EFFECT OF COOPERATIVE, COMPETITIVE AND KOLAWOLE’S PROBLEM SOLVING (KPS) METHOD OF TEACHING ON ACADEMIC ACHIEVEMENT OF STUDENTS IN MATHEMATICS
CHAPTER ONE
INTRODUCTION
Background to the Study
Mathematics without any doubt remains the most serviceable subject to all disciplines and fields of human work and it has become an indispensable tool in the study of humanities, sciences and technology and has entered into the many areas of human activities. Every individual needs some measure of mathematics for his or her day to day activities. Usefulness of mathematics in human activities cannot be underestimated because it is the precursor of scientific discoveries and inventions, of which any nation that overlooks the study of mathematics and does not take interest in it would remain underdeveloped. Mathematics, according to Kolawole and Udeh (2012) is a tool in the development of sciencebased knowledge such as technology, industry and even for sound analytical reasoning in daily living in this communication age.
Mathematics is generally recognized as the bedrock of several subjects in the school curriculum and it is also indispensable to the national goal and objectives. It is also described as an instrument to ease or facilitate the learning of other subjects (Ojaleye 2006). Ajagun (2000), identified it as a specialized language in which knowledge of the physical world has been recorded; a language in which idea originating in the minds of scientists can be encoded, transmitted to others and decoded with a much exact method and less error. The Science Teachers Association of Nigeria (1992), referred to Mathematics as the central intellectual discipline of the technology societies. Every student aiming at attaining high knowledge of science and being functional in the society must possess an average knowledge of mathematics. In this present scientific age, one cannot underestimate the important of mathematics. In his submission, Bolaji, (2005), in his submission affirmed that the knowledge of science remains superficial without Mathematics. It therefore means that, the position of Mathematics in secondary school curriculum in Nigeria is important for scientific development. It is fundamental to the understanding of science; complexities of modern technology and several scientific developments useful to mankind have their root in mathematics (Adegoke, 2003).
The importance of Mathematics to human development attracted different comments, for instance, Cangiano (2009) described it as the queen of science and the language of nature and argued that its importance should be clear to any reasonable person. In fact, the early philosopher, Plato thinks that people who are good in mathematics will do well in any other field of knowledge: “Those who have a natural talent for calculation are generally quick at every other kind of knowledge; and even the dull, if they have had an arithmetical training, although they may derive no other advantage from it, always become much quicker than they would otherwise have been and anyone who has studied geometry is infinitely quicker of apprehension than one who has not.” (Anonymous, 2005)
Brown and Porter (1996) posited that the study of mathematics can satisfy a wide range of interests and abilities. It develops the imagination and trains learners in clear and logical thought. According to them, it also develops a range of language and insights, which may then be applied to make crucial contributions to our understanding and appreciation of the world, and our ability to find and make our way in it. Considering the paramount importance such subject constitute to human life, the subject was made an essential choice of learners throughout their educational sojourn in Nigeria.
In fact, it is an essential consideration for successful outing in certificate examinations like the Secondary School Certificate Examination (SSCE) conducted by the West African Examinations Council (WAEC) and the National Examination Council (NECO) as well as placement examinations like the Unified Tertiary Matriculations Examination (UTME) conducted by the Joint Admission and Matriculation Board (JAMB).
Stressing the usefulness of mathematics, Pollak (1986) believed that the “most fundamental reason for placing so much emphasis on mathematics is that mathematics is integral to everything about life. He added that every occupation which students may choose to pursue, and much of their everyday lives are full of opportunities that need the application of mathematics. Adegboye and Adegboye (2003) observed its usefulness in other fields of study as well as in humanities such as arts, social sciences, religious mysticism, commerce, war and pastoral life. It is also applied in the description of various phenomena both in physical and economic situations. This observation points to the fact that mathematics is not only universally useful and utilitarian in nature; it is also regarded as the key to the solution of human problems (Iyekekpolor, 2007).
The Federal Government of Nigeria has for long been aware of the pivotal position of mathematics to individual fulfillments and national developmental goals with particular reference to scientific and technological emancipation and breakthrough. This understanding has consequently led educational policy makers to position mathematics as a compulsory and one of the core subjects in primary and secondary levels of education (FRN, 2004). It is also a requirement for pupils to proceed from upper basic to senior secondary level as well as for almost all courses in the tertiary level.
