathematics 18: 439-444.  
 
Portman, P.A. 1996. Preservice elementary education, major beliefs about their elementary 
physical education classes (Pt.1). Indiana Association for Health physical Education, 
Recreation and Dance Journal, 25.2: 25-28. 
 
Prescott, A., Mitchelmore, M., & White, P. 2002. Students‘ Difficulties in Abstracting Angle 
Concepts from Physical Activities with Concrete Material. In the Proceedings of the 
Annual Conference of the Mathematics Education Research Group of Australia 
Incorporated Eric Digest ED 472950. 
 
Randhawa, B.S., Beamer, J.S., & Lundberg, I. 993.   Role of mathematics self-efficacy in the 
structural model of mathematics achievement. Journal of Educational Pyschology.85.1: 
41-48. 
 
Rational Emotive Therapy RED: Albert Korzybski Memorial Lecture held in November 8, 
1991. Acesed on August 23, 2007 at http://learnings.org/library/ellis.htm.  
 
Rawnsley, D.G. 1998. Associations between classroom learning environments teacher 
 interpersonal behaviour and student outcomes in secondary mathematics classroom, 
 Perth. Curtin University of Technology. URM: adt_wcv 200 20 729.094016.  
 
Refaat, E.,  2001. Effects of Module-Based instruction on developing mathematics proof skills 
and geometry achievement of preparatory school students in Faculty of  Education, 
Suez Canal University, Egypt. 
 
Reinecke, M.A; Dattilio, F.M. and Freeman, A. (2003). Cognitive Therapy with Children and 
nd
Adolescents: A Casebook for Clinical Practice (2  ed.) Guilford Press. ISBN 1-57230-
853-2.  
 
Reis, S. M. and McCoach, D.B.2000.The underachievement of gifted students: What do we 
know and where do we go?. Gifted child quarterly, 44:152-170. 
 
 112 
UNIVERSITY OF IBADAN LIBRARY
th
Republic, 2001. Plato: Education and the value of justice. Retrieved on 20  March, 2011 from 
hhp://www.philosophy pages.com/hy2h.htn.   
 resources for low-achieving mathematics classes. Eric information analysis center for 
science and mathematics education. Columbus, Ohio.  
 
Ridlon, C.L. 2004. Article: The effect of a problem centered approach to mathematics on low-
 achieving sixth graders. Retrieved March 18, 2010 from htt://www.highbean.com 
 idoc/IGI-120635860.hm. 
 
Riley, R. 2000. Setting New expectations‖. ―seventh Annual state of American Education 
Address.  
 
Robins, R.W & Beer, J. S. 2001. Positive Illusions about the self: Short-Term Benefits and 
Long-Term Costs. Journal of Personality and social psychology, 80. 340-352.  
 
Roeser, R.W., Stobel,K. R., & Quihuis, G. 2002.  Studying early adolescents‘ academic 
motivation, social-emotional functioning, and engagement in learning: Variable-and 
person-centered approaches. Anxity, Stress, & Coping, 15. 4 : 345-368. 
 
Roeser, R.W., Strabel, K.R. and Quihuis, G. 2002. Studying early adolescents‘ academic 
 motivation, social emotional functioning, and engagement in learning: Variable and 
 person-centered approaches. Anxiety, Stress and Coping, 15.4: 345-368.  
 
Rothstein, M.G, Pownonen, S.V. Rush, J. C. And King, G.A. 1994. Personalty and cognitive 
ability. Journal of Educational Psychology. 86. 4:516-530.  
 
Round, E. L. 1998. A Study of the Potential Benefits of Using Interactive Software in High 
School Geometry Solely for Whole Class Demonstration and Discussion. Unpublished 
PhD Dissertation, The Ohio State University, USA. 
 
Ryan, W. F. 1999. The Effects of using the TI-92 Calculator to enhance Junior High 
 Students‘ Performance and Attitude toward Geometry. Eric Digest ED436414. 
 San Francisco: Jossey-Bass. 
 
San, İ. 1996.  Yaratıcılığı Geliştiren bir Yöntem ve Yaratıcı Bireyi Yetiştiren bir Disiplin: 
Eğitsel Yaratıcı Drama. Yeni Türkiye Dergisi, 2. 7: 148-160. 
 
Schalago-Schrim, C. 1995. Computer Assisted Remedial Mathematics and student scores on 
early warning test: a paper in partial fulfillment of the requirement  for the Masters of 
Arts. Kean College of New Jersey. 
 
Schank, J.A. R. & Cleary, C. 1995. Engines for education Hills dale, NJ: Lawrence Erlbaum 
Associates, Inc. 
 
Scher, D. P. 2002. Students' Conceptions of Geometry in a Dynamic Geometry Software 
Environment. Unpublished PhD Dissertation, New York University, USA. 
 
Schoenfeld, A. H. 1983. Problem Solving in the Mathematics Curriculum: a Report, 
Recommendations, and an Annotated. Washington, D.C. Mathematical Association of 
America. 
 113 
UNIVERSITY OF IBADAN LIBRARY
Schumann, H. 1994. Interactive theorem-findings in plane geometry-an example, International 
Journal of Mathematics Education in Science and Technology 25.2:285-291. 
 
Schunk, D.H. 1984. Enhancing self-efficacy and achievement through rewards and goals: 
 motivational and Information effect. Journal of Educational Research, 78:29-34.  
 
Science Daily, 2010. Few gender differences in Mathematics abilities worldwide Study finds. 
An outline. Retrieved March 19, 2011. http:www.sciencedaily.com/2010/01/05//2303.    
 
Senk, S. L. 1985. How Well do the Students Write Geometry Proofs?. Mathematics Teacher, 
78. 6: 448-456. 
 
Shang, E.L. and Doan, R.L. 1990. An investigation of the difference in attitude and 
achievement between male and female second and fifth grade students. Paper presented 
at the annual meeting of the National Association Research in Science Technology.    
 
Siegle, D. and McCoach, D.B 2007. Increasing student mathematics self-efficacy through 
teacher training. Journal of Advanced Academics, 18:278-312. 
 
Simpson, S.M., Liht, B. Grand Stader, S.R. 1996. Organization of children‘s academic ability-
related self-operations. Journal of Educational Psychology, 88.3: 387-394. 
 
Sink, C.A. & Stroh, H.R. 2003. Raising achievement test scores of early elementary school 
students through comprehensive school counselling programs. Professional school 
counselling, 6. 5: 350-365.  
 
Sink, C.A. 2005. Fostering academic development and learning: implications and  
recommendations for middle school counsellors. Professional school counselling 
9.2:128-135. Retrieved March 25, 2010 from http://www.School counselor.Org/content 
asp? Contented=241. 
 
__________2005. Comprehensive school counselling programs and academic achievement–a 
rejoinder to Brown and Trusty. Professional School Counselling, 9, 9-12.   
 
Skaalvik, E. and Rankin, R.J. 1996. April Self-concept and self-efficacy: Conceptual analysis. 
 Papers presented at the meeting of the American Educational Research Association, 
 New York.  
 
Smith, M. 2002. Outdoor and environmental education development manager curriculum 
service. Retrieved October 26, 2005. from http://www.hse.uk/school trips. 
 
Smith, M.K.  Jerome, S and Brunner 2002. The process of education. The encyclopedia 
ofinformalEducation.RetrievedJuly18,2007from http://www.infed.org/thinkers/bruner.htm.  
 
Solomando, A. M., Kendall, T.,and Whittington, C.J. 2008.  Cognitive Behavioural Therapy 
for Children and Adolescents, Current opinion in Psychiatry, 21,332-337.    
 
Sotonade, S. 2003. Gender issues in school practices and strategies. Lucky Udoni (Nig.) 
Enterprises, Ijebu-Ode. Pp. 152-153. 
 
 114 
UNIVERSITY OF IBADAN LIBRARY
Souv, L.J. Bryan of Student-faculty interactions on college outcomes for women and men. 
Journal college student development, 46.6:2-659.   
 
Sowunmi, C.O. 2007. Effects of Teaching Strategies on Students Academic Achievement in 
Selected Nursing Schools in Southwestern Nigeria.  Ph.D Thesis. University of Ibadan, 
Ibadan. xiii+181p. 
 
Spence, W. and El-Ansari, W. 2004. Portfolio assessment: practice teachers‘ early experience‖, 
Nurse Education today 24.5:388-401.   
 
Spender, D. 1982. Invisible women: The Schooling scandal. London: Writers and Readers. 
 
Stevens, T., Olivarez, A., Jr, Lan, W., & Tallent-Runnels, M.K. 2004. ―The role of 
mathematics self-efficacy and motivation in mathematics performance: Issues across 
ethnicity‖. Journal of Educational Research, 97:208-221. 
 
Stine, S. 1997. Landscapes for learning: Creating Outdoor environment for children and youth. 
 New York: John Wiley & Sons.  
 
Suit, J.P. & Lagowski, J.J. 1994. Chemistry problem-solving abilities. Gender Reasoning Level 
and Computer Simulated Experiments. Papers presented at the Annual Meeting of the 
National Association for Research in Science Teaching. Anaheim, C.A. 26-29.  
 
Surgur, S. and Telkaya, C. 2004. The Effect of Reasoning Ability and Gender on students‘ 
achievement.  Journal of Science education and Technology 121:59-64. 
 
Suveg, C., Sood,  E., Comer, J. S. and Kendal, P. C. 2009. Change in emotion regulation 
following cognitive –behavioural therapy for anxious youth. Journal of clinical child 
adolescent psychology, 38:390-401.   
 
Tahar, N.F, Ismail, Z, Zamani, N.D. & Adnan, N. 2010. Students‘ Attitude toward 
Mathematics. The use of factor analysis in determining the criteria. Procedia-social 
and behavioural Sciences. 8: 476-481.  
 
Taylor, T. L and Montgomery,  P. 2007. Can cognitive-behavioural therapy increase self-
esteem among depressed adolescents? A systematic review. Children and Youth 
Service Review 29:823-839.  
 
Tchombe, T. M-S 2004. Psychological Parameters in Teaching Collection. Science de 
Education.  
 
Tella, A. 2009. Relationships between some students Multi-Variant variables and Learning 
Outcomes in Senior Secondary School Mathematics in Oyo State. Nigeria. Ph.D Thesis 
xiv+ 259 pp. 
 
The effect of a problem centred approach to mathematics on low-achieving 6th graders. 
http://www.highbeam.com/doc/IGI-120635860.html Retrieved on 3/18/2010.   
 
 115 
UNIVERSITY OF IBADAN LIBRARY
Thirumurthy, V. 2003. Children's Cognition of Geometry and Spatial Reasoning: A Cultural 
Process. Unpublished PhD Dissertation, State University of New York At Buffalo, 
USA. 
 
Thompson, K. M. 1993.  Geometry Students‘ Attitudes toward Mathematics: An Empirical 
Investigation of Two Specific Curricular Approaches, Unpublished Master Thesis, 
California State University Dominguez Hills, USA. 
 
TIMSS, (2007). Achievement by Gender in the Mathematics Cognitive Domains at the Fourth 
and Eight Grades: TIMSS & PIRLS International Study Center, Lynch School of 
Education, Boston College: retrieved  from www.times.org/publication 2007 dated 15 
April 2009. 
 
