EFFECTS OF GAME AND POEM-ENHANCED INSTRUCTIONAL STRATEGIES ON PUPILS’ LEARNING OUTCOMES IN MATHEMATICS IN BAYELSA STATE, NIGERIA BY Toinpere Mercy FREDERICK-JONAH B.Ed.(Hons) Mathematics (Port-Harcourt), M.Ed. Mathematics Education (Ibadan) Matric No: 124195 A Thesis in the Department of Teacher Education, Submitted to the Faculty of Education In partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY of the UNIVERSITY OF IBADAN SEPTEMBER, 2014 UNIVERSITY OF IBADAN LIBRARY ABSTRACT Mathematics is a core and compulsory school subject from primary through the senior secondary school level. Reports from examination bodies have shown that the mean score of Bayelsa State pupils’ achievement in mathematics is below average. This has been attributed to the lecture instructional strategy being adopted by the teachers of the subject. Therefore, game- and poem-enhanced instructional strategies have been recommended to improve mathematics instruction at the primary school level but few studies have been carried out to determine the effectiveness of these strategies. Therefore, this study, determined the effects of game- and poem-enhanced instructional strategies on pupils’ achievement, knowledge of mathematics concepts and interest in mathematics. The moderating effects of verbal ability and gender were also determined. A pretest-posttest, control group, quasi-experimental design with 3x3x2 factorial matrix was adopted. Three hundred and forty-four primary six pupils from twelve purposively selected public schools in Yenagoa and Ogbia Local Government Areas of Bayelsa State were randomly assigned to two treatments and control groups. The study lasted for twelve weeks. The instruments used were two teachers’ assessment sheets, instructional guides on Poem-Enhanced Instructional Strategy (PEIS) and Game-Enhanced Instructional Strategy (GEIS) for the experimental groups and Modified Lecture Instructional Strategy (MLIS) for control groups, Pupils’ Mathematics Achievement Test (r=0.72), Pupils’ Mathematics Concepts Test (r=0.81), Pupils’ Interest in Mathematics Inventory (r=0.73) and Pupils’ Verbal Ability Test (r=0.85). Seven null hypotheses were tested at 0.05 level of significance. Data were analysed using Analysis of Covariance (ANCOVA) and Scheffe Post-hoc analysis. Treatment had significant main effect on pupils’ achievement in mathematics (F(2,325)= 2 2 142.473; ɳ =0.467), knowledge of mathematics concepts (F(2,325)=81.115; =0.333) 2 and interest in mathematics (F(2,325)=163.003;  =0.501). GEIS group performed better on achievement in mathematics ( =17.42) than PEIS group ( =16.40) and MLIS groups ( =12.91). The PEIS had higher posttest mean score on pupils’ knowledge of mathematics concepts ( =14.43) than GEIS ( = 13.44) and MLIS group ( =10.57). Also, PEIS had higher posttest mean score on interest in mathematics ( =15.36) than ii UNIVERSITY OF IBADAN LIBRARY GEIS group ( =14.41) and MLIS ( =10.77) groups. Verbal ability had significant 2 main effect on pupils’ achievement in mathematics (F(2,325)=35.939; =0.181), 2 knowledge of mathematics concepts F(2,325)=5.777; =0.034) and interest in mathemat 2 ics (F(2, 325)=19.320; =0.106). The posttest mean scores on pupils’ achievement in mathematics by verbal ability were high ( =16.80), medium ( =15.99) and low ( =13.95). Similarly, the posttest mean scores on pupils’ knowledge of mathematics concepts by verbal ability were high ( =13.58), medium ( =12.80) and low ( =12.06). Also, the posttest mean scores on pupils’ interest in mathematics by verbal ability were high ( =14.26), medium ( =13.76) and low ( =12.52). There was significant interaction effect of treatment and verbal ability on pupils’ knowledge of 2 mathematics concepts (F(4, 325)=2.731; =0.033). Game-enhanced instructional strategy is most effective in improving pupils’ achievement in mathematics, while poem-enhanced instructional strategy is most effective in improving pupils’ knowledge of mathematics concepts and interest in mathematics. Primary school teachers and curriculum developers should adopt these strategies to improve pupils’ learning outcomes in mathematics. Keywords: Game-enhanced instructional strategy, Poem-enhanced instructional strategy, mathematics learning outcomes Word count: 489 iii UNIVERSITY OF IBADAN LIBRARY ACKNOWLEDGEMENTS I give you thanks, Jehovah, the Almighty God, the giver of life, wisdom and opportunity, the one who brought to pass what I thought, I could not attain in life. May you, Jehovah, receive the praise, the honour and the glory, for you have done it. My heartfelt gratitude goes to my supervisor, Prof. M.K Akinsola, for his fatherly disposition to me. His particular interest in my progress was demonstrated by painstakingly going through my work promptly. His words of encouragement and outlook provided the much needed impetus to forge ahead. He is a man; God has used to prepare my table for me that I may eat for the remaining part of my life on earth. May the true God Jehovah, the Almighty, abundantly bless you and your household in everything. May God give you long life to enjoy all the blessings bestowed upon you (Amen). I cannot forget the immense contribution of Dr. Ayotola Aremu, who selflessly contributed her professional knowledge to this work as it were a co-supervisor. Such a kind gesture is difficult to find in these last days. You are truly a friend in time of need and a role model to me. May the God of heaven who has the ability to see the heart desires of every man, abundantly bless you and your household (Amen). My profound appreciation also goes to my external examiner, Prof. M. F. Salman and the internal-external examiner, Dr. D. O. A. Ajayi. Their inputs in this work, which were given promptly, sped up this work to success. May God give you added blessings. This piece of work would not have been completed without the constant interest of various lecturers who were like fathers, mothers and friends in the department who would always ask, “How is your work?”, and read it to make their various professional inputs. Worthy of note is the Head of Department, Prof. S.A. Adesoji; the sub-dean, Dr K. O. Kester; Prof. A. Olagunju; Prof. A. Abimbade; Prof. J.O. Ajiboye; Prof. S.O.Salami; Dr. D.O. Fakeye; Dr. P.A. Amosun; Dr. F.O. Ezeokoli; Dr. B. Lawal; Dr. Olusegun Akinbote; Dr. A. Tella; Dr T. Ige and Dr. A. Salami. I also extend my appreciation to the following lecturers in the other departments; Dr M.A. Odeniyi; Dr M.N. Odinko; Dr. P. Abu; Dr. B.A. Adegoke; Dr. S.A. Odebumi; Dr. Yara; Dr. A.B. Sunday of the University of Ibadan. My dear colleagues, Dr. D. Okodoko; Dr. T. Victor; Dr. Alade, Dr. A.O. Ogundiwin; Mr. O. Israel; Mr. F. Areelu. Mr. E . O. Odeyemi; Mr. T. Ajani; Mr. W. Samson, Mrs. J. N. iv UNIVERSITY OF IBADAN LIBRARY Chukwunenye and Abraham Josephine are appreciated. May the good God bless your efforts. I also appreciate the past and present vice-chancellors, registrars, deans of faculty, heads of department, colleagues and the entire staff of the Niger Delta University for their support during my absence from the University. I say big thank you to everyone. Who will I send and who will go for me? They were Messrs Tamaraulayefa. A. Singabele and Jeremiah Patrick Zidougha who designed and produced the mathematical games and photocopies of the instruments at an affordable price. They also went round with me to the various schools to take the photographs of the experiments. They were always available to be used. God should give you a fruitful life. I am also grateful to the head teachers, research assistants, pupils of various schools involved in the study. Their assistance made this research a success. I appreciate everyone. May God bless you all. I am also indebted to my parents, Mr. Reuben Frederick and Mrs. Change Frederick, for their encouragement and prayers. May you live long to enjoy the fruit of your labour. Also my brothers, sisters and wards especially Miss Taribimini Solomon, who cared for my children, though a child, yet like a mother in my absence. No wonder, my last child of less than four years of age called her “mother of mothers.” May Jehovah, your God, abundantly bless you. Let other people serve you more than the way you have served me (Amen). Finally, my deepest gratitude goes to my dear husband, Mr. C.N. Jonah, who married me as a young girl in the secondary school and continued to be beside me, coping with my absence in the family for months without being distracted. Your encouragement, prayers, emotional and financial support to ensure that I attain this academic height has made me to further trust you and confirm the true love you have for me. A man like you, who did not turn me to a full house wife in my tender age of marriage, is very rare. I cannot pay you back, but may Jehovah our God help me to humbly give you deep respect, cherish and unify my heart to always love you. I will not forget to appreciate my children, Epretari, Miepredei, Ebimoweni, Nimiyefagha and, especially, Edubamodei Jonah, who forfeited his motherly care and love in his early months on this earth. Despite all these, he has always expressed the v UNIVERSITY OF IBADAN LIBRARY love he has for me as he learns to speak, “mummy, I very so much love you. I will buy you a jeep.” I dearly love you all. May Jehovah our God, abundantly bless us. Also, I express my appreciation to all those who contributed to the success of this work in one way or the other that are not mentioned. The true God will bless you all. Toinpere Mercy Frederick-Jonah September, 2014 vi UNIVERSITY OF IBADAN LIBRARY CERTIFICATION I certify that this work was carried out by Mrs. T. M. Frederick-Jonah in the Department of Teacher Education, University of Ibadan, Nigeria. …………………………………………………. Supervisor PROF. M.K. AKINSOLA, NCE (Abeokuta), B.Sc (Ed) (Hons) Lagos, M.Ed., Ph.D. (Ibadan) (Mathematics Education), Department of Teacher Education, Faculty of Education, University of Ibadan, Nigeria vii UNIVERSITY OF IBADAN LIBRARY DEDICATION This research work is dedicated to Jehovah, the Almighty God. viii UNIVERSITY OF IBADAN LIBRARY TABLE OF CONTENTS Page Title page i Abstract ii Acknowledgements vi Certification vii Dedication viii Table of contents ix CHAPTER ONE INTRODUCTION 1 1.1 Background to the study 1 1.2 Statement of the problem 13 1.3 Hypotheses 13 1.4 Scope of the study 14 1.5 Significance of the study 15 1.6 Operational definition of terms 15 CHAPTER TWO LI ERATURE REVIEW 17 2.0 Introduction 17 2.1 Theoretical framework 17 2.1.2. Ausubel’s Subsumption Theory of Verbal Meaningful Learning (1963) 17 2.1.2 Skinner’s Operant Conditioning Theory (1938) 19 2.2 Nature and importance of mathematics 21 2.3 Primary mathematics education 22 2.4 Mathematical games as an instructional strategy 24 2.5 Characteristics of a mathematical game 25 2.6 Mathematical games and learning outcomes in mathematics 27 2.7 Mathematical poems as an instructional strategy 27 ix UNIVERSITY OF IBADAN LIBRARY 2.8 Poems and learning outcomes in mathematics 29 2.9 Knowledge of mathematics concepts and learning outcomes 30 2.10 Interest in mathematics and learning outcomes 34 2.11 Verbal ability and learning outcomes in mathematics 36 2.12 Gender and learning outcomes in mathematics 37 2.13 Appraisal of the literature reviewed 39 CHAPTER THREE METHODOLOGY 41 3.1 Research design 41 3.2 Variables in the study 42 3.3 Selection of participants 42 3.4 Research instruments 43 3.5 Teachers’ instructional guides 44 3.5.1 Instructional Guide on Poem-Enhanced Instructional Strategy (IGPEIS) 44 3.5.2 Instructional Guide on Game-Enhanced Instructional Strategy (IGGEIS) 44 3.5.2.1 Game development 45 3.5.3 Instructional Guide on Modified Lecture Instructional Strategy (IGMLIS) 47 3.6 Pupils’ Mathematics Achievement Test (PMAT) 48 3.7 Pupils’ Mathematics Concepts Test (PMCT) 50 3.8 Pupils’ Interest in Mathematics Inventory (PIMI) 50 3.9 Pupils’ Verbal Ability Test (PVAT) 51 3.10 Research procedure 52 3.11 Method of Data Analysis 54 CHAPTER FOUR ANALYSIS AND RESULTS 55 4.1 Testing of hypotheses 55 4.2 Summary of findings 68 x UNIVERSITY OF IBADAN LIBRARY CHAPTER FIVE DISCUSSION, CONCLUSION AND RECOMMENDATION 71 5.0 Discussion 71 5.1 Effect of treatment on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics 71 5.2 Effect of verbal ability on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics 73 5.3 Effect of gender on pupils’ achievement, knowledge of Mathematics concepts and interest in Mathematics 75 5.4 Interaction effect of treatment and verbal ability on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics 76 5.5 Interaction effect of treatment and gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics 77 5.6 Interaction effect of verbal ability and gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics 77 5.7 Interaction effect of treatment, verbal ability and gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics 77 5.8 Educational implications of the study 78 5.9 Conclusion 79 5.10 Recommendations 79 5.11 Limitations of the study 80 5.12 Suggestions for further study 81 REFERENCES 82 APPENDICES 98 xi UNIVERSITY OF IBADAN LIBRARY LIST OF TABLES Table No Table Description Page 1.1 Percentage performance in numeracy test by states (including Abuja) and class 4 3.1 3x3x2 factorial matrix of the design 42 3.2 Guidelines for games model validation 45 3.3 Table of specification of pupils’ achievement test 49 4.1 3x3x2 analysis of covariance (ANCOVA) of posttest scores of pupils’ achievement in Mathematics with treatment, verbal ability and gender using pre-test scores as covariates 55 4.2 Estimated marginal mean analysis of the posttest scores of pupils’ achievement in Mathematics by treatment 56 4.3 Scheffe’s post-hoc pairwise comparison analysis of treatment and pupils’ achievement in Mathematics 56 4.4 3 x 3 x 2 analysis of covariance (ANCOVA) of posttest scores of pupils’ knowledge of mathematics concepts with treatment, verbal ability and gender using pre-test scores as covariates 57 4.5 Estimated marginal mean analysis of the posttest scores of pupils’ knowledge of mathematics concepts by treatment 58 4.6 Scheffe’s post-hoc pairwise comparison analysis of treatment and pupils’ knowledge of mathematics concepts 58 4.7 3 x 3 x 2 analysis of covariance (ANCOVA) of posttest scores of pupils’ interest in Mathematics with treatment, verbal ability and gender using pre-test scores as covariates 59 4.8 Estimated marginal mean analysis of the posttest scores of pupils’ interest in Mathematics by treatment 60 4.9 Scheffe’s post-hoc pairwise comparison analysis of treatment and pupils’ interest in Mathematics 60 4.10 Estimated marginal mean analysis of the posttest scores of pupils’ achievement in Mathematics by verbal ability 61 4.11 Scheffe’s post-hoc pairwise comparison analysis of verbal ability xii UNIVERSITY OF IBADAN LIBRARY and pupils’ achievement in Mathematics 61 4.12 Estimated marginal mean analysis of the posttest scores of pupils’ Knowledge of mathematics concepts by verbal ability 62 4.13 Scheffe’s post-hoc pairwise comparison analysis of verbal ability and pupils’ knowledge of mathematics concepts 62 4.14 Estimated marginal mean analysis of the posttest scores of pupils’ interest in Mathematics by verbal ability 63 4.15 Scheffe’s post-hoc pairwise comparison analysis of verbal ability and pupils’ interest in Mathematics 63 4.16 Estimated marginal mean analysis of the posttest scores of pupils’ achievement in Mathematics by gender 64 4.17 Estimated marginal mean analysis of the posttest scores of pupils’ knowledge of mathematics concepts by gender 65 4.18 Estimated marginal mean analysis of the posttest scores of pupils’ interest in Mathematics by gender 65 xiii UNIVERSITY OF IBADAN LIBRARY LIST OF FIGURES Figure No Description Page 1 Pulos and Sneider (1994) Conceptual model for developing and evaluating games (Adopted from Aremu, 1998) 46 xiv UNIVERSITY OF IBADAN LIBRARY LIST OF APPENDICES Appendix Description Page Appendix 1 Pupils’ Mathematics Achievement Test (PMAT) 98 Appendix 2 Pupils’ Mathematics Concept Test (PMCT) 102 Appendix 3 Pupils’ Verbal Ability Test (PVAT) 104 Appendix 4 Pupils’ Interest in Mathematics Inventory (PIMI) 109 Appendix 5 Teaching Assessment Sheet for Teachers on the use of games 111 Appendix 6 Teaching Assessment Sheet for Teachers on the use of poems 112 Appendix 7 Primary mathematics topics identified as difficult by Salman (2009) 113 Appendix 8 Percentage mean and standard deviation of performance in mathematics across class 114 Appendix 9 Weekly mathematical poems 116 Appendix 10 Weekly mathematical games 139 Appendix 11 Instructional guide on Poem-Enhanced Instructional Strategy 168 Appendix 12 Instructional guide on Game-Enhanced Instructional Strategy 211 Appendix 13 Instructional guide on Modified Lecture Instructional Strategy 241 xv UNIVERSITY OF IBADAN LIBRARY CHAPTER ONE INTRODUCTION 1.1 Background to the study Primary education is the foundation of Nigeria educational system. Primary school education is the education given in institutions for children aged 6 - 12 years (Federal Republic of Nigeria, 2013). It is the foundation of every educational programme. In describing the importance of this level of education, Etukudo (2000) and Iji (2010) stated that primary school education forms the stepping stone for other levels of education and human activities. Maduagwu (2002) described it as a springboard for other levels of education. Koligili, Tumba and Zira (2007) and Kurumeh and Imoko (2008) view it as the foundation and bedrock of the Nigerian education system as well as the first step of Universal Basic Education (UBE). A firm foundation at the primary school level is pivotal to a robust educational system (Osinubi, 2004). This is because the primary education level is the key to the success and failure of the whole educational edifice; for the rest of the educational levels are built upon it (Adesina, 2011). It is because of this great importance of primary education that the present democratic government in Nigeria has revisited the issue of free basic education, so that every child can have access to education by the year 2015 in accordance with the goal for Education For All (EFA). To Okpala (2006), this is aimed at equipping learners with skills of literacy, numeracy, problem-solving as well as functional knowledge, attitude and generative skills as determined by the environment, that is the educational opportunities designed by each member country. The first two objectives of primary education are clearly stated in the National Policy on Education (Federal Republic of Nigeria, 2013) as: inculcating permanent literacy and numeracy, and the ability to communicate effectively; and laying a sound basis for scientific and reflective thinking. The inculcation of permanent numeracy stresses the need for every child to be mathematically literate at the primary school level (Iji, 2008). The National Policy on Education (Federal 1 UNIVERSITY OF IBADAN LIBRARY Republic of Nigeria, 2013) states that the mathematical development of the child cannot be ignored at the primary school level. In line with this recognition, Nurudeen (2007) avers that, if Mathematics is properly taught at the primary school level, there will be improved achievement in the subject at other levels of education. Kankia (2008) gives a clearer reason to this position by stating that Mathematics curricula content are sequential and spiral in nature. This implies that adequate understanding of Mathematics concepts at the primary school level would improve achievement at other levels of education. Adesina (2011) claims, that primary education has significant impact on Nigeria‟s social, economic and political development. Primary education is perceived as having significant impact on the attainment of the Nigeria‟s vision 20:2020. The lingering problems of under-achievement in secondary and tertiary institutions in Nigeria are traceable to the poor and shaky foundation laid at the primary school level. Salman (2009) avers that, the primary education needs to be given adequate attention. Mathematics and other science-related subjects need urgent attention for a country like Nigeria that is aspiring for scientific and technological advancement. Thus, improving the teaching and learning of Mathematics at the primary school level is imperative. Mathematics has been applied by various researchers, engineers and mathematicians according to their needs. The different ways many people see Mathematics at different times indicate how important or indispensable Mathematics is in today‟s modern world. Some try to show its elegance, precision, beauty and brevity; others show its structure and the training it provides (Ibrahim, 2004). Obodo (2000) conceptualised Mathematics as a system of sounds, words and patterns for communicating mathematical ideas. In the same vein, Harbor- Peters (2000) sees Mathematics as a culture and as well as an art. As a culture, Mathematics affords man the opportunity to know and access things and objects within his immediate and remote environment. As an art, the beauty of Mathematics is exhibited in the process where chaos of isolated facts is transformed into logical order. Mathematics plays a vital role in the achievement of the primary school objectives, particularly science and technology and science-related disciplines, for it is the language used in expressing them. Ukeje in Aguele and Usman (2007) asserts that, without Mathematics, there is no science, without science, there is no 2 UNIVERSITY OF IBADAN LIBRARY modern technology, and without modern technology, there is no modern society. This implies that Mathematics is the precursor and the queen of science and technology and the indispensible single element in modern societal development. Also, Mathematics is a core and compulsory school subject in the curricula from primary to junior secondary and to the senior secondary school levels of the Nigeria educational system (Abubakar and Bawa, 2006; Aguele and Usman 2007; Kurumeh and Imoko, 2008). Mathematics is also applied in agriculture, sports, business, medicine, transportation, public utility, communication and others (Kolawole and Oluwatayo, 2006; Iji, 2008). Further, Mathematics is important for the development of critical thinking (Agwagah, 2005). Mathematics is an important school subject; it is also important in every activity of man. It is expected that students‟ achievement at all levels would be good. However, Olayinka (2006) describes the state of mathematics education in Nigeria as depressing; implying that students‟ achievements in Mathematics at the primary, junior and senior secondary and tertiary levels are poor. Also, Bassey, Joshua and Asim (2009) note that academic achievement of students in mathematics education is still low, both in certificate and non-certificate examinations. For example, Azuka (2008) reports poor achievement of pupils in Mathematics in both internal and external examinations; Kurumeh and Imoko (2008) also express dismay in marking the pupils‟ scripts during Common Entrance Examination and Primary School Mathematics Olympaid because of the poor achievement of pupils‟ in Mathematics in these examinations. Recent research findings in Nigeria have shown that the performance of pupils in primary Mathematics is below average and also that the problem-solving skills of the pupils are poor. In the report of Education Sector Analysis (ESA, 2004) carried out in Nigeria, the national mean percentage scores of primary four and primary six pupils in numeracy were 33.7 and 35.7, respectively. Table 1.1 presents the detailed information about the performance of the pupils across the nation in 2004. 3 UNIVERSITY OF IBADAN LIBRARY Table 1.1. Percentage performance in numeracy test by State (including Abuja) and class S/N STATE PRY PRY S/N STATE PRY PRY o o IV /o VI IV /o VI o o pass /o pass pass /o pass 1 ABIA 27.63 - 20 KANO 36.51 35.71 2 ABUJA 28.33 37.67 21 KATSINA 29.85 27.64 3 ADAMAWA 22.93 27.32 22 KEBBI 41.43 45.54 4 AKIWABOM 28.29 27.7 23 KOGI 32.2 36.55 5 ANAMBRA 31.04 39.24 24 KWARA 32.59 - 6 BAUCHI 45.5 35.33 25 LAGOS 32.54 37.76 7 BAYELSA 22.61 43.12 26 NASARAWA 25.4 25.39 8 BENUE 40.78 54.82 27 NIGER 32.65 31.57 9 BORNO 19.32 20.85 28 OGUN 49.27 46.51 10 C/RIVERS 34.4 31.42 29 ONDO 35.03 33.09 11 DELTA 30.46 22.48 30 OSUN 32.4 28.96 12 EBONYI 20.21 22.48 31 OYO 36.41 41.65 13 EDO 33.64 28.64 32 PLATEAU 29.11 29.24 14 EKITI 35.63 39.67 33 RIVERS - 27.78 15 ENUGU 48.8 38.72 34 SOKOTO 27.77 30.91 16 GOMBE 36.71 34.68 35 TARABA 45.15 44.73 17 IMO 26.32 30.58 36 YOBE 39.28 40.67 18 JIGAWA 46.35 45.07 37 ZAMFARA 33.17 34.35 19 KADUNA 47.75 48.31 SOURCE: Education Sector Analysis (ESA, 2004), Nigeria Table 1.1 shows that primary 4 pupils in Ogun State had the highest mean percent score of 49.27, while pupils in Borno State had the lowest mean percent score of 19.32. Primary 6 pupils in Benue State had the highest mean percent score of 54.82, while primary 6 pupils in Delta and Ebonyi States had the lowest mean percent score of 22.48. Similarly, the final report by the National Assessment of Universal Basic Education Programme (NAUBEP, 2009) shows that the national mean score for primary six pupils in Mathematics was 42.87(see appendix 8). 4 UNIVERSITY OF IBADAN LIBRARY In Bayelsa State, primary 4 and primary 6 pupils had 22.61 and 43.12 mean percent scores, respectively. This clearly shows that neither the state mean score nor the national mean score was up to credit level in primary mathematics. Primary six pupils from other zones of Nigeria (for example, South West and South East) need a minimum of 75% pass in Mathematics and in English Language in Common Entrance Examinations into Federal Government Colleges. Most states in the Niger Delta region, for example Bayelsa State, need as low as 55% (National Examination Examiner‟s Report, 2008). It is obvious that achievement of primary school pupils in Mathematics is poor. Kurumeh and Imoko (2008) further report that the teachers who mark Junior Secondary School WAEC also complain of the poor achievement of the students in all state examinations in Mathematics. This Mathematics foundation which is very weak at the primary school level is carried to the junior secondary school and then to the senior secondary school level. This is in agreement with what Ebisine (2010) expresses: there has been a loud outcry against the frustrating achievement of secondary school students in Mathematics. Countless research works affirm the state of poor achievement in Mathematics at all levels of education (for instance, Agwagah, 1996; Ukeje, 1997; STAN, 2000; Apex, 2002; Obiniyi, 2005; Maduabum and Odili, 2006; Aburime, 2007). This reveals that poor achievement in Mathematics by students has existed for long. The problem of students‟ poor achievement in Mathematics in both internal and external examinations has been reported by mathematics educators, mathematicians and examination bodies. For instance, Kurumeh (2006) observes that students have great difficulty in understanding, comprehending, and assimilating Mathematics taught to them in the classroom. So they resort to learning by rote, resulting in consistent mass failure of students. Uwadia (2009), cited in Dahiru (2010), views inadequate coverage of syllabus, inadequate facilities for teaching, students‟ poor attitude to study, and heavy workload on teachers as causes of poor achievement in Mathematics. In his comments on the results of 2006 Common Entrance Examination in Amao (2010), the Chief Examiner noted that the majority of public primary school pupils did not do well because they could not simply make out anything of what teachers taught because of their inability to understand the language of instruction. The Chief Examiner‟s Report of WAEC (2009) notes that poor achievement of students in Mathematics is caused by poor 5 UNIVERSITY OF IBADAN LIBRARY language skills and expression, insufficient preparation, misinterpretation of questions, inadequate technical competence and poor hand writing. Other factors responsible for the poor achievement of students in Mathematics include poor background laid at the primary school level of education (Amazigo, 2002; Etukudo, 2006; Kurumeh and Imoko, 2008); lack of interest, lack of conducive learning environment, phobia and dislike of Mathematics (Olayinka, 2006; Kurumeh, 2007; Onwuka, Iweka and Moseri, 2010), poor reasoning ability and problem-solving (National Council of Teachers of Mathematics NCTM, 2000; Olkun and Toluk, 2005); teacher factor (Darling-Hammond, 2000; Ojo, 2008). Alio (1997), quoted in Nurudeen (2007), views teachers‟ strategy of presenting problem- solving as contributing factor to high failure rate in Mathematics. Many studies have identified mainly the teachers‟ strategy of teaching as the major factor contributing to poor achievement of students in Mathematics. For instance, Salman (2009) attributes the perennial low achievement of Nigerian pupils in Mathematics to inadequate knowledge of the subject matter content by teachers and poor instructional techniques and calls for imparting adequate knowledge of mathematics to pupils through the use of effective instructional techniques. Anaduaka (2011) states that the errors students make are largely as a result of deficits in the teachers‟ teaching strategies. Also, the WAEC Chief Examiner‟s Report (2001), Harbor-Peters (2001), Badmus (2002), Okoli (2006), Eze (2008), and Iji (2010) have all found teaching strategy as the major cause of poor achievement of students in Mathematics at all levels of education. The strategies adopted by the teachers do not sustain the development of students‟ interest in Mathematics. This is also one of the major causes of poor achievement in Mathematics (Agwagah, 2005). The lecture instructional strategy for example is a strategy in which the teacher presents a verbal discourse on a particular subject, theme or concept to the learners while the learners are passive listeners. The teachers deliver preplanned lessons to the students with little or no instructional aids (Okoli, 2006). The lecture instructional strategy pays more attention to teachers. The teacher begins the class by reviewing, then teaches the new lesson, and finally gives a take-home assignment. It is boring for students and diminishes students‟ interest in Mathematics because the students‟ only job in the classroom is to passively sit and watch the teacher solve mathematics exercises or problems on the chalk board and 6 UNIVERSITY OF IBADAN LIBRARY then copy what the teacher did (Peng, 2002). Also, Adesoji (2004) lists some reasons why teachers refuse to change from the lecture instructional strategy. Such reasons include lack of infrastructural facilities, overloaded curriculum and lack of training programmes/workshops for teachers. The lecture instructional strategy used in teaching Mathematics can thus be described as an authoritarian form of teaching by the teacher (Agwagah, 2005). It is also described as one that does not sustain the development of pupils‟ interest in Mathematics (Agwagah, 2004) and poorly develops learners‟ cognitive, psychomotor and affective structures (Kankia, 2008). A study of 59 public schools purposively sampled and four schools randomly selected for the study on lecture instructional strategy in a Mathematics class in Kenya revealed that teacher-pupil classroom interaction activities in the lower classes were not exploited to the full because the teachers did not involve all the pupils during classroom interaction. For instance, teachers rushed over lessons, interacting only with bright pupils ignoring weaker and slow learners; did all the work on the chalkboard; avoided group work which promotes pupil-pupil interaction; and did not demonstrate any skill (Majanga, Nasongo and Sylvia, 2011). Hence, there is the urgent need to enhance the lecture instructional strategy with some activities that provide for the pupils‟ active participation in the classroom. The effective activities recommended for the primary school level include the use of games to enhance greater understanding of concepts (Aremu, 1998; Agwagah, 2001), creating a creative corner for less capable pupils in Mathematics who may be good at arts or writing, which involves activities, such as poetry or stories about mathematical situations and geometric drawings (Ojo, 2008; Albool, 2012). Iji (2007) also recommends exhibition of poems to teachers at the primary school level. Ohuche (1990) suggests providing adequate opportunities for manipulation of materials accompanied by verbalization of materials as well as conceptualisation by means of discovery. Therefore, this study examined the effects of poem- and game-enhanced instructional strategies on pupils‟ learning outcomes in Mathematics. Poetry has vital roles to play in children learning. Owen (2010) states that memorizing poetry increases child‟s cognitive ability, for poems present language in more ordered and rhythmical ways than prose. These techniques increase a 7 UNIVERSITY OF IBADAN LIBRARY child‟s ability to reason, imagine, think, argue and experience the world in sensory and aesthetic ways. Through memorization of poetry, a child‟s mental capacity is exercised and thus increases in flexibility and strength. Poetry offer Mathematics students, new means to explore the recondite realm of abstract mathematical concepts, improving cognitive understanding and confidence (Bahls, 2009). Mathematics is not just all about calculations; it is beyond calculation (Agwagah, 2008). „There is a great and growing body of linguistic and visual metaphors that constitute a healthy understanding of mathematics in which things called fields, rings, bundles and flows play dominant roles; mastery of these concepts often involves creativity more readily expected of a poet than of a scientist‟ (Bahls, 2009: 76). Students‟ cognitive understanding of mathematical terminology and symbolism, and confidence in carrying out computation and other mathematical tasks are key coordinates of success in learning Mathematics (Bahls, 2009). Both poetry and Mathematics deals with images, ideas and metaphors. Metaphors are the currency with which poetic trade takes place, and Mathematics has the same metaphors both metaphors, alive such as spheres, balls, sinks, lattices, chains, sheaves, itineraries and distances; and dead metaphors, such as calculate, to do algebra, and to factorize. By using poetical metaphors, students become more aware of these and other mathematical metaphors and thereby gain deeper understanding of mathematical concepts that those metaphors describe. This new form of mathematical cognition is made possible through poetry (Bahls, 2009). The other activity that can be used to enhance mathematics instruction is the use of games. A game is a type of play that follows a set of rules, aims at a definite goal or outcome and involves competition against other players or against barriers imposed by nature of the game (Agwagah, 2001). A mathematical game is a game with the course of the game having mathematical structure or consideration (Onwuka, Iweka, and Moseri, 2010). Dalton (2007: p3), quoting Bright et al. (1985: p5) lists seven elements of games 1. A game is freely engaged in. 2. A game is a challenge against a task or an opponent. 3. A game is governed by a definite set of rules. The rules describe all the procedures for playing the game, including goals sought; in particular, the rules are structured so that once a player‟s turn comes to an end, that player 8 UNIVERSITY OF IBADAN LIBRARY is not permitted to retract or to exchange for another move made during that turn. 4. Psychologically, a game is an arbitrary situation clearly delimited in time and space from real-life activity. 5. Socially, the events of the game situation are considered in and of themselves to be of minimal importance. 6. A game has a finite state-space. The exact states reached during play of the game are not known prior to the beginning of play. 7. A game ends after a finite number of moves within the state-space. Games play vital roles in mathematics instruction. The use of games in teaching Mathematics makes students to be actively involved in the daily lessons since they are interested in learning mathematics as game (Abubakar and Bawa, 2006). Games relax tension, clear boredom and foster an environment where teaching and learning are pleasant, interesting, exciting, stimulating, motivating and academically rewarding (Kankia, 2008). Games provide unique opportunity for integrating the cognitive, affective, and social aspects of learning (Azuka, 2002). Many studies have been carried out on mathematical games, with positive results. Ugwuangi (2002) used game and simulation to generate students‟ interest on Sequence and Series. Dotun (2005) used ladder and tunnel game to teach algebraic expression. Okigbo (2008) employed card games to teach Percentages, Fractions and Decimals in secondary schools; Aremu (1998) used card and geoboard-based games as instructional strategies on primary school pupils‟ achievement in practical geometry. The achievement of students in all the experimental groups was better than that of the control groups. Many types of games have been developed and used by researchers and mathematics educators to enhance learning mathematics in the primary, junior and senior secondary schools. Onwuka et al. (2010) enumerate some games for teaching Number and Numeration, Algebra, Geometry, Mensuration, Trigonometry and Statistics, which are particularly useful for both primary and junior secondary schools. They are (a) Coordinate points game used, for identifying and locating coordinate points (b) Geoboard games, for identifying and calculating angles, to identify and represent geometric shapes and also calculate areas of geometrical shapes. (c) Card games, for solving linear equations and for geometrical shapes. 