Proceedngs 2016 Annual National C O N FE R E N C EUNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference Published by the Mathematical Association of Nigeria (M.A.N): Publisher of ABACUS: (The Journal of Mathematical Association of Nigeria) Copyright © M.A.N. 2016 ISBN: 97-35224-6-9 All rights reserved. N O part o f this book may be reprinted, stored in retrieval system, or transmitted, or utilized in any form or by any electronic, mechanical or other means including photocopying and recording, without the prior written permission o f the publisher. Computer typeset by: OLAD NIGERIA ENTERPRISES No. 45/70, N iger Road, Ib rin , Kwara State. 08055951854, 08069842754 Printed in Nigeria by: OLAD PUBLISHERS No. 45/70, N iger Road, Ibrin , Kwara State. ii UNIV ERSIT Y O F IB ADAN L IB RARY TABLE OF CONTENTS Page 1. Anibueze, C. O.: The Influence of Effective Communication and Class Control on Mathematics Teaching and Learning Processes in Secondary Schools in Enugu State 1 2. Ibrahim, M. O. & Busari, L. O.: Impact of Enriched-Lecture Method with Geotrigmetric Sets on Academic Performance of Secondary School Students in Trigonometric Concepts in Katsina State, Nigeria 16 3. Hassan, A. A., Abari, M. T, Ndanusa, M. A. & Anyanwu, C. R.: The Role of Cognitive Conflict in Teaching and Learning of Mathematics 25 4. Abdullahi, U.: Impact of Student Teams-achicvement Divisions Strategy on Secondary School Students Trigonometric Performance and Retention in Katsina State, Nigeria. 30 5. Azuka, B. F.: Role of Mathematics in Enhancing Good Governance in Nigeria 47 6. Tsafe, A. K. & Yusha’u, M. A.: Teaching Mathematics in the ICT-Driven Era: Imperative for National Development and Good Economic Management in Nigeria 54 7. Musa, IT, Babangida, B. & Ibrahim, L. K.: Convergence of the 2-Point Diagonally Implicit Super Class of Block Backward Differentiation Formula 61 8. Hamisu I., Sagir, A. M. & Mohammed, A.: The Effect of Different Type and Fertilizer Rates on the Yield of Maize 69 9. Obienyem, C. & Obienyem, B. I. Repositioning Instructional Methods and Strategies in Mathematics for Entrepreneurship Development and Job Opportunities 77 10. Omenka, J. E. & Tali, D. J.: The Role of Mathematics Teachers in an Inclusive Education: Implication for Poverty Alleviation in Nigeria 86 11. Folaranmi, R. O., Adcniyi, R. B. & Adeyefa, E. O. : A Chcbyshcv Collocation Block Method For Solution Of Third Order Initial Value Problems In Ordinary Differential Equations 95 12. Telia, A.: Mathematics A Tool For Success of Entrepreneurship Opportunities 111 Proceedings of September 2016 Annual National Conference IV UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference 13. Ajani, T. O. & Popoola, B. A.: Comparative Effect of Teacher- Students Relationship on Academic Achievement of Students in Mathematics 123 14. Usman, H & Sani, M.: Heat Transfer Analysis of MHD Boundary Layer Flow Past A Wedge Through Porous Medium With Thermal Radiation 131 15. Yusuf, F. Z.: Graphs From Finite Groups: An Overview 142 16. Nalado, T. K., Muntari, I. & Muhammad, S.: Circle Theorems: An Instrument for Desired Change in WAEC and NECO Performance 155 17. Okpala, J. U. & Asiegbu, F. N.: Role of Mathematics Skills in the Development of Human Capacity Building in the Private Sector for National Development 171 18. Mukhtar, M. S., Yusuf, U. & Muhammad, S. A.: The Use of Mathematical Software in Teaching and Learning: Instrument for the Desired Change in Nigeria 177 19. Muhammad, S. A., Mukhtar, M. S. & Yusuf, U.: Effect of Socio- Economic Status on Students’ Mathematics Achievement in Kebbi State Senior Secondary Schools 188 20. Ahmed, A., Nurudeen, O., Zakari, Y., Suleiman, I. & Ibrahim, A. : Modification of Yadav and Kadilar (2013) Ratio And Product Estimators For Finite Population Mean 197 21. Adeyefa, E. O., Adeniyi, R. B., Folaranmi, R. O., Odafi, N. O. & Udoye, A. M.: Orthogonal Based One-Step Algorithm 203 22. Ma’ali, A. I., Badeggi, A.Y., Abubakar, A . Abubakar, A. W. & Mohammed, U.: Derivation of Three Variants of r-Method For the Class of Non-Over Determined Ordinary Differential Equation 210 23. Salami, O. O. & Popoola, A. A.: Effects of Collaborative Method in Senior Secondary School Students’ Learning Outcomes in Mathematics in Kwara State ' 229 24. Olu-Ajayi, F. E. & Salami, O. O.: Effects of Mentoring on Secondary School Students’ Performance in Science and Mathematics in Ekiti State, Nigeria. 236 25. Adepoju, J. A. & Ipinyomi, R. A.: Construction of Asymmetric Fractional Factorial Designs 242 26. Asiru, M. A.: A Result on Perfect Numbers 251 v UNIV ERSIT Y O F IB ADAN L IB RARY 27. Ojo, V. 0 . & Ojo, O. A: Mathematics for Poverty Alleviation 255 28. Akissani, I. & Muntari, I.: Mathematics Education: A Veritable Tool for Poverty Alleviation in Nigeria 261 29. Bawa, M., Simon, A. A. & Enagi, A. I.: The Epidemiological Study of Rheumatoid Arthritis In Nigeria Encompassing Smoking As A Risk Factor Using Chi-Square Statistics 272 30. Mohammed, B. A., Chado, U. D., Isa, D. A. & Ilassan, U.: A Deterministic Model for Assessing the Impact of Poverty on Malaria Elimination 282 31. Mohammed, J., Gambo, A., Doko, C. U. & Ukwubile, O. I. : Mathematical Model of Controlling Asset and Liability Management. 