Toch, K.A. 1993. Gender and practical tasks. Science Educational Research. 35: 255-265. 
 
Travers, K.J, John,W.L. and Garth, E. R, 1971. Mathematics education reports. Teaching 
 
Tsui, Ming 2007. Gender and Mathematics Achievement in China and United States. Gender 
 issues 24.3:1-11.   
 
Turner and Beiry 2000. College counseling and student retention: research finding and 
implication for counseling centres. Journal of College counseling. Retrieved 3/8/2010. 
 
th th
Ubuz, B.  1999.  10  and 11  grade student‘s errors and misconceptions on basic  geometric 
concepts. Hacettepe Unversity journal of Education, 16, 95-104. 
 
Ubuz, B. & Üstün, I. 2003. Figural and Conceptual Aspects in Identifying Polygons. In the 
Proceedings of the 2003 Joint Meeting of PME and PMENA. 1. p.328. 
 
Uduosoro, U.J. 2000. The relative effects of computer and text assisted programmed 
instruction on students‘ learning outcomes in maths. Ph.D. Thesis. Dept. of Teacher 
Education, University of Ibadan. xviii + 279pp. 
 
Ufuktepe, U., & Ozel, C.T. 2002. Avoiding Mathematics Trauma: Alternative Teaching 
nd
Methods, Hersonissos, Crete-Greece: 2  International Conference on the Teaching of 
Mathematics, E IC Document Reproduction Service ED477833. 
 
Umoinyang, I.E. 1999. Student psychological factors as determinants of achievement in senior 
 secondary school mathematics Ph.D. Thesis. Institute of Education, University of 
 Ibadan. xiv +183pp.  
UNESCO, 2003. Gender and Education for all: The leap for  equality. Global monitoring 
report 2003/2004. http.//www.unesco/oc.unesco.org/education/eta-report  12003—
pdf/chapter 3. pgf.   
 
Üstün, I. 2003. Developing the Understanding of geometry through a computer-based learning 
environment. Unpublished Master Thesis, METU, Turkey. 
 
Vale, C. 2009. Trends and factors concerning gender and mathematics in Australasia. 
Retrieved on November 21, 2009 from http://tsg.org/document/get //169. 
 116 
UNIVERSITY OF IBADAN LIBRARY
Velo, J. 2001. The Impact of Dynamic Geometry Software on Students' Abilities to Generalize 
in Geometry. Unpublished PhD Dissertation, The Ohio State University, USA. 
 
Venkatesh, K.G. and Lissamma, S. 2011. Impact of CBT on self-efficacy and academic 
 achievement in adolescent students. University of Mysore, Mysore. Journal of the 
 Indian Academy of Applied Psychology 37:134-139.  
 
Vygotsky, L.S. 1978. Mind in Society. Cambridge MA Harvard University Press.  Pg 86.            
 
WAEC, 2005, 2007. Chief Examiners‘ Reports Yaba, Lagos. 
 
Ward, C.D. 2001. Students‘ attitudes and achievement as related to immediate remediation in 
paced algebra. Ph.D Dissertation, Georgia Southern University. Retrieved from 
www.ib.umi.com/dissertations/results.  
 
Washington-Myers, E. R. 2001. Accounting For Prospective Secondary Mathematics Teachers' 
Understandings In A Dynamic Geometry Tool Environment. Unpublished PhD 
Dissertation, The Pennsylvania State University, USA. 
 
Watson, J. 1991. Mathematics and gender.  In Elizabeth Fennema and Gilah C. Leder Eds New 
York: Teachers College Press, Columbia University.   
 
Weaver, R.R. and Qi, J. 2005. Classroom Organization and participation: College students‘ 
perception. The Journal of Higher Education, 76.5:570-601. 
 
Webb, L.D., Brigman, G.A, & Campbell, C. 2005. Linking school counselors and students 
success: A replication of the student success skills approach targeting the academic 
social competence of students. Professional School Counselling, 8.5: 407-413.  
 
Webb, L.D., Brigman, G.A. 2006. Student Success Skills: Tools and strategies for improved 
academic and social outcomes. Professional School Counselling. 10: 112-120. 
 
Wetzel, D., 2009. Teaching Strategies in math ESL students. Retrieved on March,2010 from 
 the World Wide Web: http://continuingeducation.suit101.com/article.cfm/teaching 
 math to ESL students. 
Wheel end E.; Konet, RM; & Butler, K. 2003: Perceived inhibitors to Mathematics success. 
Journal of Developmental Education 26.3:18-26 x/2005001/7836-eng.htm. Retrieved 
2/17/2009.  
 
Whiston, S.C., Sexton, T.L. 1998. A review of school counseling outcome research: 
Implications for practice. Journal of counseling and Development, 76:412-426.   
 
Williams, R.E. Omizo, M.M., & Abrams, B.C. 1984. Effect of STEP parental attitudes and 
locus of control of their learning disable children. The school counselor 126-133.  
 
Wilson, N.S. 1986. Counsellor interventions with low-achieving and underachieving 
elementary middle, and high school students. A review of the literature. Journal of  
counselling & Development: 628-634.  
 
 117 
UNIVERSITY OF IBADAN LIBRARY
th
Woolfolk, A.E.1998.  Educational Psychology  (7  edition).  Boston: Allyn and Bacon. 
 
th
Wortman, C., Loftus, E and Weaver, C. 1999. Psychology, 5  Ed Boston : McGraw Hill 
College. 
 
Yahaya, L.A. 2004. Effects of group counseling and SQ3R on the Study Habits of Secondary 
S.chool Students in Ilorin. Journal of Educational Research and Development. 3:1. 
125-136. 
 
Yara, P.O. 2009. Relationship between Teachers‘ attitude and Students academic achievement 
in Mathematics in some selected senior secondary schools in Southwestern Nigeria. 
Kampala International University, Western Campus, Bushenyi-Ishaka Uganda.   
 
Yelland, N.J. 2000. Promoting Meaningful Learning Innovations in Education Early childhood 
professionals. National Association for the Education of Young Children. Washington 
DC. 
 
Yinyinlola, W.L. 2008. Study skills training and time management strategies enhancing 
testwiseness and learning outcomes in Mathematics among Secondary School Students 
in Ibadan, Nigeria. Ph.D. Thesis, Department of Guidance and Counselling  University 
of Ibadan, Ibadan. xiii + 266 pp.     
 
Yoloye, T.W. 1999. Assessing the attitude, study habit and performance in science of some 
students after a counselling programme.   In J.O. Obemeata, S.O. Ayodele, and M.A. 
Araromi, (Eds). Evaluation in Africa in Honour of E.A. Yoloye. Ibadan. Stirling 
Horden. 193-211.  
 
Youn,A. J. 1997. I think, therefore I‘m motivated: The relations among cognitive strategy use, 
 motvational orientation and classroom perception over time.  Learning & Individual 
 Differences,9 .3: 249-284. 
Zahid Bashir,S.H.,2012. The effectiveness of co-curricular activities on academic 
achievements of second school students in district Abbottabad Pakistan-A case study. 
Journal of Education and Practice, 3.1,2012. ISSN 2222-1735(Paper). 
 
Zimmerman, B. J., Bandura. A.J., & Martinez-Pons M. 1992: Self-motivation for academic 
attainment: The role of self-efficacy beliefs and personal goal-setting. American 
Educational Research Journal 29/37 663-676. 
 
Zink, K. & Littrel L, J.M. 2000. Action research shows groups counselling effective with at-
risk adolescent girls. Professional School Counselling 4.1:50-60.  
 
Zyromski,B & Joseph,A.E.2012.  Utilizing cognitive behavioural nterventions to positively 
impact academic achievement in middle school students. Southern IIIinois University 
Carbondale, North Carolina State University. Retrieved from 
jsc.montanaedu/articles/v6n 15.pdf on 21/09/2011.    
 
 
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APPENDIX I 
ICEE DEPARTMENT) 
UNIVERSITY OF IBADAN, IBADAN 
STUDENTS’ SELECTION TEST (SST) 
 
Instruction: This test contains questions in Mathematics. Each question is followed by the 
four options: A-D, shade the letter that corresponds to the correct option on the answer sheet 
provided for you.  
 
Name:_________________________________________________ 
Class:__________________________________________________ 
Name of the school:______________________________________ 
Age:__________ Sex:___________Male (  ) Female(  )     
  
Time: 30 minutes.                      
(1) Which of the following is not an example of quadrilaterals? (a) Triangle (b) Trapezium 
(c) Square (d) Rhombus.  
(2) One of the base angles of an isosceles triangle is 70, find in degrees the other angles of 
0 0 0 0 0 0 0 0
the triangle. (a) 50 and 45 (b) 80 and10  (c) 70  and 40  (d) 60 and30  
(3)  Calculate the circumference of a circle with radius of 7cm (a) 21cm (b) 22cm (c) 28cm 
(d) 44cm 
(4)  A triangle in which all the sides are equal is ---------- (a) isosceles triangle (b) right 
angled-triangle (c) scalene triangle (d) equilateral triangle. 
(5)  The perimeter of a circle is the same as (a) circumference (b) diameter (c) chord (d) 
radius. 
(6) A polygon with six sides is called -------- (a) nonagon (b) octagon (c) hexagon (d) 
pentagon 
(7) Plane figures that are formed from straight lines are called (a) symmetry (b) polygons (c) 
isosceles triangle (d) kite 
(8)  A plane shape with four equal sides is called -------- (a) cuboid (b) parallelogram (c) 
square (d) rectangle. 
(9) A triangle in which only two of its sides are equal is called (a) equilateral (b) isosceles (c) 
scalene (d) right angled-triangle. 
(10) The perimeter of rectangle is 12cm,its length is 3cm, find the breadth (a) 6cm (b)1cm (c) 
2cm (d) 3cm 
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(11) A square has -------- line of symmetry (a) 2 (b) 4 (c) 1 (d) 3. 
(12) The longest side of a right angled-triangle is (a) line segment (b) adjacent side (c)    
hypotenuse (d) opposite side. 
(13)  A quadrilateral with one pair of parallel sides is called --------- (a) rhombus (b) 
parallelogram (c) kite (d) Trapezium 
2 3
(14)  The area of a rectangle with length 6cm and breadth 31/2  (a) 21cm  (b) 21cm (c) 21cm  
(d)21 
(15) A decagon has --------- sides (a) 20 (b) 10 (c) 15 (d) 12 
(16)  The base of a parallelogram is 6cm long and its height is 4cm.  Calculate the area of the 
2 2 2
parallelogram (a) 24cm  (b) 24cm (c) 27cm  (d) 26cm  
2
(17)  One side of the square is 6cm, calculate the area of the square (a) 26cm (b) 30cm  (c) 
2
36cm  (d) 36cm. 
(18)  If the length of one side of the square is given as x, then the perimeter of the square is (a) 
2
x (b) 4 (c) 4x (d) 4x  
(19) Calculate the perimeter of a circle of radius70m (a) 40m (b) 400m (c) 410m (d) 440m 
(20)  The special name for a polygon with all the angles equal is -------- (a) equilateral (b) 
equiangular (c) polygon (d) parallelogram.      
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APPENDIX II 
 
ICEE DEPARTMENT 
  UNIVERSITY OF IBADAN, IBADAN. 
ACHIEVEMENT TEST IN GEOMETRY (ATG) PRE-TEST AND POST-TEST 
 
Name: _________________________________________________ 
Class: __________________________________________________ 
Name of school:__________________________________________ 
Age: _______ Sex:_________  Male (    ) Female (    ) 
Religion: Christianity (    ) Islam (    ) Others (    ) 
Time: 40 minutes 
Instruction: This is a multiple choice test with only one correct answer 
Each question is followed by four options (A-D). Find the correct option and shade the letter 
that corresponds to the correct option on the answer sheet provided for you. 
 