9 UNIVERSITY OF IBADAN LIBRARY (d) Ludo game, for probability concepts. (e) Identificator game. (f) Factor card game. (g) Phythagorean triple game. Agwagah (2001) also developed different types of games for the primary school, like matchob, number race, odd-even card game, secret factor, and equation card game. She mostly developed these games for the lower basic classes. The National Mathematical Centre (NMC, 2002) Abuja developed different games on different topics in Mathematics for the secondary school level, for example, fraction grid, equation whot, mathematics circle race, geometry and statistics vocabulary, mathematics palace game and plane figure card game. The knowledge of mathematics concepts is the main outcome of any mathematics instruction process. Mathematics concepts are the mathematics words, principles, symbols, formulae and expressions understood in the context of Mathematics. In other words, they mean the language of Mathematics. Language is a way of expressing ideas and feelings using symbols, sounds, movement or rules (Olokun, 2005). The language of Mathematics thus refers to the set of mathematics words, symbols and expressions which are understood in the context of mathematics (Binda, 2006). The knowledge of mathematics concepts is prerequisite to any meaningful mathematics instruction. The ability of students to use mathematical operations to simplify or solve problems depends on a good grasp of the language of Mathematics (Obioma, 2005; Gershon, Guwal and Awuya, 2008). A student who does not know what the term factorize means will have no business with the 2 2 2 instruction to factorize the expression Cd + C d + Cd . A good knowledge of concepts is then the key to learning Mathematics, especially topics like word problems which cut across all topics in Mathematics (Nnaji, 2005). The failure of many children to understand basic mathematics concepts at a very early stage makes them to fare poorly in Mathematics (Kwok, 2009). The main objective of Mathematics learning at the primary school level is to develop in the pupils the power of reason, power to solve problems and to find responses that are novel to their experiences (Hogan, 2005). This is dependent on pupils‟ knowledge and understanding of mathematics concepts and their meanings. Olokun (2005) observes that symbolic language is another area students have to master in 10 UNIVERSITY OF IBADAN LIBRARY Mathematics. They must learn symbols for operations, relational symbols (> and <); and the meanings of parentheses and brackets. This will enhance problem- solving which is the highest level of learning that will be achieved. Therefore, in this research, knowledge of mathematics concepts was taken as a dependent variable. In order to achieve good performance in Mathematics, the interest and attitudes of students towards Mathematics need to be developed and properly harnessed right from the primary school level; this is where the solid foundation for the subject is laid (Ekine, 2010). When students generate interest in mathematics lesson and excitement about it, half of the students‟ problems in Mathematics are solved (Kankia, 2008). Interest is a condition for learning Mathematics and there can be no real mathematics education without interest in Mathematics (Udegbe, 2009). Several studies show a positive relationship between interest and achievement in Mathematics (Eccles, Denissen and Zarret, 2007). Obodo (1997) and Azuka (2002) observe that students in Nigeria have poor interest in Mathematics and Mathematics related-disciplines at all levels of education. The resultant effect of all the problems of mathematics teaching and learning is that a large pool of students express lack of interest in Mathematics at all levels of the educational system and mathematics educators are of the opinion that the development of students‟ interest in Mathematics should be a goal for mathematics teaching and learning (Anaduaka, 2011). Sotinu (2007), cited in Ekine (2010), observes that pupils‟ interest in science declines as they progress from the primary schools to their secondary school years as their performance in science subjects seems to take a decline as they progress in class. Also, Udegbe (2009) affirms that the students‟ poor interest in Mathematics is responsible for their poor achievement in both external and internal Mathematics examinations which increase students‟ hatred and phobia for Mathematics and mathematics-related courses. The low interest of students in Mathematics emanates from anxiety and fear, and this is expressed from their faces in Mathematics classes (Okigbo and Okeke, 2011). Another cause of poor interest in Mathematics is the teacher‟s strategy of teaching Mathematics, which does not sustain the development of interest in Mathematics among others (Agwagah, 2005). The WAEC Chief Examiner‟s Report (2009) suggests that teachers should help students improve their 11 UNIVERSITY OF IBADAN LIBRARY achievement and develop interest in Mathematics by reducing the abstractness of Mathematics and removing their apathy and fears of the subject. There are other factors, such as verbal ability and gender, which may have effect on the teaching and learning process, especially in Mathematics. Whetton (1994), cited in Komolafe (2010), defines verbal ability as a group intelligence tests which are largely verbal, designed to provide overall measure of scholastic ability used in an educational context. Researchers have documented the fact that students‟ verbal ability significantly influences their performance on standardized achievement tests (Maduabuchi, 2002; Fakeye, 2006). Awofala, Balogun and Olagunju (2011) state that exploring the influence of verbal ability and cognitive style on Mathematics achievement only began in recent years. Poetry is highly loaded with connotations and figurative language, which requires a reasonable level of verbal ability for students‟ competence. This study found the moderating effects of pupils of varying levels of verbal ability on learning outcomes in Mathematics. The effect of gender on learning outcomes of Mathematics and science- related subjects are still a major controversy among educators. This may be as result of conflicting results from such gender-related studies. Some studies found significant differences in favour of boys, a few in favour of girls, while others are neutral. Alio and Harbor-Peters (2001), Juhun and Momoh (2002), Onasanya (2008), and Shafi and Areelu (2010) found significant differences in favour of boys. Eniayeju (2010) found that girls achieved significantly better in all tests in the cooperative groups. Salau (2001), Etukudo (2002), Galadima and Yusha (2007), Bawa and Abubakar (2008), and Ebisine (2010) found no significant difference in the achievement of male and female students in their various studies. This inconsistency in the test achievement of boys and girls need to be further investigated in the use of poems and games to enhance mathematics instruction at the primary school level. The choice of gender as a variable was also necessitated by the current world trend and research emphasis on gender issues following the millennium declaration of September, 2000 (United Nations, 2000) which has as its goal, the promotion of gender equity, the empowerment of women and elimination of gender inequality in basic and secondary education by 2005 and at all levels by 2015 (Bassey et al., 2009). The need to ensure the achievement of this goal in school Mathematics at the primary school level and in Nigeria, in order to provide pertinent information 12 UNIVERSITY OF IBADAN LIBRARY on the level of achievement of both boys and girls and needed action to be taken also justify the inclusion of this variable in this study. 1.2 Statement of the problem Mathematics plays a significant role in virtually all activities of man, especially in this modern age of science and technology. Its demand is, therefore, at a premium position. Yet students‟ achievement in Mathematics at all levels of education is poor. The available literature shows that pupils‟ poor achievement in Mathematics is due to a number of factors, especially those related to the strategies used for teaching mathematics. The lecture instructional strategy, which is predominantly used by teachers, might have contributed to under-achievement in Mathematics at various levels of education. Some other factors that might have contributed to under-achievement in Mathematics include lack of interest in Mathematics, low understanding of mathematics concepts, and so on. Game and poem are recommended to solve the problems of teaching Mathematics at the primary school level. However, most studies on game in teaching Mathematics were carried out at the secondary school level. Also, game was used with other strategies, such as game and simulation; game and analogy; or two distinct games, like ladder and tunnel games, card and geoboard-based games, to determine the most effective strategy. Therefore, this study determined the effects of game and poem-enhanced instructional strategies on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. The study also determined the moderating effects of verbal ability and gender on the dependent variables. 1.3 Hypotheses The following null hypotheses were tested at 0.05 level of significance: H01 There is no significant main effect of treatment on pupils‟ (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. H02 There is no significant main effect of verbal ability on pupils‟ (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. H03 There is no significant main effect of gender on pupils‟ 13 UNIVERSITY OF IBADAN LIBRARY (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. H04 There is no significant interaction effect of treatment and verbal ability on pupils‟ (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. H05 There is no significant interaction effect of treatment and gender on pupils‟ (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. H06 There is no significant interaction effect of verbal ability and gender on pupils‟ (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. H07 There is no significant interaction effect of treatment, verbal ability and gender on pupils‟ (i) achievement in Mathematics (ii) knowledge of mathematics concepts (iii) interest in Mathematics. 1.4 Scope of the study The study covered primary six pupils in twelve public primary schools in Ogbia and Yenagoa Local Government Areas of Bayelsa State, Nigeria. The study examined the effects of poem and game-enhanced instructional strategies on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. It also determined the moderating effects of verbal ability and gender on the dependent variables. The content scope included fraction and decimal (addition, subtraction, multiplication and division), volume, capacity, weight, 2 and 3- dimensional figures. These are topics in the primary Mathematics curriculum listed for primary six pupils. 14 UNIVERSITY OF IBADAN LIBRARY 1.5 Significance of the study The findings of this study would provide empirical evidence on the effectiveness of using poem and game-enhanced instructional strategies in teaching the listed topics in Mathematics in Nigeria among teachers at the primary school level. It would also give insight to teachers in the choice of the most appropriate strategies and activities to enhance the lecture instructional strategy usually applied in the classroom to make it enjoyable, active, and free from the passivity and boredom usually used to describe the lecture instructional strategy. This would aid engaging both science and arts-oriented pupils actively in a mathematics classroom. The study would also provide evidence that would give direction to authors of Mathematics text-books. Thus, they can write books on mathematical poems and mathematical games thereby giving aesthetic appeal and meaningfulness to the text, reducing abstractness of text, widening the range of mathematical books and attracting more sales. The study would also provide useful information to mathematics educators, curriculum developers in Mathematics and government agencies in the area of recommending enrichment activities while teaching science and arts-oriented students in Mathematics. The larger society would also benefit from the advancement of science and technology through the improved achievement of students in Mathematics. 1.6 Operational definitions of terms Achievement in Mathematics: This is the score obtained by pupils from the Pupils‟ Mathematics Achievement Test (PMAT) based on the content covered in the Mathematics curriculum taught using game and poem-enhanced instructional strategies and modified lecture instructional strategy. Games: These are card games in which the structure of the games is purely mathematical, with definite rules and procedures which pupils play as competitive enjoyable enrichment activities to enhance mathematics instruction which focus on the concepts covered in this study. Gender: This refers to the male or female pupils in the primary schools. Interest in Mathematics: This is the likeness or dislike shown by pupils in mathematics class, mathematics-related issues, and in Mathematics as a subject. 15 UNIVERSITY OF IBADAN LIBRARY Knowledge of Mathematics Concepts: This is the score obtained by pupils from the Pupils‟ Mathematics Concepts Test (PMCT). The concepts are the mathematical language or terminologies in a topic such as words, symbols, expressions, objects, formulae, equations, principles and so on, associated with fraction and decimal, 2 and 3- dimensional figures, volume, capacity and weight. Learning Outcomes: These refer to the knowledge and attributes attained as a result of pupils‟ involvement in a particular set of educational experiences. These were measured using PMAT, PMCT, PIMI and PVAT. Modified Lecture Instructional Strategy: The strategy of teaching mathematics in which the teacher communicates orally with the use of occasional questions, demonstrations and diagrams on the chalkboard without game and poem enrichment activities and instructional materials. Poems: These are words arranged in regular patterns of rhymed and accented lines which focus on the mathematics concepts covered in this study used as enrichment activities to enhance mathematics instruction. Verbal Ability: This refers to the scholastic proficiency of a learner in the use of language without specific curriculum content. This is at three levels (high, medium and low) which the pupils express in a given test. 16 UNIVERSITY OF IBADAN LIBRARY CHAPTER TWO LITERATURE REVIEW 2.0 Introduction The literature relevant to this study is reviewed in the following order: 2.1 Theoretical framework 2.1.1 Ausubel‟s Subsumption Theory of Verbal Meaningful Learning (1963) 2.1.2 Skinner‟s Operant Conditioning Theory (1938) 2.2 Nature and importance of mathematics 2.3 Primary mathematics education 2.4 Mathematical games as an instructional strategy 2.5 Characteristics of a mathematical game 2.6 Mathematical games and learning outcomes in mathematics 2.7 Mathematical poems as an instructional strategy 2.8 Poems and learning outcomes in mathematics 2.9 Knowledge of mathematics concepts and learning outcomes 2.10 Interest in mathematics and learning outcomes 2.11 Verbal ability and learning outcomes in mathematics 2.12 Gender and learning outcomes in mathematics 2.13 Appraisal of the literature reviewed 2.1 Theoretical framework This work is anchored on the following theoretical framework. Ausubel‟s Subsumption Theory of Verbal Meaningful Learning (1963) and Skinner‟s Operant Conditioning Theory (1938). 2.1.1 Ausubel’s Subsumption Theory of Verbal Meaningful Learning (1963) Ausubel‟s subsumption theory of verbal meaningful learning applies only to reception (expository) learning in which individuals learn large amounts of meaningful materials from verbal/textual presentations in school settings. He claims that a primary process in learning is subsumption in which new material is 17 UNIVERSITY OF IBADAN LIBRARY related to relevant ideas in the existing cognitive structure on a substantive basis. Ausubel (1963) observes that meaningful verbal learning occurs when what is to be learned can be related to existing concepts (subsumers). Ausubel distinguishes reception learning from rote and discovery learning. Rote learning does not involve subsumption (that is meaningful materials) and discovery learning involves the learner in discovering information through problem-solving (Ausubel, 1978). Cooper (2009) asserts that meaning is created through some form of representational equivalence between language (symbols) and mental context. The expository (verbal) learning strategies include speech, reading, and writing, which encourage rapid learning and retention. Conversely, discovery learning facilitates transfer to other context. Also, Ausubel supports the theory that pupils form and organize knowledge themselves. Pupils gradually learn to match new knowledge with existing knowledge in their mental structures. Ausubel considers the verbal learning to be very effective for pupils of age 11 or 12 above (Slideshare, 2011). The subsumption theory involves effective linking between new knowledge and existing cognitive structure. Three linkages that are important in the learning processes in Science and Mathematics, as identified in Odili (2006), are (a) Internal linkage in the cognitive structure, which is concerned with how effectively or loosely the learner‟s knowledge is integrated. (b) Activation of a particular part of the cognitive structure for learning, which relates to the accuracy with which a particular part of cognitive structure is retrieved for use in learning a particular piece of new knowledge. (c) External linkage between an existing cognitive structure and the new learning content which is concerned with subsumption of concepts that enable the linking of the existing cognitive structure to new concepts or knowledge to be learned. Ausubel recommends the use of advance organizers where subsummers do not exist (Odili, 2006). This is the major instructional mechanism proposed by Ausubel in classroom application. The advance organizer is a tool or mental learning aid to help students integrate new information with their existing knowledge, leading to meaningful learning as opposed to memorization. It is a means of preparing the learners‟ cognitive structures for the new learning experience. It is a device to activate the relevant schema or conceptual patterns so 18 UNIVERSITY OF IBADAN LIBRARY that new information can be more readily subsumed into the learners‟ existing cognitive structures. Odili (2006) summarizes the implication of Ausubel‟s work as thus; (a) The most general ideas of a subject should be presented first and then progressively differentiated in terms of detail and specificity. (b) Instructional materials should attempt to integrate new materials with previously presented information through comparisons and cross referencing of new and old ideas. Ausubel‟s subsumption verbal meaningful learning theory is relevant to this study in the areas of using poems to enhance mathematics instruction. The use of poems involves the construction of images for appreciating Mathematics. The Califonia Infant/Toddler Learning and Development Foundation (2010) stated that social-emotional contexts unfold cognitive development. Also, Sternberg and Grigorenko (2004) assert that the cultural context is important to young children‟s cognitive development. Aspects of intelligence that have to do with social competence appear to be seen as more important than speed in some non-Western cultural contexts. The poems used in this study approach mathematics learning in the cultural context focusing on the activities of the child‟s immediate environment. The poems are verbal presentation of the mathematics concepts to be learned. Also, the mental images created from the child‟s immediate social environment reflecting the concepts serve as advance organizers or subsummers to the prior or existing knowledge of the child‟s cognitive structure to enable him learn the new concept. Furthermore, verbal meaningful learning strategies include speech, reading and writing (Cooper, 2009). The use of poetry in teaching involves these key aspects of learning. 2.1.2 Skinner’s Operant Conditioning Theory (1938) B.F Skinner is an American psychologist who developed the operant conditioning theory of learning in 1938 in order to examine what effect consequences had on behaviour. Operant conditioning theory examines the stimulus, the response to the stimulus (a behaviour) and the behaviour‟s consequence (Skinner, 1938). This theory states that the organism is in the process of operating on the environment. During this operating, the organism encounters a special kind of stimulus called a reinforcer. This special stimulus has the effect of 19 UNIVERSITY OF IBADAN LIBRARY increasing the operant, the behaviour occurring just before the reinforcer. The behaviour is followed by a consequence, and the nature of the consequence modifies the organism‟s tendency to repeat the behaviour in the future (Boeree, 2006). To illustrate this, Skinner constructed a box called the Skinner box. This box contains a bar that releases a pellet of food into a tray and at the same time automatically registers the responses at a time chart. Each time the hungry rat presses the bar and light shows, a pellet of food falls into the dish. The rat eats and presses the bar again. The food reinforces the pressing of the bar. The pressing response is responsible for producing the food (reinforcer) which then acts as a stimulus for response (bar pressing); this makes the rat to keep pressing the bar even when there is no food reward. Skinner‟s operant conditioning theory is relevant to the study in that the games were developed with this understanding. The games played are guided by rules. Whenever a pupil plays the game correctly, that child is immediately rewarded, depending on the rule of the game either by moving up a ladder or acquiring more marks. A child who plays the game wrongly will also be punished immediately by remaining at the same position, losing marks or getting out of the game (Aremu, 1998). These reinforcers will lead to behaviour change, such as pupils actively participating in the lesson, developing the spirit of competitiveness, enhancing achievement, and developing positive interest and attitude towards Mathematics. According to Obodo (1997), a positive reinforcer (reward) is an event that increases the rate of responding, such as a teacher nodding his head, smiles, assigning high grades, a pleasant statement and others. By doing this in a study, it was observed that students attitude were changed positively, interest strengthened, class attendance increased, highly motivated and were more eager to study Mathematics. The games were also constructed based on some learning principles that guide the use of games. Aremu (1998) presents these principles: (a) There is need for students‟ participation and plenty of practice since learning is activity. Games by nature are activities, thus students actively participate in learning and are involved in a lot of practice. 20 UNIVERSITY OF IBADAN LIBRARY (b) Motivation is important to the learner. It is the teacher‟s task to infuse necessary motivational forces which heighten the students‟ desire, need and interest in learning. Games enhance motivation. (c). Repetition reinforces information and makes information more enduring. A good way to repeat information is through the use of games and poems. (d) Immediate Knowledge of Results (IKOR) must be given promptly. IKOR reinforces success and gives quick correction. The use of games incorporates this principle, in that when a student has his turn in the game, right there, he knows through his mates whether he is right or wrong. This reinforces success. (e) Finally, nothing absolutely new is ever learned effectively with one exposure. Games and poems used in this study give room for repeating the presentation of the various concepts (stimuli) to be learnt. 2.2 Nature and importance of mathematics Amoo and Rahman (2004) view Mathematics as a language, a particular kind of logical structure, a body of knowledge about numbers and space, and merely as an amusing intellectual activity. Akinsola (2005) regards Mathematics as a special language that is used to identify, describe and investigate the patterns and challenges of every living entity. It is a language that helps in understanding past events, and to predict and prepare for future events so that one can fully understand the world and more successfully live in it. The American Association for the Advancement of Science (AAAS, 1990) notes that Mathematics is a theoretical discipline which explores possible relationship among abstractions without concern for whether those abstractions have counterparts in real world. The abstractions can be anything from strings of numbers to geometric figures to sets of equations. Also, Pappas (1999) describes Mathematics as a fiction which also connotes the abstract nature of Mathematics. The value of mathematics has been identified by many researchers and mathematics educators in various aspects. Kurumeh (2006) considers Mathematics as the language in which scientific ideas are expressed. It is the means by which other sciences, including Physics, Chemistry, Biology and disciplines like Engineering and Geology, are understood. Thus, Eraikhuemen and Oteze (2008) view Mathematics as the bedrock of scientific and technological development. Many other researchers and educators emphasize the vital role Mathematics plays 21 UNIVERSITY OF IBADAN LIBRARY in the scientific and technological development of a nation (STAN, 2000; Eze, 2008; Iji, 2008; Koko, 2008). Everybody needs mathematics; an engineer, a grocer, a house wife, a sportsman, an employee, and so on. Agwagah (2008) avers that a common man get on sometimes very well without learning how to read and write, but he can never pull on without learning how to count and calculate. Even insane persons know the quantity of food that can get into their mouth at a time. Mathematics is inborn with man and we cannot afford to do without it. Another important area in which the value of Mathematics is emphasized is on the development of critical thinking. Pollak (1986) posits that Mathematics is the best way to teach youngsters how to think. Mathematics is taught for its impartation of reasoning power. The Foundation of Critical Thinking (FCT, 2004) stated that lack of developing critical thinking in humans makes most of one‟s great capacity dormant and most under-developed. 2.3 Primary mathematics education Primary education is the foundation of every serious educational programme. The primary education is the success or failure and foundation of the whole education system (Agwagah, 2006; Kurumeh and Imoko, 2008). The objectives of primary education are to: (a) Inculcate permanent literacy and numeracy, and ability to communicate effectively. (b) Lay a sound basis for scientific and reflective thinking. (c) Promote patriotism, fairness, understanding and national unity. (d) Instill social, moral norms and values in the child. (e) Develop in the child the ability to adapt to the child‟s changing environment. (f) Provide opportunities for the child to develop life manipulative skills that will enable the child to function effectively in society within the limits of the child‟s capacity (FRN, 2013: 21). Odili (2006) also states the objectives of primary education in relation to mathematics education as (a) To lay a solid foundation for the concept of numeric and scientific thinking. (b) To develop in the child the ability to adapt to his changing environment. 22 UNIVERSITY OF IBADAN LIBRARY (c) To give the child opportunities for developing manipulative skills that will enable him to function effectively in society within the limits of his capacity. The activities that will guide the child to achieve these noble objectives are very vital issues in the educational system. The Federal Ministry of Education (FME, 2004) notes that the key to the success or failure of the whole educational objectives of the child hinges on the level of adequacy of the primary school subjects, such as Mathematics, English Language as well as Social Studies. Also, Iji (2007) posits that the inclusion of permanent numeracy as first among the objectives for primary education stresses the need for every child to be mathematically literate. Despite the relevance of Mathematics education at the primary school level, it is faced with many problems. Conceptual development is limited at the primary school level (Agwagah, 2001). Children dislike Mathematics at this level (Nurudeen, 2007; and Ojo, 2008). In order to solve these problems, Ojo (2008) recommends using concrete materials throughout primary school years and creating a creative corner for pupils who are less capable in Mathematics. Such pupils may be good at art or writing. They may display their creative works in the creative corner of bulletin board. Such activities include poetry or stories about mathematical situations and geometric drawings. Iji (2010) admonishes teachers to make earnest efforts geared towards making the child mathematically competent early enough. Kurumeh and Imoko (2008) assert that ideas, attitudes and beliefs acquired at this stage are usually difficult to change at adulthood. Ohuche (1990) opines that in teaching elementary Mathematics, all teaching should spring from activities, experiences and real situations or equipment. Both discovery and explanatory techniques need to be used; and provide adequate opportunities for manipulation of materials accompanied by verbalization of materials as well as for conceptualization by means of discovery. Teachers need to communicate mathematical ideas in an original fashion through demonstration and proofs; exhibits poems, research projects and further opportunities for originality (Iji, 2007). Agwagah (2001) recommends the use of games. To ensure a sound background at the primary school level in Mathematics, Etukudo (2006) emphasizes teaching Mathematics beyond counting, subtraction, multiplication and 23 UNIVERSITY OF IBADAN LIBRARY division to include ability to apply mathematical ideas in generating, developing and solving simple problems in industry, teaching and business. 2.4. Mathematical games as an instructional strategy Mathematical games take the form of puzzles, magic tricks, fallacies, paradoxes or any type of mathematics which provides amusement or curiosity. Such games provide enjoyment and recreation (Dotun, 2005). Onwuka et al. (2010) observe that game makes the teaching and learning of Mathematics easy and enjoyable. Also, the skills acquired from the game, to a considerable extent, help to arouse and sustain students‟ interest in some difficult concepts in Mathematics. Games develop pleasure, satisfaction and sense of competiveness; promote creativity skills, problem-solving ability; and bring about effective and retentive learning (Kankia, 2008). Mathematics educators could improve and promote the teaching and learning of Mathematics through games, particularly at the early stage of education; that children are natural lovers of games (Akpan, 1988). Games are used in many countries of the world to teach mathematics and science because of its importance in the educational process. In terms of general thinking skills, games offer opportunity for concentrating, thinking ahead, searching for pattern, noticing, using visual imagery, showing perseverance, reflecting, being methodical and logical (Azuka, 2002). Agwagah (2001) outlines the advantages of mathematical games to the teacher: (a) With games, the feedback to the teacher can be direct, and assessment is made more simple and relevant. (b) Games provide inexpensive instructional materials for teachers. (c) Games give the teacher added insight into the quality and level of pupils‟ work and in understanding of Mathematics. (d) Games can help to bridge the gap caused by lack of understanding on the part of the pupils and lack of communication on the teacher‟s part. (e) Games pose a quite different role for the teacher as coordinator, referee, facilitator, and observer, rather than expositor. Agwagah (2001) also lists the disadvantages of mathematical games. They include; (a) They take too long to design. 24 UNIVERSITY OF IBADAN LIBRARY (b) They tend to take longer time to use than traditional techniques. (c) Games create noise in the classroom. (d) Games may be misused, for instance by judging game success by the amount of enjoyment, instead of the amount of learning done. They may also be overused. 2.5 Characteristics of a mathematical game A mathematical game possesses some characteristics that qualify it as a mathematical game. Onwuka et al. (2010) identify the following characteristics of a mathematical game: (a) It must have a mathematical structure. (b) It must involve at least two participants. (c) There are usually rules governing each mathematical game. (d) There must be a winner and a looser, based on a systematic scoring pattern. (e) It must be activity-based or activity-oriented and should stimulate creative thinking or mental processes. These features are fundamental to the development of any mathematical games either for educational or commercial purposes. They are the guide to any game developer especially such games that are used for educational purposes. If any of these features are missing such a game is no longer called a mathematical game. These features were properly considered and incorporated in the games developed for the study. Agwagah (2001) classify mathematical games on the basis of five criteria: (i) Development and reinforcement games. Development games are used for introducing new concepts, while reinforcement games are used for consolidation or revision of factual information. (ii) Chance or strategy games. A game of chance is one in which, a player wins or loses because of chance or luck. It does not involve any skill. Strategy games involve a player devising a plan to achieve a specified goal. Thus, they involve skills such as speed, accuracy, superior memory, or quickness of thought to achieve the particular objectives. (iii) Individual or group mathematical game could either be played on individual or group bases. 25 UNIVERSITY OF IBADAN LIBRARY (iv) Mathematical games could be card, seed, board, computer, puzzles. This depends on whether the game materials are cards or seeds or game is played on a board, or a computer or they are puzzles. (v) Attribute or non-attribute games: Attribute game focuses on attributes of colour, size, shape, thickness and so on. Non-attribute games can focus on things other than the attributes listed above. Generally some games combine two or more of these classifications, but usually one mode dominates. Mathematical games served different purposes which range from whether they are to be used for the development of mathematics concepts and skills. Also, how and the materials with which the games are designed are vital issues to game developers. The games developed and used in this study are aimed at learning mathematics at the primary school level of which appropriate criteria were considered for the total development of the child. The National Mathematical Centre (NMC, 2002) Abuja identifies the component features of a mathematical game to include: (a) Title: This is the name by which a game is identified. (b) Class level: This refers to the class that will benefit from the game. (c) Topic: This indicates the mathematics topic(s) that the game purports to teach. (d) Players: This specifies the number of individuals to play the game. (e) Purpose of a game: This indicates the aim of the game in covering the mathematics topic(s). It indicates whether the game is used for initial instruction in developing the mathematics concept or for remediation, or enrichment. (f) Objectives of a game: This refers to the object of the game. It indicates what it means to win or terminate the game. For instance, the object may be to reach a particular position on the game board, or to collect the most cards, or to accumulate most points, and so on. (g) Materials: These represent the materials necessary for playing the game, such as game board, buttons, beans, seeds, cards and decision devices, like dice, coins, spinners, and so on. (h) Procedures: This specifies the processes or steps involved in playing the game. 26 UNIVERSITY OF IBADAN LIBRARY (i) Rules: The rules of a game are the clear, concise instructions that players must obey in playing the game. (j) Follow-up activities: These may be mathematical tasks, problems or exercises. 2.6 Mathematical games and learning outcomes in mathematics Abubakar and Bawa (2006) examined the effect of number base game in the study of number bases at the senior secondary school level and found a significant difference in the mean achievement scores of students taught number bases using number base game. It was equally discovered that there was no significant difference in the achievement of male and female students. Based on the findings, it was recommended, among others, that mathematics teachers as curriculum implementers should be trained by teacher educators on how to prepare different games on different concepts in Mathematics so as to build positive attitude, interest and problem-solving skills in them, that are broader in application than knowledge for its own sake. Also, Kankia (2008) found that students taught through games achieved significantly better than the students taught without games. Okigbo (2008) used card games to teach percentages, fractions and decimals and found that playing the game before and after a mathematics exercise on fraction reinforced the understanding of number values and sustained students‟ interest. Also, Aremu (1998) found that the card and geoboard game-based strategies showed significant effects on variations in pupils‟ achievement in geometry. The card-based strategy recorded the highest posttest mean scores. The geoboard-based strategy also had improved scores over the lecture strategy. No significant gender differences were observed in the pupils‟ achievement scores in game-based strategies. 2.7 Mathematical poems as an instructional strategy Literature is concerned with the literary aspect of communication using language for artistic and creative purposes with a view to creating beauty which is intellectual (Ayebola, 2006). Some literary aspects used in expressing mathematical ideas are stories, essays, poems, books, and other forms of literature that convey life experiences, real or imagined. One way of connecting school mathematics to everyday life is to draw attention to the mathematics inherent in human thinking 27 UNIVERSITY OF IBADAN LIBRARY and communication about life experiences (Haury, 2001). Studies cited in Haury (2001), gave various reasons to link mathematics instruction to children‟s literature. For instance, Usnick and McCarthy (1998) note that the literature connection motivates students, Welchman-Tischler (1992) claims that, it provokes interest, Murphy (2000) claims that it helps students connect mathematical ideas to their personal experiences, it accommodates children with different learning styles, promotes critical thinking. Melser and Leitze (1999) argue that it provides a context for using mathematics to solve problems. The aspect of literature considered in this study, poetry, has much to do in children learning. St.Cyr (2008) stated that children are natural lovers of poetry. Kids love words, rhyme, and beat. As long as the sounds have rhyme and rhythm, it will stick to the child‟s mind. When kids learn how to talk, they play with sounds, they sing, listen and they repeat. The repetitive nature of poems helps children‟s memory to learn and expand in understanding and knowledge. The world is made up of poetry and we need to help the kids appreciate the beauty of words. Children have a natural affinity for poetry which begins with their first exposure to nursery rhymes and stories of repetitive lines (Mazzucco, 1994). Children learn better and faster when rhyme is used from an early age. Rhymes are pleasing to the ear and they build listening skills which are helpful for later reading comprehension. Learning to manipulate words through rhyming and word games is an important reading skill. Rhymes also delight children and they are an introduction to music and fun of language (LeFebvre, 2004). Bahls (2009) identifies two important purposes poetry serve in Mathematics course. First, poetry offers a new sort of cognition, new lens, and one based in linguistic metaphor, through which students can examine and re-examine mathematical ideas. Second, writing poetry emboldens students and gives them confidence by allowing them familiar with idioms in which they can express themselves mathematically. Writing is an integral part of teaching poetry. The National Council of Teachers of Mathematics (NCTM, 2000) recommends that writing about mathematics be nurtured across grades. The National Institute for Literacy (2007) researches established that, like reading, improving students‟ writing skills improve their capacity to learn. In Alvermann (2002), an expert in adolescence literacy, studied students‟ self-efficacy and engagement and urged that all teachers, despite 28 UNIVERSITY OF IBADAN LIBRARY their content area expertise, to encourage students to read and write in many different ways, for writing raises the cognitive bar, challenges students to problem- solving and think critically. Urquhart (2009) states that mathematics classes previously relied on skill building and conceptual understanding activities, but today writing in Mathematics lesson is more than just a way to document information, but a way to deepen students‟ learning and a tool for helping students gain new perspective. Students whose strengths are language-based use writing as a key to understanding other disciplines, especially Mathematics. Urquhart (2009:1) avers that writing in Mathematics gives me a window into my students‟ thoughts that I don‟t normally get when they just compute problems. It shows me their roadblocks, and it also gives me, as a teacher, a road map. Also, Burns (2004:30) states, “I can no longer imagine teaching mathematics without making writing an integral aspect of students‟ learning.” Also, a teacher, as quoted in Urquhart (2009:8) explained that writing enhances the metacognitive aspect of leaning mathematics, “if there is no writing in Mathematics class, all they are doing is the evaluation-execution portion of learning. Orientation and organization come before execution, and that‟s what writing gets at. That is the most valuable piece of writing in mathematics class.” Writing in mathematics class enhances active learning, problem-solving, invention; increases reading; improves content; and is a way to participating in interdisciplinary collaboration (Urquhart, 2009). Therefore, writing should be as much at home in Mathematics class as in English Language class. Urquhart (2009) recognizes three kinds of writing prompts that reflect three aspects of learning mathematics – (1) content, (2) process and (3) affective. Content prompts deals with mathematical concepts and relationships; process prompts focus on algorithms and problem-solving; and affective prompts centre on students‟ attitudes and feelings. These areas are incorporated in the writing of the poems, especially the content and process. The affective aspect will be incorporated effectively in the pupils‟ activities and assignments together with the other prompts. 