297 32. Ojo, O. A. & Ojo, V. O.: Mathematics for Entrepreneurship and Job Opportunity 315 33. Isah, B. Y. & Bawa, H. A.: Heat Source And Chemical Reaction Effects On MUD Free Convection Heat and Mass Transfer Between Vertical Porous Plates Due to Absorption of Radiation 321 34. Azeez, O. I. & Ipinyomi, R. A.: The Impact of Modeling Level One Autocorrelated Errors in Models for Repeated Measures Data 337 35. Ilarisu, A.: The Role of Mathematics in Peace and Conflict Resolution 347 36. Ilarisu, A.: Mathematics: A Veritable Tool For Poverty Alleviation 354 37. Ilarisu, A.: Mathematics: A Viable Tool For Enhancing Entrepreneurship. 359 38. Abubakar, IE, Madugu, A. & Lawal, A.: Efficacy of Computer Assisted/ Aided Instruction on Mathematics Achievement and Retention among Junior Secondary School Students in Katsina State: Implication for Sustainable Development in Nigeria 365 39. Abdulrahman, M. K. A., Soladoyc, S. O. & Sanda, A. U. : Estimation of Constants in Sediment Transport Equation for Reservoir Network for Flood Control 381 40. Ojo, S. G.: Mathematics as a Tool for Poverty Alleviation 389 41. Fadare, A. O. & Ayeni, A. A. The Role of Mathematics in Enhancing Good Governance 397 Proceedings of September 2016 Annual National Conference vi UNIV ERSIT Y O F IB ADAN L IB RARY ( 42. Ndibe, O. F., Bello, S. & Usman, M.: Mathematics as an Instrument for the Desired Change through ICT for Good Economic Management in Nigeria. 408 43. Guwam, B.: The Mire of Retirement in Nigeria: The Place of Mathematics in Effective Change against a Corruption Ridden System. 418 44. Enemali, I. A. & Adah, O. C.: Mathematics as an Instrument for Poverty Alleviation on the farm in Nigeria. 428 45. Adah, O. C. & Enemali, I. A.: Mathematics for Agricultural Entrepreneurship in Nigeria. 433 46. Usman, I. G., Ibrahim, M. O., Hamza, M. M., Mustapha, A., Yusuf, I., & Akinyemi, S. T.: Stability Analysis of the Transmission Dynamics and Control of a Bird Flu Model 438 47. Yusuf, I., Mayaki, Z. I., Usman, I. G., Garba, Z. U., Ibrahim, M. O. Abdulrahman, S., Enagi, A. I., Abdullahi, U. A. & Adamu, G.: Stability Analysis of a Corruption-Free Equilibrium State in the Presence of Social Media 456 48. Yusuf, I., Ibrahim, M. O., Abdulrahman, S, Enagi, A. I., Usman, I. G., Isa, N., Garba, Z. U, Abdullahi, U. K.& Mayaki, Z. I. : Stability Analysis of the Recruitment Dynamics and Control of Terrorism 469 49. Yunusa, A. B., Yahaya, B. F. & Zanna, F. A.: Factors Influencing Students’ Career Choice in Mathematics 487 50. Yunusa, A. B., Yahaya, B. F. & Zanna, F. A.: Mathematics: A Tool For Eliminating Corruption 491 51. Aliyu, R. T., Olaleye, O. O. & Abd-El-Aziz, A. A.: Mathematics in Enhancing Good Governance Using 3-PI Model of IRT 497 52. Adeniji, K. A : Educational Research and Hypotheses Testing: Reason or Ritual 512 53. Aminu, I., Dahiru, A. & Luba, A. K.: Mathematics Teacher and Primary School Education in Sokoto State, Nigeria. 522 Isah, A., Kasim, L. A. & Adamu, D.: Effects of Demonstration Method of Teaching on Academic Achievement in Mathematics among NCE Students in Shehu Shagari College of Education, Sokoto. 530 Proceedings of September 2016 Annual National Conference vu UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference 55. Anyagh, I. P. & Ale, F. O.: Developing Entrepreneurial Skills in Secondary School Students Through Effective Mathematics Education. 541 56. Isaac-Oloniyo, F. O. : Mathematics As An Instrument of Desired Change in Nigeria Through the Effects of West African Examination Council Feedback Guided Teaching Approach on Students’ Performance in Mathematics 552 57. Alkali, A. J. & Isah, A. I. :a-Cuts in Fuzzy Soft Sets 569 58. Abubakar, A. If.: Enhancement Techniques for Addressing Some Privacy Issues Related to Location-Based Ubiquitous Systems 575 59. Joseph, U. J., Ogoh, M. E. & Iji, C. O.: Using Mathematics as a Desired Instrument for the Reduction of Corruption in Nigeria 586 60. Aminu, A. & Datti, A.: Min-Max Algorithm for the Solution of Solvability of A ® x > x 597 61. Aminu, A., Haruna, A.: Control solvability of an interval max-plus matrix Equation 603 62. Muhammad, R. A., Aminu, A.: A Determinant Method for Solving Interval Systems of Linear Equations 608 63. Olowo, S. E., Abdulhadi, A.: A New Hybrid Smar-Amri Conjugate Gradient Method With Sufficient Descent Properties For Unconstrained Optimization 616 64. Magami, M. S., Ibrahim, A. A., Garba, I. A., Danbaba, A., Usman, A., & Mu’azu, S. B.: Construction of Block Design From (132)-Avoiding Class of Aunu Numbers 632 65. Oyekunle, O. B.: Application of Game Theory to Decision Making in Resolving Conflicts. 