Questions 
1. One example of 3-dimensional object is (a) square (b) kite (c) parallelogram (d) cylinder.  
2. A sphere has ______faces   (a) 2 (b)1  (c)0 (d) 3 
3. The volume of a cuboid of length ɭ , breadth b and height h, = (a) ɭhv (b) ɭbv (c) ɭbh (d) 
bhv 
4. One property common to all solids is: (a) inside (b) outside (c) Inside and outside (d) 
solid and inside. 
5. The net of a square pyramid has ___ triangular shapes (a) 8 (b) 4 (c) 2 (d) 12. 
2
6. The surface area of a cone is given  by д r1 (b) д r  (c)  д1 (d) дr  
7. The surface area of a cylinder is obtained by circumference of a circle times (a) length (b) 
height (c) slanting line (d) radius.   
8. A point where two or more edges meet is called (a) face (b) vertex (c) edge (d) height. 
2 2 2
9. If the side of a cube is ɭ centimeter, what is the total surface area?(a) 6 ɭ cm  (b) 6 ɭ  cm  
3 2 4 2
(c) 6 ɭ  cm   (d) 6ɭ  cm  
10. 3 3 3Calculate the volume of a cube of length 4cm(a) 16cm   (b) 64cm  (c) 64cm   (d)24cm   
11. calculate the volume of a cuboid of length = 9cm, breadth = 7.5cm and Height= 2cm (a) 
3 3 3 3
129cm  (b) 130cm  (c) 128.5cm  (d) 135cm  
12. A  cuboid  has_____ rectangular faces  (a) 8 (b) 10  (c) 12 (d) 6 
13. Which of the following is the total surface area of a cuboid? (a) 2(bh+ ɭ)  (b) 2(ɭb + ɭh) (c) 
2(ɭb) (d)  2(ɭb +bh + ɭh)  
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3 3 3
14. The cube of dimensions, ɭ centimeter, will have  the volume v=  (a)  ɭ  cm   (b)  ɭ cm   (c)  
2 3 4 3
ɭ  cm   (d) ɭ  cm  
 3.   
15. Given the area of the base to be 40cm and the volume of a cuboid is 240cm Find the 
 
height of the cuboid (a) 2 cm (b) 4 cm (c) 6  cm  (d) 10 cm 
16. A cylinder has a base radius of 7cm and a height of 10cm.Find the curved surface area of 
2 2 2 2
the cylinder (a) 470cm  (b) 440cm  (c)400cm  (d) 450cm  
2 2 3
17. The volume of a cone is ____ of a cylinder(a) 1/3 дr (b) 1/3 дr h (c) 1/3дrh (d) 1/3дr h 
18. The volume of a cylinder of equal height and radius with a cone can be filled  with ___ 
cones of sand    (a) 4 (b) 5  (c) 3 (d) 7 
2 2
19. Find the total surface area of a cube of length 15cm  (a) 1325cm  (b)1350cm   (c)  
2 2
1332cm  (d) 1225cm  
2
20. The formula for the surface area of a  cone is  (a) д r1 (b) д r  (c)  д1 (d) дr  
21. Calculate the total surface area of a cuboid of length 8cm,breadth 6cm and height 4cm 
2 2 2 2
(a)208cm   (b)218cm  (c) 308cm  (d) 318cm  
 322. Calculate the volume of a cylinder of height 4cm and base radius 7cm (a) 620cm  (b) 
3 3 3
619cm  (c) 617cm  (d) 616cm  
 3 323. Calculate the volume of a cone of base radius of 3cm and height 7cm(a) 9cm  (b) 21cm  
3 3
(c) 81cm  (d) 66cm  
 
24. A square pyramid has ______ edges (a) 6 (b) 8 (c)  4 (d) 5 
25. Which among the following has the greatest number of vertices (a)sphere (b) cylinder  (c) 
cube (d) cone.  
26. _____ is a 3-D object because it has length, breadth and height (a) square (b) kite (c) 
cube (d) rectangle. 
27. 2 The volume of a cylinder of height h, base D and radius r is given by (a) 1/3 дr (b) 1/3 
2 3
дr h (c) 1/3дrh (d) 1/3дr h. 
28.  The total surface area of a cylinder is  (a) 2д r (h+l) (b) 2д r(h+ b) (c)2дr (h+r) (d) 2д 
2
r(h+r )  
29.  Half of a sphere is called ___(a) radius (b) circumference (c) perimeter (d) hemisphere. 
30. How many vertices has a sphere? (a) 1 (b) 0  (c) 2 (d) 3 
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APPENDIX III 
 
UNIVERSITY OF IBADAN 
INSTITUTE OF EDUCATION 
INTERNATIONAL CENTRE FOR EDUCATIONAL EVALUATION 
MATHEMATICS SELF-EFFICACY SCALE (MSES) 
 
Dear Respondents,  
 
This measuring scale is aimed at assessing the level of Mathematics self-efficacy of students. 
Any information you supply will be used for research purpose only and will be treated with 
utmost confidentiality. Please, respond to each question in the relevant box. Fill in your 
response as truthfully as possible. 
    
 
SECTION A: 
 
Name: ____________________________________________ 
Name of School_____________________________________  
My next birthday: ___________________________________ 
Age:_______ Sex:  Male (     ) female (    ) Language: English (  ) Others (   )  
Religion: Christianity (     ) Islam (     ) others (      )  
 
SECTION B: 
 
Instruction: Kindly read the following items and rate yourself accordingly. You are expected 
to tick. 
5. - Very well  
4 - Pretty well  
3 - Satisfactory  
2 - Not too well  
1 - Not well at all 
 
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Section 1  
 
The focus here is on the belief in your capability to solve Numerical Problems and Problems in 
Measurement. 
  5 4 3 2 1 
1 How well do you believe you can calculate accurately      
numerical problems mentally? 
2 How well do you believe you can calculate accurately      
numerical problems on paper? 
3 How well do you believe you can estimate and make      
approximations? 
4 How well do you believe you can interpret the      
accuracy of results and measurements?  
5 How well do you believe you can calculate the effects      
of change in variables using mathematics models? 
6 How well do you believe you can predict the rate of      
change of variables using mathematics models?  
 
 
Section 2 
The focus is on your belief in your capability to attempt successfully problems in Geometry. 
  5 4 3 2 1 
1 How well do you believe you can recognize the      
geometrical properties of objects in daily life? 
2 How well do you believe you can use geometrical      
models to solve practical problems in daily life? 
 
Section 3  
The focus is on your belief in your capability to attempt successfully problems in Algebra. 
  5 4 3 2 1 
1 How well do you believe you can recognize patterns      
and relationships in Mathematics and generalize from 
these? 
2 How well do you believe you can think abstractly and      
use symbols to communicate mathematics  concepts, 
relationships and generalizations?  
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3 How well do you believe you can think and use      
graphs and diagram to communicate mathematics  
concepts, relationships and generalizations?   
4 How well do you believe you can use algebraic      
expressions to solve practical problems?  
 
Section 4 
The focus here is on your belief in solving problems in Statistics  
  5 4 3 2 1 
1 How well do you believe you can summarize      
statistical data as reports and summaries?  
2 How well do you believe you can interpret data      
presented in chart, tables and graphs?  
3 How well do you believe you can estimate      
probabilities?  
 
Section 5  
The focus here is about your beliefs in using mathematics processes.   
  5 4 3 2 1 
1 How well do you believe you can use logical and      
systematic thinking in mathematics contexts?  
2 In a mathematical problem solving situation, how      
well do you believe you can critically reflect on the 
method you have chosen? 
3 How well do you believe you can use information      
technology in mathematics contexts? 
4 How well do you believe you can be part of a      
problem-solving team, expressing your idea, listening 
and responding to others? 
5 How well do you believe you can use the knowledge      
and skills in  mathematics to interpret presentations of  
mathematics 
6 How well do you have developed skills in using your      
own ethnic language to express mathematical ideas?  
 
Section 6 
 
Self-Belief in Motivation Strategies 
  5 4 3 2 1 
1 How well do you believe you can study in appropriate      
ways that you will be able to learn  mathematics 
2 How well do you believe that if you try hard enough      
you will be able to understand the different concepts 
in  mathematics 
3 How well do you believe that you understand the      
most complex concepts in mathematics?  
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4 How well do you believe that you can master the      
skills taught in  mathematics 
5 How well do you believe that you can do an excellent      
job on the assignment and tests in mathematics   
 
 
Section 7 
 
Self-Belief in Cognitive Strategies  
  5 4 3 2 1 
1 When studying Mathematics how well do you believe you      
can set goals for yourself to direct your activities?   
2 When you study Mathematics, how well do you believe you      
can outline the material to help organize your thoughts?  
3 When you study Mathematics, how well do you believe you      
can formulate questions to focus your thoughts?  
4 When studying Mathematics, how well do you believe you      
can go through your notes and readings to find out the most 
important concepts?  
5 When studying a new Mathematics concept, how well do      
you believe that you can skim it to see how it is organized?  
6 When studying Mathematics how well do you believe you      
can think through the topic to decide what it is you are 
supposed to learn rather than just reading it over? 
7 When studying Mathematics, how well do you believe that      
you can use information from different sources such as 
class, notes, text books and discussions?  
8 When studying Mathematics, how well do you believe that      
you can ask yourself questions to make sure that you have 
understood the material? 
9 When studying Mathematics, how well do you believe that      
you can change the way of study to fit the requirement of 
the topic?  
10 When studying Mathematics, how well do you believe you      
can memorize key words to help recall important concepts?  
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11 When studying Mathematics, how well do you believe you      
can summarize concepts of the topic of study?  
12 When studying Mathematics, how well do you believe you      
can determine the concepts you have not understood well?  
13 When studying Mathematics, how well do you believe you      
can relate ideas from Mathematics to other subjects? 
14 When studying Mathematics, how well do you believe you      
can try to relate material to what you already know?  
15 When studying Mathematics, how well do you believe you      
can sort out confusion which arises over missing note taking 
in class? 
 