2.8 Poems and learning outcomes in mathematics Very few research works are reported in the use of poetry and writing in Mathematics. Pugalee (2004) conducted a study with 9th-grade algebra students to 29 UNIVERSITY OF IBADAN LIBRARY determine if journal writing can be an effective instructional tool in mathematics education and found a positive effect in problem-solving because the writer organize and describe internal thoughts. Also, Pugalee (2005) studied the relationship between language and mathematics learning and found that writing supports mathematical reasoning and problem-solving and helps students internalize the characteristics of effective communication. Bahls (2009) found that, in writing poetry, many students seemed able to make their own mathematical ideas, yet hidden to them. Some of the students who performed poorly or at least more reluctantly than their peers on traditional mathematical exercise, such as computation, heavy home-work problems and in- class examination relished the chance to work with a new medium. Also, Samuels (1987) cited in Bahls (2009), found that performing poetry in a sociology classroom emboldened weaker students. Poetry, which may require the pupils to explain the poems, might result to storytelling, which is a strategy of teaching that is effective for motivating students‟ desire to learning (Diaw, 2009). Stories create a favourable environment for learning, reduce students‟ tension and improve students‟ memory for what they learn (Balakrishnan, 2008; Shirley, 2008). Also, storytelling in teaching mathematics can assist in understanding complex thoughts and ideas, because it encourages students to focus and think harder (Zazkis and Lijedahi, 2009). Albool (2012) found that using the storytelling strategy of teaching mathematics increased the students‟ ability to understand fraction concepts, and increased their ability to solve mathematics problems, thus increased their achievement in Mathematics. 2.9 Knowledge of mathematics concepts and learning outcomes Knowledge of mathematics concepts has to do with the language used in Mathematics (Binda, 2006). Language is a way of expressing ideas and feelings using symbols, sounds, movement or rules (Olokun, 2005). By this definition, Mathematics can be considered as a kind of language, as it deals with symbols and rules. Binda (2006) defines the language of Mathematics as the English language used for the mathematical purposes. This language consists of words, and symbols that have meanings related to particular contexts and procedures for solving mathematics problems. The language of Mathematics refers to the set of 30 UNIVERSITY OF IBADAN LIBRARY mathematics words, symbols and expressions which are understood in the context of Mathematics. From the above discussion, the language of Mathematics may be referred to as the concepts in Mathematics which students need to learn and understand to enable them perform well. For instance, in the concept of fraction, related key words, symbols or sub-concepts, like numerator, denominator, part of a whole, less than (<), greater than ( >), equal to (=) and many others that the students need to learn and understand for a better performance in fraction. Backhouse, Haggarty, Pirie, and Stratton (1992) claim that learners‟ mathematical concepts are intimately associated with words, through which the concepts are learned and with any mathematical symbols used in connection with these concepts. Nnaji (2005) defines a mathematical concept as a mental construct, whereby like properties of a set of experiences are grouped together. The elements of this set may involve objects (set objects), actions (operational concepts), processes (rational concepts) or organizational concepts. For instance, the elements are described as: (a) Set concepts: A square is a quadrilateral having all sides equal. (b) Operational concepts: The addition of any two odd numbers results in an even number. (c) Relational concepts: Closure is the common property of a mathematical group, that is, if you add integers you will always get an integer. Learning what an object is: a fraction, a polygon, an equation, a quotient, is learning the concept of that object. The importance of students having knowledge of mathematics concepts or the language of mathematics cannot be ignored. Before a student solves a mathematics task, he/she must comprehend and translate the problem statement correctly. This is influenced by the extent to which he/she understands the meanings of words or concepts taught them before they can figure out what is being said or sought for, which is a function of language (Binda, 2006). Understanding mathematical symbols and terms will help the learner in his/her mental translation of mathematical information in the learning process (Osafehinti, 1993). The understanding of the language of Mathematics is a prerequisite for high mathematics achievement (Binda, 2006). The learning of this language is not without difficulties, which include: 31 UNIVERSITY OF IBADAN LIBRARY (a) Non-availability of dictionary of Mathematics. (b) The inability of the students to retain and recall contextual meanings of mathematics words and symbols. (c) The abstractness of most mathematics words and symbols. For instance, the meaning of the words, “solve” or “simplify” can hardly be explained using concrete materials. (d) English equivalent forms for most mathematics words and symbols are difficult to find. Such words and symbols are given in other languages such as Greek and Latin, thereby rendering their learning extremely difficult. (e) Phobia and general negative attitude towards Mathematics (Binda, 2006). Also, students find it difficult to conceptualise the topics being taught not to talk of the application. Students just copy notes and struggle to memorize the mathematics topics. With these, students cannot appreciate the application of Mathematics to daily activities; they find it difficult to accept that words should be found in Mathematics (Eze, 2007). Gershon, Guwal and Awuya (2008) found that word problems are often found in Mathematics and students of colleges often complain that they least expected that there is a mathematical course that hardly uses figures. They cannot imagine how courses as Number Theory, Real Analysis and Abstract Algebra are full of worded problems. Understanding mathematics specific language, prepositions, and lexical items is another problem in Mathematics learning. Olokun (2005) notes that prepositions in general and the relationships they indicate are critical lexical items in the mathematics register that can cause a great deal of confusion. Word order, such as saying the same expression in different ways, requires a lot of reasoning. For instance, 30 divided by 6 and 6 divided by 30 mean different things. Mathematics-specific language, such as hypotenuse, minus, and exponent, must be understood. Some common words like table, product, rational, odd, and factor, have meanings in Mathematics that are different from daily language. Right means direction or correctness. However, right is used in Geometry to refer to an angle with special characteristics and has nothing to do with direction or correctness. Prepositions are conceptually challenging; they carry important but confusing functions in Mathematics. For instance, one-third of twelve oranges and reduce by 5cm. Prepositions can also signify different actions as 3 multiplied by 10 or 3 increased by 10. 32 UNIVERSITY OF IBADAN LIBRARY In an attempt to solve the above mentioned problems, Binda (2006) recommends general strategies, oral strategies, kinesthetic strategies and word origins. A brief description of each is given. a. General strategies: These strategies include building concepts first before attaching vocabularies to establish ideas. This should be followed with students recording the new term and its meaning with a diagram in a personal glossary. b. Oral strategies: These strategies involve encouraging students to work orally in groups to solve problems. While doing this, students should talk mathematics. In other words, the teacher should create opportunities for students to discuss procedures for solving mathematics problems while the teacher listens (silent teacher technique) and correct the students where necessary. c. Writing strategies: The teacher should encourage mathematical writing among the students, such as journal writing, in which the teacher provides the stem and requires the students to fill. d. Visual strategies: These strategies involve the use of structured overview, picture, dictionaries, mathematical graffiti, and mathematical cartons among others. e. Kinesthetic strategies: These involve the use of manipulative, such as algebraic tiles, making models, building three-dimensional figures, and others. Such strategies also involve group or individual projects, usually accompanied with public representations, such as drama and rehearsals. f. Word origins: It is a fact that mathematics words have their histories and roots. Teachers should teach the histories of mathematics words. This is because the knowledge of where these words came from will help students to make connections between mathematics words and the everyday English language. For example, the word perpendicular came from the root word pend which means to hang. Also, asymptote, which is related to the word symptom, is from the root sym. Some studies have been carried out by researchers and mathematics educators to ascertain students‟ level of achievement in concept development. Reys (1989) used calculators to help primary school pupils to develop conceptual understanding in finding the mean in Statistics. It was found that this enabled the 33 UNIVERSITY OF IBADAN LIBRARY pupils to concentrate on the concept rather than the tedious computation and this enhanced a better achievement. Binda (2006) carried out a study to find the relationship between understanding the language of mathematics and achievement at the secondary school level and found a weak but positive relationship between the variables studied. This suggests that mathematics teachers need to teach the language of Mathematics in order to enhance classroom communication during mathematics lessons thereby, improving achievement in the subject. Galadima and Yusha (2007) found no significant gender difference in the learning of concepts, principles, terms and symbols among Senior Secondary School (SS2) students. The study found that both boys and girls achieved poorly in the test administered on mathematical concepts, principles, terms and symbols. More than 75% of the students scored low marks in mathematical areas of Algebra, Trigonometry and Statistics as a result of the lack of understanding the basic concepts, principles, terms and symbols. Also, Inekwe (1997) found, in his study, that boys and girls achieved poorly in Geometric reasoning ability test. 2.10 Interest in mathematics and learning outcomes Interest is a significant factor that enhances the learning of Mathematics and thus improves the achievement of students in Mathematics (Udegbe, 2009). Harbor-Peters (2002) explains that interest leads the individual to make a variety of choices with respect to the activities in which he/she engages. The individual shows preference to some and aversion to others. It is the tendency to seek out and participate in certain activities or to prefer, or engage in a particular type of activities. Most secondary school students in Nigeria were found to have poor interest in Mathematics. They absent themselves in mathematics lessons and those who stay in the lesson pay little attention to their teachers. When the option is available, most students will prefer not to have anything doing with the study of Mathematics because they lack interest in it (Udegbe, 2009). Researchers and mathematics educators have investigated the factors responsible for the low interest of students in Mathematics. Nurudeen (2007) is of the view that the difficulty in understanding the technical language associated with Mathematics is one of the major factors responsible for students‟ lack of interest and even their poor achievement in Mathematics. Habor-Peters (2001) and 34 UNIVERSITY OF IBADAN LIBRARY Abakporo (2005) identify teachers‟ strategies of teaching as one of the problems of learning Mathematics that have resulted in students‟ lack of interest in Mathematics. The inability of students to understand the basic mathematical principles, computations or logical facts involved and the underlying processes that gave rise to the mathematical facts as the cause of poor achievement and lack of interest in Mathematics (Soyemi, 2003). Ukpebor (2006) attributes persistent low interest and poor achievement of students in mathematics and science education to inadequate instructional resources/materials. Various suggestions have been made by researchers and mathematics educators to solve the problem of students‟ lack of interest in Mathematics. For instance, Harbor-peters (2002) recommends to teachers to use tangible/visual representation, such as sketches/models, to concretize ideas. Such representations link up thought processes to reality. Such materials generate and sustain interest in mathematics teaching and learning. Another source of interest in Mathematics is for the teacher to vary his/her method of presenting similar ideas to take care of individual differences which, in turn, will dispel boredom and generate interest. Further suggestions are on various avenues through which teachers can explore enrichment activities. Adetula (2001) identifies sources of enrichment content such as: a. Mathematical recreation b. History of mathematics c. Application of mathematics d. Instructional resources Still, Akinsola and Popoola (2004) posit that, for teachers to meaningfully enhance learning and improve interest in Mathematics, they should tap heavily from devices which have direct sensory appeal and exhibit mathematical concepts clearly. Ukeje and Obioma (2002) stated that amusement and pleasure should be combined with mathematics instruction to make their learning more interesting. Abubakar and Bawa (2006) aver that teachers should teach Mathematics in an application-oriented form using instructional materials, such as games whose materials are readily available in the child‟s environment. This is because learning by doing is a better way to develop and sustain students‟ interest in Mathematics. Various studies quoted in Udegbe (2009) reported the effect of some strategies and activities on students‟ interest in Mathematics and other learning 35 UNIVERSITY OF IBADAN LIBRARY outcomes in Mathematics. For instance, Ezeamenyi (2002) investigated the effect of four games on junior secondary schools students‟ achievement, interest and retention in Mathematics. The study was carried out in four secondary schools in Enugu State, Nigeria. The result showed that students taught with games achieved more, generated more interest and retained more in Mathematics than those taught without games. Uchedu and Mbah (2007) investigated the effect of peer interaction in Problem-Based Learning (PBL) context on students‟ achievement and interest in Science. The result revealed that peer interaction learning strategy had positive interest in Science than traditional lecture-based learning strategy. Agwagah (2008) investigated the effect of using origami to get students interested and involved in Mathematics. She concluded that origami is one possible way to captivate and get students interested in Mathematics. Okigbo and Okeke (2011) investigated the effect of games and analogies on students‟ interest in Mathematics using 246 JSS 2 students. They found that the game was more effective in improving students‟ interest in Mathematics than analogy. It was also found that a non-significant difference existed between the mean interest scores of male and female mathematics students taught with either game and also those taught with analogy. It was recommended that teachers should be encouraged to adopt game more than instructional analogy in teaching number and numeration and algebraic processes in Mathematics. 2.11 Verbal ability and learning outcomes in mathematics Verbal ability refers to the scholastic ability of a learner, especially without any specific curriculum content. Buffery and Grey (1972) quoted in Komolafe (2010) state that learners‟ verbal abilities are linked to biological differences in the organization of the brain. Scientific research has revealed that the left cortex dominates and controls verbal functions and develops quickly in females, while the right cortex in boys is usually dominant for non-verbal functions, such as spatial relationships. To buttress this finding, Odebode (2001) reported that girls performed better in verbal tests and obtained higher grades than boys, while boys excelled in Mathematics and in all science related-subjects. Throughout the world, women are higher in verbal abilities than men, but are lower in Mathematics and spatial ability. Men are superior to women in problem-solving tasks and specific abilities related to problem-solving (Asoegwu, 2008). 36 UNIVERSITY OF IBADAN LIBRARY Idogo (2011) investigated the effects of instructional strategies on basic reading and comprehension skills on 370 primary 5 and 6 pupils and found a significant positive effect of instructional strategies on verbal ability. The high ability group performed better than the average and low ability pupils. Awofala et al. (2011) found that verbal ability and cognitive style had significant main effect on students‟ achievement in mathematical word problems using 450 JSS students. High verbal ability students performed significantly better than low verbal ability students in mathematical word problems. Hall (2004), cited in Binda (2006) found a positive correlation between students‟ verbal ability and achievement in Mathematics; stressing that, when students are strong in verbal abilities, their understanding of Mathematics will be enhanced. Iti (2005) found no significant difference of verbal ability on pupils‟ interest and class participation in primary science; but found significant difference in the achievement of male and female pupils in primary science. 2.12 Gender and learning outcomes in mathematics Gender differences are a reflection of cultural values and expected social roles for men and women. They are not as a result of biological differences or genetic deficits especially in learning Science and Mathematics (Ogunkunle, 2007). Gender refers to the social roles that are believed to belong to men and women within a particular social grouping. It is a learned perception, so anything associated with gender can be changed or reversed to achieve equality and equity for both men and women (Amoo and Onasanya, 2010). Gender differences in mathematics achievement are caused by (a) Social economic status and ethnicity. (b) Teacher-student interactions. (c) Teacher-student behaviours. (d) Characteristics of the classroom. (e) Personal beliefs in Mathematics. (f) Learning of complex mathematics (Fennema, 1995). Amoo and Onasanya (2010) point out specific school influences, such as: timetabling of subjects, assessment procedures, teacher expectations and behaviour vis-a-vis classroom practices and interpretation of mathematics curriculum, peer 37 UNIVERSITY OF IBADAN LIBRARY pressures, unequal funding, and stereotyped textbooks, as causes of gender inequality in science and mathematics teaching and learning. Researchers have found that gender plays a significant role in the learning outcomes of students. Muthukrishna (2010) carried out a study in KwaZulu-Natal in South Africa, examining whether there was a significant gender gap in Mathematics achievement, the nature of the gap, and the factors associated with the differential performance of girls and boys in mathematics class. The quantitative data was drawn from grade-six Mathematics achievement test results conducted in 2008 and 2009. The findings in the study revealed a gender gap in Mathematics achievement in favour of girls. The key factors associated with the gender gap include the issue of boys and masculinities, the dynamics of classroom cultures, and the differential attitudes to learning in respect of boys and girls in the Mathematics class. However, a study by Wilmot (2001) in Ghana revealed a general poor performance of both sexes in each class but significant differences in achievement were observed in favour of boys in only primary six (6). Opolot- Okurot (2005) investigated the students‟ attitudes toward Mathematics in Uganda secondary schools and found that, for all the attitudinal variables (anxiety, confidence and motivation), males had higher scores than females. Vale (2009) cited in Muthukrishna (2010), reported that many studies conducted between 2000 and 2004 in Australia showed no significant differences in achievement in Mathematics between males and females, although males were more likely to obtain higher mean scores. In New Zealand, studies favoured females at the primary school level, while studies conducted at the secondary school level favoured males. Also, a large scale study in the U.S.A by Hyde and Mertz (2009) revealed that, girls had now reached parity with boys in Mathematics performance, including at high school where a gap existed in earlier decades. Furthermore, girls were found to doing better than boys even for tasks that require complex problem-solving in the U.S.A. The situation in Nigeria is not different, for studies have reported gender differences from primary school to the secondary school level. For instance, Eniayeju (2010) assessed the gender differences in Mathematics using a cooperative learning strategy. Three hundred and eighty-nine primary six pupils participated in the study. The experimental groups were assigned to either homogeneous (single sex) or the heterogeneous (mixed sex) groups. The results 38 UNIVERSITY OF IBADAN LIBRARY revealed that girls in heterogeneous groups had significantly higher mean scores than their counterparts in homogeneous groups. The results of boys and girls in the cooperative groups showed that girls achieved significantly better than boys in all tests. Onasanya (2008) determined the effectiveness of team teaching using 297 J.S 2 students and found that male students achieved significantly better than female students in using team teaching in Mathematics class. Shafi and Areelu (2010) determined the effect of improvised instructional materials on 300 S.S.S 3 students‟ achievement in solid geometry and found a significant difference between the achievement of boys and girls in the experimental groups. Males achieved significantly better than females. Ebisine (2010) found no significant difference in the level of difficulty encountered by male and female students in understanding the non-technical words in multiple choice Mathematics tests. Also, Bawa and Abubakar (2008) found no significant difference in achievement of male and female students taught linear equations using weighing balance approach. Galadima and Yusha (2007) discovered no significant gender differences in Mathematics achievement of students in learning mathematical concepts, principles, terms and symbols among senior secondary school students. It is evident from the various works highlighted that gender differences still exist while learning Mathematics. 2.13 Appraisal of the literature reviewed The reviewed literature showed that the primary school level of education is considered significant in Mathematics education. This is because it is the foundation on which the secondary and the tertiary levels are built. The Mathematics curriculum is sequential and spiral in nature, which implies that a good background at the primary school level will enhance good performance at the other levels of education. The reviewed literature also revealed that pupils‟ conceptual development, interest and achievement in Mathematics was poor, which accounted for the poor achievement of students at the higher levels. As evidenced in previous researches, game and poem are recommended to solve the problems of teaching Mathematics. The use of game in teaching Mathematics makes students to be actively involved in the daily lessons. It also provides unique opportunity for integrating the cognitive, affective and social aspects of learning and is academically rewarding. 39 UNIVERSITY OF IBADAN LIBRARY Most studies on game in teaching Mathematics were carried out at the secondary school level. Also, game was used with other strategies, such as game and simulation; game and analogy; and two distinct games, like ladder and tunnel games, card and geoboard-based games, to determine the most effective strategy. The results revealed that the game instructional strategy improved students‟ interest, attitude, and achievement in Mathematics better than the other strategies. However, there is relatively no study that determines the effects of games and poems on learning outcomes in Mathematics at any level of education. Many scholars claim that poetry should be used in teaching Mathematics to help pupils who are good at arts or writing to enable them learn Mathematics. Children are natural lovers of poetry and memorizing poetry increases a child‟s cognitive ability to reason, imagine, think, argue and experience the world in sensory and aesthetic ways. There is a great and growing body of linguistic and visual metaphors that aids a healthy understanding of Mathematics. Mastery of these concepts often involves creativity more readily expected of a poet than of a scientist. Few studies have been carried out in some aspects of poetry, such as reading and writing, and in storytelling in Mathematics. The use of poetry in teaching Mathematics has been investigated in college Mathematics. However, such studies in Mathematics have not been carried out in Nigeria at any level of education. Therefore, this study determined the effects of game and poem-enhanced instructional strategies on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. Besides, studies on gender and achievement in Mathematics are inconclusive. Investigation of verbal ability on pupils‟ learning outcomes in Mathematics is a relatively new development. Therefore, the study determined gender together with verbal ability as moderating variables on pupils‟ learning outcomes in Mathematics. 40 UNIVERSITY OF IBADAN LIBRARY CHAPTER THREE METHODOLOGY This chapter deals with the research design, variables in the study, population and sample selection, research instruments, reliability and validity of the instruments, general procedure for treatment, data collection and method of data analysis. 3.1 Research design This study adopted a pretest-posttest, control group, quasi-experimental design. The design is schematically represented as: E1: 01 x1 02 E2: 03 x2 04 C: 05 x3 06 Where: 01, 03, 05 represents pretest observation for both experimental and control groups. 02, 04, 06 represents posttest observation for both experimental and control groups. X1 represents treatment 1; poem-enhanced instructional strategy X2 represents treatment 2; game-enhanced instructional strategy X3 represents the modified lecture instructional strategy This design also employs the 3x3x2 factorial matrix, shown in table 3.1 41 UNIVERSITY OF IBADAN LIBRARY Table 3.1. 3x3x2 Factorial matrix of the design Treatment Gender Verbal Ability Low Medium High Poem-Enhanced Male Instructional Female Strategy (PEIS) Game-Enhanced Male Instructional Female Strategy (GEIS) Modified Lecture Male Instructional Female Strategy (MLIS) 3.2 Variables in the study The variables considered in this study are: 3.2.1 Independent variables: The independent variable (instructional strategy) manipulated at three levels. i. Poem-enhanced instructional strategy. ii. Game-enhanced instructional strategy. iii. Modified lecture instructional strategy. 3.2.2 Moderator variables The following moderator variables were examined in the study. i. Verbal ability, at three levels (high, medium, low) ii. Gender, at two levels (male, female) 3.2.3 Dependent variables There were three dependent variables. i. Knowledge of mathematics concepts ii. Interest in Mathematics. iii. Achievement in Mathematics. 3.3 Selection of participants Two local government areas in Bayelsa State and six schools in each local government areas were purposively selected and randomly assigned to treatment 42 UNIVERSITY OF IBADAN LIBRARY and control group. The selection of the local government areas was based on the following criteria: (i) The local government areas must have roadways because of the state‟s terrain (rivers) (ii) The local government areas must have at least six (6) public primary schools that have roadways. The selection of the schools were based on the following criteria: (i) the schools must be public schools; (ii) the schools must have experienced teachers who possess teaching qualification and have been teaching Mathematics for not less than five years; and (iii) the teachers must be willing to be involved in the experiment. Six (6) schools were randomly selected from one local government area; that is, a total of twelve (12) schools from two local government areas were used for the study. One intact class of primary six (6) pupils was randomly selected from each of the twelve public primary schools in the two local government areas. Two (2) schools each were randomly assigned to treatment (i.e. groups 1 and 2) making a total of four schools to treatment and two (2) schools to control group in one local government area. Also, the same number of schools was assigned to treatment and control group in the second local government area. A total of 344 pupils (males=164, females=180) were used. 3.4 Research instruments Nine instruments were used in the study; namely: 1. Instructional Guide on Poem-Enhanced Instructional Strategy (IGPEIS) 2. Instructional Guide on Game-Enhanced Instructional Strategy (IGGEIS) 3. Instructional Guide on Modified Lecture Instructional Strategy (IGMLIS) 4. Pupils‟ Mathematics Achievement Test (PMAT) 5. Pupils‟ Mathematics Concepts Test (PMCT) 6. Pupils‟ Interest in Mathematics Inventory (PIMI) 7. Pupils‟ Verbal Ability Test (PVAT) 8. Teacher‟s Assessment Sheet for Poems (TASP) 9. Teacher‟s Assessment Sheet for Games (TASG) 43 UNIVERSITY OF IBADAN LIBRARY 3.5. Teachers’ instructional guides These were teaching guides prepared by the researcher for the teachers on Poem-Enhanced Instructional Strategy, Game-Enhanced Instructional Strategy and Modified Lecture Instructional Strategy. These were used during the training period for the experimental and control groups respectively. 3.5.1 Instructional Guide on Poem-Enhanced Instructional Strategy (IGPEIS). The main features of the guide were general information, which consisted of subject, topic, and class. It also had the procedure, general objectives, teacher activities, pupils‟ activities, materials (poems‟ manuals), pupils‟ evaluation guide and contents to be taught for eight weeks. Validation of Instructional Guide on Poem-Enhanced Instructional Strategy (IGPEIS) The instructional guide (IGPEIS) was given to experienced Mathematics teachers teaching primary six (6) classes, lecturers in Teacher Education, Science/Mathematics unit and English Language unit, University of Ibadan, to examine its content and face validity. The appropriateness of the language used and images created in the poems to the age of the children were also examined. The recommendations given were used to reconstruct the guide. 3.5.2. Instructional Guide on Game-Enhanced Instructional Strategy (IGGEIS) The main features of the guide were general information which consisted of subject, topic, and class. It also contained the procedure, general objectives, teacher activities, pupils‟ activities, deck of playing cards, game boards and game tokens, pupils‟ evaluation guide and title, objectives of the game, procedure, rules, and follow-up activities. Validation of Instructional Guide on Game-Enhanced Instructional Strategy (IGGEIS) The instructional guide on IGGEIS was given to experienced Mathematics teachers in primary schools that were teaching primary six (6), two lecturers in Teacher Education, Science/ Mathematics unit, University of Ibadan, to examine its content and face validity. The validity of IGGEIS was further ensured according to Pulos and Sneider‟s (1994) in Aremu (1998) model for game development and 44 UNIVERSITY OF IBADAN LIBRARY validation in terms of suitability, appropriateness, clarity of ideas, class level, scope and relevance to the study by two experts in the area of Educational Technology, Faculties of Education, University of Ibadan and Niger Delta University, Nigeria for scrutiny and amendments. The games also passed through the supervisor of the researcher for necessary corrections. The ratings 4, 3, 2, 1, and 0 on table 3.2 represent very good, good, average, poor and very poor respectively. Table 3.2. Guidelines for games model validation Contents 4 3 2 1 0 Relevance to learner‟s needs and ability Relevance of the objectives of the game Appropriateness of materials used Relevance of the game for the task to be learnt Attractive and sturdy Clarity of game Image familiar with the learner Balance ease, enjoyable with challenge Appropriate for the age of learners Learner‟s skill development Total 3.5.2.1 Game development The conceptual framework model adopted for the development and evaluation of the nine games is Pulos and Sneider (1994) in Aremu, (1998). The framework is based largely upon research and developments in cognitive science and developmental theories. The framework is based upon the challenge facing any game developer or evaluator. The tasks that determine the game: (i) should include the necessary components of the concepts to be taught, that is component analysis. (ii) will help learners to learn the concepts (iii) is likely to remove or reduce the difficulties students have in learning the concepts. (iv) should be interactive and enjoyable (v) should enhance learning. 45 UNIVERSITY OF IBADAN LIBRARY Fig.1. Pulos and Sneider (1994) conceptual model for developing and evaluating games (adopted from Aremu, 1998) Analysis How Analysis of Select an of concept Learners learners enjoyable learn task Evaluation Integration of task Stage 1: Analysis of concepts: The concepts of this study were from the primary six mathematics curriculum. They are identified difficult topics by Salman (2009); (see appendix 7). The researcher also carried out a survey of difficult topics in the study area in the year 2010 and found similar result. The topics were 1) Fraction and Decimal. 2) Volume. 3) Capacity. 4) Weight. 5) 2 and 3-Dimensional Figures Stage 2: How learners learn The learning theory that supports the games discussed in this study is Operant Conditioning Theory proposed by B.F Skinner (1938). This has been thoroughly discussed in chapter two of this work. Stage 3: Analysis of learners At this stage, each sub-concept was carefully considered to find out the similarities and differences that could confuse learners in learning the concepts. From the analysis and comments of teachers, the concepts that learners mixed up were identified. 46 UNIVERSITY OF IBADAN LIBRARY All the identified misunderstood concepts were borne in mind in designing the games. The most misunderstood concepts were used more frequently in the games to ensure practice that leads to better understanding. Stage 4 Selection of an enjoyable task The games used in this study were popular and interesting card games adapted from the mathematical games developed by the National Mathematical Centre (NMC, 2002), Abuja. From the words of Professor Sam O. Ale, in the foreword, these games are useful and are recommended for use by teachers and pupils in the school system to improve the teaching and the learning process in Mathematics. These games were 1. Expression Whot 2. Mathematics Palace Game 3. Capacity Board Game 4. Plane Figure Card Game 5. Circle Race Game, and 6. Mathematics Vocabulary Game Stage 5 Integration All the concepts that were analysed were integrated into the structure of the existing games and some were modified to suit the age and ability of the pupils and content to be taught in the classroom. Stage 6: Evaluation These games were evaluated by the National Mathematical Centre (NMC), Abuja and were certified as good games for improving the teaching and learning of Mathematics by Professor Sam. O. Ale (NMC, 2002) as found in the foreword. They were further certified by other experts in educational technology. 3.5.3 Instructional Guide on Modified Lecture Instructional Strategy (IGMLIS) This guide allowed some measure of interaction of pupils with teacher and materials without the poems and games. The main features of the guide were 47 UNIVERSITY OF IBADAN LIBRARY general information, which consisted of subject, topic, procedure, general objectives, teacher activities, and pupils‟ activities, contents for each week and pupils evaluation guide. Validation of Instructional Guide on Modified Lecture Instructional Strategy (IGMLIS) The instructional guide (IGMLIS) was given to experienced Mathematics teachers that were teaching primary six (6) for review and all their suggestions were considered in the guide. 3.6 Pupils’ Mathematics Achievement Test (PMAT) The PMAT was a twenty-five-item multiple choice test with four options A- D adapted from primary six pupils‟ Mathematics texts. This was to measure pupils‟ cognitive achievement in Mathematics. Section A contained the demographic data of the pupils, such as pupil number, school number, local government area, age, sex and class. Section B comprised twenty-five multiple choice items on fraction and decimal, volume, capacity, weight, 2 and 3- dimensional figures based on the curriculum and identified difficult topics (see appendix 7). The test items focused on the first three levels of cognitive domain: knowledge, comprehension, and application, as categorized by Okpala, Onocha and Oyedeji (1998) in Aremu (1998). The specification for the construction of PMAT is shown in table 3.3. 48 UNIVERSITY OF IBADAN LIBRARY Table 3.3. Table of specification of Pupils’ Mathematics Achievement Test (PMAT) Topic Knowledge Comprehension Application Total Fraction and Decimal 1 2, 3, 4 16, 7 (addition, subtraction, 17,18 multiplication and division) (1) (3) (3) Volume (cylinder, 10, 11, 20, 21 22 5 triangular prism and (4) (1) sphere) Capacity 5 9, 19 3 (1) (2) Weight 7 8 6 3 (1) (1) (1) 2 and 3-dimensional figures 12,13, 14, 15 7 23,24,25 (1) (6) Total 8 10 7 25 Validation and reliability of PMAT To validate PMAT, fifty items were initially adopted from primary six pupils‟ Mathematics text and given to a test measurement expert; a lecturer who specialized in mathematics education as well as experienced primary six mathematics teachers with the table of specification to vet the structuring, adequacy, face and content validity as well as task level of the items. Based on the recommendation of these experts, eleven (11) items were expunged and others modified. The modified test of thirty nine (39) items were administered to one hundred (100) primary six (6) pupils that were not involved in the real study to determine the discriminating indices for each item. The difficulty levels were computed manually by the researcher. The result of the analysis was used to pick twenty-five (25) items that were neither too difficult nor too easy and these were between 0.4 and 0.6. The twenty-five (25) items were then re-administered to fifty (50) pupils and a reliability coefficient of 0.72 was obtained using Kuder- Richardson formula 21 (KR-21) 49 UNIVERSITY OF IBADAN LIBRARY 3.7 Pupils’ Mathematics Concepts Test (PMCT) The PMCT was a twenty (20)-item multiple choice test with four options A-D constructed by the researcher to measure pupils‟ knowledge of mathematics concepts on the topics selected for the study. It was constructed based on what is involved in knowledge of mathematics concepts, given by Backhouse, Haggarty, Pirie and Stratton (1992); Nnaji (2005) and Binda (2006); that is, the words, symbols, principles, expressions, equations, formulae in Mathematics. Section A of PMCT contained the demographic data of pupils, such as pupil number, school number, local government area, age, sex and class. Section B consisted of twenty (20) items on the content areas. Validation and reliability of PMCT To validate PMCT, thirty six (36) items were initially developed and given to a test measurement expert; a lecturer who specialized in Mathematics Education as well as experienced primary six mathematics teachers to vet the structuring, adequacy, face and content validity as well as task level of the items. Based on the recommendation of these experts, some items were expunged and others modified. The modified test, of thirty-two (32) items, were administered to one hundred (100) primary six (6) pupils that were not involved in the real study to determine the discriminating indices for each item and difficulty levels were computed manually by the researcher. The result of the analysis was used to pick twenty (20) items that were neither too difficult nor too easy and these were between 0.4 and 0.6. The twenty (20) items were then re-administered to fifty (50) pupils and a reliability coefficient of 0.81 was obtained using Kuder-Richardson formula 21 (KR-21). 