637 66. Oyekunle, O. B.: Importance of Mathematics in Primary Schools 652 67. Ezenwa-Nebife, D. C. & Ekwueme, C. O.: Poverty Alleviation in Nigeria through Mathematical Literacy 656 68. Adeniji, S. M., Waheed, I. O., & Alabi, If. I.: Senior School Teachers’ Views on the Introduction and Implementation of Inclusive Education in Oyo State, Nigeria 663 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference MATHEMATICS A TOOL FOR SUCCESS OF ENTREPRENEURSHIP OPPORTUNITIES TELLA, A. Department o f Teacher Education, Faculty o f Education, University o f Ibadan, Nigeria. ABSTRACT Mathematics is a compulsory subject taught in both primary and secondary schools in Nigeria. The importance o f Mathematics and its applications is all encompassing and that is why the famous status accorded to as everyday subject and its’s centrality in the curriculum. Today, it is a reality that it is the creation, mastery and utilization o f modern science and technology that basically differentiates the developing from developed nations o f the world. The foundation o f science and technology, which is the basic requirement fo r development o f nation, is Mathematics. Therefore, mathematics plays a vital role in nation building and mathematics is very crucial fo r many careers and job opportunities in today’s increasing technological society. While mathematics is not only for knowledge and understanding, its other objectives includes skill application/development, attitude formation appreciation, problem-solving skill, brevity> generalization, drawing inferences, interpreting, future vocational/ life skills, reasoning ability, systematic and critical thinking and others. Entrepreneurship is a creative and innovative response to the environment such responses can take place in any field o f social endeavour, business, industry, agriculture, education, social work and the like. This paper explores the various skills o f mathematics as a tool fo r the creation o f success in diverse entrepreneurship opportunities. INTRODUCTION In recent past, it has been observed that issues of high unemployment rates, businesses collapsing and folding off, insecurity and instability economy are major challenges facing Nigeria and other developing countries. This has been attributed largely to lack of creativity, innovative skills and mathematical skills Entrepreneurship has become a popular career path in developed and developing countries, a phenomeon that has contributed to the intense interest in the subject shown by researchers and policy makers around the world (Berger, 1991). Public policy makers recognise the importance of entrepreneurship as promoter of economic development and hence support instruments like entrepreneurship education to increase entrepreneurial activity (Fayolle, Gailly, & Lassas-Clerc, 2006). The European Commission, for example, endorses such support, noting that the "primary purpose of entrepreneurship education [at higher education level] is to develop entrepreneurial capacities and mindsets" (European Commission, 2008) and recommends integrating entrepreneurship more fully into university curricula. Shane, Locke and Collins (2003) suggested four important reasons for acquisition of entrepreneurship skills. First of all, Schumpeter argued long ago that entrepreneurship is central to the generation of economic growth since it drives the innovation and technical change required for growth to occur (Baumol, 1986; Gutterman, 2015). Second, entrepreneurial action has been cited as the means for balancing supply and demand in the market place (Gutterman, 2015; Kirzer, 1997). I l l UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference Third, entrepreneurship has been praised as the process that facilities the conversion of new knowledge and ideas into innovative products and services (Shane and Venkataraman, 2000). Finally, as described above, entrepreneurship is now widely viewed as a distinct vocation and, as such, it is important and useful to gain a better understanding of the role that entrepreneurship plays in the development of human and intellectual capital (Gutterman, 2015). To this end, Mathematics should be able to solve the problems of high unemployment rates, businesses collapsing and folding off, insecurity and instability economy. It is supposed to provide the basic tools for industrialization and national development (Maduabum, 1999). Hartog, van Praag and van der Sluis (2010) use the U.S. National Longitudinal Study of Youth to examine the effects of various personal characteristics among entrepreneurs and employees. They find that verbal abilities appear to be more