Section 8 
 
Self-Belief in resource Management Strategies 
  5 4 3 2 1 
1 How well can you believe you can explain a topic in      
Mathematics to your classmate/friend? 
2 How well do you believe you can work on your own,      
even if you have trouble learning the material in 
Mathematics class?  
3 How well do you believe you can use your study time      
for Mathematics?  
4 How well do you believe you can work with your      
classmates to complete the course assignments? 
5 How well do you believe you can work in class even      
if you don‘t like what is being done? 
6 How well do you believe you can stick to your study      
schedule? 
7 How well do you believe you can seek clarifications      
from your Mathematics teacher when you do not 
understand a concept?  
8 How well do you believe you can persist on the topic      
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in Mathematics when you find the material difficult? 
9 How well do you believe you can ask a peer/another      
student in class for help in Mathematics when you 
cannot understand the material being taught? 
10 How well do you believe you can keep up with topics      
and assignment in Mathematics?   
11 How well do you believe you can manage to keep      
working in Mathematics even when you find the 
material uninteresting? 
12 How well do you believe you can review your      
Mathematics notes/readings before an exam? 
 
Section 9 
Self-Belief for Self-Regulated Learning 
  5 4 3 2 1 
1 How well do you believe you can finish your      
Mathematics homework/assignments by deadlines?    
2 How well do you believe you can learn Mathematics      
when there are other interesting things to do? 
3 How well do you believe you can concentrate on      
school subjects? 
4 How well do you believe you can concentrate in      
Mathematics in the classroom? 
5 How well do you believe you can take notes of class      
instruction? 
6 How well do you believe you can take notes of      
Mathematics during class instruction? 
7 How well do you believe you can use the internet      
facilities to get information for class assignment?  
8 How well do you believe you can plan your school      
work? 
9 How well do you believe you can remember      
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information presented in class and text book?  
10 How well do you believe you can arrange a place to      
study without distractions? 
11 How well do you believe you can motivate yourself to      
do school work? 
12 How well do you believe you can motivate yourself to      
do school work in Mathematics?  
13 How well do you believe you can participate in class      
discussions? 
14 How well do you believe you can classify doubts in      
Mathematics in class? 
 
 
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APPENDIX IV 
 
UNIVERSITY OF IBADAN 
INSTITUTE OF EDUCATION 
INTERNATIONAL CENTRE FOR EDUCATIONAL EVALUATION 
GEOMETRY ATTITUDE SCALE (GAS) 
 
Instruction: Please respond to each question in the relevant box. Fill in your response as 
truthfully as possible. Note that the information you provide is for research purposes only and 
will be treated with utmost confidentiality. Thank you.  
 
Section A: About yourself and the school  
Name:___________________________________________________  
Name of school: __________________________________________ 
Age:_______ Sex: Male (     ) Female       (       ) Language: English (      ) others (       )  
 
 
KEY: SA for strongly agree, A for agree, U for undecided, D for disagree SD for strongly 
disagree. 
 
Section B: Instruction  
Tick (√) good in the space which best indicates how appropriately you agree or disagree with 
feeling expressed in each statement below. 
S/N Item SA A U D SD 
1 Students forget geometry easily.       
2 Students are happy on the day they do not have geometry.        
3 Geometry textbook is too hard.       
4 Student remembers most of the things he/she learned in      
geometry  
5 Geometry is not practiced during the long vacation.       
6 Geometry is not being discussed with my friends.       
7 Geometry tests are easy for me.       
8 Geometry has always been liked by me.      
9 Geometry book is interesting.       
10 Students do not like being asked questions in geometry.      
11 Not getting good marks in geometry does not border me.       
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12 Students worry about their marks in geometry.        
13 Other books about geometry should be read besides the one      
used in class. 
14 Geometry book is liked better than most school books.       
15 Students wish geometry classes were shorter.        
16 Geometry classes are preferred to be missed.       
17 Geometry is the best of all my school subjects.       
18 Students dislike taking tests in geometry.         
19 Geometry classes are enjoyable.       
20 Students do not enjoy studying from geometry book.      
21 Geometry problems are often been forgotten after working      
on other kinds. 
22 Geometry homework is not easy for me to do      
23 Student often thinks ―he can‘t do geometry‖ when a work      
problem seems hard.   
24 Geometry homework can be done in the class.      
25 Geometry is easy for me.      
26  Much geometry is not remembered over the summer      
vacation. 
27 Students like geometry.        
28 Geometry is preferred than other subjects.      
29 Students like to answer questions in geometry classes.       
30 Geometry is interesting to students.      
31 Failing to get solution to geometry problems does not      
discourage students   
32 A student is sure of himself/herself in geometry.       
33 Fewer geometry problems are often wished to be done.      
34 Geometry problems that are alike are preferred rather than      
the mixed problems. 
35 Students wish that geometry tests were easier.        
36 Geometry is hard for students.      
37 Students are glad when it is time for geometry class.      
38 Students enjoy working harder problems in geometry.       
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39 Geometry problems take too much time.       
40 Most of my friends think geometry is dull.       
41 Geometry is one of my favorite subjects.      
42 Students would rather do geometry than read books.      
43  Students enjoy talking to their teacher about geometry.       
44 Students like to do word problem in geometry.       
45 Students would take geometry next year even if they do not      
have to. 
46 Students like the easy problem in geometry.       
47 Students like to do extra work in geometry when they have      
time. 
48 Student likes to work geometry problems with his/her      
friends.  
49 Students would rather be authors than scientists.       
50 Students prefer a job involving geometry.       
51 Students like taking tests in geometry.       
52 Students prefer a job which never used any geometry.      
53 A job which used a great deal of geometry is accepted by      
students.  
54 It is not enjoyable talking to parents about geometry.       
55 Geometry homework often takes more time than any other      
school subjects.  
56 Students hate geometry.       
57 Geometry is not student‘s best subject.      
58 Writing a story is better than working geometry problems      
59 Students do not like doing geometry homework.      
60 Students do not have to spend much time on geometry to      
pass it. 
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APPENDIX V 
 
EXPERIMENTAL GROUP 1: OUT-OF-CLASS- ACTIVITY STRATEGY 
 
WEEK 1 
 
Topic: Orientation and administration of instrument to obtain baseline data.  
 
Objectives: 
 To do self introduction. 
 To acquaint the participants with the benefits of the training programme and the roles they 
would play. 
 To inform the participants the rules of the training.  
 To obtain the baseline data.  
 
Step I: The teacher welcomed the participants and introduced herself to familiarize with and 
sensitize the participants. The participants were also instructed to introduce themselves 
individually by mentioning their names only. The teacher urged the participants to feel free to 
make their contributions to the programme by expressing their own views and opinions in a 
polite way by respecting the views of others. 
 
Step II:  Acquitting the participants with the benefits of the programme. 
 
The teacher acquitted participants with the nature and benefits of the training programme.  The 
teacher highlighted the benefits the participants might derive from the training, if they 
participate meaningfully. Such benefits might include the development of positive attitude 
towards mathematics, particularly in the area of Geometry; high level of self-efficacy and 
improvement in their academic performance. 
The teacher emphasized the need for participants to cooperatively participate effectively in all 
the eight training sessions, as this would enable them to follow the programme sequentially 
and logically, since the outcome of the programme depended on their complete participation in 
the training programme, and the training programme was cumulative in nature. This implied 
that any break in session would create a gap in knowledge, which might deprive the 
participants of the full benefits of the programme and therefore prevent the programme from 
producing the desired result.   
 
 
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Step III: Administration of the pre-test measures. 
 
The teacher informed the participants that they would complete some tests   Participants were 
advised to complete all items in the test and give correct information. She informed the 
participants that the scores on the tests had nothing to do with their school grades. The teacher 
did this to reduce anxiety from the participants.  
 
The teacher highlighted her role in the programme, which included assisting, guiding, 
discussing and advising participants as well as coordinating the training programme in such a 
way that the psychological, as well as the academic performance of the participants might be 
enhanced. 
 
The teacher administered the instruments for the pre-test measures.  SST, ATG MSES and 
GAS were distributed to all the participants.   She explained to them what they supposed to do 
and how they were expected to respond to the instruments.  After the explanation, she inquired 
from the participants if the procedure was clear, giving them the opportunity to signify where 
they did not.  The teacher reiterated the need for participants to objectively respond to the 
items in each of the tests as scores on the instruments were for research purpose and not related 
to their school grade.  The teacher collected the instruments after the participants had 
responded to each of the instruments one after the other.  Scores obtained from the tests during 
this session formed the pre-test scores. 
 
Step IV: Agreement on time and venue 
 
The teacher discussed the issue of time and venue of meeting with each of the groups.  The 
teacher picked the school hall as the venue and Tuesday, 11.20 AM-12.00 Noon as the time of 
meeting.  This period fell into the break period of the school.  Since this period is meant for the 
students to take refreshment and the teacher has already taken care of this, hence, the 
participants were not disadvantaged.  The teacher picked this time in order not to disrupt the 
school programme and overstay the participants in the school. This was because; the 
participants were equally engaged in the afternoon lesson being organized by the school.  
Having done that, the teacher then emphasized the need to be regular and punctual at the 
sessions, so that once the training commences, there would be no going back, so as to 
maximize the time of training. 
      
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Step V: Home -assignment 
 
The teacher concluded the session by thanking the participants for volunteering to participate 
in the training programme. The teacher encouraged the participants to ensure that they 
participated fully in all the sessions and gave them the following home -assignment. 
The participants were requested to (a) list from home reasons why they go to school and (b) to 
collect some specified 3-Dimensional and 2-Dimensional objects  
 
WEEK 2 
Topic: Identification of 3-Dmensional Objects   
Objectives:  
 To review the previous home-assignment. 
 To guide the participants in knowing why they go to school. 
 To guide the participants in knowing why the training is being organized. 
 To identify 3-Dimensional objects.  
 To differentiate between the 3-D and 2-D objects 
 
Step I: The teacher took the participants out of the classroom to collect geometrical   objects 
within the school community. Teacher reviewed the previous home-assignments with the 
participants on why students go to school. The teacher asked the participants reason why they 
come to school. The participants responded that they have come to school to learn. The teacher 
informed the participants that they have come to school to learn, so that after leaving the Junior 
School, they will transit to Senior School where they will write the Senior School Certificate 
Examination (SSCE) with which they will gain admission into tertiary institution (University, 
Polytechnic, College of education, School of nursing, and School of Surveying).  The teacher 
informed the participants that before they can gain admission into any of these tertiary 
institutions, they must obtain credit pass in certain school subjects, especially English and 
Mathematics.  Research findings have shown that most students could not transit to the tertiary 
institution because students‘ performance in mathematics was poor. The Joint Examiners‘ 
reports as well as Adeleke (2007) and Adegoke (2002) have shown that the major area where 
students have problem is in the area of Geometry (a branch of mathematics).  It has also been 
observed that the method of teaching this aspect of   mathematics was problematic and 
therefore should be corrected.  It is in line with this that this training programme tagged Out-
of-Class-Activity (OCA) is being organized. The principles involved in this programme 
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include the popular Chinese   proverb, which states that:  
What I hear, I forget.  
What I see, I remember.  
What I do, I understand (Alemni, 2008. abstract. P .v) 
 
Step III: Identification of 3-Dimentional (3-D) objects.  The teacher let the participants know 
the purpose of taking them out of the class. The teacher took the participants out of class to 
allow them collect geometrical objects within the school community. To let the participants 
realize that mathematics is real and can be done outside the four walls of classroom. The 
teacher collected all the geometrical objects gathered by the participants from home and those 
ones within the school community, to improvise mathematics laboratory. The teacher 
distributed both the 2-Dimensional (2-D) (square, triangle kite, etc) and 3-D (matchbox, cubes 
of sugar, Milo tin, etc) objects to the participants to enable them identify 3-D objects and also 
to differentiate 3-D objects from 2-D ones. What can you say about their shapes, sizes and 
lengths? The teacher told the participants that they are familiar with some common 2-D and 3-
D objects in their homes and outside their homes. The only problem is that they may not know 
the name and the significance of what they are playing with. She guided the participants in 
outlining the difference between the 2-D and 3-D objects. A 3-D object is one that has length, 
breadth and height. It occupies space. There are many types of 3-D objects. Examples are cube, 
cuboids, cone, pyramid, cylinder and sphere. A 2-D figure is one that has only length and 
breadth (width). Examples are square, rectangle, triangle and circle. The teacher got the 
participants directly involved in identifying the 3-D objects.   
  