3.8 Pupils’ Interest in Mathematics Inventory (PIMI) This instrument was adapted from Ekine (2010). It consisted of twenty items with which the pupils were to indicate their like and dislike for Science. Ekine (2010) noted that the instrument was structured as dichotomous (yes/no) inventory, because the primary school pupils could not respond clearly to a Likert scale used at first. Ekine (2010) citing Akinbote (1993) reported that the yes/no response mode have been found to be more appropriate and better understood by primary school pupils. The only change made on PIMI in this study was replacement of Science with Mathematics. 50 UNIVERSITY OF IBADAN LIBRARY The instrument addressed three characteristics interest-oriented actions which include cognitive stabilization that shows a person‟s knowledge of the subject, emotional status and personal value of the person‟s interest. These three areas were considered in structuring the items in Mathematics. Ekine (2010) had a reliability coefficient of 0.79 using Cronbach Alpha. Validation and reliability of PIMI To validate PIMI, the twenty items were subjected to expert review to assess the content and face validity in respect of the suitability of language presentation, clarity and application to the investigation. The suggestions were incorporated into the items. The test items were then given to thirty (30) pupils that were not involved in the main study to determine the reliability of the scores using Kuder-Richardson 20 (KR-20), since the PIMI is structured dichotomous yes/no and had a reliability coefficient of 0.73. 3.9 Pupils’ Verbal Ability Test (PVAT) The PVAT was a thirty (30)-item test; an Intelligence Quotient (IQ) test for children called the Wechsler Intelligence Scale for Children Revised (WISC-R) test, adopted from Komolafe (2010). This revised edition was published in 1974, as WISC-R for children between the age ranges of 6-16 years (Wechsler, 1974). The only modification made by Komolafe was a careful selection taken into consideration, the cultural setting of the pupils, the school curriculum, among others, that are relevant to the level of the respondents. The instrument was to test pupils‟ ability to reason, discover differences and similarities between words, and also used to categorize pupils into high, medium and low verbal abilities. A correct answer attracted one (1) mark, while a wrong answer was scored zero (0). Pupils who score from 1-10 marks, 11-20 marks, and 21-30 marks were grouped as low, medium and high verbal abilities, respectively. The test was used as pre-test only. Komolafe (2010) had a reliability coefficient of 0.81 using KR-21. Validation and reliability of PVAT To validate PVAT, the test was given to lecturers in Language Education and two teachers teaching English Language in primary six classes to vet the structuring, clarity of language and appropriateness of the content in terms of its difficulty for primary six pupils. Then the test was administered to fifty (50) pupils 51 UNIVERSITY OF IBADAN LIBRARY that were not part of the main study to determine the reliability of the test using Kuder-Richardson 21 formula (KR-21), which yielded a reliability coefficient of 0.85. 3.10 Research procedure The researcher obtained a letter of introduction from the Department of Teacher Education, University of Ibadan, to the head teachers of the selected schools to be allowed to use their schools, teachers and pupils for the study. This was necessary in order to seek the cooperation of the head teachers and primary six teachers that were involved in the study because the topics taught during the treatment period were not in order with the school scheme of work. Preliminary activities 1. Training of teachers The researcher personally visited the participating teachers in their respective local government areas and trained them on how to adhere strictly to the instructional and experimental procedures. Two teachers were trained as research assistants for each experimental group. They were asked to use the instructional guides IGPEIS and IGGEIS, while the teachers for control group were asked to adhere to the steps on the Instructional Guide on the Modified Lecture Instructional Strategy (IGMLIS). The first two weeks were used for training the participating primary six teachers in each of the local government areas by the researcher. 2. Pre-test The third week was used for the administration of pre-test by the teachers and researcher in the order: PIMI, PMAT, PMCT and PVAT. 3. Procedure for treatment The fourth to eleventh weeks (eight weeks) were used for the administration of the treatment to experimental groups (PEIS and GEIS) and control group (MLIS). Experimental Group I: Steps in Instructional Guide on Poem-Enhanced Instructional Strategy (IGPEIS) The pupils in this group were taught using the following steps: Step1:  The teacher briefly reviews the previous lesson/introduces the new topic. 52 UNIVERSITY OF IBADAN LIBRARY Step 2:  The teacher distributes the poems manuals to pupils.  Pupils read the poems aloud (choral reading by the whole class, small groups in rows and individually at random).  Pupils explain the images and dramatize or role-play the actions in the poems.  Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. Step 3:  Teacher gives few problems to solve as class work.  Teacher marks pupils‟ work and do corrections for them.  Teacher concludes the lesson by giving home work to pupils. 2. Experimental Group 2: Steps in Instructional Guide on Game-Enhanced Instructional Strategy (IGGEIS) Step1:  The teacher briefly reviews the previous lesson/ introduces the new topic. Step 2:  Teacher teaches the new topic.  Teacher rearranges the class/distributes game materials  Teacher explains the game materials, rules and the objectives of the lesson.  Pupils play the games with minimum teacher intervention Step 3:  Teacher‟s debriefing session, to further clarify the concept and problems.  Follow-up activities by way of pupils coming to the board to solve problems/give assignment.  Collection of materials and rearrange the class. 3. Control Group: Steps in Instructional Guide on Modified Lecture Instructional Strategy (IGMLIS) Step1:  Teacher reviews the previous lesson and introduces the new topic. Step 2:  Teacher teaches the new topic.  Teacher draws models on the chalk board to represent the concept. 53 UNIVERSITY OF IBADAN LIBRARY  Teacher allows some form of interaction with pupils (pupils ask questions and solve problems on the chalk board).  Teacher allows pupils to copy the notes. Step 3:  Teacher gives pupils few problems to solve as class work.  Teacher marks pupils‟ work and do corrections for them.  Teacher concludes the lesson by giving home work to pupils. 4. Posttest Week twelve was used for the administration of posttest by the teachers and researcher in the order: PIMI, PMAT and PMCT. 3.11 Method of Data Analysis The data collected were analysed using Analysis of Covariance (ANCOVA). This was adopted to test the hypotheses using pre-test scores as covariates. Estimated Marginal Means (EMM) analysis was used to determine the magnitude of performance of the various groups. Scheffe‟s post-hoc test was also used when significant differences were observed to show the pairs of groups that were significantly different and to determine the direction of the difference. 54 UNIVERSITY OF IBADAN LIBRARY CHAPTER FOUR ANALYSIS AND RESULTS This chapter presents the results and the interpretation of the analysis of data. Analysis of Covariance (ANCOVA) using pretest scores as covariates, Estimated Marginal Mean (EMM) analysis and Scheffe‟s multiple comparison test (post-hoc analysis) were used to test the null hypotheses at 0.05 level of significance. The results of the analysis of data are presented in Tables 4.1 to 4.18. 4.1 Testing of hypotheses 4.1.1 H01 (i): There is no significant main effect of treatment on pupils‟ achievement in Mathematics. Table 4.1. 3x3x2 Analysis of Covariance (ANCOVA) of posttest scores of pupils’ achievement in Mathematics with treatment, verbal ability and gender using pre-test scores as covariates Source of variation Type III Df Mean F-cal. Sig. Partial Sum of Square Eta Squares squared Corrected Model 5230.539 18 291.085 153.801 0.000 0.895 Intercept 398.600 1 398.600 210.608 0.000 0.393 Pretest scores 918.251 1 918.251 485.175 0.000 0.599 Treatment 529.293 2 269.647 142.473 0.000* 0.467 Verbal ability 136.037 2 68.019 35.939 0.000* 0.181 Gender 1.598 1 1.598 0.844 0.359 0.003 Treatment*Verbal ability 5.461 4 1.365 0.721 0.578 0.009 Treatment*Gender 1.663 2 0.831 0.439 0.645 0.003 Verbal ability*Gender 5.288 2 2.644 1.397 0.249 0.009 Treatment*Verbal ability*Gender 10.537 4 2.634 1.392 0.236 0.017 Error 615.101 325 1.893 Total 89558.000 344 Corrected Total 5854.640 343 R. Squared = .895 (Adjusted R Squared = .889) * = Significant at p < 0.05 alpha level 55 UNIVERSITY OF IBADAN LIBRARY Table 4.1 indicates that the main effect was significant on pupils‟ achievement in Mathematics (F2, 325 = 142.473; p < 0.05; partial eta squared = 0.467), which gives an effect size of 46.7 percent. Thus, H01 (i) was not accepted. Consequent upon the observed main effect, Table 4.2 is presented to determine the magnitude of the mean scores of the groups‟ performance. Table 4.2. Estimated marginal mean analysis of the posttest scores of pupils’ achievement in Mathematics by treatment Grand Mean =15.575 Mean Std Error 95% Confidence interval Treatment Lower Upper GEIS 17.417 0.176 17.070 17.764 Bound Bound PEIS 16.400 0.203 16.001 16.799 MLIS 12.909 0.213 12.490 13.327 Table 4.2 shows that, the pupils exposed to GEIS had the highest adjusted posttest mean score of 17.417, followed by pupils exposed to PEIS, with a mean score of 16.400, while pupils exposed to MLIS had the lowest adjusted posttest mean score of 12.909. However, the grand mean was 15.575. The source of the significant difference obtained was determined using Scheffe‟s post-hoc test, as shown in Table 4.3 Table 4.3. Scheffe’s post-hoc pairwise comparison analysis of treatment and pupils’ achievement in Mathematics Treatment N Mean GEIS PEIS MLIS GEIS 116 17.417 * * PEIS 128 16.400 * * MLIS 100 12.909 * * *Pairs of group significantly different at p < 0.05. Table 4.3 shows that pupils exposed to GEIS performed significantly better, with a mean score of 17.417, than pupils exposed to PEIS, with a mean score of 16.400. Also pupils exposed to PEIS were better than those exposed to MLIS, with a mean score of 12.909. This further indicates that the significant difference shown by the ANCOVA analysis was as a result of the difference between GEIS and PEIS, GEIS and MLIS as well as that of PEIS and MLIS. 4.1.2 H01 (ii): There is no significant main effect of treatment on pupils‟ knowledge of mathematics concepts. 56 UNIVERSITY OF IBADAN LIBRARY Table 4.4. 3 x 3 x 2 Analysis of Covariance (ANCOVA) of posttest scores of pupils’ knowledge of mathematics concepts with treatment, verbal ability and gender using pre-test scores as covariates Source of variation Type III Df Mean F Sig. Partial Sum of Square Eta Squares squared Corrected Model 3829.104 18 212.728 94.824 0.000 0.840 Intercept 488.881 1 488.920 217.920 0.000 0.401 Pretest scores 933.110 1 933.110 415.937 0.000 0.561 Treatment 383.947 2 181.974 81.115 0.000* 0.333 Verbal ability 25.921 2 12.961 5.777 0.003* 0.034 Gender 0.980 1 0.980 0.437 0.509 0.001 Treatment*Verbal ability 24.505 4 6.126 2.731 0.029* 0.033 Treatment*Gender 11.271 2 5.636 2.512 0.083 0.015 Verbal ability*Gender 2.766 2 1.383 0.616 0.540 0.004 Treatment*Verbal ability*Gender 6.407 4 1.602 0.714 0.583 0.009 Error 729.102 325 2.243 Total 61273.000 344 Corrected Total 4558.206 343 R. Squared = 0.840 (Adjusted R Squared = 0.831); * = Significant at p < 0.05 alpha level Table 4.4 shows that the main effect was significant on pupils‟ knowledge of mathematics concepts (F2, 325 = 81.115; p < 0.05; partial eta squared = 0.333), which gives an effect size of 33.3 percent. Hence, the null hypothesis (H01 (ii)) was not accepted. To find the magnitude of the mean scores of performance of each group, Table 4.5 is presented. 57 UNIVERSITY OF IBADAN LIBRARY Table 4.5. Estimated marginal mean analysis of the posttest scores of pupils’ knowledge of mathematics concepts by treatment Grand Mean = 12.812 Mean Std Error 95% Confidence interval Treatment Lower Upper GEIS 13.439 0.192 13.061 13.817 PEIS 14.429 0.221 B13o.u9n9d4 1B4o.u8n6d3 MLIS 10.567 0.233 10.110 11.025 Table 4.5 shows that pupils exposed to PEIS had the highest adjusted posttest mean score of 14.429, followed by pupils exposed to GEIS, with mean score of 13.439, while pupils exposed to MLIS, had the lowest adjusted mean score of 10.567. However, the grand mean was 12.812. The source of the significant difference obtained was determined using Scheffe‟s post-hoc test, as shown in Table 4.6 Table 4.6. Scheffe’s post-hoc pairwise comparison analysis of treatment and pupils’ knowledge of mathematics concepts Treatment N Mean GEIS PEIS MLIS GEIS 116 13.439 * * PEIS 128 14.429 * * MLIS 100 10.567 * * *Pairs of group significantly different at p < 0.05. Table 4.6 reveals that, pupils exposed to PEIS performed significantly better, with a mean score of 14.429 than pupils exposed to GEIS, with a mean score of 13.439. Also pupils exposed to GEIS, were better than those exposed to MLIS, with a mean score of 10.567. This further shows that the significant difference shown by the ANCOVA analysis was as a result of the difference between GEIS and PEIS, G IS and MLIS as well as that of PEIS and MLIS. This means that the three groups differed in their mean scores on pupils‟ knowledge of mathematics concepts. This further implies that all the possible pairs contributed to the significant effect obtained on pupils‟ knowledge of mathematics concepts. 58 UNIVERSITY OF IBADAN LIBRARY 4.1.3. H01 (iii): There is no significant main effect of treatment on pupils‟ interest in Mathematics Table 4.7. 3 x 3 x 2 Analysis of Covariance (ANCOVA) of posttest scores of pupils’ interest in Mathematics with treatment, verbal ability and gender using pre-test scores as covariates Source of variation Type III Df Mean F Sig. Partial Sum of Square Eta Squares squared Corrected Model 3696.065 18 205.337 124.682 0.000 0.874 Intercept 674.351 1 674.351 409.471 0.000 0.558 Pretest scores 765.782 1 765.782 464.988 0.000 0.589 Treatment 536.894 2 268.447 163.003 0.000* 0.501 Verbal ability 63.636 2 31.818 19.320 0.000* 0.106 Gender 0.639 1 0.639 0.388 0.534 0.001 Treatment*Verbal ability 15.573 4 3.893 2.364 0.053 0.028 Treatment*Gender 2.126 2 1.063 0.646 0.525 0.004 Verbal ability*Gender 5.040 2 2.520 1.530 0.218 0.009 Treatment*Verbal ability*Gender 14.089 4 3.522 2.139 0.076 0.026 Error 535.238 325 1.647 Total 68228.000 344 Corrected Total 4231.302 343 R. Squared = .874 (Adjusted R Squared = .866) * = Significant at p < 0.05 alpha level Table 4.7 indicates that the main effect was significant on pupils‟ interest in Mathematics (F2, 325 = 163.003; p<0.05; partial eta squared = 0.501), which gives an effect size of 50.1 percent. Therefore, the null hypothesis H01 (iii) was not accepted. Consequent upon the observed main effect, estimated marginal mean analysis was used to determine the magnitude of the mean scores of the groups‟ performance, as shown in Table 4.8. 59 UNIVERSITY OF IBADAN LIBRARY Table 4.8. Estimated marginal mean analysis of the posttest scores of pupils’ interest in Mathematics by treatment Grand Mean = 13.512 Mean Std Error 95% Confidence interval Treatment Lower Upper GEIS 14.411 0.167 14.083 14.739 Bound Bound PEIS 15.355 0.189 14.984 15.726 MLIS 10.772 0.197 10.385 11.158 Table 4.8, shows that the pupils exposed to PEIS had the highest adjusted posttest mean score of 15.355, followed by pupils exposed to GEIS, with a mean score of 14.411, while pupils exposed to MLIS, had the lowest adjusted posttest mean score of 10.772. However, the grand mean was 13.512. The source of the significant difference obtained was determined using Scheffe‟s post-hoc test, as shown in Table 4.9 Table 4.9. Scheffe’s post-hoc pairwise comparison analysis of treatment and pupils’ interest in Mathematics Treatment N Mean GEIS PEIS MLIS GEIS 116 14.411 * * PEIS 128 15.355 * * MLIS 100 10.772 * * *Pairs of group significantly different at p < 0.05. Table 4.9 indicates that pupils exposed to PEIS performed significantly better, with a mean score of 15.355, than pupils exposed to GEIS, with a mean score of 14.411. Also pupils exposed to GEIS were better than those exposed to MLIS, with a mean score of 10.772. This further indicates that the significant difference shown by the ANCOVA analysis was as a result of the difference between GEIS and PEIS, GEIS and MLIS as well as that of PEIS and MLIS. This means that the three groups differed in their mean scores on pupils‟ interest in Mathematics. This further implies that all the possible pairs contributed to the significant effect obtained on pupils‟ interest in Mathematics. 4.2.1 H02 (i): There is no significant main effect of verbal ability on pupils‟ achievement in Mathematics. Table 4.1 shows that the main effect was significant on pupils‟ achievement in Mathematics (F2, 325=35.939; p<0.05; partial eta squared = 0.181), which gives an effect size of 18.1 percent. Hence, the null hypothesis (H02 (i)) was not 60 UNIVERSITY OF IBADAN LIBRARY accepted. Consequent upon the observed main effect, estimated marginal mean analysis was used to determine the magnitude of the mean scores of the groups‟ performance, as shown in Table 4.10. Table 4.10. Estimated marginal mean analysis of the posttest scores of pupils’ achievement in Mathematics by verbal ability Grand Mean =15.575 Mean Std Error 95% Confidence interval Verbal Ability Lower Upper Low 13.945 0.188 13.574 14.315 Bound Bound Medium 15.986 0.109 15.771 16.200 High 16.796 0.342 16.124 17.468 Table 4.10 shows that, pupils with high verbal ability had the highest adjusted posttest mean score of 16.796, followed by pupils with medium verbal ability, with a mean score of 15.986, while pupils with low verbal ability had the lowest adjusted posttest mean score of 13.945. However, the grand mean was 15.575. The source of the significant difference obtained was determined, using Scheffe‟s post-hoc test, as shown in Table 4.11 Table 4.11. Scheffe’s post-hoc pairwise comparison analysis of verbal ability and pupils’ achievement in Mathematics Verbal N Mean Low Medium High Ability Low 109 13.945 * * Medium 202 15.986 * * High 33 16.796 * * *Pairs of group significantly different at p < 0.05. Table 4.11 shows that, there was a significant difference on pupils‟ achievement in Mathematics. Pupils with low and medium verbal ability had a significant difference. Again, it was also revealed that a significant difference existed between pupils with low and high verbal ability. Similarly, a significant difference existed between pupils with medium and high verbal ability. This implies that the three groups differed in their mean scores on pupils‟ achievement in Mathematics. In other words, all the possible pairs contributed to the significant main effect obtained on pupils‟ achievement in Mathematics. 4.2.2 H02 (ii): There is no significant main effect of verbal ability on pupils‟ knowledge of mathematics concepts. 61 UNIVERSITY OF IBADAN LIBRARY The result presented in Table 4.4 indicates that the main effect was significant on pupils‟ knowledge of mathematics concepts (F2, 325 = 5.777; p<0.05; partial eta squared = 0.034), which gives an effect size of 3.4 percent. Therefore, the null hypothesis H02 (ii) was not accepted. Consequent upon the observed main effect, estimated marginal mean analysis was used to determine the magnitude of the mean scores of the groups‟ performance, as shown in Table 4.12. Table 4.12. Estimated marginal mean analysis of the posttest scores of pupils’ Knowledge of mathematics concepts by verbal ability Grand Mean =12.812 Mean Std Error 95% Confidence interval Verbal Ability Lower Upper Low 12.057 0.197 11.669 12.445 Bound Bound Medium 12.798 0.116 12.571 13.025 High 13.580 0.373 12.846 14.314 Table 4.12 indicates that, pupils with high verbal ability had the highest adjusted posttest mean score of 13.580, followed by pupils with medium verbal ability, had a mean score of 12.798, while pupils with low verbal ability, had the lowest adjusted posttest mean score of 12.057. However, the grand mean was 12.812. The source of the significant difference obtained was determined using Scheffe‟s post-hoc test, as shown in Table 4.13 Table 4.13. Scheffe’s post-hoc pairwise comparison analysis of verbal ability and pupils’ knowledge of mathematics concepts Verbal Ability N Mean Low Medium High Low 109 12.057 * * Medium 202 12.798 * * High 33 13.580 * * *Pairs of group significantly different at p < 0.05. On pupils‟ knowledge of mathematics concepts, Table 4.13 shows that, pupils with low and medium verbal ability had a significant difference. A significant difference also existed between pupils with low and high verbal ability. Similarly, there was a significant difference between pupils with medium verbal ability and those with high verbal ability. This means that the three groups differed in their mean scores on pupils‟ knowledge of mathematics concepts. Thus, all the possible pairs therefore contributed to the significant main effect obtained on pupils‟ knowledge of mathematics concepts. 62 UNIVERSITY OF IBADAN LIBRARY 4.2.3 H02 (iii): There is no significant main effect of verbal ability on pupils‟ interest in Mathematics. Table 4.7 reveals that the main effect was significant on pupils‟ interest in Mathematics (F2, 325 = 19.320; p<0.05; partial eta squared = 0.106), which gives an effect size of 10.6 percent. Hence, the null hypothesis (H02 (iii) was not accepted. Estimated marginal mean analysis was used to determine the magnitude of the mean scores of the groups‟ performance, as shown in Table 4.14. Table 4.14. Estimated marginal mean analysis of the posttest scores of pupils’ interest in Mathematics by verbal ability Grand Mean=13.512 Mean Std Error 95% Confidence interval =V1e2rb.8a1l 2A 1b2il.i8ty1 2 Lower Upper Low 12.524 0.159 12.211 12.837 Bound Bound Medium 13.759 0.097 13.568 13.950 High 14.255 0.312 13.640 14.870 Table 4.14 shows that pupils with high verbal ability had the highest adjusted posttest mean score of 14.255, followed by pupils with medium verbal ability, with a mean score of 13.759, while pupils with low verbal ability, had the lowest adjusted posttest mean score of 12.524. However, the grand mean was 13.512. The source of the significant difference obtained was determined using Scheffe‟s post-hoc test, as shown in Table 4.15 Table 4.15. Scheffe’s post-hoc pairwise comparison analysis of verbal ability and pupils’ interest in Mathematics Verbal Ability N Mean Low Medium High Low 109 12.524 * * Medium 202 13.759 * * High 33 14.255 * * *Pairs of group significantly different at p < 0.05. Table 4.15 reveals that pupils with high verbal ability performed significantly better, with a mean score of 14.255 than pupils with medium verbal ability, with a mean score of 13.759. Also pupils with medium verbal ability were better, than those with low verbal ability, with a mean score of 12.524. This further shows that, the significant difference revealed by the ANCOVA analysis was as a result of the differences between high and medium verbal ability, high and low verbal ability, as well as that of medium and low verbal ability. This means that the three groups differed in their mean scores on pupils‟ interest in Mathematics. This 63 UNIVERSITY OF IBADAN LIBRARY further implies that all the possible pairs contributed to the significant effect obtained on pupils‟ interest in Mathematics. 4.3.1 H03 (i): There is no significant main effect of gender on pupils‟ achievement in Mathematics. The result presented in Table 4.1 reveals that the main effect was not significant on pupils‟ achievement in Mathematics (F1, 325 = 0.844; p>0.05; partial eta squared = 0.003). This gives an effect size of 0.3 percent. Hence, the null hypothesis (H03 (i)) was retained. This implies that gender had no main effect on the pupils‟ achievement in Mathematics. Despite the fact that gender had no main effect on the pupils‟ achievement in Mathematics, there is need to determine the magnitude of the mean scores of the groups‟ performance, as shown in Table 4.16. Table 4.16. Estimated marginal mean analysis of the posttest scores of pupils’ achievement in Mathematics by gender Grand Mean = 15.575 Mean Std Error 95% Confidence interval Gender Lower Upper Male 15.681 0.194 15.299 16.062 Bound Bound Female 15.470 0.126 15.222 15.719 The result presented in Table 4.16 shows that the male pupils had a posttest mean score of 15.681, higher than the female pupils, with posttest mean score of 15.470. 4.3.2 H03 (ii): There is no significant main effect of gender on pupils‟ knowledge of mathematics concepts. The result presented in Table 4.4 indicates that the main effect was not significant on pupils‟ knowledge of mathematics concepts (F1, 325 = 0.437; p>0.05; partial eta squared = 0.001), which gives an effect size of 0.1 percent. Therefore, the null hypothesis (H03 (ii)) was retained. This simply means that gender had no main effect on pupils‟ knowledge of mathematics concepts. Despite the fact that gender had no main effect on the pupils‟ knowledge of mathematics concepts, there is need to determine the magnitude of the mean scores of the groups‟ performance, as shown in Table 4.17. 64 UNIVERSITY OF IBADAN LIBRARY Table 4.17. Estimated marginal mean analysis of the posttest scores of pupils’ knowledge of mathematics concepts by gender Grand Mean = 12.812 Mean Std Error 95% Confidence interval Gender Lower Upper Male 12.729 0.213 12.310 13.147 Bound Bound Female 12.895 0.137 12.624 13.165 The result presented in Table 4.17 shows that the male pupils had a posttest mean score of 12.729, less than the female pupils, with a posttest mean score of 12.895. 4.3.3 H03 (iii): There is no significant main effect of gender on pupils‟ interest in Mathematics. The result presented in Table 4.7 reveals that the main effect was not significant on pupils‟ interest in Mathematics (F1, 325 = 0.388; p>0.05; partial eta squared = 0.001). This gives an effect size of 0.1 percent. Hence, the null hypothesis (H03 (iii)) was retained. This implies that gender did not have main effect on the pupils‟ interest in Mathematics. Despite the fact that gender had no main effect on the pupils‟ interest in Mathematics, there is need to determine the magnitude of the mean scores of the groups‟ performance, as indicated in Table 4.18. Table 4.18. Estimated marginal mean analysis of the posttest scores of pupils’ interest in Mathematics by gender Grand Mean = 13.512 Mean Std Error 95% Confidence interval Gender Lower Upper Male 13.446 0.181 13.090 13.802 Female 13.579 0.118 1B3o.u3n4d7 B13o.u8n1d1 The result presented in Table 4.18 indicates that the male pupils had a posttest mean score of 13.446, less than the female pupils with a posttest mean score of 13.579. 4.4.1 H04 (i): There is no significant interaction effect of treatment and verbal ability on pupils‟ achievement in Mathematics. The result presented in Table 4.1 indicates that the interaction effect was not significant on pupils‟ achievement in Mathematics (F4, 325 = 0.721; p>0.05; partial eta squared = 0.009). This gives an effect size of 0.9 percent. Hence, the null 65 UNIVERSITY OF IBADAN LIBRARY hypothesis (H04 (i)) was upheld. This implies that treatment and verbal ability did not have interaction effect on pupils‟ achievement in Mathematics. 4.4.2 H04 (ii): There is no significant interaction effect of treatment and verbal ability on pupils‟ knowledge of mathematics concepts. The result presented in Table 4.4 indicates that the interaction effect was significant on pupils‟ knowledge of mathematics concepts (F4, 325 = 2.731; p < 0.05 partial eta squared = 0.033). This gives an effect size of 3.3 percent. Therefore, the null hypothesis (H04 (ii) was not accepted. This implies that treatment and verbal ability had interaction effect on pupils‟ knowledge of mathematics concepts. 4.4.3 H04 (iii): There is no significant interaction effect of treatment and verbal ability on pupils‟ interest in Mathematics. The result presented in Table 4.7 reveals that the interaction effect was not significant on pupils‟ interest in Mathematics (F4, 325 = 2.364; p > 0.05 partial eta squared = 0.028). This gives an effect size of 2.8 percent. Hence, the null hypothesis (H04 (iii)) was retained. This implies that treatment and verbal ability had no interaction effect on the pupils‟ interest in Mathematics 4.5.1 H05 (i): There is no significant interaction effect of treatment and gender on pupils‟ achievement in Mathematics. The result presented in Table 4.1 indicates that the interaction effect was not significant on pupils‟ achievement in Mathematics (F2, 325 = 0.439; p > 0.05; partial eta squared = 0.003). This gives an effect size of 0.3 percent. Therefore, the null hypothesis (H05 (i)) was retained. This implies that treatment and gender had no interaction effect on the pupils‟ achievement in Mathematics. 4.5.2 H05 (ii): There is no significant interaction effect of treatment and gender on pupils‟ knowledge of mathematics concepts. Table 4.4 shows that the interaction effect was not significant on pupils‟ knowledge of mathematics concepts (F2, 325 = 2.512; p > 0.05; partial eta squared = 0.015). This gives an effect size of 1.5 percent. Hence, the null hypothesis (H05 (ii)) was retained. The implication is that treatment and gender had no interaction effect on the pupils‟ knowledge of mathematics concepts. 66 UNIVERSITY OF IBADAN LIBRARY 4.5.3 H05 (iii): There is no significant interaction effect of treatment and gender on pupils‟ interest in Mathematics. The result presented in Table 4.7 reveals that the interaction effect was not significant on pupils‟ interest in Mathematics (F2, 325 = 0.646; p > 0.05; partial eta squared = 0.004). This gives an effect size of 0.4 percent. Therefore, the null hypothesis (H05 (iii)) was retained. This implies that treatment and gender had no interaction effect on the pupils‟ interest in Mathematics. 4.6.1 H06 (i): There is no significant interaction effect of verbal ability and gender on pupils‟ achievement in Mathematics. The result in Table 4.1 shows that the interaction effect was not significant on pupils‟ achievement in Mathematics (F2, 325 = 1.397; p > 0.05; partial eta squared = 0.009). This gives an effect size of 0.9 percent. Therefore, the null hypothesis (H06 (i)) was retained. This implies that verbal ability and gender did not have any interaction effect on the pupils‟ achievement in Mathematics. 4.6.2 H06 (ii): There is no significant interaction effect of verbal ability and gender on pupils‟ knowledge of mathematics concepts. The result presented in Table 4.4 indicates that the interaction effect was not significant on pupils‟ knowledge of mathematics concepts (F2, 325 = 0.616; p > 0.05; partial eta squared = 0.004). This gives an effect size of 0.4 percent. Therefore, the null hypothesis (H06 (ii)) was retained. This implies that verbal ability and gender had no interaction effect on the pupils‟ knowledge of mathematics concepts. 4.6.3 H06 (iii): There is no significant interaction effect of verbal ability and gender on pupils‟ interest in Mathematics. The result presented in Table 4.7 reveals that the interaction effect was not significant on pupils‟ interest in Mathematics (F2, 325 = 1.530; p > 0.05; partial eta squared = 0.009). This also gives an effect size of 0.9 percent. Therefore, the null hypothesis (H06 (iii)) was retained. This implies that verbal ability and gender had no interaction effect on the pupils‟ interest in Mathematics. 4.7.1 H07 (i): There is no significant interaction effect of treatment, verbal ability and gender on pupils‟ achievement in Mathematics. 67 UNIVERSITY OF IBADAN LIBRARY Table 4.1 shows that the interaction effect was not significant on pupils‟ achievement in Mathematics (F4, 325=1.392; p>0.05; partial eta squared = 0.017). This result gives an effect size of 1.7 percent. Hence, the null hypothesis (H07 (i)) was retained. This implies that treatment, verbal ability and gender had no interaction effect on the pupils‟ achievement in Mathematics. 4.7.2 H07 (ii): There is no significant interaction effect of treatment, verbal ability and gender on pupils‟ knowledge of mathematics concepts. The result presented in Table 4.4 indicates that the interaction effect was not significant on pupils‟ knowledge of mathematics concepts (F4, 325 = 0.714; p > 0.05; partial eta squared = 0.009). This gives an effect size of 0.9 percent. Therefore, the null hypothesis (H07 (ii)) was retained. This implies that treatment, verbal ability and gender had no interaction effect on the pupils‟ knowledge of mathematics concepts. 4.7.3 H07 (iii): There is no significant interaction effect of treatment, verbal ability and gender on pupils‟ interest in Mathematics. Table 4.7 reveals that the interaction effect was not significant on pupils‟ interest in Mathematics (F4, 325 = 2.139; p > 0.05; partial eta squared = 0.026). This gives an effect size of 2.6 percent. Hence, the null hypothesis (H07 (iii)) was upheld. This implies that treatment, verbal ability and gender had no interaction effect on pupils‟ interest in Mathematics. 4.2 Summary of findings (1i). There was a significant main effect of treatment on pupils‟ achievement in Mathematics. Pupils exposed to GEIS were significantly better than those exposed to both PEIS and MLIS in their achievement in Mathematics. The result showed that 46.7 percent of the total variance of pupils‟ achievement in Mathematics was attributable to the influence of treatment. (1ii). There was a significant main effect of treatment on pupils‟ knowledge of mathematics concepts. Pupils exposed to PEIS were significantly better than those exposed to both GEIS and MLIS in their knowledge of mathematics concepts. The result showed that 33.3 percent of the total variance of pupils‟ 68 UNIVERSITY OF IBADAN LIBRARY knowledge of mathematics concepts was attributable to the influence of treatment. (1iii). There was a significant main effect of treatment on pupils‟ interest in Mathematics. Pupils exposed to PEIS were significantly better than those exposed to both GEIS and MLIS in their interest in Mathematics. The result indicates that 50.1 percent of the total variance of pupils‟ interest in Mathematics was attributable to the influence of treatment. (2i). There was a significant main effect of verbal ability on pupils‟ achievement in Mathematics. Pupils with high verbal ability were significantly better than those with medium and low verbal ability respectively in their achievement in Mathematics. The result showed that 18.1 percent of the total variance of pupils‟ achievement in Mathematics was attributable to the influence of verbal ability. (2ii). There was a significant main effect of verbal ability on pupils‟ knowledge of mathematics concepts. Pupils with high verbal ability were significantly better than those with both medium and low verbal ability in their knowledge of mathematics concepts. The result also showed that 3.4 percent of the total variance of pupils‟ knowledge of mathematics concepts was attributable to the influence of verbal ability. (2iii). There was a significant main effect of verbal ability on pupils‟ interest in Mathematics. Pupils with high verbal ability were significantly better than those with both medium and low verbal ability in their interest in Mathematics. The result also revealed that 10.6 percent of the total variance of pupils‟ interest in Mathematics was attributable to the influence of verbal ability. (3i). There was no significant main effect of gender on pupils‟ achievement in Mathematics. (3ii). There was no significant main effect of gender on pupils‟ knowledge of mathematics concepts. (3iii). There was no significant main effect of gender on pupils‟ interest in Mathematics. (4i). There was no significant interaction effect of treatment and verbal ability on pupils‟ achievement in Mathematics. 69 UNIVERSITY OF IBADAN LIBRARY (4ii). There was a significant interaction effect of treatment and verbal ability on pupils‟ knowledge of mathematics concepts. The result also revealed that 3.3 percent of the total variance of pupils‟ knowledge of mathematics concepts was attributable to the combined influence of treatment and verbal ability. (4iii). There was no significant interaction effect of treatment and verbal ability on pupils‟ interest in Mathematics. (5i). There was no significant interaction effect of treatment and gender on pupils‟ achievement in Mathematics. (5ii). There was no significant interaction effect of treatment and gender on pupils‟ knowledge of mathematics concepts. (5iii). There was no significant interaction effect of treatment and gender on pupils‟ interest in Mathematics. (6i). There was no significant interaction effect of verbal ability and gender on pupils‟ achievement in Mathematics. (6ii). There was no significant interaction effect of verbal ability and gender on pupils‟ knowledge of mathematics concepts. (6iii). There was no significant interaction effect of verbal ability and gender on pupils‟ interest in Mathematics. (7i). There was no significant interaction effect of treatment, verbal ability and gender on pupils‟ achievement in Mathematics. (7ii). There was no significant interaction effect of treatment, verbal ability and gender on pupils‟ knowledge of mathematics concepts. (7iii). There was no significant interaction effect of treatment, verbal ability and gender on pupils‟ interest in Mathematics. 70 UNIVERSITY OF IBADAN LIBRARY CHAPTER FIVE DISCUSSION, CONCLUSION AND RECOMMENDAITONS This study determines the effects of game and poem-enhanced instructional strategies on pupils‟ learning outcomes in Mathematics. The effect of verbal ability and gender as moderator variables on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics was also examined. Seven hypotheses were tested at 0.05 level of significance. The discussion of result is presented in this chapter. 