Based upon reports from these examination bodies, performances of Nigerian learners in this subject have not been encouraging, making some curriculum and pedagogical pundits to beam their searchlights on teaching methods, curriculum contents, instructional materials, and other ancillary factors which they believe may influence the ability of the learners to want to learn more. It is highly disheartening that approaches and strategies for teaching and learning of this subject at both primary and secondary levels are not probably being put to use effectively that could promote learners’ activity and provide learners’ guided practice enabling them to retain concepts taught and solve problems. Generally students fear and hate and/or dislike mathematics because they see it as abstract. This has resulted to their lack of interest and low retention rate which leads to poor performance in mathematics examinations, both internally and externally (Obodo,2004).
Reporting to the National Council on Education (NCE) on students’ performance in the May/June Senior Secondary School Certificate Examinations (SSCE), the West African Examinations Council (WAEC, 2006), expressed worries over the low achievement due to poor retention rate and interest in mathematics by Nigerian candidates. Kurumeh (2007) maintained that the inappropriate, inadequate, elitist and eurocentric teaching techniques and methods used by mathematics teachers is instrumental to learners inability to understand and retain the basic mathematical principles, computations or logical facts involved. And the underlying process that gave rise to the mathematical facts resulted to learning by rote memorization, which led to poor retention, low performance and lack/loss of interest in mathematics.
According to Child cited by Iji (2010), man is endowed with limited capacity for memorization. Thus the ability to memorize difficult subjects by rote learning calls for exercising the minds and the muscles of the mind and brain. However, mathematics is not a subject that can be learnt by rote memorization but for one to remember and recall information demand passing through one’s experience. This goes to mean that the task before a teacher is how to help learners improve on their ability to assimilate information towards effective recalling/retrieving when the need arises. Resourcefulness in mathematics teaching demands that the mathematics teacher should focus attention on methods of teaching that stimulates learner’s zeal, interest and higher retention rate, taking into cognizance of individual differences of learners.
Different teaching techniques have been adopted by pedagogues in order to shore up students’ performance in Mathematics ranging from some teachercentred techniques to other learnercentred methods. In this part of the world, the commonest type of teaching technique seems to be the teachercentred wholeclassroom teaching referred to as conventional teaching strategy (CTS). This technique requires that the learners sit and listen to the teacher as he presents the content of the day’s lesson, with students asking few questions when necessary and supplying responses when asked to do so by the teacher.
Another popular approach used in teaching Mathematics is the cooperative learning strategy (CLS). Cooperative learning is instructional contexts in which peers work together on a learning task, with the goal of all participants benefiting from the interaction. Cooperation can be treated as synonymous, as a truly cooperative context is always collaborative (O’donnell, 2002). She highlighted three types of cooperative interaction strategies. The scripted cooperation in which partners work together to learn text material, broken down into sections such that both partners read the first section and one partner summarizes the material for his or her partner, who in turn provides a critique of the summary. They then alternate roles for the second section of the text, continuing in this way until they have completed the reading.
Cooperative learning is a mode of learning in which students of different levels of ability work together in small groups to achieve a purpose (Akinbobola, 2006). It involves the use of a variety of learning activities to improve their understanding of a subject (Slavin, 1992). Students in a group interact with each other, share ideas and information, seek additional information, make decisions about their findings to the entire class (Kort, 1992). Cooperative learning is student centred versus teacher centred leading to a stronger emphasis on the goal of learning instead of a performance goals. It encourages teachers to use alternative assessment techniques further reducing the emphasis on competitive examinations (Slavin, 1992). Pressel (1992), opined that cooperative learning helps to improve student achievement and retention, increase selfesteem and intrinsic motivation and develop more positive attitude towards learning skills and social skills.
Cooperation is working together to accomplish shared goals.Within cooperative activities, individuals seek outcomes that are beneficial to themselves and beneficial to all other group members. Cooperative instruction involves the use of small groups so that students work together to maximize their own and each other’s learning. Class members are organized into small groups after receiving instruction from the teacher. They then work through the assignment until all group members successfully understand and complete it. Cooperative efforts result in participants striving for mutual benefit so that all group members gain from each other’s effort. In cooperative learning situations there is a positive interdependence among students’ goal attainments because students perceive that they can reach their learning goals if and only if the other students in the learning group also reach their goals (Deutsch, 1962; Johnson, 1989).
Competitive learning exists when one student goal is achieved but all other students fail to reach that goal (Johnson and Johnson, 2001). Competitive learning can be interpersonal (between individuals), or intergroup (between groups), where a group setting is appropriate. This strategy has been described as the most appropriate when students need to review learned material (Griffiths and Podirsky, 2001). Competitive learning is most appropriate when student need to view learned materials. It can be interpersonal (between individuals) or intergroup (between groups), (Johnson et al., 1986). When competition occurs between wellmatched competitors, is done in the absence of a normreferenced grading system, and is not used too frequently, it can be an effective way of motivating students to cooperate with each other (Cohen, 1994).