important for employees, while mathematical, technical and social abilities are more important for entrepreneurs. They also argue that general ability and balance across the various kinds of ability generate higher incomes for entrepreneurs. In developing individual’s inner resources, the role that mathematics plays were mostly about thinking, clarity of thought and pursuing assumptions to logical conclusions are central to the mathematical enterprise. There are many ways of thinking, and the kind of thinking one learns in mathematics is an ability to handle abstractions. Even more importantly, what mathematics offers is a way of doing things: to be able to solve mathematical problems, and more generally, to have the right attitude for problem solving and to be able to attack all kinds of problems in a systematic manner. It is generally agreed that Mathematics is a critical skill for all (Hodgen & Marks, 2013). Further, an argument is put forward that in today’s world of ‘rapid change’ (ACME, 2011a), particularly in terms of technological change, the demand for mathematical skills is increasing (Burghes, 2011; Norris, 2012). The main arguments for the importance of mathematics, however, fall into three areas: mathematics is a core skill for all adults in life generally; a contribution to the country’s economic prosperity; and mathematics is important for its own sake (Mathematics Reports, 2015). Hence, this paper explores the various skills of mathematics as a tool for success in diverse entrepreneurship opportunities. Importance of Mathematics Education in Nation Sustainability Development Today, it is a reality that it is the creation, mastery and utilization of modem science and technology that basically distinguishes the so- called developing from the developed nations of the world. That is to say that the standard of living of a nation is dependent on the level, of science and technology of that nation. While science is the bedrock that provides the spring-board for the growth of technology, mathematics is the gate and key to the sciences. In other words, it is the level of mathematics that determines the level of the science and technological component of any nation. The foundation of science and technology, which is the basic requirement for development of nation, is mathematics. Therefore, mathematics plays a vital role in nation building and in particularly in enhancing entrepreneurial opportunities The general objectives for mathematics education among others include; i to generate interest in mathematics and to provide a solid foundation for everyday living. 112 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference ii to develop computational skills. iii to foster the desire and ability to be accurate to a degree relevant to the problem at hand. iv to develop precise, logical and abstract thinking. v to develop the ability to recognize problems and to solve them with related mathematical knowledge. vi to provide necessary mathematical background for further education. vii to stimulate and encourage creativity. According to Sidhu (2006), the aim of learning mathematics is not only for knowledge and understanding objectives, it includes Skill Application, Attitude, Appreciation and Interest Objectives of which among other things, the learner; acquires and develops skill in the use and understanding of mathematics, acquires and develops speed, neatness, accuracy, brevity and precision in mathematical applications, learns and develops technique of problem-solving, develops the ability to estimate, check and verify results, develop ability to think correctly, to draw conclusions, generalizations and inferences, develops, appreciate skill in drawing, reading, interpreting graphs and statistical tables, develops skill in measuring, weighing and surveying, develops the ability to apply mathematics in his future vocational life, develops the habit of systematic thinking and objective reasoning, develops self-confidence for solving mathematical / other problems and shows originality and creativity. As Vorderman, Porkess, Budd, Dunne, R. & Rahman-hart (2011) imply, mathematical skills underpin the attributes such as problem solving which are of critical importance within modern industrial environments, such as the pharmaceutical industry. Objectives of Mathematics Education as the Basis for Developing Entrepreneurial Skills. According to Uka (2015) the following entrepreneurial skills, traits/ behaviours are major attributes of mathematical mind: optimistic, initiative, risk- taker, drive and persistence, resilience, critical and creative thinking, problem-solving ability, goal­ setting, decision-making and planning and organizing. These entrepreneurial skills were based on the national objectives of primary and Secondary education as it relates to mathematics to include: 1. to lay a solid foundation for the concept of numeracy and scientific thinking, 2. to give the child opportunities for developing manipulative skills that will enable him function effectively in the society within the limits of his capacity, 3. to develop in the child the ability to adapt to his changing environment 4. to provide the basic tools for further advancement as well as prepare him for trades and crafts of his locality, 5. at the secondary level, to build on the foundation of the primary level, so that the child can make a useful living professionally, economically, politically and socially. 