5.0 Discussion 5.1 Effect of treatment on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics The findings from the study revealed that there was a significant main effect of treatment on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. Pupils exposed to Game-Enhanced Instructional Strategy (GEIS) obtained the highest mean score, followed by pupils exposed to Poem- Enhanced Instructional Strategy (PEIS), while the pupils exposed to Modified Lecture Instructional Strategy (MLIS) had the least mean achievement score. This shows that the GEIS and PEIS were found to have facilitated achievement in Mathematics more than the MLIS. The findings of the study are consistent with many previous studies on the effectiveness of the use of game in mathematics instruction (Aremu, 1998; Ezeamenyi in Udegbe, 2009; Dotun, 2005; Onwuka, Iweka and Moseri, 2010; Okigbo and Okeke 2011), that students who are exposed to game instructional strategy achieved significantly better in Mathematics than the lecture instructional strategy. On the use of PEIS, this study agrees with the views of Pugalee (2005), Bahls (2009) and Albool (2012) that poems and poetic aspects of learning Mathematics increase achievement in Mathematics. The superiority of the GEIS over the PEIS in achievement could be as a result of the fact that pupils exposed to GEIS had the opportunity to solve whole 71 UNIVERSITY OF IBADAN LIBRARY mathematics problems while pupils in PEIS solved a part or step in mathematics problems because it was a role-play. Again the writing activity of PEIS also failed, which might have enhanced pupils‟ achievement in Mathematics. Also, that GEIS had advantage over MLIS, with an improved mean score, could be due to the fact that pupils exposed to GEIS were all actively involved in solving series of mathematics problems through games. This finding confirms the assertion of Abubakar and Bawa (2006) and Kankia (2008) that the use of game makes students to be actively involved in the daily lesson and academically rewarding. The pupils exposed to PEIS also had an edge over the MLIS group. This was because the pupils in PEIS were exposed to reading or reciting the poems, dramatizing or role- play and writing, which made them to be actively involved in parts of the lesson. This agrees with the findings established by the National Institute for Literacy (2007), that reading and writing skills improves students‟ capacity to learn. Urquhart (2009) and Burns (2004) aver that writing enhances the meta-cognitive aspect of learning Mathematics, problem-solving, and invention, increased reading and improved content understanding. This also confirms the statement of Owen (2010) and St.Cyr (2008) that memorizing poetry increases a child‟s cognitive ability, ability to reason, think, imagine and helps children‟s memory to learn, grow and expand in understanding and knowledge. However, the pupils exposed to MLIS were not exposed to group work, which promotes pupils‟ interaction and did not demonstrate any skill. This explains why their performance was not as good as the other groups (Majanga, Nasongo, and Sylvia, 2011). The findings also revealed that pupils exposed to GEIS and PEIS had a significant difference in knowledge of mathematics concepts. Also GEIS and MLIS, then PEIS and MLIS had significant differences. This finding agrees with the assertion of Aremu (1998), Agwagah (2001) and other studies, that the use of game enhances greater understanding of mathematics concepts. Also, the use of poems in developing pupils‟ knowledge of mathematics concepts confirms the assertion of Bahls (2009), that mastery of mathematics concepts often involves creativity more readily expected of a poet than a scientist. With poetical metaphors, students become more aware of mathematical metaphors and gain deeper understanding of mathematics concepts those metaphors describe. The advantage PEIS had over GEIS could be as a result of the opportunity pupils of the PEIS group had, that is repeatedly reciting the poems beyond the 72 UNIVERSITY OF IBADAN LIBRARY classroom, which helped them to examine and re-examine mathematical ideas (Bahls, 2009). This is in conformity with the claim of St. Cyr (2008) and LeFebvre (2004) that the repetitive nature of poems helps children‟s memory to learn, expand and build listening skills. Furthermore, the findings also showed that pupils exposed to PEIS had significantly better mean interest score than pupils exposed to MLIS. Also pupils exposed to GEIS were better than those exposed to MLIS. Similarly, there was a significant difference between those exposed to GEIS and PEIS (see Table 4.9). This implies that the significant difference shown by the ANCOVA analysis was as a result of the difference between GEIS and PEIS, GEIS and MLIS as well as that of PEIS and MLIS. These findings agree with the findings of Ezeamenyi in Udegbe (2009) that students taught with game achieved more and generate more interest than those taught with the lecture strategy. It also supports the findings of Okigbo and Okeke (2011), that game was effective in improving students‟ interest in Mathematics. Also pupils exposed to PEIS had better mean interest scores than those exposed to GEIS and MLIS. This supports the assertion of St Cyr (2008), that children are natural lovers of poetry. Also, Mazzuco (1994) noted that children have a natural affinity for poetry. Ekine (2010), found a significant main effect of treatment on pupils‟ interest in primary science. All these results show that learner friendly strategies should be adopted in the teaching and learning of science, mathematics and technology (Aremu, 2008). These factors must have accounted for the better interest mean scores of GEIS and PEIS over MLIS. This confirms the assertions of some mathematics educators that the lecture instructional strategy diminishes students‟ interest in Mathematics, does not sustain the development of pupils‟ interest in Mathematics and poorly develops learners‟ cognitive, psychomotor and affective structures (Peng, 2002; Agwagah, 2004; Kankia, 2008). 5.2 Effect of verbal ability on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics The result showed that pupils with high verbal ability obtained the highest mean achievement score, followed by the medium verbal ability group, while pupils with low verbal ability obtained the lowest mean achievement score. The study confirms the findings of Idogo (2011) that the high verbal ability group 73 UNIVERSITY OF IBADAN LIBRARY performed better than the average and low verbal ability pupils in reading and comprehension skills. Also, Awofala et al. (2011) lend credence to this finding that the high verbal ability students perform significantly better than the low verbal ability students in mathematical word problems. Hall in Binda (2006) found a positive correlation between students‟ verbal ability and Mathematics achievement, stressing that, when students are strong in verbal abilities, their understanding of Mathematics will be enhanced. Also, Iti (2005) found significant difference of verbal ability in the achievement of pupils in primary science. However, Oladunjoye (2003) and Adeosun (2004) assert that learners‟ verbal ability does not have any effect on learners‟ academic achievement in their various studies. This study also showed that pupils of high verbal ability obtained the highest mean score, followed by medium verbal ability pupils, while the low verbal ability pupils obtained the lowest mean score in knowledge of mathematics concepts. Mathematics itself is a language (Amoo and Rahman, 2004; Akinsola, 2005) and understanding this language needs some level of verbal ability. Binda (2006) found a weak but positive correlation between the language of Mathematics and achievement in Mathematics. This confirms the findings of this study, that verbal ability significantly affects pupils‟ knowledge of mathematics concepts. Thus, pupils‟ level of verbal ability may enhance or impede a better performance in understanding the language of mathematics, which this study has established. This further justifies the findings of Awofala et al. (2011), that pupils with high verbal ability obtained the highest mean achievement score in worded mathematics problems, which depends on the understanding of the language of mathematics that is knowledge of mathematics concepts. The findings of the study revealed that the high verbal ability group obtained the highest mean interest score, followed by the medium verbal ability pupils, while the low verbal ability group obtained the lowest mean interest score. This result contradicts Iti (2005), who found no significant difference of verbal ability on primary 3 pupils‟ interest in science. It also contends with the findings of Komolafe (2010) that there is no significant effect of verbal ability on primary 4 and primary 5 pupils‟ attitude in composition writing. This study found a significant effect of verbal ability on primary 6 pupils‟ interest in Mathematics. The difference in the results of these studies could be the nature of the instruments used for data collection. The interest and attitude scales of Iti (2005) and Komolafe 74 UNIVERSITY OF IBADAN LIBRARY (2010) are on a four-point adapted Likert scale which according to Akinbote in Ekine (2010), note that the yes/no response mode, has been found to be more appropriate and better understood by the primary school pupils. Iti (2005) attributed the non-significant effect of verbal ability on pupils‟ interest in primary science to the method of data collection and immaturity of the pupils to appreciate what is of interest to them. Komolafe (2010), citing Akinbote (1999), gave a similar report. However, the findings of this study are in conformity with those of Yoloye (2004), who notes that when students‟ level of participation in an instruction increases, students‟ interest is aroused; consequently their achievement also increases. Lazar (2004) asserts that verbal fluency of pupils determines easy understanding, comprehension and recall. The above reports are practical, especially in PEIS, where pupils boldly read, explain, write and role-play the actions in the poems. 5.3 Effect of gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics. The findings of this study showed that there was no significant difference in the mean achievement scores of male and female pupils in Mathematics. This finding supports the report of Bawa and Abubakar (2008), who found no significant difference in the achievement of male and female students, taught linear equations using weighing balance approach. It also lend credence to the report of Ebisine (2010) that both male and female students had no significant difference in the level of difficulties encountered in understanding non-technical words in multiple choice mathematics tests. Contrary reports were made by Ogunkunle (2007), Onasanya (2008) and Shafi and Areelu (2010) that males achieved significantly better than females in Mathematics. However, Ogunkunle (2007) concludes that the result does not show any gender superiority. Also Muthukrishna (2010) and Eniayeju (2010) reported that the females achieved significantly better than the male students in Mathematics. The result further showed that there was no significant main effect of gender on pupils‟ knowledge of mathematics concepts. The result of this study supports Inekwe (1997) and Galadima and Yusha (2007), who did not find significant differences of gender on pupils‟ knowledge of mathematics concepts. 75 UNIVERSITY OF IBADAN LIBRARY Both male and female students performed poorly in the test administered on mathematics concepts, principles, terms and symbols. The study also revealed no significant effect of gender on pupils‟ interest in Mathematics. The results of this study support the findings of Okigbo and Okeke (2011), who found no significant difference in the mean scores of males and females, using game and analogy, on the interest of students in Mathematics. It also supports Imoko and Agwagah (2006), that concepts mapping technique enhanced male and female students‟ interest in trigonometry. Iti (2005) also found no significant main effect of gender on pupils‟ interest in primary science. However, a contradicting finding was reported by Ekine (2010), that female pupils obtained a higher mean interest score in primary science than their male counterparts. 5.4 Interaction effect of treatment and verbal ability on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics The study showed that the interaction effect of treatment and verbal ability was not significant on pupils‟ achievement in and interest in Mathematics. This implies that no particular treatment mode favoured one verbal ability group more than the other; neither did any of the instructional strategies facilitated learning more than the other. The result supports the assertion of Wilkinson and Ortiz (2000) and Komolafe (2010) that treatment of a group of learners and their verbal ability do not have anything to do with achievement of the learners in and attitude in language learning. This, however, negates the findings of Iti (2005) and Awofala et al. (2011), who used two levels of verbal ability in primary science and mathematical word problems on achievement, respectively. The study also showed that the interaction effect of treatment and verbal ability was found significant on pupils‟ knowledge of mathematics concepts. Therefore, the teacher must take into consideration the treatment he/she gives to the pupils along with their verbal ability levels in order for all to improve their performance equally, since different verbal ability pupils are in the same class. 76 UNIVERSITY OF IBADAN LIBRARY 5.5 Interaction effect of treatment and gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics The results of the study showed that there was no significant interaction effect of treatment and gender on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. This implies that treatment is gender insensitive; in other words, the effects of treatment on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics does not vary from male to female. This result lends credence to the findings of Aremu (1998), Olagunju (2001), Imoko and Agwagah (2006), Ekine (2010) and Okigbo and Okeke (2011). It, therefore, follows that teachers of Mathematics should apply games and poems to enhance mathematics instruction irrespective of the pupils‟ gender in order to improve their achievement, knowledge of mathematics concepts and interest in Mathematics. 5.6 Interaction effect of verbal ability and gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics The findings of the study revealed no significant interaction effect of verbal ability and gender on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. These findings agree with those of Adeosun (2004), Iti (2005) and Komolafe (2010), who found no significant interaction effect of verbal ability and gender on the dependent variables. The result, suggests that verbal ability and gender do not interact to affect pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. Therefore, teachers should realize that irrespective of the level of pupils‟ verbal ability and their gender, the learners are teachable and their performance can improve in Mathematics. 5.7 Interaction effect of treatment, verbal ability and gender on pupils’ achievement, knowledge of mathematics concepts and interest in Mathematics The results of the study showed that there was no significant interaction effect of treatment, verbal ability and gender on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. The results support those of Olowoyaiye (2004) and Komolafe (2010) on achievement measure. This result is also consistent with the findings of Iti (2005) and Awofala et al. (2011), that 77 UNIVERSITY OF IBADAN LIBRARY treatment, verbal ability and gender/cognitive style have no significant interaction effect on primary science and mathematics, respectively. The result implies that pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics do not vary according to high verbal ability male and female, medium verbal ability male and female and low verbal ability male and female. That is, games and poems could be used to improve pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics irrespective of their verbal ability and gender. 5.8 Educational implications of the study The study has the following implications for classroom practices. The findings in this study revealed that the use of game-enhanced instructional strategy is more effective in improving the achievement of pupils in mathematics at the primary school level. The implication of this to classroom teaching is that the achievement of pupils in primary mathematics will be enhanced with the introduction of game-enhanced instructional strategy in the teaching and learning process. The use of poem-enhanced instructional strategy is more effective in improving pupils‟ knowledge of mathematics concepts and interest in Mathematics. This implies that, if teachers are encouraged to create and use poems in the mathematics classroom, it will enhance pupils‟ understanding and recall of mathematics concepts readily and also improve their interest in mathematics. The significant verbal ability on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics is worthy of note as the high verbal ability pupils had higher mean score in all the variables of study. The implication of this to classroom teaching is that the medium and low verbal ability pupils‟ are at disadvantage and so appropriate measures be taken to enhance these two levels of verbal abilities of pupils. One way is to engage all public primary school pupils from primary one to primary six in the verbal reasoning exercise, which some of the schools in this study area are doing. A non-significant main effect of gender on pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics was observed. The implication is that boys and girls can learn mathematics without much difference at the primary school level. It therefore means that both boys and girls could be given 78 UNIVERSITY OF IBADAN LIBRARY the same opportunity in the classroom and exposed to the same activities like responding to questions without fear and intimidation. It then implies that game and poem-enhanced instructional strategies are good for this purpose. 5.9 Conclusion On the basis of the findings in this study, it could be concluded that: Game-enhanced instructional strategy is most effective in improving pupils‟ achievement in Mathematics, while poem-enhanced instructional strategy is most effective in improving pupils‟ knowledge of mathematics concepts and interest in Mathematics. Therefore, GEIS and PEIS are better activities to improve pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics than the modified lecture instructional strategy. Pupils‟ verbal ability has a significant effect on pupils‟ achievement, knowledge of mathematics concepts and interest in mathematics. Thus, pupils‟ verbal ability has a significant role to play in learning Mathematics. Gender difference in achievement, knowledge of mathematics concepts and interest in Mathematics was not significant. Thus, females can perform as good as the males in mathematics. Therefore, teachers should give equal attention to the two groups while teaching mathematics. 5.10 Recommendations Based on the findings of this study, the following recommendations are made: Mathematics teachers should use games and poems to enhance pupils‟ achievement, knowledge of mathematics concepts and interest in Mathematics. Teachers of Mathematics should give special attention to the use of poems to enhance pupils‟ knowledge of mathematics concepts and interest in Mathematics. Teachers should find a means of enhancing the verbal ability of the pupils by engaging all public primary school pupils in the verbal reasoning exercise taught in schools. Another way is to use activities like poems, where every child is involved in reading, writing, verbal communication with the whole class and teachers. Teachers should give both males and females‟ equal opportunity to ask and respond to questions without fear and intimidation in the classroom. This will 79 UNIVERSITY OF IBADAN LIBRARY create conducive learning environment for both boys and girls and also enhance their performance in mathematics. The National Mathematical Centre (NMC) and the state government should embark on in-service training for Mathematics teachers to equip them with new skills, such as the use of games and poems needed for effective teaching. Nigeria Educational Research and Development Council (NERDC) should emphasize that teachers should embrace the use of innovative strategies, like the use of games and poems while implementing the Mathematics curriculum. Games and poems should be included in the curriculum as activities to enhance mathematics instruction. Authors of mathematics text books should write books on mathematical poems as they have done on mathematical games for easy access and use. 5.11 Limitations of the study There were many factors that constituted one impediment or the other to this study. Some of them are mentioned below. It was not possible to go round all the public primary schools in Bayelsa State to carry out the investigation; only 2 local government areas out of 8 were used in the study. Within the local government areas, only 12 schools were used and only primary 6 pupils were used. This militated against the generalizability of the results of the study. On the moderating variables, only verbal ability and gender were considered among other variables. All these may impose a limitation on the extent to which the results of this study could be generalized. The duration of the experiment was another major constraint. The period of 8 weeks for treatment may not be adequate for a comprehensive study. Therefore, it imposed a limitation on generalization of results. Also, not all the pupils in the classes could read and write. Thus, the writing activity of the pupils of the poem-enhanced instructional strategy failed because most pupils could not write their poems meaningfully, and as poets. This must have made the game-enhanced instructional strategy have an edge over the poem- enhanced instructional strategy in achievement test. 80 UNIVERSITY OF IBADAN LIBRARY 5.12 Suggestions for further study In view of the fact that this study was carried out using only public primary schools, further studies could be done using private schools. The use of only public schools for the study was done to ensure relatively uniform standard of schools and pupils in the conduct of the research. The use of games and poems to enhance mathematics instruction can further be replicated in other local government areas of the state and any state of the federation. The study can also be carried out at the secondary school level since the writing activity of the poem-enhanced instructional strategy failed at the primary school level. This study can also be further investigated with other mathematics concepts not used in this study. 81 UNIVERSITY OF IBADAN LIBRARY REFERENCES AAAS. 1990. 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A lead paper presented at the 34th annual national conference of the mathematical association of Nigeria (MAN). Ukpebor, N.J. 2006. The use of information and communication technology as instructional material in school mathematics: implication for secondary schools. ABACUS: Journal of mathematical association of Nigeria 31.1: 80-86. Urquhart, V. 2009. Using writing in mathematics to deepen student learning. Retrieved Oct. 5, 2011, from http://www.mcrel.org/pdf/mathematics/0121tg_writing_in_mathematics.pdf Wechsler, D. 1974. The Wechsler intelligence scale for children-revised. New York: psychological corporation. 96 UNIVERSITY OF IBADAN LIBRARY West African Examination Council (WAEC). 2001. West African Secondary School Certificate Examination May/June 1998/2002: Nigeria statistics of entries and results: Lagos. West African Examination Council (WAEC). 2005. Chief examiners‟ report of West African Examination Council. West African Examination Council (WAEC). 2009. Chief examiners‟ report in senior secondary certificate examinations in mathematics. Yoloye, T. W. 2004. That we may learn better. Inaugural lecture, University of Ibadan Wilkinson, C. Y. and Ortiz, A. 2000. Test review: the bilingual verbal abilities tests (BVAT). Communique, 28, 2-3. Retrieved April 7, 2002, from http:/www.nku.edu/-walkerst/ceds.htm Wilmot, E. M. 2001. Gender differences in mathematics achievement in primary schools in Ghana. Retrieved June 2, 2012 from www.ajol.info/index.php/mc/article/view/21479 Zazkis, R. and Lijedahl, P. 2009. Teaching mathematics as storytelling. Retrieved Dec. 19, 2010 from http://www.sensepublishers.com/catalog/files/978908 7907358PR. pdf 97 UNIVERSITY OF IBADAN LIBRARY APPENDICES Appendix 1 PUPILS’ MATHEMATICS ACHIEVEMENT TEST (PMAT) Instruction: Answer all the questions. Use pencil to tick the correct option on the answer sheet provided. Do not write on the question paper. Time Allowed: 1hour 4 9 1. Arrange the following fractions in descending order. ¾ , /5, ½ , /10. 9 4 9 4 4 9 (a) ¾, ½, /10, /5 (b) /10, /5, ¾, ½, (c) ½, ¾, /5, /10 4 4 (d) /5, ½ , ¾, /5 2 3 2. Calculate the value of 5 /3 – 1½ + 3 /4 1 11 5 (a) 8 /3 (b) 3¼ (c) 7 /12 (d) /12. 3. Find the difference between 188.371 and 240.642. (a) 51.271 (b) 52.271 (c) 62.271 (d) 52.371. 4. Find the product of 6.02 x 0.4. (a) 2408 (b) 240.8 (c) 2.408 (d) 24.08 5. Simplify 8950 litres + 10,000 litres + 9,050 litres giving your answer in kilolitres. (a) 28kl (b) 280kl (c) 2.8kl (d) 2800kl 6. An empty box weighing 0.95kg is filled with 36 tins of milk, each of which weighs 0.75kg. What is the total weight of the box? (a) 27kg (b) 28kg (c) 26kg (d) 27.95kg. 7. Express 11.75kg in grams. (a) 117.50g (b) 11750g (c) 1175g (d) 117500g 8. The weights of five boys are 45kg, 42kg, 40kg, 36kg and 37kg. Find the average weight of the boys. (a) 35kg (b) 40kg (c) 50kg (d) 25kg 9. A tank measures 100cm long by 40cm wide and it is filled with water up to a depth of 30cm. What is the capacity of the tank in litres? (a) 120litres (b) 1200litres (c) 170litres (d) 195litres. 2 10. Calculate the volume of a triangular prism whose base area is 6cm and height 25cm. 3 3 3 3 (a) 300cm (b) 32cm (c) 100cm (d) 150cm 11. What is the volume of a sphere whose radius is 3cm? (Take π = 3.14cm). 3 3 3 3 (a) 113.14cm (b) 112.04cm (c) 103.04cm (d) 113.04cm 98 UNIVERSITY OF IBADAN LIBRARY 12. Find the size of the marked angle B 1150 0 x 30 A C 0 0 0 0 (a) 85 (b) 20 (c) 35 (d) 25 13. In the diagram below, name the triangle that is equilateral. A F B E 0 25 C D (a) ABC (b) EDC (c) AFE (d) ACE 14. The diagram below is a kite. How many lines of symmetry do a kite has. B C A D (a) 1 (b) 2 (c) 3 (d) 4. 15. Calculate the sum of angles of a 4-sided polygon? 0 0 0 0 (a) 540 (b) 180 (c) 360 (d) 720 2 3 16. A nail 3 /5cm is driven into a piece of wood. If 2 /10 cm of the nail protrudes from the surface, what is the length of the nail embedded in the wood? 3 4 2 1 (a) 5 /10cm (b) 1 /10cm (c) 5 /5cm (d) 1 /10 cm. 1 17. In a class, there are 39 pupils. If /3 of them wear spectacles, how many pupils do not wear spectacles? 99 UNIVERSITY O 1200 F IBADAN LIBRARY (a) 26 (b) 23 (c) 13 (d) 24 18. A dress requires 2.7m of cloth. How many such dresses can be made from a piece of cloth measuring 45.9m? (a) 43.2 (b) 17 (c) 123.93 (d) 48.6. 19. A 504 saloon car consumes 1 litre of petrol covering a distance of 9km. How many litres of petrol will it consume for a journey of 288km? (a) 25 litres (b) 20 litres (c) 32 litres (d) 9 litres 3 20. Calculate the height of the triangular prism below if its volume is 140cm . 4cm 5cm (a) 20cm (b) 9cm (c) 28cm (d) 14cm. 21. Calculate the volume of a cylinder of radius 7cm and height 4cm (Take π = 22 /7). 3 3 3 3 (a) 600cm (b) 28cm (c) 616cm (d) 520cm 22. A cylinder is filled with water. The water level is 16cm in the cylinder. If the radius of the cylinder is 14cm, what is the volume of the water in the 22 cylinder? (Take π = /7). 3 3 3 3 (a) 9856cm (b) 9846cm (c) 9756cm (d) 8946cm 23. How many faces, edges and vertices do the square pyramid has. 100 UNIVERSITY OF IBADAN LIBRARY E D C A B (a) 5 faces, 7 edges, 4 vertices (b) 5 faces, 6 edges, 5 vertices (c) 5 faces, 8 edges, 5 vertices (d) 4 faces, 8 edges, 5 vertices 24. In the diagram below, list 2 pairs of parallel lines. S R Q P D C A B (a) AB and PA, DS and BC (b) AB and PQ, DC and SR (c) SR and PA, BQ and AB (d) RC and PQ, SD and BC 25. Give the name of the solid made from the net below 4cm 4cm 4cm 4cm 4cm 4cm (a) Cube (b) Cuboid (c) Pyramid (d) Cylinder 101 UNIVERSITY OF IBADAN LIBRARY Appendix 2 PUPILS’ KNOWLEDGE OF MATHEMATICS CONCEPT TEST (PKMCT) Instruction: Answer all the questions. Use pencil to tick the correct option on the answer sheet provided. Do not write on the question paper. Time Allowed: 30 mins 1. A four sided figure is called _______ (a) Triangle (b) Polygon (c) Quadrilateral (d) Pentagon. 2. ______ is the word that describe part of whole (a) Fraction (b) Decimal (c) Numerator (d) Quotient 3. Find the product is the same as ______ (a) Addition (b) Subtraction (c) Division (d) Multiplication. 4. A seven sided polygon is called _____ (a) Octagon (b) Heptagon (c) Pentagon (d) Hexagon. 5. A triangle that has all its sides equal is called _____ triangle (a) Equilateral (b) Scalene (c) Isosceles (d) Right-angle 6. ______ is the name of a quadrilateral. (a) Triangle (b) Pyramid (c) Square (d) Cuboid. 7. Find the sum is the same as __________ (a) Multiplication (b) Addition c) Subtraction (d) Division. 8. ______ is not a 3-dimensional shape. (a) Cube (b) Cylinder (c) Rectangle (d) Pyramid. 9. Find the difference is the same as (a) Addition (b) Subtraction (c) Multiplication (d) Division. 10. Find the quotient is the same as _______ (a) Addition (b) Subtraction (c) Multiplication (d) Division. 11. A rectangle has _____ lines of symmetry. (a) 1 (b) 2 (c) 3 (d) 4 12. ______ is called the space an object occupies. (a) Capacity (b) Weight (c) Volume (d) Litre 13. Mathematically, volume is expressed as _______ (a) Length x breadth (b) ½ x base x height 2 (c) πr (d) Area of cross section x height 14. ____ is the formula for volume of a triangular prism. 102 UNIVERSITY OF IBADAN LIBRARY 2 (a) ½ a x b x height (b) Length x breadth x height (c) πr x height 4 3 (d) /3πr 15. ______ represents the volume of a cylinder. 4 2 2 2 (a) /3πr (b) πr x h (c) ½ a x b x height (d) πr . 16. _____ describes the amount a container can hold. (a) Volume (b) Weight (c) Capacity (d) Polygon. 17. _____ is the term that describe how heavy an object is (a) Volume (b) Weight (c) Capacity (d) Circumference. 18. _____ is called the line that divides a shape into two equal fitted parts (a) Perpendicular (b) Edge (c) Symmetry (d) Parallel 19. _____ best describes parallel lines. 0 (a) They form 90 (b) They move at equal distance apart 0 (c) They form 360 (d) They are polygons. 20. Two faces of a 3-dimensional shape meet to form______ (a) Vertex (b) An edge (c) Circle (d) Perimeter. 103 UNIVERSITY OF IBADAN LIBRARY Appendix 3 PUPILS’ VERBAL ABILITY TEST (PVAT) Instruction: Use pencil to tick the correct answer among the options (a) – (d) on the answer sheet provided. Do not write on the question paper. Time allowed: 45 mins Which of the following is different from the others? 1. a) Monday b) Thursday c) January d) Saturday 2. a) Duck b) Turkey c) Cock d) Aeroplane 3. a) Yam b) Sweet Potato c) Cocoyam d) Water 4. a) Tree b) Hibiscus flower c) Arm d) Stem 5. a) Mushroom b) Apple c) Mango d) Pawpaw 6. a) Fish b) Crayfish c) Lizard d) Crab 7. a) December b) Wednesday c) October d) June 104 UNIVERSITY OF IBADAN LIBRARY 8. a) Teacher b) Pupil c) Principal d) Farmer 9. a) Parrot b) Camel c) Cat d) Dog 10. a) Friday b) Morning c) Evening d) Afternoon Which words are the correct ones to complete each of the following statements? Tick the correct answer on the answer sheet provided. 11. As thin as a a) Biro b) Cain c) Broomstick d) Candle 12. As white as a) Cloth b) Cotton wool c) Iron d) Bronze 13. As gentle as a a) Dove b) Lamb c) Baby d) Duck 14. As dirty as a a) Duck b) Cat c) Pig d) Rat 105 UNIVERSITY OF IBADAN LIBRARY 15. As cunning as a a) Goat b) Parrot c) Tortoise d) Monkey 16. As beautiful as a a) Bride b) House c) Car d) Man 17. As sharp as a a) Sharpener b) Razor blade c) Tooth d) Cutlass Tick the correct answer on the answer sheet provided. 18. Hat (Cowboy), Head tie ( ) a) Man b) Father c) Woman d) Grandfather 19. Finger (Hand), Head ( ) a) Feet b) Hair c) Leg d) Hear 20. Fisherman (hook) Farmer ( ) a) Gun b) Dog c) Hoe d) Animal 21. Sit (chair) Sleep ( ) a) Marked b) Tree 106 UNIVERSITY OF IBADAN LIBRARY c) Bed d) Pot 22. Candle (light) Water ( ) a) Eat b) Bed c) Axe d) Drink 23. Shirt (nicker), Skirt ( ) a) Wrapper b) Scarf c) Blouse d) Trouser 24. Piano (pianist), Drum ( ) a) Hunter b) Swimmer c) Drummer d) Farmer 25. Laugh (Happy), Cry ( ) a) Wonder b) Sad c) Hide d) Laugh 26. Cow (Milk), Hen ( ) a) Chick b) Egg c) Food d) Feather 27. Fly (Disease), Cleanliness ( ) a) Health b) Sickness c) Medicine d) Water 28. First (last), Front ( ) a) Led 107 UNIVERSITY OF IBADAN LIBRARY b) Head c) Back d) Middle 29. She – goat (He-goat), Sheep ( ) a) Dog b) Rat c) Cat d) Ram 30. Moon (Night), Sun ( ) a) Star b) Water c) Hot d) Day 108 UNIVERSITY OF IBADAN LIBRARY Appendix 4 PUPILS’ INTEREST IN MATHEMATICS INVENTORY (PIMI) This inventory is designed to show your interest in mathematics as a subject. It includes several areas pertaining to mathematics and showing interest oriented actions. SECTION A: GENERAL INFORMATION Student Number: …………………………………………………………… School Number: …………………………………………………………… Class: Primary ( ) L. G. A: Yenagoa ( ) Ogbia ( ) Age:……………………… Sex: Male ( ) Female ( ) SECTION B: INSTRUCTION Consider the following statements and indicate your answer by a tick in the appropriate column. Code: Y - Yes N - No ITEM YES NO 1. Do you like being in the Mathematics class? 2. Do you hate reading Mathematics books or notes? 3. Do you enjoy doing Mathematics exercise? 4. Is Mathematics a good subject? 5. Do you hate discussing about Mathematics subject with your friends? 6. Do you find Mathematics test difficult? 7. Do you listen attentively during Mathematics lessons? 8. Do you understand what your Mathematics teacher teaches you? 9. Is Mathematics an easy subject to understand? 10. Is Mathematics for boys? 11. Does Mathematics teach what you need to know about life? 12. Do you get to know more things during the Mathematics class? 13. Do you think that someone who does not learn Mathematics is an illiterate? 14. Do you want to do Mathematics -related jobs in future? 109 UNIVERSITY OF IBADAN LIBRARY 15. Can you become what you want to be without doing Mathematics? 16. Do you think that you need Mathematics to live at all? 17. Mathematics is too difficult to read and pass. 18. Will you do everything necessary to become a Mathematician? 19. Only the intelligent can do Mathematics. 20. Mathematics is not for someone like me. 110 UNIVERSITY OF IBADAN LIBRARY Appendix 5 Teaching Assessment Sheet for Teachers on the use of games Name of Teacher:………………………………………………………………. School: …………………………………………………………………………… Date: ……………………………………………………………………………… Guidelines Involved V. Good Good Average Poor V. Poor 5 4 3 2 1 Teacher introduction of the lesson whether it is based on pupils‟ previous knowledge. Teacher‟s ability to teach the new topic. Teacher‟s ability to organize the class, distribute and explanation of game materials and rules to pupils. Teacher‟s ability to give pupils opportunity to play game with less intervention. Teacher‟s ability to ask pupils questions to further clarify the concept and problems Teachers‟ ability to give follow-up activities and homework. 111 UNIVERSITY OF IBADAN LIBRARY Appendix 6 Teaching Assessment Sheet for Teachers on the use of poems Name of Teacher:………………………………………………………………. School: ………………………………………………………………………… Date: ………………………………………………………………………… Guidelines Involved V. Good Good Average Poor V. Poor 5 4 3 2 1 Teacher introduction of the lesson whether it is based on pupils‟ previous knowledge. Teacher‟s ability to give pupils opportunity to read poems aloud (choral, in small groups, individually and at random). Teacher‟s ability to ask pupils to explain and role play the actions in the poems. Teacher‟s ability to ask pupils questions to clarify the concept. Teacher‟s ability to teach the new topic with reference to the poems. Teachers‟ ability to give pupils class work/ homework which also involves writing of poems in content, process and affective. 112 UNIVERSITY OF IBADAN LIBRARY Appendix 7 Primary Mathematics topics identified as difficult by Salman (2009) S/No Identified difficult primary Frequency Percentages of mathematics topics counts respondents 1 Practical & descriptive 65 76.5 geometry (solids or 3-D figures) 2 Word problems 59 69.4 3 Weight, capacity & volume 51 54.1 4 Graphs 46 44.7 5 Compound interest 37 43.5 6 Decimal fraction 35 41.2 7 Everyday statistics 33 38.8 8 Ratio & proportion 32 37.6 9 Measurement (length & area) 31 36.5 10 Place value 29 34.1 11 Algebra (simple equations) 28 32.9 12 Number line 27 31.8 13 Approximation & estimation 26 30.6 14 Binary number 26 30.6 15 Equivalent fractions 24 28.2 113 UNIVERSITY OF IBADAN LIBRARY Appendix 8 Percentage mean and standard deviation of performance in Mathematics across classes States Primary 6 JSS 1 JSS 2 JSS 3 X SD X SD X SD X SD (%) (%) (%) (%) ABIA 48.86 16.79 36.41 11.19 29.18 8.48 NA NA ADAMAWA 45.69 18.27 39.32 16.10 35.17 9.08 40 12.25 AKWAIBOM 47.24 15.41 50.96 12.22 39.35 10.54 45 14.30 ANAMBRA NA NA 57.22 16.21 53.59 17.37 NA NA BAUCHI 44.91 17.93 23.85 6.61 24.48 6.31 28.13 7.40 BAYELSA 55.96 17.53 40.00 11.66 34.11 7.01 32.14 10.30 BENUE 38.27 13.02 33.15 9.75 33.07 13.41 NA NA BORNO 38.52 19.13 37.38 17.35 24.48 6.31 29.45 9.35 CROSS RIVER 39.00 12.96 44.05 14.47 33.10 10.31 27.68 9.63 DELTA 29.73 8.93 38.46 13.31 27.84 6.92 NA NA EBONYI 34.51 11.94 33.85 11.05 27.89 7.30 NA NA EDO 38.40 13.21 47.01 14.44 33.10 10.31 27.68 9.63 ENUGU 43.89 17.35 36.33 11.16 21.84 5.99 NA NA EKITI 48.40 18.23 25.79 10.43 35.73 7.69 28.13 7.40 GOMBE 44.91 17.93 33.95 13.04 24.48 6.31 49.58 15.48 IMO 46.49 19.12 40.26 11.30 30.85 9.74 NA NA JIGAWA 58.26 15.71 54.55 17.79 41.37 12.81 49.58 15.48 KADUNA 38.42 13.45 37.34 11.03 30.85 8.91 34.18 4.08 KANO 23.35 6.20 42.76 13.16 36.09 8.96 27.35 6.68 KASTINA 44.27 15.32 28.78 9.29 27.11 6.30 29.40 7.85 KEBBI 43.91 17.50 35.56 11.05 31.41 7.81 36.15 17.20 KOGI 45.70 18.10 41.94 18.78 33.28 18.45 24.90 7.78 KWARA 43.56 16.23 32.14 7.41 29.74 8.08 24.28 7.78 LAGOS 45.06 16.29 40.36 11.04 34.32 8.69 NA NA NASARAWA 36.46 14.95 26.78 7.66 27.07 6.79 31.50 10.53 NIGER 34.84 13.62 32.81 12.84 33.28 18.45 24.90 7.78 114 UNIVERSITY OF IBADAN LIBRARY OGUN 42.27 16.22 36.80 11.37 32.59 8.66 NA NA ONDO 39.23 14.56 33.44 10.13 32.27 5.78 26.04 8.23 OSUN 54.00 16.77 34.14 12.34 31.80 7.47 30.60 10.22 OYO 47.16 15.44 50.96 12.22 39.35 10.54 45.83 14.42 PLATEAU 32.44 12.34 33.15 9.06 28.52 8.20 NA NA RIVERS 36.03 20.61 37.19 19.43 24.53 7.34 NA NA SOKOTO 47.98 17.50 31.78 10.18 32.94 11.81 29.90 11.16 TARABA 44.63 13.60 35.52 9.97 32.47 12.36 34.50 14.93 YOBE 45.22 14.98 38.36 12.11 51.51 19.08 44.49 16.46 ZAMFARA 34.66 14.68 30.05 12.58 27.50 7.13 34.24 12.65 FCT, ABUJA 27.24 15.49 44.74 14.08 36.44 12.87 42.00 14.82 National 42.87 17.51 37.68 14.72 34.42 12.28 13.63 Source: Final Report (NAUBEP), January, 2009. 115 UNIVERSITY OF IBADAN LIBRARY Appendix 9 Weekly mathematical poems Week 1 1. Concept of Fraction Chnedu can break bread, Latei learns Latin. In Latin, fractio means „break‟ In English, fraction means „to break‟. Have you seen a valley dividing two mountains? Have you seen cream dividing biscuits? Have you seen nose dividing two eyes? So does a line divide a fraction? Like my new cap on my head, Like my meat on my rice, a number stands on another to form a fraction. Your younger brother, a fraction of your family; My smiling sister, the little lily of our house, A fraction of our family Bassey baked bread for breakfast. If his six smiling sisters share from it; They take a fraction each. Oh fraction! Come divide this drink for us, Come share this shrimp for us. 2. Concept of Decimal 1 1 1 2 1 3 Numoebi defines different numbers /10 , /10 , /10 . . . Edidubamo defines even number as divisible by 2 1 1 1 Fipadei defines fraction as part of a whole /10, /100, /1000 . . . Dipamo defines decimal as a number expressed in powers to base tenth parts. Alas! Alamini exclaim 116 UNIVERSITY OF IBADAN LIBRARY 0.5, 0.65, 0.781 are decimals. 3. Express Fractions as Decimals Chwukudi converts corn to popcorn Chika converts cassava to garri Francis converts fraction to decimal too. Fraction to decimal Takes three steady steps Francis expresses fraction denominator in powers to base 10 By multiplying numerator and denominator By the same number. Bright from the right, Count the places of decimal represented, By the number of zeroes on the denominator Pat put the decimal point Finah has her final answer. Oh! Fraction to decimal A sweet simple formula For any fraction Is the long division method Telma tells teacher Show us example 4. Express Decimals as Fractions Epretari expresses good morning as nuwan Eyitayo expresses good afternoon as ekaasun Decimal can be expressed as fraction. Decimal change to fraction 117 UNIVERSITY OF IBADAN LIBRARY In six steady steps Starting from the decimal point, Express the decimal in powers to base tenth parts. 1st number Fentei expresses first number in tenth part /10 2nd number Selepre expresses second number in hundredth part. /100 3rd number Telemo expresses third number in thousandth part /1000 . . . So it goes on and on to last number Adifere add the ordinary fraction. Enifiyemi expresses the final answer in its lowest term Oh! Decimal with whole number, Add it to the ordinary fraction. 5. Ordering of Fractions Left! Right! Left! Right! At ease! On a single file! Like Captain Columbus of Colombian Cantonment, I will order my fractions. From the least to the highest With less than sign, Go in ascending order. From the highest to the least, With greater than sign, Go in descending order With „equal to‟ sign, You are equal fractions; Going together like a couple. 