Step IV: Home-assignment: Participants were asked to give (i) three examples of 3-D and 
three examples of 2-D objects each. (ii) To bring from home some specified 3-D objects.   
 
WEEK  3 
Topic: Surface area of cube and cuboid. 
Objectives: 
 To discuss the previous assignment. 
 To take the participants out of class.  
 To lead the participants discover the formula for the surface area of cube and cuboid.  
 
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Step I: Take the participants out of the class. Using the 3-D objects collected from home and 
school community by the participants, the teacher guided them to measure the sides of cubes of 
different sizes. What can you say about the sides of a cube? 
 
Step II: The teacher led the participants to discover properties of a cube. The teacher also 
2.
helped them discover that surface area (outside of an object) of cube is 6L  All the sides of a 
cube are equal. To find the area of one face of a cube, it is length  
= (ɭ) x Breadth (B). But a cube has six equal faces which you have seen. This implies that the 
surface area of a cube = ɭ x B + ɭ x B + B x H + B x H + ɭ x H + ɭ x H ( But ɭ =B = H) 
Therefore the surface area of a cube =6 (ɭ x ɭ) 
 2
          = 6 ɭ  
 
Step III: Surface area of a cuboid. Participants were guided to measure the dimensions of 
different given cuboids. They were led to discover both the properties of a cuboid and the 
formula for the surface area of a cuboid as thus:  
Surface area of a cuboid = L x B + L x B + B x H +B x H + L x H + L x H  
= 2LB+2BH+2LH.  A cuboid has six rectangular faces of two equal faces. This implies that the 
surface area of a cuboid  
= 2(L B+BH+LH).  
 
Step IV: Home-assignment: Group assignments were given to the participants. Participants are 
to measure the dimensions of their mathematics text book and use the measurements to find the 
surface area of the cuboid. (b) Measure the dimensions of a cube of sugar and use it to find the 
surface area of a cube. (c) They were asked to collect from their home environment some 
specified 3-D objects like funnel, Bornvita tin etc.  
 
WEEK 4  
Topic:  Surface Area of cylinder and Cone 
Objectives: 
 To take the participants out. 
 To discuss the previous assignment.  
 
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To use the 3-D objects around the participants‘ immediate environment to lead them to 
discover the surface area of cylinder and cone 
 
r  
 
 A  2πr  A  
 A   
 h  h  
 
 r  B  
 B  B  
  
 Fig. a Fig. b 
Fig. c 
 
Participants in this group were taken out of the class to school community to gather some 3-D 
objects. The 3-D objects gathered from home and school were used by the participants to 
deduce the surface area of cylinder and cone under the guidance of the teacher.   
 
Step II: Deduction of formula. The core of a toilet roll in figure (b) above was cut open using 
scissors and was spread out to form a rectangle in figure (c).  Measure the length and breadth 
of the rectangle and calculate the area of the rectangle. You are familiar with area of rectangle, 
which is Lx B. 
 
Step III: What is the relationship between the area of the rectangle and the curved surface area 
of the cylinder in figure (a)? The breadth B of the rectangle is the height h of the cylinder, 
while the length L of the rectangle is the circumference of the circular base of the cylinder 
which is 2r .   
Area of the rectangle is L x B = curved surface area of a cylinder = 2r x h = 2r h. Therefore, 
area of the curved surface of a cylinder, height h, base radius r is given by 2r h.    
 
While the total surface area of a cylinder is the area of curved surface + area of the top + area 
of the base. Therefore, for a cylinder of radius r and height h, the total surface area is  
2r 2 2  h + r + r
 = 2r 2h + 2r  
 = 2r (h + r) 
 
Step IV: A model of cone with a given radius, from cardboard and a piece of paper which is 
cut in the shape of a circle in figure2 is made from figure1.  The participants and teacher 
constructed the model of the cone.  The cone was used to deduce the curved surface area of a 
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cone.   
 
B 
 
 B h ɭ 
  Ɵ  
 O r ɭ 
 O  
 A The sector C A Cone  A C Fig. 3 
 fig.1 fig.2 
 
The formula for the curved surface area of a cone isrl where r=radius of a cone, l= slant 
2 
height of a cone. The area of the base of the cone is r
2 
 the total surface area of the cone is rl  + r = r  (ɭ + r)  
 
Step V: Home-assignment. Participants were given cardboard to construct a cone with a given 
specified radius. Participants were asked to collect 3-D objects that are spherical in nature. 
Examples of spherical shapes as ball, onion, apple etc.  
 
 
WEEK  5 
 
Topic: Properties of Pyramid and Sphere.  
 
Objectives:  
 
 To review the previous lesson. 
 To take the participants out of class. 
 To construct the net of square -based pyramid using cardboard  
 To discover the properties of a pyramid and a sphere. 
 To draw a sphere 
 
Step I: The teacher welcomed the participants and reviewed the previous lessons with them. 
Participants were taken out of the class to collect 3-D objects within the school community. 
The 3-D objects collected from school and the ones from home environment were used to form 
mathematics laboratory. 
Step II: The teacher distributed the spherical object and wooden pyramid to the participants to 
feel and to observe. The participants were led in identifying the properties of a square-based 
pyramid modeled by the researcher.  With card-board, a net of a square based pyramid was 
constructed.  
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Step III:  A chart of a square-based pyramid was given to the participants to use to answer the 
following questions:  V 
 
 
The net of a pyramid  
 
 
 
 
 D 
Questions C 
A 
a. What is the shape of face VDA? 
b. What is the true shape of face ABCD? B 
c. How many edges meet at the vertex V? 
d. How many faces has the pyramid? 
e. How many faces are triangular and how many are square in shape? 
 
Step IV: The participants examined different spherical objects which led to the identification 
of the properties of a sphere. Use the knife to cut onion into two equal parts. What can you say 
about each half of the onion?  What is the name given to it? What can you say about the edge 
of the ball, face and vertices? They were led to discover the properties themselves. Home-
assignment: Participants were given card-board to construct a net of a pyramid and also collect 
empty cylindrical objects and conical objects. 
 
WEEK  6 
 
Topic:  volume of cube and cuboids  
 
Objectives:    
 To take the participants out of class  
 To improvise the mathematics laboratory using the collected local materials 
 To review the previous assignment 
 To guide the participants discover the volume of cube and cuboids  
 
Step I: Taking participants out of class. Improvisation of mathematics laboratory 
The teacher used the 3-D objects collected by the participants from their local environment to 
improvise mathematics laboratory  
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Step III:  Discussion on the previous session  
The teacher reviewed the previous session with the participants.  
Step IV: Calculation of the volume of cube and cuboids.    
 
Step VI: The participants were given different sizes of cube and cuboid to measure their 
dimensions and record in their note book. With those dimensions, the participants were led to 
the volume of a cube and cuboids. Thus, length of the block (L) = 12cm, Breadth of the blocks 
(B) = 6cm and Height of the block (H) = 4cm.  
Volume of the block (V) = L x B x H x cm x cm x cm 
3
Volume  = 12x6x4xcm  
3
        = 288cm  
 
Volume of the cube of sugar measured by the participants implied length (L) x Breadth (B) x 
height (H) x cm x cm x cm  
3
1½cm x 1½cm x 1½cm   3/2 x 3/2 x 3/2 cm  = 27/8 
 
Step VII: Home-assignment 
Participants were asked to measure the dimensions of a cube of magi and box of match and 
calculate their volumes.    
 
WEEK  7 
 
Topic: Volume of Cylinder and Cone 
 
Objectives:  
 To discuss the  previous home-assignment  
 To take the participants  out of class  
 To improvise mathematics laboratory  
 To construct cylinder and cone  
 
Step I: The teacher welcomed the participants and expressed appreciation for their cooperation 
and regular attendance.   
 
Step II: Out of class activity  
The teacher took the participants out of the class to collect the 3-D objects that relate to 
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participants‘ real life situation 
 
Step III: Discussion on the previous session  
Previous session was reviewed and home-assignment was discussed. 
 
Step IV: Construction of cylinder and cone 
The teacher distributed the 3-D objects (cylinder and cone) to the participants. The teacher 
guided the participants in constructing a cylinder and a cone with the same radius and the same 
height. The teacher used the constructed cylinder and cone to let the participants establish the 
relationship between the volume of a cylinder and cone. The participants were asked to fill a 
cone with sand and pour the sand into the cylinder until the cylinder is filled up. How many 
cones of sand fill the cylinder? To deduce the formulae of the volumes of cylinder and cone, 
1 2
you have seen that the volume of cone = /3 r h. 
Step V: summarize the whole session  
The completion of the table of identification.  
The participants identified and related the given 3-D objects to real world Common solids  
 
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Table 1: This was done to see the extent they could identify and relate geometrical objects to 
their real world.  
S/N Name of objects Freehand drawing  Name of basic shape 
1 Tin of margarine     
 
2 A plastic funnel     
 
3 Block     
 
4 Onions    
 
5 Exercise book -  
 
6 A mound of groundnut     
 
7 A cube of magi    
 
8 Milk tin     
 
9 Sharp-end of a pencil     
 
10 Half of the orange     
 
11 Moon    
 
Sorting and classification table 
 
Step VI: Home -assignment 
Participants were asked to construct a cylinder and a cone having the same radius and the same 
height in groups of five consisting of 8 members each. Card-boards and cellotapes were given 
to them by the teacher. The teacher instructed the participants to use the cylinder they have 
constructed to find the number of faces, edges and vertices a cylinder has. Also the  
participants were asked to collect five local 3-D geometrical objects and relate them to their 
real world like the table above. 
 
WEEK  8 
 
Topic: Administration of post-test measures and official termination of the training. 
Objectives:  
 To obtain post-test measures  
 To summarize the whole session 
 To formally terminate the training  
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 To appreciate the participants 
Step I: General summary of all the sessions 
Step II: Administration of post-test measures  
 
Step III: The teacher administered achievement test in Geometry and Geometry attitude scale 
to the participants and collected them back at completion.  
 
Step IV: Formal Termination of the training. The teacher appreciated the participants and 
commended the participants for their active role they played all through the training. The 
participants were encouraged to see that mathematics is real and not abstract. Secondly, 
mathematics is culture of people Participants were enjoined to develop positive attitude 
towards geometry as geometry is useful in their lives.   
 