6. secondary education should also prepare the child for higher education. Concepts of Entrepreneurship Entrepreneurship is recognised both nationally and internationally as a key driver of growth (Fitzsimons and O’Gorman, 2003; Commission of the European Communities, 113 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference 2004), with future prosperity depending on the creation of indigenous businesses (Orhan and Scott, 2001). Martin and Laing (1998) believed that a country’s future economic development is dependent upon increasing its growing entrepreneurial talent. Morrison (1998) agreed with this, proposing that the successful entrepreneur is the “first among equals in the process of wealth creation” (Morrison, 1998). Entrepreneurship is a complex concept, which many scholars in the field of economy, sociology, psychology and sciences have tried to define. Despite all efforts, no consensus has been reached regarding the boundaries of the definition of entrepreneurship. However, many scholars agree that the field of entrepreneurship positively influences on a country’s economy. According to Kjeldsen and Nielsen (2000), creating new enterprises constitute the base for maintaining a country’s international competitive power, economic development, employment, and standard of living. Baumol (1990) viewed entrepreneurs as persons who are ingenious and creative in finding ways that add to their own wealth, power and prestige. Entrepreneurship is the act of creating new things. Entrepreneurship can be described as a creative and innovative response to the environment. Such responses can take place in any field of social endeavour, business, industry, agriculture, education, social work, and the like. Thus doing new things or doing things that are already being done in a new way is therefore a simple definition of entrepreneurship. The capacity and willingness to develop organize and manage a business venture along with any of its risks in order to make a profit. The most obvious example of entrepreneurship is the starting of new businesses (Businessdictionary.com). According to Schumpeter’s (1934) system entrepreneurship is essentially a creative activity. These definitions have been used in many studies to study the characteristics of those who have started business ventures. However, the contributions of these to the understanding of concept of entrepreneurship is not substantial because they have not tried to focus on the critical function of the entrepreneur and so the concept remains elusive. According to Bloomberg (2010) defined entrepreneurship as the activity of the entrepreneur involving three main parts, which are generating business ideas which involves formation and formulation of goals, organization of cases which includes effective ways of enforcing such goals, and enforcement of such cases which could involve generating the choice of activities of course, no one can succeed in life endeavours in general and in entrepreneurship in particular through sheer luck except through creative ideas, extensive research work, plenty of trials, doggedness, innovative ideas, precise decision making, accurate problem solving, good managerial ideas and consistent persistence of efforts all these and more that make entrepreneurship activities a success can be provided through the knowledge of mathematics. E Entrepreneurship to be an ability to create and build something from practically nothing. Sugumar (2006) refers to entrepreneurship as the qualities which are required to innovate and start a new enterprise accept the challenge and bear the risk. In India the term entrepreneurship connotes a restricted meaning. It generally veers round efforts which result in establishing and running factories and industrial enterprise alone. Moreover, there is a market tendency to relate it only to operations, which exceed a particular size. This narrow overview of the concept perhaps reflects the preponderance of values nurtured by urban white collar class in the society. According to Rashmi (2010) entrepreneurship has been viewed as a phenomenon occurring around the individual and benefiting only an individual. It is rarely appreciated 114 