118 UNIVERSITY OF IBADAN LIBRARY Week 2 1. Addition and Subtraction of Like Fractions Orange to orange Mango to mango Number to number Fraction denominator to fraction denominator Equal denominator to equal denominator Is all about like fractions. I have like fractions, I want to add like fractions, I want to subtract like fractions, I have two tasks. I have few steps to follow. I have three steps to follow. Step one: I add or subtract the numerators; Step two: I write result over single denominator; Step three: I write final answer in lowest term. 2. Addition and Subtraction of Fractions with Different Denominators Principal Patani‟s podium On the academy‟s assembly. It has six steeply steps, Six steeply steps That shakes like skeletons. Unlike those steeply steps; Addition and subtraction of fraction Has six solid steps: You find the denominator‟s LCM; You divide LCM by denominator; You multiply result by numerator; You add or subtract the result; You write the answer over LCM; You write the final answer in lowest term. 119 UNIVERSITY OF IBADAN LIBRARY 3. Addition and Subtraction of Mixed Numbers Madam Pat‟s porridge Makes my mouth salivate. It is a mixture of many edibles. Like that palatable porridge, Where snail meets with shrimps, Where yam meets with oil, Numbers can mix. When numbers mix, We have mixed numbers. We can add and subtract mixed numbers. Like willing workers at Madam‟s Pat‟s pots; We add or subtract whole number, We find LCM of denominator, We divide LCM by each denominator, We multiply result by numerators, We add or subtract the result, We write answers over LCM, with the whole number. We write final answer in lowest term. Oh! When I involve carrying What I carry Is equal to my L.C.M. 4. Word Problems on Addition Blow a balloon, You increase the size. Blow a ball, You increase the size. Blow a tube, You increase the size. It is all about addition! 120 UNIVERSITY OF IBADAN LIBRARY To find the sum Is addition, To find the total Is addition, To add together Is addition, Sign of plus (+) Is addition, Any extra Is addition. 5. Word Problems on Subtraction David draws water from well, Dre drinks Dano every day, Esther eats plates of rice, When he drinks Dano, When she eats rice, Quantity decrease. Find the difference is subtraction; Act of removal is subtraction, Act of waste is subtraction; Act of use is subtraction; Act of spending is subtraction; Act of decrease is subtraction; Sign of minus (-) is subtraction. 6. Standard to Compare Fraction. The whole is one (1), Dividing to fractions; The whole is one (1), Breaking to fractions; The whole is one (1), 121 UNIVERSITY OF IBADAN LIBRARY Creating the fraction 7. Addition and Subtraction of Given Decimals Ade and Susan add or subtract whole numbers Adeleke and Francis add or subtract fractions Adebi and Desmond add or subtract decimals too. Five steady steps to add or subtract decimals Bright writes whole numbers on one column according to place value. Desmond writes decimal points on one column Numobi and Columbus write numbers After decimal point in their columns according to place value. Ade and Susan add or subtract Numbers by their columns from the right Finah and Anita write final answer 122 UNIVERSITY OF IBADAN LIBRARY Week 3 1. Multiply Fraction by Fraction Whyte Nubere multiplies whole numbers by whole numbers Detonye multiplies decimal by decimal Francis multiplies fraction by fraction too. To multiply fraction involves five steady steps Sample simplify numerators and denominators By cancelling with a common factor Arthur Murphy multiply the numerators To get the numerator of the answer Desmond Murphy multiply the denominators To get the denominator of the answer Whyte writes numerator‟s answer Over denominator‟s answer Andrew Bright writes final answer in its lowest term Finah has her final answer. Look! A mixed number fraction Change to improper fraction Then, apply the five steady steps. 2. Word Problems on Multiplication Grandma Golden has a gold pot Fostinah add four cups of corn in it Florence add another four cups of corn in it Foster add another four cups of corn in it It is all about multiplication. 123 UNIVERSITY OF IBADAN LIBRARY Repeated addition, is multiplication Find the product, is multiplication Sign of „×‟, is multiplication Oh! Operation on „of‟, is multiplication. 3. Multiply Decimal by Decimal Promise multiplies her provision shop Whyte Noble multiplies whole numbers by whole numbers Destiny multiplies decimal by decimal too. To multiply decimal by decimal involves five steady steps Desmond writes the decimal numbers as whole numbers Mustapha Wole multiply the whole numbers Adabel add the result County Dila-emi count all the decimal places Pat Decard put the decimal point Counting from the right to left Finah has her final answer. 4. Divide Decimal by 2 or 3-Digit Numbers Have you seen things dividing to 13 places? Have you seen whole numbers dividing to 606 places? Like Banabas‟ bunch of banana dividing to 13 places Like Florence‟s fried fish dividing to 14 places. Like 3,636, dividing to 606 places It is all about division by 2 or 3-digit numbers. So, Dila-emi divides decimals by 2 or 3-digit numbers. Terrified! Destiny asks Dila-emi, how? 124 UNIVERSITY OF IBADAN LIBRARY By long division method, Divide as in whole numbers Telma tells teacher Show us example! 5. Word Problems on Division of Decimals Bere share her bread into two Banabas share his banana into three Finima share her fish into four It is all about division. Find the quotient, is division Sign of „†‟, is division a Sign of /b is division Ah! Action of share is division. 125 UNIVERSITY OF IBADAN LIBRARY Week 4 1. Volume Airplane flies on air and occupies a space Benidou sleeps on bed and occupies a space John Bull jump into water and occupies a space Seiye sits on chair and occupies a space It is all about volume. It is the occupied space To mathematicians, volume is area of cross-section × height Triangular Prism 2. Volume of a Triangular Prism Oh! Tarima find triangular prism Meet triangular prism at prison Your formula for volume fools me! Terrified! Triangular prism said My formula for volume is, ½ a × b × h 3. Volume of Cylinder Chima meets cylinder at the chamber Zachy Zoo zooms out of the chamber And ask cylinder; What is your formula for volume? Cylinder With loud voice 2 My formula for volume is πr × h 4. Volume of a Sphere Sphere Seiyefa meets sphere on the space Ask the formula for volume But spheroid a friend to sphere said 4 3 The formula for volume of sphere is /3 × π × r 126 UNIVERSITY OF IBADAN LIBRARY 5. Word Problems on Volume of Triangular Prism, Cylinders and Spheres We have words bringing us together We have words defining us We are defined by shape and formula while solving word problems Like Wole who gives word problems on volume Wode lookout for solution in word problems Stephen outline seven sequential steps Sharon shares the seven sequential steps. Redeem reads question carefully Idisemi identifies the shape Noble notes the shape of the cross-section Claudius calculate the area of the cross-section Wilson writes down the equation for volume Whyte writes the given values in the equation So, Solomon solves the equation And Domotimi writes down the answer. 127 UNIVERSITY OF IBADAN LIBRARY Week 5 1. Capacity Cup contains an amount of water Classroom contains certain number of pupils Cupboard contains certain number of books It is all about capacity It is the amount a container can hold It is the same as length × breadth × height And the unit of capacity is the litre. 2. Compare Capacities of Containers Seiye‟s Spoon contains small water Bolade‟s bottle contains more water. Buky‟s bucket contains still more water Domotimi‟s drum contains still more water It is all about capacities of containers So, different containers contain different amounts. Spoon Bottle Bucket 3. Table of Capacity 3 1 litre = 1,000 cubic centimeter (cm ) Drum 1 litre = 1,000 millilitres (ml) 1,000 litres = 1 kilolitre (kl) 3 1,000 litres = 1 cubic metre (m ) 4. Conversion of Capacities Martha grandma convert corn to popcorn Chika convert cassava to garri Mathematicians convert units of capacities too. 128 UNIVERSITY OF IBADAN LIBRARY Ha! Ha! Ha! How? Mama Maria puts soup From a big pot to small pots By multiplying the number of small pots Rita puts rice From a small bag to a big bag By dividing the big bag From larger unit to smaller unit, multiply. So, from kilolitre to litre, multiply From smaller unit to larger unit, divide. So, from litres to kilolitres, divide. So, mathematicians convert capacities of containers. 5. Word Problems on Capacity Bruce always brushes mouth Beatrice always takes breakfast Banabas always takes bath Solving word problems on capacity, always requires the following too. Redeem reads the question carefully Idendou identifies the units Chima converts to the same units Idris identifies the related operation; Addition, subtraction, multiplication or division Catherine carries out the operation Whyte writes the answer. It is all about word problems on capacity. 129 UNIVERSITY OF IBADAN LIBRARY Week 6 1. Weight How heavy is Luke‟s lunch box How heavy is Sola‟s school bag How heavy is Catherine‟s car It is all about weight It measures how heavy an object is Its‟ units are the kilogram (kg) and gram (g) 2. Weights of Objects Miela measures his milk tin in grams West measures his weight in kilograms Carmela measures his car in tonnes Makama, the mathematician Measures small objects in grams Measures medium sized objects in kilograms Measures heavy objects in tonnes 3. Tables of Weight 1000 grams (g) = 1 kilogram (Kg) 1000 kilograms = 1 tonne (t) So, 1 tonne = 1,000,000 grams (g) 4. Conversion of Weights Florence converts flour to bread Grandma converts groundnut to groundnut oil Mathematician Comfort converts different weights. Hail ! Hail ! How? From a larger unit to a smaller unit, multiply So, 5 kg = (5 × 1000)g = 5000g 4t = (4 × 1000)kg = 4000kg. 130 UNIVERSITY OF IBADAN LIBRARY From a smaller unit to larger unit, divide 5000 So, 5000g = /1000 kg = 5kg 5000 5000kg = /1000 t = 5t 5. Express the Same Weight in Different Units: Grams, Kilograms and Tonnes Comfort converts cassava to fufu, farina and garri. Comfort converts corn to pap, agidi and popcorn. Martha, the mathematician expresses The same weight of object in grams, kilograms and tonnes. Epretari expresses 80,000 grams to kilograms and tonnes. Hail! Hail! Shout Sharon 80,000 80,000 grams = /1000 kg = 80kg What! What! Esther exclaim 80 80kg = /1000 t = 0.08 tonnes Oh! What an amazing knowledge 80,000 grams = 80 kilograms = 0.08 tonnes. 6. Word Problems on Weight Bruce always brushes mouth Beatrice always takes breakfast Banabas always takes bath Solving word problems on weight Always requires the following too. Redeem reads the question carefully Idendou identifies the units Comfort converts to the same units Idris identifies the related operation Addition, subtraction, multiplication or division. Catherine carries out the operation Whyte writes the answer. It is all about word problems on weight 131 UNIVERSITY OF IBADAN LIBRARY Week 7 1. 2-Dimensional Shapes Dinky 2-Dimensional shapes Length I want to know you well. 2-Dimensions, I have F a c e Breadth Length, I have Trapezium Breath, I have I am a plane shape Like a plane sheet of paper I have one face Know me by length, breadth and one face So, Kite belongs to me Kite Parallelogram belongs to me Rectangle belongs to me Rectangle Rhombus belongs to me Rhombus Square belongs to me Trapezium belongs to me Oh! Triangle, you belong to me 2. Names of Quadrilaterals A table has four legs Triangle A table has four sides Square A table is a shape It is all about quadrilaterals. Quadrilaterals are four sided shapes. Kite is a quadrilateral Parallelogram is a quadrilateral Rectangle is a quadrilateral Parallelogram Rhombus is a quadrilateral Square is a quadrilateral So! Trapezium is a quadrilateral 132 UNIVERSITY OF IBADAN LIBRARY 3. Features of Quadrilaterals Handy has two hands equal Legacy has two legs equal Sympathy Noble‟s nose is a line of symmetry of her face It is all about features of quadrilaterals Square Square has four equal sides Square has four right angles Square has four lines of symmetry Rectangle Rectangle has its opposite sides equal Rectangle has four right angles Rectangle has two lines of symmetry. Rhombus has its four sides equal Parallelogram Rhombus has its opposite angles equal Rhombus Rhombus has two lines of symmetry. Parallelogram has its opposite sides equal Parallelogram has its opposite angles equal Parallelogram has no line of symmetry. Trapezium Trapezium has sides of different lengths Trapezium has angles of different sizes Kite Trapezium has no line of symmetry Like my little lilies of different heights Kite has its neighboring sides equal Kite has one pair of opposite angles equal Kite has one line of symmetry. 133 UNIVERSITY OF IBADAN LIBRARY 4. Types and Features of Triangles Triangle has three sides o Triangle has three angles, total to 180 Triangles are four types in all. Equilateral triangle Like a table that has four legs. Right angled triangle Oh! Ha! See my types and features. I am right angled triangle When I have a right angle I am equilateral triangle When my three sides are equal When my three angles are equal Isosceles triangle When I have three lines of symmetry. I am isosceles triangle When two sides are equal When my base angles are equal Scalene triangle When I have one line of symmetry. I am scalene triangle When my three sides are unequal When my three angles are unequal When I have no line of symmetry Like three unequal triplets, so I look. 5. Regular Polygons Remi Difiye defines regular polygons Polygons are plane shapes With at least three straight sides And three angles. Triangle 134 UNIVERSITY OF IBADAN LIBRARY 6. Types of Polygons Triangle has types Quadrilateral has types So, polish polygon has types Quadrilateral o With three sides and sum of angles equals 180 Call me triangle o With four sides and sum of angles equals 360 Call me quadrilateral. o With five sides and sum of angles equals 540 Pentagon Call me pentagon o With six sides and sum of angles equals 720 Call me hexagon. o With seven sides and sum of angles equals 900 Hexagon Call me heptagon. o With eight sides and sum of angles equals 1080 Call me octagon. So ,I end at the primary school. But as polish and pretty, I am Octagon I have simple fine formula For the sum of my angles o It is pretty as (n-2) × 180 Heptagon 135 UNIVERSITY OF IBADAN LIBRARY Week 8 1. 3-Dimensional Shapes Dinky 3-Dimensional shapes I want to know you well. 3 dimensions, I have Length, I have Breadth, I have Height, I have More than one face, I have So, Cube like sugar belongs to me Cuboid like match box belongs to me Cylinder like bournvita tin belongs to me Know me by length, breadth, height and more than one face 2. Faces, Vertices and Edges of 3-Dimensional Shapes FACE Peter‟s face is pretty round face Earth‟s face is flat surface So, solid‟s face is flat or curve surface Like a plane sheet of paper Like a face of a table fan. It is all about face of 3-D shapes EDGE Pat close her two palms to pray Flat face Vertex Martha‟s and Maria‟s faces meet X A Solid‟s two faces meet Curved fac e B A B Like two walls meeting together y It is all about an edge So, two faces meet to form an edge Face A meet face B Form edge XY Look, an edge XY is a line 136 UNIVERSITY OF IBADAN LIBRARY VERTEX A table has sides and corners One side of the table AB Meet and end at point B Another side of the table BC Meet and end at point B Form a corner at point B So, edges AB and BC of 3-D shapes Meet each other to form a corner It is all about vertex. So, edges meet to form a vertex. 2. 3-Dimensional Shapes and their Features. Cube is a 3-D shape Cube has all sides equal Cube Cube has 6 flat faces Cube has 12 edges Cube has 8 vertices Oh! Cube looking like the cube sugar Cuboid is a 3-D shape Cuboid has two opposite sides equal Cuboid has 6 flat faces Cuboid has 12 edges Cuboid Cuboid has 8 vertices Oh! Cuboid, looking like a match box. Cylinder is a 3-D shape Cylinder Cylinder has 1 curved and 2 flat faces Cylinder has 2 circular edges Cylinder has no vertex Oh! Cylinder, looking like a milk tin. 137 UNIVERSITY OF IBADAN LIBRARY 4. Measurement of Angles of 3-Dimensional Shapes Ruler measures length Thermometer measures temperature Speedometer measures speed So, protractor measures angles. 5. Perpendicular and Parallel lines Perpendicular line Hurry! Hurry! Hurry! Vero drop vertical line down A Hit horizontal line CD hot Form perpendicular line at B 0 o 90 Form right angle or 90 Line AB perpendicular to line CD B Form right angle at B. C D Parallel lines Ernest is an enemy to Eremo Nestor never meets with Nimi Railway lines never meet at a point It is all about parallel lines Two parallel lines never meet at a point With equal distance apart They move on and on C D M N 138 UNIVERSITY OF IBADAN LIBRARY Appendix 10 Weekly mathematical games Week 1 game (adapted from NMC (2002) Abuja. Title: Fraction/Decimal Grid Class level: Primary 6 Topic: Fraction and Decimal Objectives: Pupils should be able to: 1. Arrange a set of fractions and decimals in order of magnitude 2. Express fractions as decimals 3. Express decimals as fractions Materials: 45 cards containing all positive fractions and decimals with highest denominator of 10 are used for the game. 2. A checklist showing the order of magnitude of each fraction and decimal Plan: The game can be played by two or more pupils at a time. Each player is to arrange four cards in order of magnitude. To check for correctness, the judge will check from the check list of cards and their orders of magnitude. For example, the four cards 2 5 /7 /7 0.1 0.125 Their orders of magnitude on the check are 9 17 1 3 Procedure: Each player is dealt four cards after shuffling and players are to arrange their cards from left to right in increasing order (ascending). The first player to complete correctly becomes the winner. Strategies: Players must use a strategy of comparing two fractions by finding two other fractions which are equivalent to the given fractions but whose denominators are the same. Then comparing the numerators gives the correct order. Also fast ways of reducing fractions to l owest term will help the player. Again, expressing fractions as decimals or decimals as fractions depending on the cards a player has will be of help. Follow-up activities: The pupils are asked to arrange sets of numbers in ascending or descending order. 139 UNIVERSITY OF IBADAN LIBRARY Sample cards 140 UNIVERSITY OF IBADAN LIBRARY Week 2 game (adapted from NMC (2002) Abuja). Title: Expression Whot Topic: Fraction and Decimal Class level: Primary 6 Objectives: Pupils should be able to: 1. Add fractions and decimals 2. Subtract fractions and decimals 3. Solve word problems on addition and subtraction of fractions and decimals. Materials: 30 question cards of (9x12cm). Plan: The game may involve two or more players (maximum of six). The teacher or a pupil so appointed can serve as judge. The player with the highest value is declared the winner. Procedure: After shuffling, each player is dealt with 5 cards (in case of 6 players). A player will also be given 5 game tokens of the same color. A total of 10 minutes will be given to each player to solve the five questions, i.e. 2 minutes for each question. If a player solves a problem and got the correct answer, he/she takes a token and places it on the game board that has that answer. Then, the judge will check the correct answer to that question from the check list. If it is correct, the token will remain on the game board. If it is wrong, the token will be removed and the question card will be placed face down on the floor for any other players who may finish his/her question cards before the allotted time. Players that got their answers wrong will be corrected during the follow-up activities. The winner of the game is the player with the highest score when the allotted time is finished. Scores are as follows: Black = Scores 4 points Green = Scores 3 points Red = Scores 2 points White = Scores 1 point Wrong answers score zero point. Strategies: Each player considers the cards that are easier to solve first in less than 2 minutes with speed and accuracy in solving each card. Follow-up activities: Pupils will be asked to solve 2 cards on the board and explain to the class. 141 UNIVERSITY OF IBADAN LIBRARY 142 UNIVERSITY OF IBADAN LIBRARY Sample cards 143 UNIVERSITY OF IBADAN LIBRARY Week 3 game (adapted from NMC (2002) Abuja). Title: Mathematics Circle Race Game Class level: Primary 6 Topic: Fraction and Decimal Objectives: Pupils should be able to; 1. Multiply decimals by decimals 2. Multiply fractions by fractions 3. Divide decimals by 2- digit and 3- digit numbers 4. Solve word problems on multiplication and division of fraction and decimal Materials: 1. A game board. This board is in circular form and centre is where the race starts and ends at where „out‟ is written. There are 42 squares of six different colors excluding the empty zone. 2. 36 Problem cards 3. A die 4. Cards slots‟ (6) 5. Game tokens 6. Checklist 7. Pen and paper Plan: The game is played by 2 or at most 3 players. A time keeper is essential. A maximum of 2 minutes is given to solve a problem. A time keeper can also be the recorder and the checker. There is a check list with the checker. Procedure: (1) To start the game, a die is tossed. A player with a six will start the game. The game starts from the area marked centre. 2. The cards‟ slots are numbered 1-6 and each slot will be placed 6 problem cards after shuffling properly. 3. The cards are well shuffled before the start, the number shown on the die will determine what problem square the player finds himself, i.e. if a player plays a „six‟, he gets to the centre, if he plays a „four‟ at the second throw he counts four, looks at the color, then goes to the appropriate cards slot and picks a problem card. 4. If the player solves the problem correctly he looks for the reward at the bottom of the problem card i.e. move 2 or 3 steps forward. If wrong, move 2, 3, or 4 steps backward. 144 UNIVERSITY OF IBADAN LIBRARY 5. F and E on the game board represent free and empty zones respectively. If a player falls in free zone (F), he will relax; he will not forfeit his chance. But if in empty zone (E), he will forfeit his chance; that is, come back to the former position and wait for another turn. Scoring: 1. For 3 players, the first player to get out will score 30 points, while the second and third players score 20 and 10 points respectively. 2. For 2 players, it will be 20 and 10 points respectively. 3. The total mark will depend on the number of rounds they play and the player with the highest point declared the winner. Strategy: Each player struggles to get high numbers in order to run very fast and get out. But if numbers shown are always low, the chance of getting out fast is very low. Follow-up activities: Students should try to go over their textbooks and solve related problems on the topics. 145 UNIVERSITY OF IBADAN LIBRARY 146 UNIVERSITY OF IBADAN LIBRARY Sample cards 147 UNIVERSITY OF IBADAN LIBRARY Week 4 game (adapted from NMC (2002) Abuja Title: Mathematics Palace Game Topic: Volume Class level: Primary 6 Objectives: Pupils should be able to: 1. Use formula to calculate the volume of triangular prisms 2. Use formula to calculate the volume of cylinders. 3. Use formula to calculate the volume of spheres 4. Solve word problems involving the volume of the shapes. Materials: 1. Game board made from cardboard sheets. 2. Pack of 13 cards with questions on volume of solids 3. A die and eight game tokens of four colors and two tokens for each color. 4. Check list Plan: The game board is prepared by drawing about 30 squares on a cardboard sheet. The square spaces contain instructions which involve reciting some formulae and picking questions from a pack of questions. The questions will be on a topic under discussion. The questions are numbered for easy identification. There is a solution sheet showing all the answers to the questions in the pack. A die and game tokens used in ordinary ludo could be used for this game or the teacher could improvise the game tokens. Besides, the teacher should write out a summary of the basic concepts on the topic to help players to recollect some basic facts. This will help them to respond to the questions involved in the game. The game could be played by at least two players but a maximum of four players is recommended. There should be only one judge to monitor the game. The judge should keep the solution sheet and checks answers for the players. But where there is no judge, the solution sheet could be turned face down by the players and should be referred to when necessary. Procedure: Any of the players can start the game by throwing the die and other players will play in a clockwise direction. But to qualify his entering any of his game tokens on the game board, a player must get a six and the second throw will determine where to place his game token. He has to follow the instruction on that number square. For example, „pick a question and solve‟. 148 UNIVERSITY OF IBADAN LIBRARY Correct response will move the game token forward to the number shown on the arrow. Wrong answer implies that the player will move his game tokens backward as directed on the game board. In this case he has to perform the instruction on the number square again as part of penalty. If he gets it right, he moves forward to the former position. Otherwise, he will remain in that number square. He could then refer to his note book or ask the teacher for correction. If a player falls in a square where he has to recite a formula in mathematics, he has to do so loudly. If he gets it correct, he can move forward, otherwise he will remain there. A player should spend a maximum of two minutes on a question. A winner is decided by the first player to get all his game tokens to the „mathematics palace numbered thirty on the game board. Strategies: The interest of every player is to get to the Mathematics Palace first. Since each player has two game tokens, he has to move the one that will reward him more at any particular throw of the die. As much as possible, a player should avoid penalties that will move him backwards. Another defensive strategy is that if your game token meets another player‟s game token, then that token should be taken back by two steps. Variations: This game „Mathematical Palace‟ could be prepared for any level of the education system. It could be used to revise or practice any topic with the students. Many game boards could be prepared to enable more students participate in the game. But, the game could be played in schools, homes, offices and relaxation centers to generate interest of the people in mathematics. 149 UNIVERSITY OF IBADAN LIBRARY 150 UNIVERSITY OF IBADAN LIBRARY Sample cards 151 UNIVERSITY OF IBADAN LIBRARY Week 5 game (adapted from Agwagah, 2001) Title: Capacity Board Game Class level: Primary 6 Topic: Capacity Objectives: Pupils should be able to: 1. Solve word problems involving capacity Materials: 1. A 4 by 4 square board made of card board or wood which contains answers of problems to be solved. 2. A deck of sixteen question cards of 9cm by 12cm on capacity made of cardboard and answer to the problem on the reverse side. 3. Four different sets of colored game tokens or ludo seeds, for covering the correct answers on the small squares in the game board. 4. A die 5. Checklist 6. Paper and pencil or pen Plan: The game may involve two or more players (maximum of four). The teacher or a pupil appointed can serve as judge or caller. Procedure: The deck of cards is shuffled and placed on the table with problems face up in front of the caller or judge to open the problem cards on the table. When a problem is opened, the players solve it on their paper, and the first to finish, places one of his game tokens on the small square that contains the answer on the game board. The caller then checks the number covered by the player to make sure it tallies with the answer of that problem card on the checklist. Game continues until a player covers four numbers in a row horizontally, vertically or diagonally, and calls out „Down’. Rules: Once a player covers a number, he does not remove his token unless he is wrong, after the check by the caller. In this case, another player has the chance of covering the correct answer. Winner: The first player to cover four correct numbers in a row horizontally, vertically, or diagonally wins the game. 152 UNIVERSITY OF IBADAN LIBRARY 153 UNIVERSITY OF IBADAN LIBRARY Sample cards 154 UNIVERSITY OF IBADAN LIBRARY Week 6 game (adapted from NMC (2002) Abuja) Title: Mathematics Palace Game Topic: Weight Class level: Primary 6 Objectives: Pupils should be able to: 1. Express the same weight in different units: grams, kilograms and tonnes. 2. Convert weights in tonnes to kilograms and vice versa. 3. Identify objects whose weights could be expressed in tonnes, kilograms and grams. 4. Solve word problems on weight Materials: 1. Game board made from cardboard sheets 2. Pack of 17 cards with questions on weight 3. A die and eight game tokens of four colors and two tokens for each color. 4. Check list Plan: The game board is prepared by drawing about 30 squares on a cardboard sheet. The square spaces contain instructions which involve reciting some formulae and picking questions from a pack of questions. The questions are based on the topic under discussion. The questions are numbered for easy identification. There is a solution sheet showing all the answers to the questions in the pack. A die and game tokens used in ordinary ludo could be used for this game or the teacher could improvise the game tokens. Besides, the teacher should write out a summary of the basic concepts on the topic to help players to recollect some basic facts. This will help them to respond to the questions involved in the game. The game could be played by at least two players but a maximum of four players is recommended. There should be only one judge to monitor the game. The judge should keep the solution sheet and checks answers for the players. But where there is no judge, the solution sheet could be turned face down by the players and should be referred to when necessary. Procedure: Any of the players can start the game by throwing the die and other players will play in a clockwise direction. But to qualify a player entering any of his game tokens on the game board, a player must get a six and the second throw will determine where to place his game token. He has to follow the instruction on that number square. For example, „pick a question and solve‟. 155 UNIVERSITY OF IBADAN LIBRARY Correct response will move the game token forward to the number shown on the arrow. Wrong answer implies that the player will move his game tokens backward as directed on the game board. In this case he has to perform the instruction on the number square again as part of penalty. If he gets it right, he moves forward to the former position. Otherwise, he will remain in that number square. He could then refer to his note book or ask the teacher for correction. If a player falls in a square where he has to recite a formula in mathematics, he has to do so loudly. If he gets it correct, he can move forward, otherwise he will remain there. A player should spend a maximum of two minutes on a question. A winner is decided by the first player to get all his game tokens to the „mathematics palace numbered thirty on the game board. Strategies: The interest of every player is to get to the „Mathematics Palace‟ first. Since each player has two game tokens, he has to move the one that will reward him more at any particular throw of the die. As much as possible, a player should avoid penalties that will move him backwards. Another defensive strategy is that if your game token meets another player‟s game token, then that token should be taken back by two steps. Variations: Th is game „Mathematical Palace‟ could be prepared for any level of the education system. It could be used to revise or practice any topic with the students. Many game boards could be prepared to enable more students participate in the game. But, the game could be played in schools, homes, offices and relaxation centers to generate interest of the people in mathematics. Follow-up activities: At the end of the game, the teacher should give students more problems to solve on the topics covered in the game to ensure mastery of the key concepts in the topics. 156 UNIVERSITY OF IBADAN LIBRARY 157 UNIVERSITY OF IBADAN LIBRARY Sample cards 158 UNIVERSITY OF IBADAN LIBRARY Week 7 game (adapted from NMC (2002) Abuja) Title: Plane Figure Card Game Class level: Primary 6 Topic: 2- Dimensional shapes Objectives: Pupils should be able to: 1. Identify plane figures 2. Identify common properties of plane figures 3. Identify peculiar properties of plane figures Materials: 60 cards (60mmX40mm) cards made of cardboard paper on which sketches of variety of plane figures are drawn. Five plane figures each on square, trapezium, rectangle, kite, rhombus, parallelogram, equilateral triangle, right-angle triangle, isosceles triangle, scalene triangle, 3-sided polygon, and 6-sided polygon. Plan: There are normally two players at a time. Nevertheless, 3 or 4 persons can play at a time. Procedure: Player „A‟ shuffled the cards and shares them out at random to both of them. Each player gets 5 cards for a start. One card is thrown open by „A‟ from the pile. Player „B‟ starts the game by placing another card with a common property with the open one on its top and the judge ensures the common property. If player „B‟ has no such card he draws a card from the pile. Then it is the next player‟s turn to place a correct card. If he cannot, he draws from the pile and it goes round. The game is played alternatively till one of the players announces „last card‟ when he/she has played second to the last card in his/her hand. If he/she successfully plays his/her last card, he calls for a check. The number of cards remaining in the opponent‟s possession is counted and the number recorded against the opponent. This is one round of the game. The game is played for four rounds before a winner emerges. The winner is the one with the least sum of all the rounds scores. Rules of the game 1. A card with a sketch of scalene is known as Whort 2. A Whort is used to respond to any property requested for. 3. When a Whort card is placed, the player is free to request for any property in response. 4. If one calls for last card and is not able to end the game, he goes ‟to market‟. 5. A card with a sketch of polygon is known as hold-on card. 159 UNIVERSITY OF IBADAN LIBRARY 6. If a player plays a hold-on card, his/her opponent waits for him to play again. 7. A card with sketch of trapezium sends the opponent „to market‟ to pick two cards. Strategies Reserve cards with plane figures with many common properties and/or WHORT for your last card call to enable you end the game, in your favor. Knowledge of which plane figure is a sub-set of the other e.g. a square is a special rectangle while a rectangle is a special parallelogram, enables one to clear his/her cards to win. Common Properties in use for the Game 1. All sides are equal (AS) 2. Opposite sides are equal (OS) 3. All angles are equal (AA) 4. Base angles are equal (BA) 5. Opposite angles are equal (OA) 6. Equal pairs of parallel lines (P) 7. Two pairs of parallel lines (PP) 8. One line of symmetry (S1) 9. Two lines of symmetry (S2) 10. Three lines of symmetry (S3) 11. Four lines of symmetry (S4) Follow-up activities: Try to produce a graphic representation of relationship between the plane figures; one for triangles and another for quadrilaterals. Try to produce a table of plan figures against the properties of plan figures and observe their relationship as well as the special property for each plan figure. Hence or otherwise try to define each plane figure. 160 UNIVERSITY OF IBADAN LIBRARY Sample cards 161 UNIVERSITY OF IBADAN LIBRARY Week 8 game (adapted from NMC (2002) Abuja) Title: Mathematics Circle Race Game Class level: Primary 6 Topic: 2 and 3-dimensional shapes Objectives: Pupils should be able to 1. Identify 2-dimensional shapes not exceeding the octagon. 2. Identify 3-dimensional shapes 3. Solve problems on 2 and 3-dimensional shapes. Materials: 1. A game board. This board is in circular form and centre is where the race starts and ends at where „out‟ is written. There are 42 squares of six different colors excluding the empty zone. 2. 30 Problem cards 3. A die 4. Cards slots‟ (6) 5. Game tokens 6. Pen and paper Plan: The game is played by 2 or at most 3 players. A time keeper is essential. A maximum of 2 minutes is given to solve a problem. A time keeper can also be the recorder and the checker. There is a check list at the back. Procedure: (1) To start the game, a die is tossed. A player with a six will start the game. The game starts from the area marked centre. 2. The cards‟ slots are numbered 1-6 and each slot will be placed 5 problem cards after shuffling properly. 3. The cards are well shuffled before the start, the number shown on the die will determine what problem square the player finds himself, i.e. if a player plays a „six‟, he gets to the centre, if he plays a „four‟ at the second throw he counts four, looks at the color, then goes to the appropriate cards slot and picks a problem card. 4. If the player solves the problem correctly he looks for the reward at the bottom of the problem card i.e. move 2 or 3 steps forward. If wrong, move 2, 3, or 4 steps backward. 5. F and E on the game board represent free and empty zones respectively. If a player falls in free zone (F), he will relax; he will not forfeit his chance. But if in 162 UNIVERSITY OF IBADAN LIBRARY empty zone (E), he will forfeit his chance that is come back to the former position and wait for another turn. Scoring: 1. For 3 players, the first player to get out will score 30 points, while the second and third players score 20 and 10 points respectively. 2. For 2 players, it will be 20 and 10 points respectively. 3. The total mark will depend on the number of rounds they play and the player with the highest point declared the winner. Strategy: Each player struggles to get high numbers in order to run very fast and get out. But if numbers shown are always low, the chance of getting out fast is very low. Follow-up activities: Students should try to go over their textbooks and solve related problems on the topics. 163 UNIVERSITY OF IBADAN LIBRARY 164 UNIVERSITY OF IBADAN LIBRARY Sample cards 165 UNIVERSITY OF IBADAN LIBRARY Game 9 for also week 8 (adapted from NMC (2002) Abuja) Title: Mathematics Vocabulary Game Class level: Primary 6 Topic: Fractions and Decimals, Volume, Capacity, Weight and Geometry. Objectives: Pupils should be able to: Explain common vocabulary within the above topics in the primary school mathematics curriculum Materials: 30 cards (numbered 1-30) each containing a mathematical term within the topics specified and a check list. A referee to determine the correctness or otherwise of response and ensure time keeping, proper scoring, addition of scores and declaration of winner. Plan: Prepare and number problem cards that test knowledge of mathematics concepts in specified areas within the primary school curriculum. Set up a rule for deciding who plays first. Award 2 marks for each correct response for normal turn and 1 mark for each incorrect response whether during normal turn or bonus chance. Score zero for no response within stipulated time. Allow for 2 to 5 players. Procedure: Toss for a start, shuffle the cards and place on the table with questions face down. Each player picks five cards one at a time in turn. The first player drops a card with question facing up and offers solution within 1 minute. The referee decides on the correctness or otherwise of a response and awards score as appropriate. The referee gives bonus chance where necessary or gives answer where no one gets it. After every player might have dropped all cards in his hand, the total score for each player is calculated. Strategy: A player should play his cards beginning with whichever the solution appears well known and most sure of. A player should play last the one that he finds the solution to be most difficult. Follow-up activities: Teacher should arrange some lessons for a review of the topics by going over the various vocabularies to discuss related concept. 