 
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APPENDIX VI 
 
TRANINING PROGRAMME (GCS) 
WEEK 1 
General Orientation and Administration of Pre-test measures 
Topic: Orientation and administration of instrument to obtain baseline data.  
 
Objectives: 
 To introduce one another. 
 To acquaint the participants with the benefits of the training programme and the roles they 
would play. 
 To inform the participants about the rules of the training.  
 To obtain the baseline data. 
 
Step1: Self-introduction between the researcher and the participants.  
 
The counsellor welcomed the participants and introduced herself to familiarize with and 
sensitize the participants. The participants were also instructed to introduce themselves 
individually by mentioning their names only. The counsellor urged the participants to feel free 
to make their contributions to the programme by expressing their own views and opinions in a 
polite way by respecting the views of others. 
 
Step II: Acquitting the participants with the benefits of the programme. 
 
The counsellor acquitted participants with the nature and objectives of the training programme.  
The counsellor highlighted the benefits the participants might derive from the training, if they 
participated meaningfully. Such benefits might include the development of positive attitudes 
towards Mathematics (geometry included), high level of self-efficacy and improvement in their 
academic performance. 
 
The counsellor emphasized the need for participants to cooperatively participate effectively in 
all the eight training sessions, as this would enable them to follow the programme sequentially 
and logically, since the outcome of the programme depended on their complete participation in 
the training programme, and the training programme was cumulative in nature. This implied 
that any break in session would create a gap in knowledge, which might deprive the 
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participants of the full benefits of the programme and therefore prevent the programme from 
producing the desired result.   
 
Step III: Administration of the pre-test measures. 
The counsellor informed the participants that they would complete some tests.   Participants 
were advised to complete all items in the test and give correct information.  She informed the 
participants that the scores on the tests had nothing to do with their school grades. The 
counsellor did this to reduce anxiety from the participants.  
The counsellor highlighted her role in the programme, which included assisting, guiding, 
discussing, teaching and advising participants as well as coordinating the training programme 
in such a way that the psychological, as well as the academic performance of the participants 
might be enhanced. 
 
The counsellor administered the instruments for the pre-test measures.  SST, ATG MSES and 
GAS were distributed to all the participants.  She explained to them what they were supposed 
to do and how they were expected to respond to the instruments.  After the explanation, she 
inquired from the participants if the procedure was clear, giving them the opportunity to 
signify where they did not.  The counsellor reiterated the need for participants to objectively 
respond to the items in each of the tests as scores on the instruments were for research purpose 
and not related to their school grade. The counsellor collected the instruments after the 
participants had responded to each of the instruments one after the other.  Scores obtained from 
the tests during this session formed the pre-test scores. 
 
Step IV: Agreement on time and venue of meeting. 
 
The venue and time of meeting was same as in group 1(OCA) except that the day of meeting 
was Thursday.  
 
Step V: Home-assignments 
 
The counsellor also emphasized the need for the participants to do the home-assignments that 
would be given to them.  The counsellor informed the participants that assignment would 
provide greater opportunity for them to practice and familiarize themselves with the skills that 
were being taught. The counsellor concluded the session by thanking the participants for 
volunteering to participate in the programme. The counsellor encouraged the participants to 
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ensure that they participated fully in all the sessions and gave them the following home-
assignment. 
 
The participants were requested to list from home reasons why they attend schools.  The aim is 
to enable participants to see the need of setting a goal in their study.  This is also meant to 
assist them in self-appraisal before the next session. 
 
WEEK  2 
Topic: The goal of coming to school 
Objectives:  
 To appreciate the participants for coming. 
 To discuss the previous home-assignment. 
 To inform the participants about the goal of coming to school 
 
Step I:  The counsellor welcomed the participants and appreciated them for their punctuality. 
 
Step II: Review of the previous homework 
 
Step III:  The counsellor asked the participants the reason why they come to school. The 
participants responded that they have come to school to learn. The counsellor informed the 
participants that they have come to school to learn, so that after leaving the Junior School, they 
will transit to Senior School where they will write the Senior School Certificate Examination 
(SSCE) with which they will gain admission into tertiary institution (University, Polytechnic, 
College of education, School of nursing, and School of Surveying).  The counsellor informed 
the participants that before they can gain admission into any of these tertiary institutions, they 
must obtain credit pass in certain school subjects, especially English and Mathematics. 
Research findings have shown that most students could not transit to the tertiary institution 
because students‘ performance in mathematics was poor. The Joint Examiners‘ reports as well 
as Adeleke (2007) and Adegoke (2002) have shown that the major area where students have 
problem is in the area of geometry (a branch of mathematics).   
 
Step IV: Home-assignment.  
What are the reasons for not performing well in mathematics (geometry included)?  What are 
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the conditions for gaining admission into institutions of higher learning? 
  
WEEK 3    
Topic:  The concept of Cognitive Behaviour Therapy and Cognitive Distortions  
Objectives:  
 To discuss the previous home-assignment  
 To explain the concept of CBT. 
 To identify some cognitive distortions. 
 
Step I: review of the previous home-assignment  
 
The counsellor reviewed the discussion of the previous session home-assignments with the 
participants. She asked the participants to read out the information they recorded on their note 
books on the condition for gaining admission to institution of higher learning.. 
 
Step II: the concept of CBT 
 
It has been observed that among the reasons listed by the participants why students are not 
performing well in mathematics is that the subject is difficult and also, that it is too abstract. 
This is a misconception (wrongly-held notion about mathematics).  Psychologists say that most 
of our emotions and behaviours are the results of what we think or believe about ourselves, 
other people, and the world. These cognitions shape how we interpret and evaluate what 
happens to us, influence how we feel about it, and provide a guide to how we should respond.  
Unfortunately, sometimes our interpretations, evaluations, and underlying beliefs thoughts 
contain distortions, errors, or biases that are not very useful or helpful. This results in 
unnecessary suffering and often causes us to react in ways that are not in our best interest.   It 
is on this line that this training programme tagged Cognitive Behaviour Therapy (CBT) is 
being organized. This programme, CBT is intended to assist you in modifying your negative 
thought patterns about the subject, mathematics.  The principles involved in this programme 
include a systematic and goal-oriented procedure through the use of cognitive behaviour 
therapy techniques. These techniques were discussed below in the subsequent sessions. 
 
Step III: identification of some cognitive distortions. 
The term ―cognitive distortion‖ refers to errors in thinking or patterns of thought that are 
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biased in some ways. They may include (A) interpretations that are not very accurate and 
selectively filter the available evidence, (B) evaluations that are harsh and unfair, and/or (C) 
expectations for one and for others that are rigid and unreasonable. The more a person‘s 
thinking is characterized by these distortions, the more they are likely to experience disturbing 
emotions and to engage in maladaptive behaviour.  For example, if a student thinks or believes 
that the subject is difficult, that feeling or that thinking may affect his performance in that 
subject.  A number of cognitive distortions have been identified. These include:  
 
(1)  Mind reading: This implies reading more into the mind of others more than is really 
there or can be described as when you jump to conclusions or make assumptions 
(usually negative about what others may be thinking about you or what you talk about 
yourself ).   
(2)  Mental filter:  Focusing on a single negative detail and dwelling on it exclusively  until 
 one‘s vision of reality becomes darkened.  
(3)  Name-calling or Labeling criticism: Attaching a negative name (label) to oneself  or 
 others instead of discussing the actual behaviour or action.  Or continually  putting 
 oneself down (often more than you would others).  
(4)  Magnification or minimization: magnifying the negative and minimizing the 
 positive.   
 
Step IV: Homework. The counsellor asked the participants to write down two examples of 
cognitive distortions and their meanings.  
 
WEEK 4 
Topic:  CBT Techniques (case study) 
Objectives:  
 To welcome the participants. 
 To review the previous home-assignment  
 To modify maladaptive thought patterns using CBT techniques (a) Cognitive Rehearsal and 
(b) Validity Testing) 
 
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Step I: The counsellor welcomed the participants to another session and requested for the 
home-assignment that was given to them.  This was discussed and more light was shed on the 
participants‘ given responses.  
 
Step III: CBT Techniques  
The counsellor introduced the topic for discussion cognitive rehearsal and validity testing.  
 
Discussion:  
 
The counsellor informed the participants that the essence of this (cognitive rehearsal) was to 
allow the participants to imagine a difficult situation they have faced in the past. The 
participants were then informed to list the problems they have encountered in the past in the 
process of learning mathematics. The participants listed the problematic situations they have 
encountered. The counsellor in a step-by-step manner probed the genuiness of those problems 
(validity testing). The counsellor guided the participants on the possible solution to those 
problems. The counsellor advised the participants to be practicing all what they have discussed 
during the session. 
 
A case study of a student with self-defeating thought patterns about mathematics . 
 
 
 
 
 I hate mathematics, it is my 
 problem in school  
 I fear the subject mathematics      
I am always failing mathematics  
 
 
 
 
 
 
 
Step III: Effects of self-defeating thought patterns about mathematics (geometry 
included).  
It promotes negative attitude towards the learning of mathematics.   
It could result to poor academic performance.   
It can reduce motivation towards the acquisition of mathematical skills.   
It could debar one from achieving one‘s life goals.             
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Step IV: Home-assignment:  The counsellor informed the participants to imagine any 
difficult situation they may face in the course of learning and suggest possible solution(s).  
 
WEEK 5 
Topic: Writing in a Journal and guided discovery. 
Objectives:  
 To appreciate the participants. 
 To discuss the participants‘ home-assignment.   
 To explain the CBT techniques. 
 
Step I: appreciation 
The counsellor thanked the participants for their punctuality and regularity. She equally 
appreciated them for the cooperation and contribution during each session.   
 
Step II: The counsellor reviewed the previous session.   
 
Step III: The counsellor requested for the homework given to the participants last session. The 
various problems imagined and possible solutions suggested were discussed.  
 
Step IV: The counsellor introduced the new topic for the session __Writing in a Journal and 
Guided discovery. 
 
Discussion  
The counsellor asked the participants to mention aids to memory. Among the aids listed was 
record keeping.  The counsellor informed the participants that they need to maintain a diary to 
keep an account of situations that arise in their day-to-day activities. They were advised to 
write the thoughts that were associated with those situations and behaviours they exhibited 
toward the situation. The counsellor gave an example of a student who thought that the 
mathematics counsellor would not come to school; the situation that arose was that he did not 
bother to bring his math notebook to school and the counsellor came. The behaviour exhibited 
was absenteeism in the math class because he felt that his math teacher might discover this and 
punish him.  
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The counsellor explained what is meant by cognitive distortion and explained to the 
participants what to do in order to modify their behaviours.  
 
Step V The counsellor responded to various questions being asked by the participants.  
 
Step VI: Home Assignment: The counsellor instructed the participants to write three names 
of people they would wish to be like, as well as the reason why they want to be like them. 
 
WEEK  6 
Topic: Modelling and Homework  
Objectives: 
 To welcome the participants 
 To discuss the previous home-assignment.   
 To modify cognitive distortions using the techniques of modelling and homework  
 
Step I:  Welcoming participants   
The counsellor commended the participants for their regularity and cooperation.  
Step II: The counsellor reviewed the previous session. The given home-assignment was 
collected by the counsellor and discussed.  
Step III: Modelling and Homework 
 
Discussion  
The counsellor introduced the topic for the session_ modelling and homework. The counsellor 
prompted the participants to identify the names they would wish to be like with reasons. Each 
response was used to treat expected behaviour.   
 