However, there have been many criticisms of this type of learning, including promoting high anxiety levels, selfdoubt, selfishness, and aggression. It may also promote cheating and interfere with learners’ capacity to problemsolve. Competitive interaction strategy as used in this study is where students work in subgroups. Members of each subgroup work strictly on his/her own, strive to be the best in the subgroup for price or reward.
Kolawole (2013) postulated a comprehensive easytouse problemsolving method called; Kolawole’s ProblemSolving (KPS) method which by design deliberately takes care of teaching (i.e. Content versus Behavioural Objective for the teacher), learning (i.e. Content versus Behavioural Objectives for students) and evaluation Processor blueprint (i.e. Taxonomy of Educational Objectives, which incorporates content versus illustrative verbs).
The unique feature of KPS method is that the teacher can use it for teaching and evaluating the students. In this regard, the KPS method involves a combination of content, teacher’s activities, student’s activities and evaluation that could be operated concurrently or simultaneously.
The KPS method deals with:
 Identification of all relevant keywords, terms and terminologies
 Direct the problem/opic mathematical concept ability level step
 “Devecquit” problem the topic/mathematical language ability level
 “Sc3ript” problem the topic/mathematical computation and manipulation ability level
 Appraise problem the topic/mathematical level ability appraisal
This then suggest that Mathematics educators should be able to develop new teaching techniques/methods to take care of the individual abilities of learners in the class room. Mari (2002) maintained that teaching strategies is a variable that can easily be manipulated by teachers to increase students’ retention rate and performance as well as reduce or eliminate sexrelated differences in science and mathematics performance. Paden and Dereshiwsky (2007) and Omenka (2010) as well attributed the low performance in mathematics of students particularly among sexes to instructional modality adopted by teachers. In view of the above situation there is need to develop or adopt teaching methods which are capable of improving the reasoning and logical ability of the learners to enable them perform well in mathematisc. Hence, the study examine the effect of cooperative, competitive and Kolawole’s Problem Solving (KPS) teaching method on academic achievement of students in secondary school in Ondo State.
Statement of the Problem
There had been mass failure of students in mathematics over the years in secondary schools. Kurumeh (2007) maintained that the mathematics taught in schools is foreign, eurocentric in origin and built on western cultural background, making students to learn by rote memorization in which the attendant result is consistent mass failure of students. Hence students no longer have interest towards the study of the subject. Ashafi and Areelu (2010) assert that in mathematics, boys achieved significantly higher than girls as a result of retentive rate. In the view of Aiyedun, (2000), there is no significant difference in the performance of boys and girls in mathematics and that they both retain equally well. This conflicting results call for continuous investigation specially with teaching methods to bring equity in gender achievement in mathematics.. For instant, Table I below shows the percentage distribution of credit pass of students who sat for Senior School Certificate Examination (SSCE) Mathematics conducted by West African Examination council (WAEC) between 2008 and 2011. The table shows poor and fluctuation in the students’ achievement in Mathematics.
Table1: Students’ Achievement in May/June Senior School certificate Examination (SSCE) 20082011
Year  Total Number of Candidates

Credit
A1C6 (%) 
Pass
D7E8 (%) 
Fail
F9 (%) 
Absent
(%) 
2008  1189271  41.12  31.09  24.93  2.86 
2009  1219524  33.99  28.16  34.41  3.44 
2010  1254853  46.75  24.52  25.68  3.05 
2011  1324981  47.61  27.47  23.15  1.77 
Source: WAEC, Lagos (2012)
From table 1, in 2008 when 1,189,271 enrolled for Mathematics, 41.12% had credit pass (i.e A1 C6), 31.09% had ordinary pass (i.e. D7E8), 24.93% had F9 while 2.86% were absent. From this result, it shows that only 41.12% of the enrolled candidates have the opportunity of furthering their education provided they also have credit passes in four other relevant subjects, including English language. In 2009, from 1,219,524 candidates that enrolled, 33.99% had credit pass, 28.16% had ordinary pass i.e between D7 and E8, 34.41% had F9 while 3.44% candidates were absent. Further, in 2010, 46.75% had between A1 and C6, 24.52% had between D7 and E8, while 25.68% failed. Finally, in 2011, 1,324,981 candidates enrolled, 47.61% had credit pass, 27.47% had ordinary pass, 23.15% failed while 1.77% absent from the examination. Though there is a steady increase in the percentage of students with credit pass, the conclusion drawn from students’ achievement in Mathematics between 2008 and 2011 is that, more than 50% of students enrolled had below credit pass i.e. A1C6. This is a source of worry to Educational stakeholders and researchers.