166 UNIVERSITY OF IBADAN LIBRARY 167 UNIVERSITY OF IBADAN LIBRARY Appendix 11 INSTRUCTIONAL GUIDE ON POEM-ENHANCED INSTRUCTIONAL STRATEGY (IGPEIS) Experimental group 1 (lesson schedule) Week I Lesson I Duration: 40 mins Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to 1. Explain the concept of fraction 2. Explain the concept of decimal 3. Express fractions as decimals 4. Express decimals as fractions. 5. Order fractions and decimals 168 UNIVERSITY OF IBADAN LIBRARY Topic Duration Steps Day Teacher’s Activities Pupils’ Teaching Evaluation Guide Activities Aids Fracti 5 mins 1 to Ask pupils questions on Listen and on and 3 the previous lesson and answer the Decim introduce the new topic. questions al 25mins 2 1 1.Distribute the poems‟ 1. Choral Give home work manual to pupils and ask reading of to: pupils to read poems poems aloud express: 1,2&3 in wk1( aloud by by the whole 1. fractions as the whole class, in small class, in decimals (correct groups by rows and small groups to 2 or 3 decimal individually at random). by rows and places) 2. Ask pupils to explain individually. and role play the 2. Explain following as pictured in and role play the poems. the images a. Concept of fraction. pictured in b. Concept of decimal the poems. c. Processes involve in 3. Listen to expressing fractions as the teacher, decimals. ask questions d. Solve problems on the and copy chalk board e.g. express their notes. ¾ as a decimal 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 169 UNIVERSITY OF IBADAN LIBRARY 25mins 2 1.Distribute the poems‟ 1. Choral Give home work manual to pupils and ask reading of to: pupils to read poem 4&5 poems aloud express: in wk1( aloud by the by the whole 1. Decimals to whole class, in small class, in fractions. Give groups by rows and small groups answers in the individually at random). by rows and lowest term. 2. Ask pupils to explain individually. 2. Order decimals and role play the 2. Explain in ascending following as pictured in and role play order. the poems. the images 3. Order a set of a. Processes involve in pictured in decimals in expressing decimals as the poems. descending order. fraction. 3. Listen to b. Solve problems on the the teacher, chalk board e.g. express ask questions 0.75 as a fraction; give and copy answer in its lowest term their notes. c. Processes involved in ordering decimal numbers d. Order decimals in ascending or descending order of magnitude. 3.Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems 170 UNIVERSITY OF IBADAN LIBRARY 25 mins 3 1. Distribute the poems‟ 1. Choral Give home work manual to pupils and ask reading of to: 1.Order pupils to read poems 3&5 poems aloud fractions in in wk1( aloud by the by the whole ascending order. whole class, in small class, in 2. Order a set of groups by rows and small groups fractions in individually at random). by rows and descending order 2. Ask pupils to explain individually. and role play the 2. Explain following as pictured in and role play the poems. the images 40mins 4 1a.. P Prroecseesnst itnhveo plvoe mins for 1p.i cLtuisrteedn iann d 1. Give more othred ewrienegk ftroa cptuiopnilss . Poems rtheaed p woeimths t.h e exercises as home 1b -.5O irnd ewr kf1ra. ction in t3ea. cLhiestre n to work. a2s. cReenaddin pgo oerm dse aslcoeund iwngit h t2h. eR teadc hiner , 2.Give pupils oemrdoetri onf sm. agnitude. samska qllu gersotiuopnss poems to write 3.. ATesakc phuepr ialsk tso preuapdil s and copy a. Their feelings pquoemstiso (ncsh toor acll arreiafdyi tnhge by ithndeirv indoutaelsl.y . about cthoen cwehpot/ltee acclahsess, tshmea nlle w 3. . Explain mathematics. gtorpoiucp ws bityh roefwe raendc e to the t he images b. The content for pinodeimvisd.u ally at random). a nd role play the week. 4. Ask pupils to explain the actions in c. Process of the images and role play the poems. solving a problem the actions in the poems. 4. Listen to 5. Revise the week‟s work the revision with reference to the and ask poems questions 40 mins. 5 1. Give test for the weeks 1. Write the Give test to: work test. 1. Order a set of 171 UNIVERSITY OF IBADAN LIBRARY 2. Mark the test and do 2. Do their fraction in the correction. corrections. ascending and descending order. 2. Order a set of decimal in ascending and descending order. 3. Express fractions as decimals. 4. Express decimals as fractions. Give answers in the lowest term. 10mins 3 1. Give pupils problems to 1. Solve Give 1 or 2 solve in the class. problems questions as class 2. Go round to mark given by the work. pupils work and do the teachers. correction. 2. Do their 3. Conclude the lesson by correction. giving home work to 3. Copy the pupils. home work in their notes. 172 UNIVERSITY OF IBADAN LIBRARY Week 2 Lesson 2 Duration: 40 mins Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to: 1. Add fractions and decimals 2. Subtract fractions and decimals 3 .Combined addition and subtraction of fraction 4. Solve word problems on addition of fraction and decimal 5. Solve word problems on subtraction of fraction and decimal. Topic Duration Steps Day Teacher’s Activities Pupils’ Teaching Evaluation Activities Aids Guide Addition 5 mins 1 1 to Ask pupils‟ questions Listen and and 3 on the previous answer the subtraction lesson and introduce questions. (Sub-topic) the new topic. 25mins 2 1 1.Distribute the 1. Choral Give home poems‟ manual to reading of work to: pupils and ask pupils poems aloud 1. Add to read poems 1&2 in by the whole fractions only wk2( aloud by the class, in 2. Subtract whole class, in small small groups fractions only. groups by rows and by rows and individually at individually. random). 2. Explain 173 UNIVERSITY OF IBADAN LIBRARY 2. Ask pupils to and role play explain and role play the images the following as pictured in pictured in the the poems. poems. 3. Listen to a. Process involve in the teacher, solving problems on ask questions addition of fraction. and copy b. Process involve in their notes solving problems on subtraction of fraction. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 2 1. Distribute the 1. Choral Give home poems‟ manual to reading of work to pupils and ask pupils poems aloud 1. Solve to read poems 3, by the whole problems on 4,5&6 in wk2 (aloud class, in combined by the whole class, in small groups addition and small groups by rows by rows and subtraction of and individually at individually. fraction. random). 2. Explain 2. Solve 2. Ask pupils to and role play problems that 174 UNIVERSITY OF IBADAN LIBRARY explain and role play the images involve the following as pictured in carrying. pictured in the the poems. 3. Solve word poems. 3. Listen to problems a. Process involve in the teacher, involving solving problems on ask questions addition and combined addition and copy subtraction of and subtraction of their notes fraction. fraction. b. Process involve in solving word problems on addition and subtraction of fraction. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 3 1. Distribute the 1. Choral Give home poems‟ manual to reading of work to pupils and ask pupils poems aloud 1. Solve word to read poems 7& by the whole problems on repeat 4,5 in wk2 class, in addition of (aloud by the whole small groups decimal. class, in small groups by rows and 2. Solve word by rows and individually. problems on 175 UNIVERSITY OF IBADAN LIBRARY individually at 2. Explain subtraction of random). and role play decimal. 2. Ask pupils to the images 3. Solve word explain and role play pictured in problems the following as the poems. involving pictured in the 3. Listen to addition and poems. the teacher, subtraction of a. Process involve in ask questions decimal solving problems on and copy addition of decimal. their notes b. Process involve in solving problems on subtraction of decimal. c. Process involve in solving word problems on addition and subtraction of decimals. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 176 UNIVERSITY OF IBADAN LIBRARY 40mins 4 1. Present the poems for 1. Listen and 1. Give more the week to pupils. read poems exercises as home 2. Read poems aloud with with the work. emotions. teacher 2.Give pupils 3. Ask pupils to read poems 2. Read poems poems to write (choral reading by the in small groups a. Their feelings whole class, in small groups and about mathematics. by row and individually at individually. b. The content for random). 3. Explain the the week. 4. Ask pupils to explain the images and c. Process of images and role play the role play the solving a problem actions in the poems. actions in the 5. Revise the week‟s work poems. with reference to the poems 4. Listen to the revision and ask questions 40mins 5 1. Give test for the week‟s 1. Write the Give Test to work. test. 1. Add and 2. Mark the test and do the 2. Do the subtract fractions. correction. correction. 2. Add and subtract fraction involving carrying. 177 UNIVERSITY OF IBADAN LIBRARY 3. Word problems on addition and subtraction of fraction. 4. Add and subtract decimal. 5. Word problems on addition and subtraction of decimal. 10 3 1. Give pupils problems to 1. Solve Give 1 or 2 mins solve in the class problems given questions as class 2. Go round to mark pupils by the teacher. work. work and do the correction. 2. Do their 3. Conclude the lesson by correction giving home work to pupils. 3. Copy the home work in their notes. 178 UNIVERSITY OF IBADAN LIBRARY Week 3 Lesson 3 Duration: 40 minutes Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to 1 Multiply fraction by fraction 2 Solve word problems on multiplication of fraction 3 Multiply decimal by decimal 4 Divide decimal by 2-digit and 3 digit numbers 5 Solve word problems on multiplication and division of decimal. Topic Duration Steps Day Teacher’s Activities Pupils’ Teaching Evaluation Activities Aids Guide Multiplication 5mins 1 1 to Ask pupils questions Listen and and Division 3 on previous lesson answer the (sub-topic) and introduce the questions. new lesson. 25mins 2 1 1. Distribute the 1. Choral Give home to poems‟ manual to reading of 1. Multiply pupils and ask pupils poems aloud fraction by to read poems 1&2 by the whole fraction in wk3( aloud by the class, in small 2. Solve word whole class, in small groups by problems on groups by rows and rows and multiplication of individually at individually. fraction. random). 2. Explain 179 UNIVERSITY OF IBADAN LIBRARY 2. Ask pupils to and role play explain and role play the images the following as pictured in pictured in the the poems. poems. 3. Listen to a. Process involve in the teacher, solving problems on ask questions the multiplication of and copy their fraction by fraction. notes b. Process in solving word problems on multiplication of fraction. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25mins 2 1. Distribute the 1. Choral Give home work poems‟ manual to reading of to pupils and ask pupils poems aloud 1. Multiply to read poems 3& by the whole decimal by repeat 2 in wk3 class, in small decimal (correct (aloud by the whole groups by to 2 or 3 places class, in small rows and of decimal. groups by rows and individually. 2. Solve word individually at 2. Explain problems on 180 UNIVERSITY OF IBADAN LIBRARY random). and role play multiplication of 2. Ask pupils to the images decimal. explain and role play pictured in the following as the poems. pictured in the 3. Listen to poems. the teacher, a. Process involve in ask questions solving and copy their multiplication of notes decimal by decimal. b. Process involve in solving word problems on the multiplication of decimal. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 3 1. Distribute the 1. Choral Give home work poems‟ manual to reading of to: pupils and ask pupils poems aloud 1. Divide to read poems 4& 5 by the whole decimal by 2- in wk3 (aloud by the class, in small digit and 3-digit whole class, in small groups by numbers. groups by rows and rows and 2. Solve word 181 UNIVERSITY OF IBADAN LIBRARY individually at individually. problems on random). 2. Explain division of 2. Ask pupils to and role play decimals. explain and role play the images the following as pictured in pictured in the the poems. poems. 3. Listen to a. Process involve in the teacher, solving problems on ask questions division of decimals and copy their by 2-digit and 3-digit notes numbers. b. Process involve in solving word problems on division of decimals. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 40 mins 4 1. Present the poems 1. Listen and 1. Give more for the week to read with the exercises as pupils. teacher home work. 2. Read poems aloud 2. Read in 2.Give pupils with emotions. small groups poems to write 3. Ask pupils to read and about 182 UNIVERSITY OF IBADAN LIBRARY poems (choral individually. a. Their feelings reading by the whole 3. Explain the about class, in small images and mathematics. groups and role play the b. The content individually at actions in the for the week. random). poems. c. Process of 4. Ask pupils to 4. Listen to solving a explain the images the revision problem and role play the and ask actions in the poems. questions 5. Revise the week‟s work with reference to the poems 40 mins 5 1. Give test for the 1. Write the Give test to: week‟s work. test 1. Multiply 2. Mark the test and 2. Do the fraction by do the correction. correction. fraction 2. Solve word problems involving the multiplication of fraction. 3. Multiply decimal by decimal and solve word problems. 4. Divide decimal by 2 & 183 UNIVERSITY OF IBADAN LIBRARY 3-digit numbers. 5. Solve word problems on division of decimal. 10 mins 3 1. Give pupils 1. Solve Give 1 or 2 problems to solve in problems questions as the class given by the class work. 2. Go round to mark teacher pupils‟ work and do 2. Do their the correction for corrections them. 3. Pupils copy 3. Conclude the the home lesson by giving work in their home work to pupils. notes. 184 UNIVERSITY OF IBADAN LIBRARY Week 4 Lesson 4 Duration: 40 minutes Topic: Volume Objectives: At the end of the lesson, pupils should be able to 1. Calculate volume of triangular prism 2. Calculate volume of cylinders 3. Calculate volume of spheres 4. Solve word problems on volume Topic Duratio Steps Day Teacher’s Activities Pupils’ Teachin Evaluation n Activities g Aids Guide Volume 5 mins 1 1 to Ask pupils questions on Listen and 3 previous lesson and answer introduces the new questions. topic. 25 mins 2 1 1. Distribute the poems‟ 1. Choral Diagram Give home manual to pupils and reading of s of work to: ask pupils to read poems aloud triangula 1. Solve poems 1,2& 5 in wk4 by the whole r prism problems on (aloud by the whole class, in small on the volume at class, in small groups groups by rows chalk triangular prism by rows and and board. using the individually at random). individually. formula 2. Ask pupils to explain 2. Explain and 2. Solve word and role play the role play the problem 185 UNIVERSITY OF IBADAN LIBRARY following as pictured in images involving the poems. pictured in the volume of a. Concept of volume poems. triangular prism. b. Formula for 3. Listen to the calculating volume of teacher, ask triangular prism questions and c. Process involve in copy their solving problems on notes volume of triangular prisms d. Process involve in solving word problems on triangular prisms. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 2 1. Distribute the poems‟ 1. Choral Diagram Give home to: manual to pupils and reading of of 1. Solve ask pupils to read poems aloud Cylinder problems on poems 3& 5 in wk4 by the whole on the volume of (aloud by the whole class, in small chalk cylinders using class, in small groups groups by rows board the formula. by rows and and 2. Solve word individually at random). individually. problems 2. Explain and involving 2. Ask pupils to explain role play the volume of and role play the images Cylinder. 186 UNIVERSITY OF IBADAN LIBRARY following as pictured in pictured in the the poems. poems. a. Formula for 3. Listen to the calculating the volume teacher, ask of cylinders questions and b. Process involve in copy their solving problems on notes volume of cylinders c. Process involve in solving word problems on volume of cylinder. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 3 1. Distribute the poems‟ 1. Choral Diagram Give home work manual to pupils and reading of of sphere to: ask pupils to read poems aloud on the 1. Solve poems 4& 5 in wk4( by the whole chalk problems on aloud by the whole class, in small board volume of class, in small groups groups by rows sphere using the by rows and and formula individually at random). individually. 2. Solve word 2. Ask pupils to explain 2. Explain and problems and role play the role play the involving the following as pictured in images volume of the poems. pictured in the sphere. a. Formula for poems. 187 UNIVERSITY OF IBADAN LIBRARY calculating volume of 3. Listen to the sphere teacher, ask b. Process involve in questions and solving problems on copy their volume of sphere notes c. Process involve in solving word problems on volume of sphere. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 40 mins 4 1. Present the poems 1. Listen and 1. Give more for the week to pupils. read with the exercises as 2. Read poems aloud teacher home work. with emotions. 2. Read in 2.Give pupils 3. Ask pupils to read small groups poems to write poems (choral reading and about by the whole class, individually. a. Their small groups by row 4. Explain the feelings about and individually at images and mathematics. random). role play the b. The content 4. Ask pupils to explain actions in the for the week. the images and role poems. c. Process of play the actions in the 4. Listen to the solving a poems. revision and problem 5. Revise the week‟s ask questions work with reference to 188 UNIVERSITY OF IBADAN LIBRARY the poems 40 mins 5 1. Give test for the 1. Write the Give test to: week‟s work test 1. Solve 2. Mark the test and do 2. Do the problems on corrections corrections volume of a triangular prism, cylinder and sphere. 10 mins 3 1. Give pupils problems 1. Solve Give 1 or 2 to solve in the class. problems given questions as 2.Go round to mark by the teacher. class work. pupils‟ works and do 2. Do their the corrections for them corrections 3. Conclude the lesson 3. Pupils copy by giving home work to the home work pupils. in their notes. 189 UNIVERSITY OF IBADAN LIBRARY Week 5 Lesson 5 Duration: 40 minutes Topic: Capacity Objectives: At the end of the lesson, pupils should be able to 1. Explain the concept of capacity 2. Solve word problems on capacity. Topic Duration Steps Day Teacher’s Activities Pupils’ Teaching Evaluation Activities Aids Guide Capacity 5 mins 1 1 to Ask questions on Listen and 3 previous lesson and answer introduce the new questions. topic. 25 mins 2 1 1. Distribute the 1. Choral Give home work poems‟ manual to reading of to: pupils and ask pupils poems aloud 1. Name and to read poems 1& 2 in by the whole compare the wk5 (aloud by the class, in small capacities of whole class, in small groups by containers in the groups by rows and rows and home. individually at individually. random). 2. Explain and 2. Ask pupils to role play the explain and role play images the following as pictured in the pictured in the poems. poems. a. Concept of capacity 3. Listen to the 190 UNIVERSITY OF IBADAN LIBRARY b. Various containers teacher, ask and compare their questions and capacities. copy their 3. Teacher asks pupils notes questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 2 1. Distribute the 1. Choral Give home work poems‟ manual to reading of to: pupils and ask pupils poems aloud 1. Solve problems to read poems 3& 4 in by the whole on conversion of wk5( aloud by the class, in small units of capacity. whole class, in small groups by groups by rows and rows and individually at individually. random). 2. Explain and 2. Ask pupils to role play the explain and role play images the following as pictured in the pictured in the poems. poems. a. Tables of capacity 3. Listen to the b. Conversion of units teacher, ask of capacity. questions and 3. Teacher asks pupils copy their questions to clarify the notes concept/teaches the new topic with 191 UNIVERSITY OF IBADAN LIBRARY reference to the poems. 25 mins 3 1. Distribute the 1. Choral Give home work poems‟ manual to reading of to: pupils and ask pupils poems aloud 1. Solve word to read poems 4& 5 in by the whole problems wk5 (aloud by the class, in small involving whole class, in small groups by capacity. groups by rows and rows and individually at individually. random). 2. Explain and 2. Ask pupils to role play the explain and role play images the following as pictured in the pictured in the poems. poems. a. Process involve in 3. Listen to the solving word problems teacher, ask involving capacity. questions and 3. Teacher asks pupils copy their questions to clarify the notes concept/teaches the new topic with reference to the poems. 40 mins 4 1. Present the poems 1. Listen and 1. Give more for the week to pupils. read with the exercises as home 2. Read poems aloud teacher work. with emotions. 2. Read in 2.Give pupils 3. Ask pupils to read small groups poems to write poems (choral reading and about 192 UNIVERSITY OF IBADAN LIBRARY by the whole class, in individually. a. Their feelings small groups and 4. Explain the about individually at images and mathematics. random). role play the b. The content for 4. Ask pupils to actions in the the week. explain the images and poems. c. Process of role play the actions in 4. Listen to the solving a problem the poems. revision and 5. Revise the week‟s ask questions work with reference to the poems. 40 mins 5 1. Give test for the 1. Write the Give test to week‟s work test 1. Solve problems 2. Mark pupils work 2. Do the on conversion of and do corrections. corrections units of capacity 2. Solve word problems involving capacity. 10 mins 3 1. Give pupils 1. Solve Give1 or 2 problems to solve in problems questions as class the class. given by the work. 2. Go round to mark teacher. pupils‟ works and do 2. Do their the corrections for corrections them. 3. Pupils copy 3. Conclude the lesson the home work by giving home work in their notes. to pupils. 193 UNIVERSITY OF IBADAN LIBRARY Week 6 Lesson 6 Duration 40 minutes Topic: Weight Objectives: At the end of the lesson, pupils should be able to: 1 Explain the concept of weight 2 Express the same weight in different units: grams, kilograms, and tonnes 3 Solve word problems involving weight. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Guide Activities Aids Weight 5 mins 1 1 to Ask pupils questions Listen and 3 on previous lesson and answer the introduce the new questions. topic. 25 mins 2 1 1. Distribute the 1. Choral Give home work to poems‟ manual to reading of list 5 objects each that pupils and ask pupils to poems aloud can be expressed in read poems 1& 2 in by the whole 1. Grams wk6 (aloud by the class, in 2. Kilograms whole class, in small small groups 3. Tonnes groups by rows and by rows and individually at individually. random). 2. Explain 2. Ask pupils to explain and role play and role play the the images following as pictured in pictured in 194 UNIVERSITY OF IBADAN LIBRARY the poems. the poems. a. Concept of weight 3. Listen to b. Weight of small the teacher, objects is expressed in ask questions grams, medium sized and copy objects in kilograms, their notes while heavy objects are expressed in tonnes. c. Name examples of objects and the unit of expression of weight. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 2 1. Distribute the 1. Choral Give home work to poems‟ manual to reading of convert weights pupils and ask pupils to poems aloud 1. in grams to kg read poems 3,4& 5 in by the whole 2. Kg to tonnes wk6 (aloud by the class, in 3. Grams to tonnes whole class, in small small groups 4. Tonnes to Kg and groups by rows and by rows and grams individually at individually. random). 2. Explain 2. Ask pupils to explain and role play and role play the the images following as pictured in pictured in the poems. the poems. 195 UNIVERSITY OF IBADAN LIBRARY a. Tables on weight on 3. Listen to the chalk board. the teacher, b. Tables on conversion ask questions of weight and copy c. Express the same their notes weight in different units, e.g. 80,000 grams = 80kg = 0.08 tonnes. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 3 1. Distribute the 1. Choral Give home work to poems‟ manual to reading of 1. Solve word pupils and ask pupils to poems aloud problems involving read poem 6 in wk6 by the whole weight. (aloud by the whole class, in class, in small groups small groups by rows and by rows and individually at individually. random). 2. Explain 2. Ask pupils to explain and role play and role play the the images following as pictured in pictured in the poems. the poems. a. Process in solving 3. Listen to word problems on the teacher, 196 UNIVERSITY OF IBADAN LIBRARY weight on the chalk ask questions board. and copy 3. Teacher asks pupils their notes questions to clarify the concept/teaches the new topic with reference to the poems. 40 mins 4 1. Present the poems 1. Listen and 1. Give more exercises for the week to pupils. read with the as home work. 2. Read poems aloud teacher 2.Give pupils poems with emotions. 2. Read in to write about 3. Ask pupils to read small groups a. Their feelings about poems (choral reading and mathematics. by the whole class, in individually. b. The content for the small groups and 4. Explain week. individually at the images c. Process of solving a random). and role play problem 4. Ask pupils to explain the actions in the images and role the poems. play the actions in the 4. Listen to poems. the revision 5. Revise the week‟s and ask work with reference to questions the poems. 40 mins 5 1. Give test for the 1. Write the Give test to; week‟s work test 1. Convert weights to 2. Mark pupils work 2. Do the different units. and do corrections. correction. 2. Solve word problems involving 197 UNIVERSITY OF IBADAN LIBRARY weight. 10 Mins 3 1. Give pupils 1. Solve Give 1 or 2 questions problems to solve in problems class work. the class. given by the 2. Go round to mark teacher pupils work and do the 2. Do their correction for them. corrections. 3. Conclude the lesson 3. Copy the by giving home work home work to pupils. in their note. 198 UNIVERSITY OF IBADAN LIBRARY Week 7 Lesson 7 Duration: 40 minutes Topic: 2-Dimensional figures Objectives: At the end of the lesson, pupils should be able to 1. Explain what 2-dimensional shapes are 2. Identify 2-dimentional shapes by name 3. Identify the essential properties of 2-dimensional shapes 4. Identify polygons not exceeding the octagon 5. Solve more difficult problems on 2-dimensional shapes. Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide 2- 5 mins 1 1 to Ask pupils Listen and Dimensional 3 questions on answer the Figures previous lesson and questions. introduce the new topic. 25 mins 2 1 1. Distribute the 1. Choral reading Diagrams Give home poems‟ manual to of poems aloud of 2- D work to: pupils and ask by the whole shapes 1. Name seven pupils to read class, in small 2-dimensional poems 1& 2 in wk7 groups by rows shapes. (aloud by the whole and individually. 2. Name the class, in small 2. Explain and types of groups by rows and role play the triangles. 199 UNIVERSITY OF IBADAN LIBRARY individually at images pictured random). in the poems. 2. Ask pupils to 3. Listen to the explain and role teacher, ask play the following questions and as pictured in the copy their notes poems. a. What 2- dimensional shapes are? b. Names of 2- dimensional shapes on the chalk board. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 200 UNIVERSITY OF IBADAN LIBRARY 15 mins 2 1. Distribute the 1. Choral reading Diagrams Give Home poems‟ manual to of poems aloud showing work to pupils and ask by the whole the 1. Complete a pupils to read class, in small features chart of shapes poems 3& 4 in wk7 groups by rows of 2- indicating lines (aloud by the whole and individually. dimensio of symmetry, class, in small 2. Explain and nal and number of groups by rows and role play the shapes. sides. individually at images pictured Draw 2. Number of random). in the poems. triangles, angels 2. Ask pupils to 3. Listen to the compoun contained in explain and role teacher, ask d shapes the shape. play the following questions and on the 3. Name the as pictured in the copy their notes chalk types of poems. board. triangles a. Features of 2- 4. Write the dimensional shapes features of each on the chalk board. triangle. b. Solve problems 5. Identify on 2-dimensional different shapes. shapes in a 3. Teacher asks compound pupils questions to figure. clarify the 6. Find sizes of concept/teaches the angles of new topic with triangles. reference to the poems. 201 UNIVERSITY OF IBADAN LIBRARY 25mins 3 1. Distribute the 1. Choral reading Diagram Give home poems‟ manual to of poems aloud of work to; pupils and ask by the whole polygons 1. List the pupils to read class, in small on the names of poems 5& 6 in wk7 groups by rows chalk- polygons. (aloud by the whole and individually. board 2. Calculate the class, in small 2. Explain and angle at the groups by rows and role play the centre of each individually at images pictured polygon. random). in the poems. 3. Calculate the 2. Ask pupils to 3. Listen to the sum of angles explain and role teacher, ask of each play the following questions and polygon. as pictured in the copy their notes 4. Deduce the poems. formula for the a. What a polygon sum of angles is. of n-sided b. Call polygons not polygon. exceeding the octagon. c. Solve problems on polygons 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 202 UNIVERSITY OF IBADAN LIBRARY 40 mins 4 1. Present the 1. Listen and . 1. Give more poems for the week read with the exercises as to pupils. teacher home work. 2. Read poems 2. Read in small 2.Give pupils aloud with groups and poems to write emotions. individually. about 3. Ask pupils to 4. Explain the a. Their read poems (choral images and role feelings about reading by the play the actions mathematics. whole class, in in the poems. b. The content small groups and 4. Listen to the for the week. individually at revision and ask c. Process of random). questions solving a 4. Ask pupils to problem explain the images and role play the actions in the poems. 5. Revise the week‟s work with reference to the poems. 40 mins 5 1. Give test for the 1. Write the test. Give test to week‟s work 2. Do the 1. Name and 2. Mark pupils work correction. identify and do corrections. features of 2- dimensional shapes. 2. Name types of triangles and 203 UNIVERSITY OF IBADAN LIBRARY their features. 3. Identify shapes in a given compound figure. 4. Calculate angles in a given triangle. 5. Name the types of polygons 6. Calculate the sum of angles of a given polygon. 10 mins 3 1. Give pupils class 1. Solve Give 1 or 2 work problems given questions as 2. Go round to mark by the teacher. class work. pupils‟ work and do 2. Do their the correction. corrections 3. Conclude the 3. Copy the home lesson by giving work. home work to pupils. 204 UNIVERSITY OF IBADAN LIBRARY Week 8 Lesson 8 Duration: 40 minutes Topic: 3-Dimensional shapes Objectives: At the end of the lesson, pupils should be able to 1. Explain what 3-dimensional shapes are 2. Identify 3-dimentional shapes by name 3. Identify number of edges, faces and vertices of 3-dimensional shapes 4. Identify nets of 3-dimensional shapes 5. Measure angles of 3-dimensional shapes 6. Identify lines that are parallel and perpendicular in 3-dimensional shapes. Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide 3- 5 mins 1 1 to Ask pupils Listen and Dimensional 3 questions on answer the Shapes previous lesson and questions. introduce the new topic. 25 mins 2 1 1. Distribute the 1. Choral Diagrams of Give home poems‟ manual to reading of 3- work to: pupils and ask poems aloud dimensional 1. List 3- pupils to read by the whole shapes on the dimensional poems 1 in wk8 class, in small chalk board. shapes. (aloud by the whole groups by 2. Draw and class, in small rows and label 3- 205 UNIVERSITY OF IBADAN LIBRARY groups by rows and individually. dimensional individually at 2. Explain shapes. random). and role play 2. Ask pupils to the images explain and role pictured in play the following the poems. as pictured in the 3. Listen to poems. the teacher, a. What 3- ask questions dimensional shapes and copy their are? notes b. Names of 3- dimensional shapes on the chalk board. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 2 1. Distribute the 1. Choral Diagrams Give home poems‟ manual to reading of showing the work to: pupils and ask poems aloud edges, faces 1. Make 3- pupils to read by the whole and vertices dimensional poems 2&3 in wk8 class, in small of 3- shapes with (aloud by the whole groups by dimensional cardboard. class, in small rows and shapes. 2. Complete a groups by rows and individually. chart of 3- 206 UNIVERSITY OF IBADAN LIBRARY individually at 2. Explain dimensional random). and role play shapes 2. Ask pupils to the images indicating explain and role pictured in numbers of play the following the poems. edges, faces and as pictured in the 3. Listen to vertices. poems. the teacher, 3. Prepare nets a. What are edges, ask questions of 3- faces and vertices and copy their dimensional of a given 3- notes shapes. dimensional shape? b. Indicate the edges, vertices and faces of 3-D shapes 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 25 mins 3 1. Distribute the 1. Choral 1. Diagram Give home poems‟ manual to reading of of 3- work to: pupils and ask poems aloud dimensional 1. Measure sizes pupils to read by the whole shapes. of angles in 3- poems 4&5 in wk8 class, in small 2. Diagram dimensional (aloud by the whole groups by of parallel shapes. class, in small rows and and 2. List lines that groups by rows and individually. perpendicular are 207 UNIVERSITY OF IBADAN LIBRARY individually at 2. Explain lines. perpendicular. random). and role play 3. List lines that 2. Ask pupils to the images parallel to each explain and role pictured in other. play the following the poems. as pictured in the 3. Listen to poems. the teacher, a. Measure the ask questions sizes of angles in 3- and copy their dimensional notes shapes. b. Indicate lines that are parallel and perpendicular 3- dimensional shapes. 3. Teacher asks pupils questions to clarify the concept/teaches the new topic with reference to the poems. 40mins 4 1. Present the 1. Listen and 1. Give more poems for the week read with the exercises as to pupils. teacher home work. 2. Read poems 2. Read in 2.Give pupils aloud with small groups poems to write emotions. and about 208 UNIVERSITY OF IBADAN LIBRARY 3. Ask pupils to individually. a. Their feelings read poems (choral 3. Explain the about reading by the images and mathematics. whole class, in role play the b. The content small groups and actions in the for the week. individually at poems c. Process of random). 4. Listen to solving a 4. Ask pupils to the revision problem explain the images and ask and role play the questions actions in the poems. 5. Revise the week‟s work with reference to the poems. 40 mins 5 1. Give test for the 1. Write the Give test to: week‟s work test. 1. List the 2. Mark pupils 2. Do the names of 3- work and do correction. dimensional corrections. shapes. 2. Identify the number of edges, faces and vertices of 3- dimensional shapes. 3. Use protractor to 209 UNIVERSITY OF IBADAN LIBRARY measure the sizes of angles of 3- dimensional shapes. 4. List pair of parallel and perpendicular lines in a given 3-dimensional shape. 5. Identify nets of 3- dimensional shapes. 10 mins 3 1. Give pupils class 1. Solve the Give 1 or 2 work. problems questions as 2. Go round to given by the class work. mark pupils work teacher. and do the 2. Do their corrections. corrections 3. Conclude the 3. Copy the lesson by giving home work. home work to pupils. 210 UNIVERSITY OF IBADAN LIBRARY Appendix 12 INSTRUCTIONAL GUIDE ON GAME-ENHANCED INSTRUCTIONAL STRATEGY (IGGEIS) Experimental group 2 (lesson schedule) Week I Lesson I Duration: 40 minutes Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to: 1. Explain the concept of fraction 2. Explain the concept of decimal 3. Express fractions as decimals 4. Express decimals as fractions 5. Order fractions and decimals Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide Fraction 2 mins 1 1 to Ask pupils questions on Listen and and 3 the previous lesson and answer the Decimal introduce the new topic. questions 25mins 2 1 1.Teach the new topic 1. Listen, Give home work 2.Distribute week 1 game ask to: materials/re-arrange the questions express: class and copy the 1. fractions as 3. Explain the game note. decimals (correct 211 UNIVERSITY OF IBADAN LIBRARY materials, rules and 2. Play week to 2 or 3 decimal objectives of the lesson. 1 game places) 25 mins 2 1.Teach the new topic 1. Listen, Give home work 2. Distribute week 1 ask to: game materials/re-arrange questions express: the class and copy the 1. Decimals as 3. Explain the game note. fractions. Give materials, rules and 2. Play week answers in the objectives of the lesson. 1 game lowest term. 2. Order decimals in ascending order. 3. Order a set of decimals in descending order. 25 mins 3 1.Teach the new topic 1. Listen, Give home work 2.Distribute week 1 game ask to: 1.Order materials/re-arrange the questions fractions in class and copy the ascending order. 3. Explain the game note. 2. Order a set of materials, rules and 2. Play week fractions in objectives of the lesson. 1 game descending order 40mins 4 1.Revise the week‟s work 1. Listen, Give more 2.Distribute week 1 game ask exercises as materials/re-arrange the questions home work and class and copy the follow up 212 UNIVERSITY OF IBADAN LIBRARY 3. Explain the game note. activities. materials, rules and 2. Play week objectives of the lesson. 1 game 40 mins. 5 1. Give test for the 1. Write the Give test to: weeks work test. 1. Order a set of 2. Mark the test and do 2. Do their fraction in the correction. corrections. ascending or descending order. 2. Order a set of decimal in ascending or descending order. 3. Express fractions as decimals. 4. Express decimals as fractions. Give answers in the lowest term. 13mins 3 De- briefing session 1. Pupils 1. Ask questions 1. Ask pupils questions to answer the base on the day‟s further clarify the questions. work. concept and problems. 2. Pupils 2. Call pupils to 2. Ask pupils to come to solve the solve question the board to solve problems on cards that were problems as follow-up the board. difficult. 213 UNIVERSITY OF IBADAN LIBRARY activities. 3. Pupils 3. Give home 3. Give home work. copy their work covering 4. Collect materials/re- home work the day‟s work. arrange the class. 214 UNIVERSITY OF IBADAN LIBRARY Week 2 Lesson 2 Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to: 1. Add fractions and decimals 2. Subtract fractions and decimals 3. Combined addition and subtraction of fraction 4. Solve word problems on addition of fraction and decimal 5. Solve word problems on subtraction of fraction and decimal. Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide Addition 2 mins 1 1 to Ask pupils questions Listen and and 3 on the previous lesson answer the subtraction and introduce the new questions. (sub-topic) topic. 25mins 2 1 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 2 questions and to game materials/re- copy the note. 1. Add fractions arrange the class 2. Play week only 3. Explain the game 2 game 2. Subtract materials, rules and fractions only. objectives of the lesson. 25 mins 2 1.Teach the new topic 1. Listen, ask Give home work 215 UNIVERSITY OF IBADAN LIBRARY 2.Distribute week 2 questions and to game materials/re- copy the note. 1. Solve arrange the class 2. Play week problems on 3. Explain the game 2 game combined materials, rules and addition and objectives of the subtraction of lesson. fraction. 2. Solve problems that involve carrying. 3. Solve word problems involving addition and subtraction of fraction. 25mins 3 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 2 questions and to: game materials/re- copy the note. 1. Solve word arrange the class 2. Play week problems on 3. Explain the game 2 game addition of materials, rules and decimal. objectives of the 2. Solve word lesson. problems on the subtraction of decimal. 3. Solve word problems 216 UNIVERSITY OF IBADAN LIBRARY involving addition and subtraction of decimal 4 1.Revise the week‟s 1. Listen, ask Give more work questions and exercises as 2.Distribute week 2 copy the note. home work and game materials/re- 2. Play week follow up arrange the class 2 game activities. 3. Explain the game materials, rules and objectives of the lesson. 