Modelling: Modelling is a behaviour change method that provides ample experience to the 
observer who might imitate the observed behaviour. The counsellor instructed the participants 
about the models of great mathematicians to enable them formulate appropriate cognitive 
logical thought patterns for dealing with mathematics problems. The pictures were displayed. 
The counsellor asked the following questions from the participants:  
 
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The model of great mathematicians 
 
 
 
 
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Are these models of mathematicians‘ only males?  
What can you say about their ages? 
Are they old?  
Do they have positive attitude towards mathematics?  
 
The counsellor let them know that gender is not a barrier in studying mathematics. Both male 
and female can achieve greatness in mathematics if they have positive thought patterns and 
attitude towards mathematics and also work hard like these great mathematicians.  For 
example, Ezilo & Katherine Okikiola achieved great success in mathematics. Secondly, the 
counsellor informed them that age is not the determinant of success in the learning of 
mathematics. Any person can learn mathematics irrespective of their ages, whether young or 
old. For you to be as successful as those models you mentioned and these mathematicians also, 
you must be a self-regulating (self- control) students who must be ready to do his or her own 
mathematics homework (homework techniques).  
 
Doing homework helps to broaden one‘s knowledge and facilitates understanding. It is 
therefore necessary that homework should be seriously carried out without procrastination 
(postponement). The counsellor instructed the participants that any homework given to them 
by teacher must be done immediately. Any homework that is difficult should not be kept aside, 
because if you do, the homework might either not be done or it might be poorly done or it 
might not be done at all. The counsellor further informed the participants about the importance 
of homework using a case study of a student who does his homework conscientiously and 
these leads to better understanding of mathematics, which eventually leads to enhanced 
performance in mathematics. The counsellor instructed the participants to always do their 
homework.                               
 
Step IV: A case study of a student who does his homework regularly and also having positive 
thought patterns about mathematics. 
   A happy student who likes 
mathematics  
 
I always do my homework in 
 mathematics without 
 procrastination.  I score high 
 marks in mathematics. 
 examination   
 
 
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The counsellor explained that it is the liking in mathematics with the doing of his homework 
that might have brought about good performance in mathematics. That is  
A- Liking for mathematics   
B- Regular doing of homework  
C- High scores 
 
Step V: Home-assignment 
The counsellor asked the participants to write three importance of homework to them.  
The counsellor asked the participants to write three things to be done by a student who wants 
to acquire ability to know mathematics.     
 
WEEK 7 
 
Topic:  Cognitive Behaviour Therapy Technique - systematic positive reinforcement  
Objectives:  
 To appreciate the participants  
 To discuss the previous session  and  the given home-assignment   
 To acquire mathematical skills using  the CBT technique, systematic positive 
reinforcement  
 
Step I: Appreciation 
The counsellor appreciated the participants for their cooperation and regularity from the 
beginning of the training.  
 
Step II:  The home-assignment was requested for, collected and discussed by both the 
counsellor and the participants.  
 
Step III: The counsellor introduced the new topic for discussion- systematic positive 
reinforcement. 
 
Discussion  
The counsellor told the participants the story of a girl, Felicia who wanted to study Mechanical 
Engineering in the university but was deficient/weak in mathematics. She was good in other 
subjects but her major problem centered on mathematics which was the major skill needed for 
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Felicia to be able to fulfill her desire.  The counsellor asked the participants to tell her what 
they (the participants) think that Felicia should do in order to improve her mathematics ability? 
The counsellor first of all wants to know what the participants would suggest the Felicia could 
do so as to possess mathematical skills.  The counsellor prompted the participants to give their 
own suggestions to the class. The Participants were actively involved in the discussions.  
 
Step IV: Interaction and discussion ensured between the participants and the counsellor.  
Responses of the participants  
i) ―Felicia should read her mathematics book every day.‖  
ii) ―She  should  make sure that she does her mathematics assignment promptly‖ 
iii) ―If she does not have mathematics text book, she should buy one‖ 
iv) ―Felicia should  move with friends who know math better than her so that they would   
teach her ‖ 
v) ― she should employ the lesson teacher to teach her mathematics at home ‖      
vi) ―She should tell her math teacher about her problem‖. 
 
Step V: However, the counsellor told them that they all answered well. She informed the 
participants what Felicia did in other to improve her mathematics ability.  Felicia sought   the 
help of a counsellor who gave her counselling remedy on mathematics. 
 
Step VI: The counsellor explained that the past records of Felicia‘s mathematics scores were 
checked and it was discovered that Felicia has not been performing well in mathematics.  
Felicia was instructed that self-defeating thought can affect academic performance. Therefore, 
she should first of all believe that she can perform well in the subject in question, mathematics. 
The counsellor explained the importance of mathematics to Felicia and enjoined her to work 
harder. After the counselling, Felicia was determined to be studying mathematics everyday. 
The Continuous Assessment test was given, Felicia out performed the whole class. The 
mathematics teacher asked the class to clap for her (positive reward).  Also, at the end of the 
term, Felicia scored the highest mark in mathematics and she was given a new mathematics 
text book (positive systematic reinforcement). Positive systematic reinforcement can be 
described as the step –by- step method of giving reward to individual in order to increase the 
probability of emission of desirable behaviour in that individual. 
 
 
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Step VII: The counsellor used the case of Felicia to inform the participants about the 
importance of mathematics also, letting them know that rational thinking can promote good 
performance in mathematics. The counsellor explained that one of the profitable things a 
student who wants to learn could do is to have determination to achieve and then, to study. 
Determination is by personal choice and all profitable life enterprises require the force of 
determination and hard work. The counsellor stressed that learning mathematics is a profitable 
exercise that requires regular attendance of classes, prompt doing of assignment and constant 
study. Counsellor emphasized that any student that does that would be rewarded just as the 
same way Felicia was rewarded for passing her mathematics examinations.  The story was 
summarized by the counsellor as follows: Cognitive Behaviour Therapy. Table of a student 
who requires improvement on general mathematical ability. 
 
Situation  Requiring improvement of general mathematical ability. 
Automatic I can not achieve my dream of becoming a Mechanical Engineer if I am 
thoughts  deficient in Mathematics. I am a failure (name –Calling, magnifying negative 
and  minimizing positive     
Emotions Sad/depressed, Discouraged   
Behaviour Not studying mathematics. 
Counsellor  Evaluate and modify the behaviour.  
Baseline data were sought by digging into her previous mathematics records. 
How many times do you study mathematics a week?  Don‘t you think that 
increasing the period of studying mathematics per week can improve your 
proficiency? Allocate more time to mathematics since it is identified as a 
problem subject. Regular attendance of classes, promt doing of home-
assignment and determination to succeed. Success is the product of hardwork, 
so work hard.  
 
Step VIII:  Home-Assignment.  
The counsellor asked the participants to (a) enlist ten other things a student can do to acquire 
mathematical ability and (b) seven CBT techniques they had learnt in the course of training. (c) 
Give one reason why they study the techniques.  
 
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WEEK  8    
 
Topic: Administration of Post-test measures and Termination of the training 
Objectives: 
 To  summarize the whole session  
 To obtain post-test measures  
 To formally terminate the training programme 
 To appreciate the participants 
 
Step I: General Summary of all the sessions  
The counsellor, using the previous home-assignment summarized the whole session. She 
elicited questions and provided answers. She clarified issues that were mentioned by the 
participants. 
 
Step II: Administration of post-test measures  
The counsellor assisted the researcher in administering Achievement Test in Geometry and 
Geometry Attitude Test Scale and collected them on completion .  
 
Step III: Formal termination of the training  
The counsellor appreciated the participants for their active participation and cooperation. She 
enjoined the participants to maintain the gain of the training.  
    
  
   
 
 
 
 
 
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APPENDIX VII 
 
RESEARCHER’S INSTRUCTIONAL GUIDE IN GEOMETRY (RIGG) 
 
WEEK 1           SAME AS IN OCA AND GCS           
 
 
WEEK  2  
 
Subject: Geometry 
Topic: Identification of 3-Dimensional objects. 
Instructional Objectives: By the end of the lesson, the participants should be able to:  
(i) Define 3-Dimensional objects.  
(ii) List six examples of 3-Dimensional objects. 
(iii) Differentiate 3-D from 2-D objects.  
 
Instructional Materials: Chalkboard and diagrams relating to the concept of the day. 
Previous Knowledge: Participants are familiar with different shapes such as square, 
rectangles, circle and triangles. 
 
Presentation: The explanation of the topic 
 Concept of 3-Dimensional objects 
 Teacher instructed the participants to give examples of 2-Dimensional shapes they had 
studied in JSI (square, rectangle, circle etc.). The teacher instructed them to list other solid 
shapes they can see around their homes or in their school environment (Milo tin, play ball, 
funnel, a cube of sugar, magi cube and a matchbox). Teacher explained that these other 
solid shapes  such as Milo tin, play ball, funnel, a cube of sugar, magi cube an hut and a 
matchbox are called 3-Dimensional shapes. They are different from the 2-Dimensional 
shapes you have studied in JSI. 3-Dimensional shapes have a common property, an inside 
and an outside.  While 3-Dimensional shapes have length, breadth and height, the 2-D 
shapes have only length and breadth.  3-Dimensional objects can be written as 3-D shapes 
or 3-D objects. Examples of 3-Dimensional shapes were written and drawn on the 
chalkboard.  
 
 
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The following questions were asked from the participants to review the whole lesson. 
(a) Explain what is meant by 3-D objects.  
(b) Name six types of 3-D objects.  
(c) Give an example of each of the 3-D objects mentioned in (b).  
(d) What is the shape of (i) a sheet of paper? (ii) a hut (iii) the moon 
(e)    What is the difference between 3-D and 2-D objects? 
 
Participants responded to the questions above.  
Home-assignment: Participants were asked to write down five everyday objects that are 3-D 
in shape and five that are 2-D. 
 
WEEK 3 
 
Topic: Surface area of cube and cuboids  
Duration: 40 minutes  
Instructional Objective: By the end of the lesson, the participants should be able to: 
1) Identify the following terms (i) ii) faces (iii) edges and vertices of cube and cuboid. 
ii)      Define each of (i) above  
iii) Explain the properties of cube and cuboids 
iv) Calculate the surface area of cube and cuboids      
 
Previous Knowledge: Participants could explain the meaning of 3-Dimensional objects  
Instructional Material: chalkboard. 
Presentation: Explanation of the concept. 
Teacher discussed the properties of cube and cuboid with the participants.  
 