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference as one that could be harnessed to benefit the larger groups. Likewise, there is a tendency to view the occurrence only in terms of the total aggregate society. This approach ignores the distinctly varying social environments which confront the large variety of smaller groups and which present both opportunities as well as challenges dissimilar in nature. This consideration of entrepreneurship has also negated the role that the joint family system played in the sphere of economic development (Rashmi, 2010). Moreover, it is often not recognized that the process of transformation from the rural and agricultural society to entrepreneurial society, would have to cover all sizes, shapes and types of economic activities. Harbinsen (cited by Singh 1992) defines entrepreneurship as a skill to build an organization. He spots the crux of entrepreneurship in the ability to multiply by effectively delegating responsibilities to others. He further stresses that the ability to create an organization is the most crucial skill as it facilitates the economic use of other innovations and that in the absence of this skill other innovations fail to stimulate economic development. Thus entrepreneurship is basically concerned with the development and coordination of entrepreneurial functions (Rashmi, 2010). Advantages of Entrepreneurship According to Bolarinwa (2001), entrepreneurship education has the following advantages: (1) It will help the students to form a base of knowledge about the function and operation of a business and develop some level of familiarity and comfort with business environment, since technology changes micro-enterprises; (2) It will play as a complementary role in developing the occupational knowledge, job skills, and work experience; (3) It offers opportunities to students for job experience and for earning, saving, and investing money at an earlier stage of life than their peers, contributing to their belief in their abilities and a sense of self-worth; (4) There will be a great reduction in the high rate of unemployment in the society, and self-employment and business ownership will become viable and appealing goals for today’s students. One pertinent question that we should ask ourselves or ponder over is that do entrepreneurs need to be good at math? One might contest that the days of paperwork and performing tedious manual calculations are long past, as ample market software compensates for what an individual may lack in basic skill. In what situation then, does one require math knowledge? The point in having a strong grasp of math concepts is not as essential for the actual computations as it is for the understanding of the big picture. These days, software does much of the actual mathematics for you. An entrepreneur has to merely put in the appropriate numbers, and the software displays professional results. It helps to forecast project sales, expenses, and cash flow quickly and accurately. It also suggests financial projections with reports and charts; you do not have to make any calculations, create formulas, or design and build reports or graphs yourself. You can obtain profit/loss statements; balance sheets; cash plans; sales forecasts; expense budgets; ratio analysis; breakeven analysis; sales by category; and expenses by category by simply feeding the software the required numbers. All this sounds very convenient. Nonetheless, you have to be able to interpret the results. In fact, efficiently feeding the numbers into the software 115 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference also calls for accuracy. Instead of blindly depending on software, having mathematical knowledge to authenticate the results certainly works for your benefit (Scheper, 2015). A background in science, technology, engineering and mathematics offers a great start to developing the knowledge and many of the skills necessary to be an entrepreneur. In fact, many of the skills you learn and practice in science, technology and mathematics have similarities with entrepreneurial thinking skills - creative problem solving, divergent thinking, data collection, organisation and analysis of information and clear communication of results, to name a few (Let’s Talk Science, 2015). Again the second question is whether entrepreneurs generally good at mathematics? ! To Scheper (2015) an entrepreneur with average mathematical skills can manage his entrepreneurial work efficiently. Nonetheless, the importance of the subject in the world of business is such that most successful entrepreneurs are, by default, good at mathematics. According to Let’s Talk Science (2015) a good grounding in STEM can really help new entrepreneurs. A recent study by TheStar.com (2015) of Canadian small business owners showed that 39 per cent failed a 10-question