The mass failure had been linked with the choice of teachers’ method of teaching which had not effectively enhanced students’ achievement in mathematics. Most of the current teaching method in the educational system is based upon cooperative and competition methods. On the other hand, the Kolawole’s Problem Solving (KPS) teaching method is sparsely used in teaching mathematics. But researchers support the use of cooperative learning as increasing retention, fostering team building and developing higher level thinking skills. The main problem which the study investigated is which of these learning methods will bring out better achievement of the students in Mathematics and to what extent do these teaching methods affect gender in learning outcomes.
The problem of this study therefore, is to find answers to the following question:
 What is the level of achievement of students before being exposed to treatment in the three methods under study?
 What is the level of achievement of students after being exposed to treatment in the three methods under study?
 What is the performance of male and female students exposed to treatment in the three methods under study?
Purpose of the Study
The purpose of the study is to find out the effect of cooperative, competitive and Kolawole’s Problem Solving (KPS) method of teaching on academic achievement of students in mathematics in Ondo State. Specifically, the study is to examine:
 The differences in the mean academic achievement of students taught mathematics under cooperative, competitive and Kolawole’s Problem Solving (KPS) method of teaching before and after treatment.
 The differences in the mean academic achievement of male and female students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching after treatment.
 The differences in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in rural and urban areas.
 The differences in academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in day and boarding school.
 The differences in academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in private and public schools.
Research Questions
The study attempts to find answer to the following questions:
 Is there any difference in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching before and after treatment?
 Is there any difference in the mean academic achievement of male and female students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching after treatment?
 Is there any difference in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in rural and urban areas?
 Is there any difference in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in day and boarding schools?
 Is there any difference in mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in private and public schools?
Hypotheses
In attempting to find solutions to the specific questions raised, the following were proposed to be tested.
 There is no difference in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching before and after treatment?
 There is no difference in the mean academic achievement of male and female students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching after treatment?
 There is no difference in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in rural and urban areas?
 There is no difference in the mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in day and boarding schools?
 There is no difference in mean academic achievement of students taught mathematics under cooperative, competitive and kolawole’s Problem Solving (KPS) method of teaching in private and public schools?
Significance of the Study
It is hoped that the findings of this study would help to improve the teaching and learning of mathematics in several ways.
Through feedback, publication of the findings of this study, learners, especially the low ability learners could benefit immensely from the findings in that they would interact with the high performance learners thereby enhancing their learning experiences. It is hoped that the study would help students to effectively articulate and recall information, sharpen their listening faculty and arithmetic skills. Findings of this study could also enhance the critical problem solving skills of learners.
Teachers, for instance could benefit from the findings in that they will make their classroom activities more learnercentred as against teacherdominated activities popularly used in mathematics lessons. This can be achieved if teachers incorporate these methods into their teaching. Also, teacher trainers like universities and colleges of education would see the need to reorientate teachers in training on the skills for successful implementation of cooperative instruction.
Although vast literature exist within and outside Nigeria on cooperative, competitive and individualistic methods on students learning outcomes, none or probably a very few in relation to the comparative effects of Kolawole’s Problem Solving Teaching methods exist to the best of the researcher’s knowledge in Nigeria.
Thus, this study could serve as reference source for researchers in the
related aspects of Mathematics. In addition, textbook writers would equally benefit from the findings, in that group activity and activities in pairs would be
incorporated into major mathematics topics for use in schools.
Through the findings of this study, educators, federal and state ministries of education and other stakeholders would organize conferences and workshops for teachers where they can learn innovative techniques and methods for teaching mathematics.
Moreover, the findings of this study could serve as guide to researchers and other mathematics educators on how to use other models of cooperative instruction, competitive and KPS method.
Finally, the findings could help curriculum planners and curriculum developers to design a curriculum that will effect positive changes in learning experiences of learners in mathematics.
Delimitation of the Study
The study will be delimited to Ondo State secondary schools. Only the senior classes (SS2SS3) will be covered in the study.
Definition of Terms
 Cooperative method of teaching: – This is a method that requires a small number of students working together on a common task, supporting and encouraging one another to improve their learning through interdependence and cooperation with one another.
 Competitive: This is a method whereby students are concerned with their individual grades and where they fit into grade curve
 KPS: Kolawole’s Problem Solving method of teaching
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