40mins 5 1. Give test for the 1. Write the Give test to: week‟s work. test. 1. Add and 2. Mark the test and do 2. Do the subtract the correction. correction. fractions. 2. Add and subtract fraction involving carrying. 3. Word problems on addition and subtraction of fraction. 4. Add and subtract 217 UNIVERSITY OF IBADAN LIBRARY decimal. 5. Word problems on addition and subtraction of decimal. 13mins 3 De- briefing session 1. Pupils 1. Ask questions 1. Ask pupils questions answer the base on the to further clarify the questions. day‟s work. concept and problems. 2. Pupils 2. Call pupils to 2. Ask pupils to come solve the solve question to the board to solve problems on cards that were problems as follow-up the board. difficult. activities. 3. Pupils 3. Give home 3. Give home work. copy their work covering 4. Collect materials/re- home work the day‟s work. arrange the class. 218 UNIVERSITY OF IBADAN LIBRARY Week 3 Lesson 3 Duration: 40 minutes Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to 1. Multiply fraction by fraction 2. Solve word problems on multiplication of fraction 3. Multiply decimal by decimal 4. Divide decimal by 2-digit and 3 digit numbers 5. Solve word problems on multiplication and division of decimal. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Activities Aids Guide Multiplication 2mins 1 1 to Ask pupils questions Listen and and Division 3 on previous lesson answer the (sub-topic) and introduce the questions. new lesson. 25mins 2 1 1.Teach the new 1. Listen, ask Give home to topic questions and 1. Multiply 2.Distribute week 3 copy the note. fraction by game materials/re- 2. Play week fraction arrange the class 3 game 2. Solve word 3. Explain the game problems on materials, rules and multiplication of objectives of the fraction. lesson. 219 UNIVERSITY OF IBADAN LIBRARY 25mins 2 1.Teach the new 1. Listen, ask Give home work topic questions and to: 2.Distribute week 3 copy the note. 1. Multiply game materials/re- 2. Play week decimal by arrange the class 3 game decimal (correct 3. Explain the game to 2 or 3 places materials, rules and of decimal. objectives of the 2. Solve word lesson. problems on multiplication of decimal. 25 mins 3 1.Teach the new 1. Listen, ask Give home work topic questions and to: 2.Distribute week 3 copy the note. 1. Divide game materials/re- 2. Play week decimal by 2- arrange the class 3 game digit and 3-digit 3. Explain the game numbers. materials, rules and 2. Solve word objectives of the problems on lesson. division of decimals. 40 mins 4 1.Revise the week‟s 1. Listen, ask Give more work questions and exercises as 2.Distribute week 3 copy the note. home work and game materials/re- 2. Play week follow up arrange the class 3 game activities. 3. Explain the game materials, rules and 220 UNIVERSITY OF IBADAN LIBRARY objectives of the lesson. 40mins 5 1. Give test for the 1. Write the Give test to: week‟s work. test 1. Multiply 2. Mark the test and 2. Do the fraction by do the correction. correction. fraction 2. Solve word problems involving multiplication of fraction. 3. Multiply decimal by decimal and solve word problems. 4. Division of decimal by 2 & 3-digit numbers. 5. Word problems on division of decimal. 13mins 3 De- briefing session 1. Pupils 1. Ask questions 1. Ask pupils answer the base on the day‟s questions to further questions. work. clarify the concept 2. Pupils 2. Call pupils to and problems. solve the solve question 2. Ask pupils to problems on cards that were 221 UNIVERSITY OF IBADAN LIBRARY come to the board to the board. difficult. solve problems as 3. Pupils copy 3. Give home follow-up activities. their home work covering 3. Give home work. work the day‟s work. 4. Collect materials/re-arrange the class. 222 UNIVERSITY OF IBADAN LIBRARY Week 4 Lesson 4 Duration: 40 minutes Topic: Volume Objectives: At the end of the lesson, pupils should be able to 1. Calculate volume of triangular prism 2. Calculate volume of cylinders 3. Calculate volume of spheres 4. Solve word problems on volume Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide Volume 2 mins 1 1 to Ask pupils questions on Listen and 3 previous lesson and answer introduces the new questions. topic. 25 mins 2 1 1.Teach the new topic 1. Listen, ask Diagrams Give home work 2.Distribute week 4 questions and of to: game materials/re- copy the note. triangular 1. Solve arrange the class 2. Play week 4 prisms on problems on 3. Explain the game game the chalk volume of materials, rules and board. triangular prism objectives of the lesson. using the formula 2. Solve word problems 223 UNIVERSITY OF IBADAN LIBRARY involving volume of triangular prisms. 25 mins 2 1.Teach the new topic 1. Listen, ask Diagram Give home work 2.Distribute week 4 questions and of to: game materials/re- copy the note. Cylinder 1. Solve arrange the class 2. Play week 4 on the problems on 3. Explain the game game chalk volume of materials, rules and board cylinders using objectives of the lesson. the formula. 2. Solve word problems involving volume of Cylinder. 25mins 3 1.Teach the new topic 1. Listen, ask Diagram Give home work 2.Distribute week 4 questions and of sphere to: game materials/re- copy the note. on the 1. Solve a arrange the class 2. Play week 4 chalk problem on 3. Explain the game game board volume of sphere materials, rules and using the objectives of the lesson. formula 2. Solve word problems involving the volume of sphere. 40 mins 4 1.Revise the week‟s 1. Listen, ask Give more 224 UNIVERSITY OF IBADAN LIBRARY work questions and exercises as 2.Distribute week 4 copy the note. home work and game materials/re- 2. Play week 4 follow up arrange the class game activities. 3. Explain the game materials, rules and objectives of the lesson. 40 mins 5 1. Give test for the 1. Write the Give home work week‟s work test to: 2. Mark the test and do 2. Do the 1. Solve corrections corrections problems on volume of a triangular prism, cylinder and sphere. 13mins 3 De- briefing session 1. Pupils 1. Ask questions 1. Ask pupils questions answer the base on the day‟s to further clarify the questions. work. concept and problems. 2. Pupils solve 2. Call pupils to 2. Ask pupils to come to the problems solve question the board to solve on the board. cards that were problems as follow-up 3. Pupils copy difficult. activities. their home 3. Give home 3. Give home work. work work covering 4. Collect materials/re- the day‟s work. arrange the class. 225 UNIVERSITY OF IBADAN LIBRARY Week 5 Lesson 5 Duration: 40 minutes Topic: Capacity Objectives: At the end of the lesson, pupils should be able to 1. Explain the concept of capacity 2. Solve word problems on capacity. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Activities Aids Guide Capacity 2 mins 1 1 to Ask pupils questions Listen and 3 on previous lesson and answer introduce the new questions. topic. 25 mins 2 1 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 5 questions and to: game materials/re- copy the note. 1. Name and arrange the class 2. Play week 5 compare the 3. Explain the game game capacities of materials, rules and containers in the objectives of the home. lesson. 226 UNIVERSITY OF IBADAN LIBRARY 25 mins 2 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 5 questions and to: game materials/re- copy the note. 1. Solve problems arrange the class 2. Play week 5 on conversion of 3. Explain the game game units of capacity. materials, rules and objectives of the lesson. 25mins 3 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 5 questions and to: game materials/re- copy the note. 1. Solve word arrange the class 2. Play week 5 problems 3. Explain the game game involving materials, rules and capacity. objectives of the lesson. 40 mins 4 1.Revise the week‟s 1. Listen, ask Give more work questions and exercises as home 2.Distribute week 5 copy the note. work and follow game materials/re- 2. Play week 5 up activities. arrange the class game 3. Explain the game materials, rules and objectives of the lesson. 40 mins 5 1. Give test for the 1. Write the test Give test to: week‟s work 2. Do the 1. Solve problems 2. Mark pupils work corrections on conversion of 227 UNIVERSITY OF IBADAN LIBRARY and do corrections. units of capacity 2. Solve word problems involving capacity. 13mins 3 De- briefing session 1. Pupils answer 1. Ask questions 1. Ask pupils the questions. base on the day‟s questions to further 2. Pupils solve work. clarify the concept and the problems on 2. Call pupils to problems. the board. solve question 2. Ask pupils to come 3. Pupils copy cards that were to the board to solve their home work difficult. problems as follow-up 3. Give home activities. work covering the 3. Give home work. day‟s work. 4. Collect materials/re- arrange the class. 228 UNIVERSITY OF IBADAN LIBRARY Week 6 Lesson 6 Duration: 40 minutes Topic: Weight Objectives: At the end of the lesson, pupils should be able to: 1. Explains the concept of weight 2. Express the same weight in different units: grams, kilograms, and tonnes 3. Solve word problems involving weight. Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide Weight 2 mins 1 1 to Ask pupils questions on Listen and 3 previous lesson and answer the introduce the new topic. questions. 25 mins 2 1 1.Teach the new topic 1. Listen, ask Give Home work 2.Distribute week 6 questions and to list 5 objects game materials/re-arrange copy the note. each that can be the class 2. Play week 6 expressed in: 3. Explain the game game 1. Grams. materials, rules and 2. Kilograms. objectives of the lesson. 3. Tonnes. 25 mins 2 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 6 questions and to convert game materials/re-arrange copy the note. weights: the class 2. Play week 6 1. in grams to kg 3. Explain the game game 2. Kg to tonnes 229 UNIVERSITY OF IBADAN LIBRARY materials, rules and 3. Grams to objectives of the lesson. tonnes 4. Tonnes to Kg and grams etc. 25mins 3 1.Teach the new topic 1. Listen, ask Give home work 2.Distribute week 5 questions and to: game materials/re-arrange copy the note. 1. Solve word the class 2. Play week 5 problems 3. Explain the game game involving weight. materials, rules and objectives of the lesson. 40 mins 4 1.Revise the week‟s 1. Listen, ask Give more work questions and exercises as home 2.Distribute week 6 copy the note. work and follow game materials/re-arrange 2. Play week 6 up activities. the class game 3. Explain the game materials, rules and objectives of the lesson. 40 mins 5 1. Give test for the 1. Write the Give test to; week‟s work test 1. Convert 2. Mark pupils work and 2. Do the weights to do corrections. correction. different units. 2. Solve word problems involving weight. 13mins 3 De- briefing session 1. Pupils 1. Ask questions 1. Ask pupils questions answer the base on the day‟s 230 UNIVERSITY OF IBADAN LIBRARY to further clarify the questions. work. concept and problems. 2. Pupils solve 2. Call pupils to 2. Ask pupils to come to the problems solve question the board to solve on the board. cards that were problems as follow-up 3. Pupils copy difficult. activities. their home 3. Give home 3. Give home work. work work covering the 4. Collect materials/re- day‟s work. arrange the class. 231 UNIVERSITY OF IBADAN LIBRARY Week 7 Lesson 7 Duration: 40 minutes Topic: 2-Dimensional figures Objectives: At the end of the lesson, pupils should be able to 1. Explain what 2-dimensional shapes are 2. Identify 2-dimentional shapes by name 3. Identify the essential properties of 2-dimensional shapes 4. Identify polygons not exceeding the octagon 5. Solve more difficult problems on 2-dimensional shapes. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Guide Activities Aids 2- 2 mins 1 to 3 Ask questions on Listen and Dimensional previous lesson and answer the Figures introduce the new questions. topic. 25 mins 2 1 1.Teach the new topic 1. Listen, ask Diagram Give home work 2.Distribute week 7 questions and of 2- to; game materials/re- copy the note. dimension 1. Seven 2- arrange the class 2. Play week 7 al shapes dimensional shapes. 3. Explain the game game on the 2. Name the types materials, rules and chalk of triangles. 232 UNIVERSITY OF IBADAN LIBRARY objectives of the board. lesson. 25 mins 2 1.Teach the new topic 1. Listen, ask Diagrams Give home work to: 2.Distribute week 7 questions and showing 1. Complete a chart game materials/re- copy the note. the of shapes indicating arrange the class 2. Play week 7 features of lines of symmetry, 3. Explain the game game 2- and number of materials, rules and dimension sides. objectives of the al shapes. 2. Number of lesson. 2.Draw angels contained in triangles, the shape. compound 3. Name the types shapes on of triangles the chalk 4. Write the board. features of each triangle 5. Identify different shapes in a compound figure. 6. Find sizes of angles of triangles. 233 UNIVERSITY OF IBADAN LIBRARY 25mins 3 1.Teach the new topic 1. Listen, ask Diagram Give home work to: 2.Distribute week 7 questions and of 1. List the names of game materials/re- copy the note. polygons polygons. arrange the class 2. Play week 7 on the 2. Calculate the 3. Explain the game game chalk- angle at the centre materials, rules and board. of each polygon. objectives of the 3. Calculate the lesson. sum of angles of each polygon. 4. Deduce the formula for the sum angles of n-sided polygon. 40 mins 4 1.Revise the week‟s 1. Listen, ask Give more work questions and exercises as home 2.Distribute week 7 copy the note. work and follow up game materials/re- 2. Play week 7 activities. arrange the class game 3. Explain the game materials, rules and objectives of the lesson. 234 UNIVERSITY OF IBADAN LIBRARY 40 mins 5 1. Give test for the 1. Write the Give test to week‟s work test. 1. Name and 2. Mark pupils work 2. Do the identify features of and do corrections. correction. 2-dimensional shapes. 2. Name types of triangles and their features. 3. Identify shapes in a given compound figure. 4. Calculate angles in a given triangle. 5. Name the types of polygons 6. Calculate the sum of angles of a given polygon. 13mins 3 De- briefing session 1. Pupils 1. Ask questions 1. Ask pupils answer the base on the day‟s questions to further questions. work. clarify the concept and 2. Pupils solve 2. Call pupils to 235 UNIVERSITY OF IBADAN LIBRARY problems. the problems solve question cards 2. Ask pupils to come on the board. that were difficult. to the board to solve 3. Pupils copy 3. Give home work problems as follow-up their home covering the day‟s activities. work work. 3. Give home work. 4. Collect materials/re- arrange the class. 236 UNIVERSITY OF IBADAN LIBRARY Week 8 Lesson 8 Duration: 40 minutes Topic: 3-Dimensional shapes Objectives: At the end of the lesson, pupils should be able to: 1. Explain what 3-dimensional shapes are 2. Identify 3-dimentional shapes by name 3. Identify number of edges, faces and vertices of 3-dimensional shapes 4. Identify nets of 3-dimensional shapes 5. Measure angles of 3-dimensional shapes 6. Identify lines that are parallel and perpendicular in 3-dimensional shapes. Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide 3- 2 mins 1 1 to Ask pupils questions Listen and Dimensional 3 on previous lesson answer the Shapes and introduce the questions. new topic. 25 mins 2 1 1.Teach the new 1. Listen, ask Diagrams of Give home topic questions and 3- work to: 2.Distribute week 8 copy the note. dimensional 1. List 3- game materials/re- 2. Play week 8 shapes on the dimensional arrange the class game board. shapes. 3. Explain the game 2. Draw and materials, rules and label 3- objectives of the dimensional 237 UNIVERSITY OF IBADAN LIBRARY lesson. shapes. 25 mins 2 1.Teach the new 1. Listen, ask Diagrams Give home topic questions and showing the work to: 2.Distribute week 8 copy the note. edges, faces 1. Make 3- game materials/re- 2. Play week 8 and vertices dimensional arrange the class game of 3- shapes with 3. Explain the game dimensional cardboard. materials, rules and shapes. 2. Complete a objectives of the chart of 3- lesson. dimensional shapes indicating numbers of edges, faces and vertices. 3. Prepare nets of 3- dimensional shapes. 25mins 3 1.Teach the new 1. Listen, ask 1. Diagram Give home topic questions and of 3- work to 2.Distribute week 8 copy the note. dimensional 1. Measure game materials/re- 2. Play week 8 shapes. sizes of angles arrange the class game 2. Diagram in 3- 3. Explain the game of parallel dimensional materials, rules and and shapes. objectives of the perpendicular 2. List lines that 238 UNIVERSITY OF IBADAN LIBRARY lesson. lines. are perpendicular. 3. List lines that parallel to each other in 3-D shapes. 40 mins 4 1.Revise the week‟s 1. Listen, ask Give more work questions and exercises as 2.Distribute week copy the note. home work and 8&9 games 2. Play week follow up materials/re-arrange 8&9 games activities. the class 3. Explain the game materials, rules and objectives of the lesson. 40 mins 5 1. Give test for the 1. Write the 1. List the week‟s work test. names of 3- 2. Mark pupils work 2. Do the dimensional and do corrections. correction. shapes. 2. Identify the number of edges, faces and vertices of 3-dimensional shapes. 3. Use protractor to measure the 239 UNIVERSITY OF IBADAN LIBRARY sizes of angles of 3- dimensional shapes. 4. List pair of parallel and perpendicular lines in a given 3-dimensional shape. 5. Identify nets of 3- dimensional shapes. 13mins 3 De- briefing session 1. Pupils 1. Ask 1. Ask pupils answer the questions base questions to further questions. on the day‟s clarify the concept 2. Pupils solve work. and problems. the problems 2. Call pupils to 2. Ask pupils to on the board. solve question come to the board to 3. Pupils copy cards that were solve problems as their home difficult. follow-up activities. work 3. Give home 3. Give home work. work covering 4. Collect the day‟s work. materials/re-arrange the class. 240 UNIVERSITY OF IBADAN LIBRARY Appendix 13 INSTRUCTIONAL GUIDE ON MODIFIED LECTURE INSTRUCTIONAL STRATEGY (IGLMIS) Control group (lesson schedule) Week I Lesson I Duration: 40 mins Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to: 1. Explain the concept of fraction 2. Explain the concept of decimal 3. Express fractions as decimals 4. Express decimals as fractions. 5. Order fractions and decimals Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide Fraction 5 mins 1 1 to Ask pupils questions on the Listen and and 3 previous lesson and answer the Decimal introduce the new topic. questions 15 mins 2 1 1. Explain the concept of 1.Listen to Give home fraction the work to: 2. Explain the concept of explanation express: decimal of the 1. fractions 3. Express fractions as concept of as decimals decimals fraction, (correct to 2 241 UNIVERSITY OF IBADAN LIBRARY 4. Solve problems on the decimal and or 3 decimal chalk board e.g. express express places) ¾ as a decimal fractions as decimals 2.Listen, ask questions and copy the note. 15 mins 2 1. Explain the processes 1. Listen to Give home involve in expressing the processes work to: decimals as fraction. involve in express: 2. Solve problems on the expressing 1. Decimals to chalk board e.g. express decimal as fractions. 0.75 as a fraction; give fraction. Give answers answer in its lowest term 2. Listen, in the lowest 3. Explain the processes ask questions term. involve in ordering decimal and copy the 2. Order numbers note. decimals in 4. Order a set of decimals in ascending ascending and descending order. order of magnitude 3. Order a set of decimals in descending order. 3 1. Explain the process 1. Listen to Give home involve in ordering fractions the processes work to: 2 .Order fraction in involve in 1.Order ascending or descending ordering fractions in order of magnitude. fractions . ascending 242 UNIVERSITY OF IBADAN LIBRARY 2. Listen, order. solve 2. Order a set examples of fractions in with the descending teacher and order copy the note. 15mins 4 1. Revise the week‟s work. 1. Listen and Give more ask questions exercises as 2. Solve more examples on 2. Participate home work. the week‟s work. in solving the examples. 40 mins. 5 1. Give test for the weeks 1. Write the Give test to work test. 1. Order a set 2. Mark the test and do the 2. Do their of fraction in correction. corrections. ascending or descending order. 2. Order a set of decimal in ascending or descending order. 3. Express fractions as decimals. 4. Express decimals as fractions. 243 UNIVERSITY OF IBADAN LIBRARY Give answers in the lowest term. 20 mins 3 1. Give pupils problems to 1. Solve Give class solve in the class. problems work covering 2. Mark pupils work and do given by the the day‟s the correction. teacher. lesson. 3. Conclude the lesson by 2. Do their giving home work to pupils. correction. 3. Copy the home work in their notes. 244 UNIVERSITY OF IBADAN LIBRARY Week 2 Lesson 2 Duration: 40 mins Topic: Addition and Subtraction Objectives: At the end of the lesson, pupils should be able to: 1. Add fractions and decimals 2. Subtract fractions and decimals 3. Combined addition and subtraction of fraction 4. Solve word problems on addition of fraction and decimal 5. Solve word problems on subtraction of fraction and decimal. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Activities Aids Guide Addition 5 mins 1 1 to Ask pupils questions Listen and and 4 on the previous lesson answer the subtraction and introduce the new questions. (sub-topic) topic. 2 1 1. Give pupils a 1. Participate Give home revision of addition of in the revision work to: whole numbers. exercise. 1. Add 2. Lead pupils to solve 2. Listen, and fractions only problems on addition solve 2. Subtract of fraction. examples with fractions only. 3. Lead pupils to solve the teacher problems on and copy the subtraction of fraction. note on 245 UNIVERSITY OF IBADAN LIBRARY addition of fraction. 3. Listen and solve examples on subtraction of fraction and copy the note. 15 mins 2 1. Solve problems on 1. Listen and Give home combined addition and solve work to subtraction of fraction. problems with 1. Solve 2. Solve word the teacher problems on problems on addition and copy the combined and subtraction of note. addition and fractions. 2. Listen, ask subtraction of questions and fraction. copy the note. 2. Solve problems that involve carrying. 3. Solve word problems involving addition and subtraction of fraction. 3 1. Lead pupils to solve 1. Listen and Give home problems on addition solve work to: of decimal. problems with 1. Solve 246 UNIVERSITY OF IBADAN LIBRARY 2. Lead pupils to solve the teacher problems on problems on and copy the addition of subtraction of decimal. note. decimal. 2. Listen, and 2. Solve solve the problems on problems on the subtraction subtraction of of decimal. decimal with the teacher. 4 1. Solve word Listen, ask Give home problems on addition questions and work to: of decimals. copy the note. 1. Solve word 2. Solve word problems on problems on addition of subtraction of decimal. decimals. 2. Solve word problems on subtraction of decimal. 3. Solve word problems involving addition and subtraction of decimal. 40mins 5 1. Give test for the 1. Write the Give test to: week‟s work. test. 1. Add and 2. Mark the test and do 2. Do the subtract the correction. correction. fractions. 247 UNIVERSITY OF IBADAN LIBRARY 2. Add and subtract fraction involving carrying. 3. Word problems on addition and subtraction of fraction. 4. Add and subtract decimal. 5. Word problems on addition and subtraction of decimal. 20 mins 3 1. Give pupils 1. Solve Give class problems to solve in problems work covering the class given by the the day‟s 2. Mark pupils work teacher. lesson. and do the correction. 2. Do their 3. Conclude the lesson correction by giving home work 3. Copy the to pupils. home work in their notes. 248 UNIVERSITY OF IBADAN LIBRARY Week 3 Lesson 3 Duration: 40 minutes Topic: Fraction and Decimal Objectives: At the end of the lesson, pupils should be able to: 1. Multiply fraction by fraction 2. Solve word problems on multiplication of fraction 3. Multiply decimal by decimal 4. Divide decimal by 2-digit and 3 digit numbers 5. Solve word problems on multiplication and division of decimal. Topic Duration Steps Day Teacher Activities Pupils’ Teaching Evaluation Activities Aids Guide Multiplication 5mins 1 1 to Ask pupils questions Listen and and Division 3 on the previous lesson answer the (sub-topic) and introduce the new questions. lesson. 15mins 2 1 1. Give pupils a 1. Participate in Give home to: revision on the revision of 1. Multiply multiplication of multiplication fraction by whole numbers. of whole fraction 2. Solve some numbers. 2. Solve word examples on the 2. Listen and problems on multiplication of solve examples multiplication fraction by fraction. with the of fraction. 3. Solve examples of teacher and 249 UNIVERSITY OF IBADAN LIBRARY word problems on the copy the note. multiplication of 3. Listen, ask fraction. questions and copy the note. 15mins 2 1. Solve some 1. Listen, solve Give home examples on the examples with work to: multiplication of teacher and 1. Multiply decimal by decimal. copy the note. decimal by 2. Solve word 2. Listen; ask decimal problems on the questions and (correct to 2 multiplication of copy the note. or 3 places of decimal. decimal). 2. Solve word problems on multiplication of decimal. 15 mins 3 1. Give pupils revision 1. Participate in Give home on the division of the revision on work to: whole numbers by 2- division of 1. Divide digit and 3-digit whole decimal by 2- numbers. numbers. digit and 3- 2. Solve some 2. Listen and digit numbers. examples of division solve examples 2. Solve word of decimals by 2-digit with the problems on and 3-digit numbers. teacher and division of 3. Solve word copy the note. decimals. problems involving the 3. Listen, ask division of decimals. questions and copy the note. 250 UNIVERSITY OF IBADAN LIBRARY 15 mins 4 1. Give revision on 1. Participate in Give home the week‟s work. the revision in work to: 2. Solve more the revision 1. Solve problems on the exercise problems week‟s work 2. Listen, ask covering the questions and week‟s work copy the notes. 40 mins 5 1. Give test for the 1. Write the Give test to: week‟s work. test 1. Multiply 2. Mark the test and do 2. Do the fraction by the correction. correction. fraction 2. Solve word problems involving the multiplication of fraction. 3. Multiply decimal by decimal and solve word problems. 4. Division of decimal by 2 & 3-digit numbers. 5. Word problems on division of decimal 251 UNIVERSITY OF IBADAN LIBRARY 3 1. Give pupils 1. Solve Give class problems to solve in problems given work covering the class by the teacher the day‟s 2. Mark pupils work 2. Do their lesson. and do the correction corrections for them. 3. Pupils copy 3. Conclude the lesson the home work by giving home work in their notes. to pupils. 252 UNIVERSITY OF IBADAN LIBRARY Week 4 Lesson 4 Duration: 40 minutes Topic: Volume Objectives: At the end of the lesson, pupils should be able to: 1. Calculate volume of triangular prism 2. Calculate volume of cylinders 3. Calculate volume of spheres 4. Solve word problems on volume Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Guide Activities Aids Volume 5 mins 1 1 to Ask pupils questions on Listen and 3 previous lesson and answer introduces the new questions. topic. 15 mins 2 1 1. Explain the concept 1. Listen to the Diagrams 1. Give home of volume explanation of of work to: 2. Present the formula the concept of triangular 1. Solve a for calculating volume volume prism on problem on of triangular prism 2. Listen and the chalk volume of 3. Solve two example, write down the board. triangular prism on volume of triangular formula of using the formula prism volume of 2. Solve a word 4. Solve examples of triangular problem involving word problems on prism. volume of 253 UNIVERSITY OF IBADAN LIBRARY triangular prism. 3. Listen and triangular prisms. write the note 4. Listen, ask questions and write the note. 15 mins 2 1. Present the formula 1. Listen and Diagram Give home work for calculating the write down the of to: volume of cylinders formula of the Cylinder 1. Solve problems 2. Solve two examples volume of on the on volume of on volume of cylinders cylinder chalk cylinders using 3. Solve examples of 2. Listen and board the formula. word problems on write the note 2. Solve word volume of cylinder. 3. Listen, ask problems questions and involving volume write the note. of Cylinder. 15mins 3 1. Present the formula 1. Listen and Diagram Give home work for calculating the write down the of sphere to: volume of sphere formula of the on the 1. Solve problems 2. Solve two examples volume of a chalk on volume of on volume of sphere sphere board sphere using the 3. Solve examples of 2. Listen and formula. word problems on write the note 2. Solve word volume of sphere. 3. Listen, ask problems questions and involving volume write the note of sphere. 15 mins 4 1. Revise the week‟s 1. Listen and Give home work work ask questions to: 2. Solve more examples 2. Participate 1. Solve a word 254 UNIVERSITY OF IBADAN LIBRARY on the week‟s work. in solving the problem each on examples. volume of triangular prism, cylinder and sphere. 40 mins 5 1. Give test for the 1. Write the Give test to: week‟s work test 1. Solve a 2. Mark the test and do 2. Do the problem on corrections corrections volume of a triangular prism, cylinder and sphere. 20 mins 3 1. Give pupils problems 1. Solve Give class work to solve problems covering the day‟s 2. Mark pupils works given by the lesson. and do the corrections teacher. for them 2. Do their 3. Conclude the lesson corrections by giving home work to 3. Pupils copy pupils. the home work in their notes. 255 UNIVERSITY OF IBADAN LIBRARY Week 5 Lesson 5 Duration: 40 minutes Topic: Capacity Objectives: At the end of the lesson, pupils should be able to 1. Explain the concept of capacity 2. Solve word problems on capacity. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Guide Activities Aids Capacity 5 mins 1 1to Ask pupils questions Listen and 4 on previous lesson and answer introduce the new questions. topic. 15 mins 2 1 1. Explain the concept 1. Listen to the Give home work of capacity explanation of to: 2. Mention various the concept of 1. Name and containers and ask capacity compare the pupils to compare their 2. Compare by capacities of capacities. stating the containers in the container that home. has higher or lower capacity. 15 mins 2 1. Revise tables of 1. Listen and Give Home work capacity write down to: 256 UNIVERSITY OF IBADAN LIBRARY 2. Revise conversion table of 1. Solve problems of units of capacity. capacity. on conversion of 2. Listen and units of capacity. copy the note. 15mins 3 1. Write word 1. Write down Give home work problems involving the word to: capacity on the chalk problems 1. Solve word board. involving problems 2. Solve the word capacity on the involving problems involving note. capacity. capacity on the chalk 2. Listen and board. ask questions and write the note. 15 mins 4 1. Solve more word 1. Listen and Give home work problems involving ask questions to: capacity on the chalk and write the 1. Solve more board. note. word problems involving capacity. 40 mins 5 1. Give test for the 1. Write the Give test to: week‟s work test 1. Solve problems 2. Mark pupils‟ work 2. Do the on conversion of and do corrections. corrections units of capacity 2. Solve word problems involving capacity. 20 mins 3 1. Give pupils 1. Solve Give class work 257 UNIVERSITY OF IBADAN LIBRARY problems to solve problems covering the day‟s 2. Mark pupils‟ works given by the lesson. and do the corrections teacher. for them 2. Do their 3. Conclude the lesson corrections by giving home work 3. Pupils copy to pupils. the home work in their notes. 258 UNIVERSITY OF IBADAN LIBRARY Week 6 Lesson 6 Duration: 40 minutes Topic: Weight Objectives: At the end of the lesson, pupils should be able to 1. Explain the concept of weight 2. Express the same weight in different units: grams, kilograms, and tonnes 3. Solve word problems involving weight. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Activities Aids Guide Weight 5 mins 1 1to Ask pupils questions Listen and 4 on previous lesson and answer the introduce the new questions. topic. 15 mins 2 1 1. Explain the concept 1. Listen to the Give Home of weight teacher‟s work to list 5 2. Explain that the explanation of objects each weight of small the concept of that can be objects is expressed in weight. expressed in: grams, medium sized 2. Listen to the 1. in grams objects in kilograms, explanation of 2. Kilograms while heavy objects objects and the 3. Tonnes. are expressed in unit of tonnes. expression of 3. Ask pupils to name weight. objects and the unit of 3. Name the 259 UNIVERSITY OF IBADAN LIBRARY expression of weight. objects and the unit of expression of weight. 15 mins 2 1. Write tables on 1. Copy tables Give home weight on the chalk on weight in the work to convert board. note book. weights 2. Explain the tables 2. Listen to the 1. in grams to on weight explanation of kg 3. Express the same the tables of 2. Kg to tones weight in different weight. 3. Grams to units, e.g. 80,000 3. Listen and tones grams = 80kg = 0.08 copy the notes. 4. Tonnes to Kg tonnes. and grams. 15mins 3 1. Write word 1. Copy the Give home problems involving word problems work to weight on the chalk involving 1. Solve word board. weight in the problems 2. Solve the word note. involving problems involving 2. Listen, ask weight. weight on the chalk questions and board. copy the note. 15 mins 4 1. Solve more word 1. Listen and Give home problems involving ask questions work to; weight on the chalk and write the 1. Solve word board. note. problems involving 260 UNIVERSITY OF IBADAN LIBRARY weight. 40 mins 5 1. Give test for the 1. Write the test Give test to: week‟s work 2. Do the 1. Convert 2. Mark pupils work correction. weights to and do corrections. different units. 2. Solve word problems involving weight. 20 Mins 3 1. Give pupils 1. Solve Give class work problems to solve in problems given covering the the class. by the teacher day‟s lesson. 2. Mark pupils work 2. Do their and do the correction corrections. for them. 3. Copy the 3. Conclude the lesson home work in by giving home work their note. to pupils. 261 UNIVERSITY OF IBADAN LIBRARY Week 7 Lesson7 Duration: 40 minutes Topic: 2-Dimensional figures Objectives: At the end of the lesson, pupils should be able to 1. Explain what are 2-dimensional shapes 2. Identify 2-dimentional shapes by name 3. Identify the essential properties of 2-dimensional shapes 4. Identify polygons not exceeding the octagon 5. Solve more difficult problems on 2-dimensional shapes. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Activities Aids Guide 2- 5 mins 1 1 to Ask pupils questions Listen and Dimensional 4 on previous lesson answer the Figures and introduce the questions. new topic. 15 mins 2 1 1. Explain what 2- 1. Listen to the Give home dimensional shapes explanation of work to: are. what 2- 1. Name seven 2. List the names of dimensional 2-dimensional 2-dimensional shapes are. shapes. shapes on the chalk 2. Copy and 2. Name the board. call the names types of 3. Draw and label of the shapes. triangles. the shapes on the 3. Draw and 262 UNIVERSITY OF IBADAN LIBRARY chalk board. label the shapes in the note. 15 mins 2 1. List and call the 1. Copy the Diagrams Give Home features of each 2- note, and call showing the work to dimensional shape the features of features of 1. Complete a on the chalk board. the 2- 2- chart of shapes 2. Draw the shapes dimensional dimensional indicating on the chalkboard shapes. shapes. lines of and lead pupils to 2. Copy the symmetry, and see the features. note and label number of the features on sides. the shapes. 2. Number of angels contained in the shape. 3. Name the types of triangles 4. Write the features of each triangle 15 mins 3 1. Solve problems 1. Listen, ask Draw Give home on 2-dimensional questions and triangles, work to: shapes. copy the note. compound 1. Identify shapes on different the chalk shapes in a board. compound 263 UNIVERSITY OF IBADAN LIBRARY figure. 2. Find sizes of angles of triangles. 15 mins 4 1. Explain what a 1. Listen to the Diagram of Give home polygon is. explanation of polygons work to; 2. List and call what a on the 1. List the polygons not polygon is. chalk- names of exceeding the 2. Copy and board. polygons. octagon. listen to the 2.Calculate the 3. Solve problems names of the angle at the on polygons polygons. centre of each 3. Listen, ask polygon questions and 3. Calculate copy the note. the sum of Listen, ask angles of each questions and polygon. copy the note. 4. Deduce the formula for the sum of angles of n-sided polygon. 40 mins 5 1. Give a test for the 1. Write the Give test to: week‟s work test. 1. Name and 2. Mark pupils work 2. Do the identify and do corrections. correction. features of 2- dimensional shapes. 2. Name types 264 UNIVERSITY OF IBADAN LIBRARY of triangles and their features. 3. Identify shapes in a given compound figure. 4. Calculate angles in a given triangle. 5. Name the types of polygons 6. Calculate the sum of angles of a given polygon. 20 mins 3 1. Give pupils class 1. Solve Give class work problems work covering 2. Mark pupils work given by the the day‟s and do the teacher. lesson. correction. 2. Do their 3. Conclude the corrections lesson by giving 3. Copy the home work to home work. pupils. 265 UNIVERSITY OF IBADAN LIBRARY Week 8 Lesson 8 Duration: 40 minutes Topic: 3-Dimensional shapes Objectives: At the end of the lesson, pupils should be able to 1. Explain what are 3-dimensional shapes 2. Identify 3-dimentional shapes by name 3. Identify number of edges, faces and vertices of 3-dimensional shapes 4. Identify nets of 3-dimensional shapes 5. Measure angles of 3-dimensional shapes 6. Identify lines that are parallel and perpendicular in 3-dimensional shapes. Topic Duration Steps Day Teacher Activities Pupils Teaching Evaluation Activities Aids Guide 3- 5 mins 1 to Ask pupils questions on Listen and Dimensiona 3 previous lesson and answer the l Shapes introduce the new topic. questions. 15 mins 2 1 1. Explain what 3- 1. Listen to the Diagrams of Give home work dimensional shapes are. explanation of 3- to: 2. List the names of 3- what 3- dimensional 1. List 3- dimensional shapes on dimensional shapes on dimensional the chalk board. shapes are. the board. shapes. 3. Draw and label the 2. Copy and call 2. Draw and label shapes on the chalk the names of 3- 3-dimensional board. dimensional shapes. shapes. 266 UNIVERSITY OF IBADAN LIBRARY 3. Draw and label the shapes in the note. 15 mins 2 1. Explain what are 1. Listen to the Diagrams Give home work edges, faces and vertices explanation of showing the to: of a given 3-dimensional edges, surfaces edges, faces 1. Make 3- shape. and vertices of and vertices dimensional 2. Draw and ask pupils 3-D shapes. of 3- shapes with to indicate the edges, 2. Examine the dimensional cardboard. vertices and faces of 3-D shapes to shapes. 2. Complete a shapes. determine the chart of 3- 3. Draw nets or models number of dimensional of 3-D shapes on the edges, faces and shapes indicating chalkboard. vertices. numbers of edges, 3. Examine and faces and vertices. determine the 3. Prepare nets of nets to the 3-dimensional respective 3- shapes. dimensional shape. 4. Copy all the notes. 15 mins 3 1. Lead pupils to 1. Use a 1. Diagram Give home work measure the sizes of protractor to of 3- to: angles in each 3- determine the dimensional 1. Measure sizes dimensional shape. size of angles in shapes. of angles in 3- 2. Lead pupils to a given shape. 2. Diagram dimensional indicate lines that are 2. Identify lines of parallel shapes. 267 UNIVERSITY OF IBADAN LIBRARY parallel and that are parallel and 2. List lines that perpendicular in 3- and perpendicul are perpendicular. dimensional shape. perpendicular in ar lines. 3. List lines that 3-dimensional parallel to each shapes. other in 3-D shapes. 15mins 4 1. Revise the week‟s 1. Listen and Give more home work. participate in work. answering and asking questions. 15 mins 5 1. Give test for the 1. Write the test. 1. List the names week‟s work 2. Do the of 3-dimensional 2. Mark pupils work and correction. shapes. do corrections. 2. Identify the number of edges, faces and vertices of 3-dimensional shapes. 3. Use protractor to measure the sizes of angles of 3-dimensional shapes. 4. List pair of parallel perpendicular lines in a given 3- 268 UNIVERSITY OF IBADAN LIBRARY dimensional shape. 5. Identify nets of 3-dimensional shapes. 20 mins 3 1. Give pupils class 1. Solve the Give class work work. problems given covering the day‟s 2. Mark pupils work and by the teacher. work. do the corrections. 2. Do their 3. Conclude the lesson corrections by giving home work to 3. Copy the pupils. home work. 269 UNIVERSITY OF IBADAN LIBRARY