financial literacy quiz, and 57 per cent achieved a score of 50 per cent or less. These results highlight the real need to have knowledge and skills in mathematics as well as great ideas to start a business because successfully staying in business also relies on understanding profit margins, fixed assets and the balance sheet of your business. Mathematics Education and Entrepreneurial Skills According to Zvobwo in Dludla (2015) all entrepreneurs can benefit from having a solid grasp of mathematical concepts as it forms the basis of good problem solving, decision making and leadership. Mathematics can help entrepreneurs grapple with numbers, graphs, accounts, maximise profits and minimise costs," he says. The ability to figure out what the numbers say and how they can be improved upon is the secret to success, he adds that Mathematics as a subject, Zvobwo claims, is composed of a series of problems that have to be solved which is analogous to business. "If a business is to progress past the start-up stage, instincts need to be supported by down and dirty number crunching and mathematics models." He also says the resilience and definiteness of purpose afforded in a mathematics class is a necessary and sufficient ingredient for success in business. "Mathematics skills can also be used to provide savvy solutions to complex, real-world problems through mathematical modelling. A knowledge and comfort with STEM and the innovations in STEM provide opportunities for the use of these discoveries and technologies in new business ventures. Entrepreneurial thinking is usually the key ingredient in turning a new scientific discovery or innovation in technology into a usable product. Entrepreneurs with a sound knowledge of mathematics often perform better than their counterparts who are not proficient in the subject. Being able to accurately calculate and interpret figures allows you to analyze data, compute probabilities and statistics, understand investment systems, evaluate target consumers, and understand taxes (Scheper, 2015). A study by Sarasvathy (2003), a cognitive scientist, showed that expert entrepreneurs share a common way of thinking that defines them. Contrary to common belief, entrepreneurs do not use “causal thinking”. The latter is mostly followed by managers who employ given means to achieve predetermined goals. In contrast, entrepreneurs use “effectual thinking” which is similar to entrepreneurial thinking which is a learning style propelled by the desire to solve 116 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference problems and create. They form new ideas and imagine new possibilities based on available means. While causal reasoning does not necessarily involve creative thinking, creativity is an innate attribute of effectual reasoning (Katirtzoglou, 2014). Effectual thinking is a heuristic way of reasoning that requires imagination and risk-taking. And it this heuristic attribute of the entrepreneurial reasoning that makes mathematical training advantageous to any aspiring entrepreneur (Katirtzoglou, 2014). A heuristic is a problem solving technique, widely used in mathematics, whose purpose is to discover. It involves creating a speculative formulation and then use investigation to reach an outcome. Saunders (1995) in Katirtzoglou (2014), offered intuition, trial, error, speculation, conjecture, proof as the sequence in which we come to understand and develop mathematics. Intuition emerges from existing knowledge and experience. Ideas, like money, do not fall from a helicopter. Mathematicians and entrepreneurs get ideas for their next research project or venture from what they know and what they are good at. Trial and error is used to test whether an idea works: Trial and error is a process with an uncertain outcome during which new knowledge and experience is gained. Trying out an idea for the first time can be daunting. It is the phase of discovery that one is faced with uncharted territory. It is the time that one has to face and deal with failure. Mathematicians learn to do this by viewing every failed trial as a step closer to success. A failed trial just eliminates one possible path and improves one’s insight about what does and what does not work. Trial and error is a dynamic process where the original idea is tested, shaped and re-shaped. At the end of this process either we have an idea that seems workable or we are looking for new goals. Is this process any different for entrepreneurs? Mathematicians and entrepreneurs learn to embrace failure and uncertainty. Speculation: after a sufficient number of trials and errors one is now able to make an informed guess on whether the initial intuition led to a workable idea. Conjecture: for a mathematician a conjectured is a proposition that seems to be correct (based on the previous