Definition  
Surface: The outer view of a solid is called its surface  
A face: A face is any of the pieces which make up a surface  
An edge: An edge is a line where two or more surfaces meet. It may be curve or straight  
A Vertex: A vertex is a point or corner where three or more edges meet.  
Properties of a cube and cuboid  
A cube: A cube is a 3-diemnsional object with equal size. It has equal length, breadth and 
height. It may be described as a cuboid in which all the six faces are square.   
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A cube has six faces, eight vertices and twelve edges. Examples are magi cube, ludo dice. 
 A cuboid  
  
A  H Vertex   
A Cube  
   Top Surface 
 F G F 
 F    
Left Surface 
 ESdugref a  c
 C E    Front Surface e   
B  D 
 
 
Cuboids:    cuboids are examples of 3-D objects. Each of the faces of cuboids has the shape of 
a rectangle. The face of the cuboids could either be flat (plane) or curved. Cuboids also have 
six faces, eight vertices and 12 edges. Examples of cuboids are chalk box, match boxes, 
textbooks,  
 
Calculation of surface area of cube and cuboids. Explanation of how to calculate the surface 
areas of cube and cuboids was given by the teacher. Thus, cube has 6 equal faces. Each of the 
faces is a square.  Area of one of the square faces is Length x Breadth = Lx B =Lx L (since 
2 
L=B), that is, L  
2 2 
To find surface area of the 6 faces implies 6xL = 6L square unit 
 
Cuboids: cuboids have 6rectangular faces. Surface area of cuboids is, LB +LB + BH + BH + 
LH+ LH  
= 2LB + 2BH + 2LH  
= 2 (LB+ BH + LH) square unit.  
Examples are done on the chalkboard.  What is the surface area of a cube of 7cm long? (b)  
Calculate the surface area of a cuboid with dimensions 6m by 5m by 3m.  
 
Solved examples 
Cube: length  =7cm, Breadth  
=7cm,  
i.e, L=B =7cm Surface area of a cube  
2    
= 6ɭ = 6 x ɭ x ɭ
2
Surface area = 6 x 7x 7 cm  
2
= 294cm  
 
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Cuboids with length 6, breadth 5 and height 3 has the 
Surface area = 2 (LB+ BH + LH)  
=2(6x5 + 5x3+ 6x3)  
2
= 126cm  
 
Home-assignment   
Find the surface area of (i) a cube of sugar and (i) cuboid of a chalk box. 
 
WEEK 4 
 
Topic: Surface Area of Cylinder and Cone  
 
Duration: 40 minutes  
 
 
Instructional Objectives: By the end of the lesson, the participants should be able to:  
(i) Explain the properties of cylinder and cone. 
(ii) State the formulae for the surface area of a cylinder and a cone. 
(iii)  Calculate the surface area of (a) cylinder and (b) cone 
 
Previous Knowledge: The participants could explain the properties of cube and cuboid. 
Instructional Materials: Chalkboard, meter ruler and a sheet of paper.  
Presentation: The teacher reviewed the previous session and introduced the new lesson to the 
participants. 
The objects like milk tin and Bornvita tin you know are called 3-D objects. They have some 
properties which can be used to identify them. 
Cylinder: Cylinder can be described as a 3-D object with round ends and long straight side. 
The surface of a cylinder consists of three faces: flat top face, round face and bottom flat face. 
The cylinder has two plane faces and one curved one. It has two edges and no vertices. The 
two plane faces are both circles.  
 
Cone is another example of 3-D object and examples are funnel, a sharp end of a pencil,or 
biro. The base of a cone is a plane circle. It has two faces, one vertex and one edge. 
 
 
 r  
 
h ɭ 
 
 h 
 r 
 
r  
A  Cone    
Cyli nder 
 
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Surface area of cylinder and cone. 
 
Cylinder: Participants are familiar with the areas of the circle and rectangle. A plane sheet of 
paper was folded into a cylindrical shape. This is made up of three regions.  
A=the circular top 
B = curved surface 
 C= the circular base. The circumference of the circle is 2r . The circular top of the cylinder 
becomes the length of the rectangle 2r  and the height of the cylinder becomes the breadth of 
rectangle. The formula for the area of the curved surface of the  
cylinder = L x B = 2r  x h 
 = 2r h.  
While the total surface area of a cylinder is the area of curved surface + area of the top + area 
of the base. Therefore, for a cylinder of radius r and height h, the total surface area is  
 2r 2 2 h + r + r
 = 2r 2h + 2r  
 = 2r (h + r) 
 
Curved surface area of a cone is given by πrɭ where radius of the cone =r and slight height ɭ = ɭ.  
2 
The area of the base of the cone is r
2 
 the total surface area of the cone is rl  + r = r  (ɭ + r)  h ɭ 
 
Example one.   
r 
Calculate the surface area of the cylinder of r= 2cm, h = 14cm.  
A Cone  
Solved problem  
Radius of the cylinder = 14.   
Height of the cylinder = 2cm  
Area of the curved surface of the cylinder = 2r h 
 =2 x22 x2 x14/7 
2
= 176cm  
 
Cone. Curved surface area of a cone is given by πrɭ. Find the area of curved surface of cone 
with radius 7cm and length of slighting side 10cm. 
2 
Area is given by nrl = 22/7 x7 x 10 cm
2
=220cm  
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Home- assignments. Calculate the surface area of each of the following cylinders.  
Radius=3cm, height =21cm (b) radius =28, height = 10 (c) what is the radius of a cone with 
2?
slight side of length 10cm and curved surface area of 220cm  
 
 
WEEK 5  
 
Topic: Basic properties of Pyramid and Sphere 
 
Duration: 40 minutes  
 
Instructional Objective: By the end of the lesson, the participants should be able to: 
(i) State the properties of a pyramid and sphere.  
(ii) Draw pyramid and sphere.  
(iii) Give examples of pyramid and sphere. 
 
Previous Knowledge: Participants are familiar with the mound of ground, rice, beans, hut, 
ball. 
 
 
Instructional Materials: Chalkboard, diagrams. 
 
 
Concept of pyramid and Sphere  
The teacher reviewed the previous assignment and introduced the new lesson to the 
participants. V 
 
 
 
 
 
 
 
 
 D 
 C 
 A 
 
  B 
 
 
A Pyramid 
 
The name pyramid is derived from the shape of its base-face. 
 
A square-based pyramid has five faces, five vertices and eight edges. Four of the faces are 
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triangular and one is square.  Examples of pyramid are huts, mounds of ground, rice, beans  
 
Sphere:  A sphere is another type of 3-dimensional object. It is described as a solid figure that 
is not completely round but spherical in shape; and every point on its surface is at equal 
distance from the centre. Examples of a sphere are play ball, the shape of the earth, apple. Half 
of a sphere is called a hemisphere. A typical example of a hemisphere is half of a moon  
 
Properties of a sphere  
A sphere has no edge. 
It does not have any vertex.  
 
A sphere has only one face.  
 
 
 
 
 
 
 
 
 A Sphere  
 
Summary Table  
 
Name No. of Vertices  No. of edges No. of faces 
Pyramid 5 8 5 
Sphere 0 0 1 
 
Home-Assignment: Give three objects each under the following 3-D shapes: 
(a) Pyramid (b) sphere  
(2) How many vertices has a pyramid and how many has a sphere?  
 Draw a net of a pyramid on the given cardboard and submit to the teacher. 
 
 
WEEK  6  
 
Topic: Calculation of Volume of a cube and a cuboid   
 
Duration: 40 minutes  
 
Instructional Objectives: By the end of the lesson, the participants should be able to:  
(i) Define the following terms: (a) volume  (b) capacity.  
(ii) Identify the unit of (a) volume  (b) capacity 
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(iii) Write down the formulae for the volume of cube and cuboid. 
(iv) Calculate the volume of a cube and cuboid  
 
Previous Knowledge: The participants are familiar with things in their local environments  
 
 
Presentation: Explanation of the volume.   
 
 
Volume: Volume refers to the amount of space an object can occupy. Or the measure of the 
space occupied by a solid shape is called the volume of the shape. The units of volume are 
cubic centimeters and cubic meters. Teacher explained that every measurement that is carried 
3
out has its units. The unit of volume can be measured in cubic centimeters (cm ) or in cubic 
3
meters (m ), the choice of a unit of measurement to a large extent should depend on the 
               
object(s) being measured.  
Capacity: The capacity of a container is the amount of liquid it holds. The basic unit of 
capacity is the liters or centiliters. For example, the capacity of the liquid in Coca-Cola bottle is 
35cl or 50cl and the capacity of engine oil in a gallon is 4 liters. 
 
Volume of a cuboid  
 
A cuboid  
  
 A H Vertex  
 1m 
F G F 
 
F    Edge   
 
Surface   
 1m 
1m 
C E 
 
B D 
 
The volume of 3-D object is base area multiply 
by height. But cuboid has a rectangular  
shape, therefore, 
Volume=Base area x height 
Where base area =length x breadth 
Hence,  
 Volume of the cuboid is  
= L x B x H cubic centimetre  
Example1: A match box has lenght 4cm, breadth 3cm and height 2 cm.  
 
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Volume = LxBx H 
3
= 24cm   
Example2 
What is the volume of a cube whose length, breadth and height are 6cm, 6cm and 6cm, 
respectively. 
 
Volume of a cube = L x B x H =6 x 6 x 6 x cm x cm x cm 
3
     =216cm  
Home-Assignment: (a) Find the volume of the following  
L = 6cm, B = 3cm and H = 4cm  
3cm, 3cm and 3cm  
5cm, 5cm and 5cm  
10cm, 5cm and 3cm 
 
WEEK 7  
 
Topic:  Volume of Cylinder and Cone.  
 
Instructional Objective: By the end of the lesson, the participants would be able to: 
  review the previous  assignment 
 Calculate the volume of Cylinder and Cone applying the formulae. 
 
Volume of Cylinder  
Participants should remember that  
Volume =base area x height.  
Again, remind the participants that cylinder has a circular base. 
Therefore, the volume of cylinder is circular base x height 
2
= nr  x h  
2
= nr h cubic unit  
Example1: Calculate the volume of cylinder of height 7cm and radius of 7/2 
2
   Volume = nr h 
        = 22/7 x7/2 x7/2 x 7 
3
=1191/2cm    
 
Volume of cone:  
Volume of the cone = 1/3 of the cylinder volume 
2
=1/3πr h 
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Example2: calculate the volume of a cone with base 8cm and height 5cm. 
2
Volume of the cone = 1/3πr h 
           = 1/3 x 22/7 x 8 x 8 x 5 
3 
           = 335cm
 
3
Home-Assignment: (1) Find the radius of a cone whose volume and height are 1100cm  and 
        7cm respectively. 
3
   (2) If the volume of the cylinder is 1408cm  and the radius is 9cm find 
        the height in cubic metre. 
 
WEEK 8 
Administration of post-test measures.  
Instructional Materials: Chalkboard, all the post-test instruments: Achievement Test in 
Geometry and Geometry Attitude Scale.  
 
Objectives:  
 To generally review all the sessions and conduct final evaluation. 
 To appreciate the participants. 
 To obtain post-test measures. 
 
Presentation: The teacher reviewed all the sessions and emphasized that all the activities were 
aimed at enhancing their attitude and improving performance in mathematics generally, 
especially in the area of Geometry.  Achievement Test in Geometry (ATG) and Geometry 
Attitude Scale (GAS) were administered with the help of the Research Assistants. They were 
collected on completion.  
The teacher appreciated the participants for their patience, regularity and full participation 
throughout the sessions. The teacher‘s Instructional Guide in Geometry (RIGG) was used to 
teach the three groups the Geometry instruction. 
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