process) and needs to be proven. For an entrepreneur it could be a new product or service that needs consumer approval. Proof is the last step of the investigation and it can lead either to success or to failure. A mathematician needs to use rigorous analytical tools to verify the conjecture and an entrepreneur needs to devise a marketing strategy to promote a new product and gain customer support. Although proof seems to be the last step in a creative reasoning process it is also the first for the next idea. According to Dludula (2015) African countries continue to rank low in mathematics and science education according to a 2013 report by the World Economic Forum. This has resulted in African countries having a skills shortage in the science, technology, engineering and science sectors. Zvobwo says this is worrying as problem­ solving and critical thinking are sought after skills in modem economies the world over. To overcome the skills shortage, what is needed is a more holistic subject approach, says Zvobwo in Dludla (2015). According to him, "Mathematics is 117 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference everywhere, it permeates every business and household.” For mathematics education to take its proper place in developing entrepreneurial skills in our students, the present methods of teaching mathematics in our schools which are expository, rote leaming/memorisation, recitations, large group instruction, mental drilling to mention but a few must be dropped. This method according to Bot (2007) emphasizes the development of mathematics concepts and computational competences among learners using standard rules and procedures at the detriment of genuine understanding. They deny the learner active involvement and participation in the learning process because the teacher always provides explanations for any mathematical thinking and reasoning. However, mathematics education must cover the following ability to develop entrepreneurial skills in students (Anyagh and O’kwu, 2008), Mathematical computation, formal reasoning, problem solving and mathematics as a creative medium of application to everyday activities entrepreneurial inclusive. This can only be possible if the teaching of mathematics will go beyond rote learning, drill and teacher centered approaches which permeates in our schools system today instead of engaging students with participatory, active learning and innovative strategies that can leads to proper understanding of mathematical concepts. These are students- centered, problems solving and problems- based learning among others. According to Anyagh and O’kwu (2008), these methods of teaching mathematics will shape the thinking of the learner and arouse their curiosity to find out what is happing around them, to discover opportunities and utilize them, which are basic qualities of an entrepreneur. However, the big problem is that learners do not receive any motivation in doing mathematics outside the school environment. But if we can teach students how to apply mathematics in every sphere of their lives, that it is not only about solving an X, then students can also see how easy the subject is and how it contributes to solving everyday problems (Zvobwo in Dludla, 2015). CONCLUSION This paper reviewed the relevance of mathematics in the success of entrepreneurship opportunities. It looked at the nature and objectives of mathematics in the development of sustainable development in Nigeria and submitted that mathematics has a great role to play in the enhancement of entrepreneurship skills. For Nigeria to be able to minimize the rate of unemployment in the country, then the need for the development of entrepreneurial skills in our students cannot be overemphasized through the teaching of Mathematics in our schools. Efforts must be made by stake holders to put mathematics on a sound footing in Nigeria in order to inculcate in students various skills of mathematics as a tool for success in diverse entrepreneurship opportunities Specifically, the study recommends: 1. Shifting the focus of mathematics education from achieving ‘narrow’ goals to ‘higher’ goals 2. Direct support for the mathematical enterprise, which is primarily the responsibility of national governments; 3. Strengthening successful existing mechanisms, most notably regional training and research networks; 4. Enriching teachers with a variety of mathematical resources. 118 UNIV ERSIT Y O F IB ADAN L IB RARY Proceedings of September 2016 Annual National Conference REFERENCES ACME. (2011a). Mathematical Needs Mathematics in the workplace and in Higher Education. London. Anyagh, P.I. and O’kwu, E.I. (2008). Developing entrepreneurial skills through school mathematics education. Journal o f Teacher Perspective, 545 - 549. Baumol, W. 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