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Effect of Problem solving method on students achievement in mathematics at Ibadan North East Local government Are of Oyo State

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EFFECT OF PROBLEM SOLVING METHOD ON STUDENTS ACHIEVEMENT IN
MATHEMATICS AT IBADAN NORTH EAST LOCAL GOVERNMENT AREA OF OYO STATE BY RAJI AYOBAMI AKEEM 22006/IK/SD/4800 DEPARTMENT OF MATHEMATICS, FACULTY OF EDUCATION. UNIVERSITY OF NIGERIA, NSUKKA OCTOBER, 2010

EFFECT OF PROBLEM SOLVING METHOD ON STUDENTS ACHIEVEMENT IN MATHEMATICS AT IBADAN NORTH EAST LOCAL GOVERNMENT AREA OF OYO STATE BY RAJI AYOBAMI AKEEM 2006/IK/SD/4800 A RESEARCH PROJECT PRESENTED TO DEPARTMENT OF MATHEMATICS UNIVERSITY OF NIGERIA (NSSUKA) IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE AWARD OF BACHELOR OF SCIENCE IN EDUCATION (BSC. ED) OCTOBER, 2010

CERTIFICATION
I certify that this project was carried out by RAJI AYOBAMI AKEEM under my supervision and that the work is original.

................................................ ............................................................
Project Supervisor Student

............................................... ..............................................................
Date Date

DEDICATION

This project work is dedicated to the glory of Almighty Allah and to my junior sister LATE RUKAYAT ADUKE (IYA ROKIBA) MAY HER SOULD REST IN PEACE

TABLE OF CONTENT

Title Page Page
Certification i
Dedication ii
Table of Contents iii
Abstract iv-v

Chapter One - Introduction
1.1 Background of the study 1-3
1.2 Purpose of the Study 4
1.3 Significance of the Study 4-5
1.4 Research Question/Hypothesis
1.5 Scope of the Study
1.6 Definition of Terms

Chapter Two - Review of Related Literature
2.0 Literature Review
2.1 Definition of Mathematics
2.2 The Nature of Mathematics
2.3 The Nature of Problem Solving
2.4 Other methods of Teaching
2.5 Researches in Problem-Solving Strategies
2.6 The Ideals in Teaching Problem Solving
2.7 Appraisal of Related Literature Review

Chapter Three - Research Methodology
3.0 Research Methodology
3.1 Research Design
3.2 Population
3.3 Sample and Sampling Techniques
3.4 Instrumentation
3.5 Validation of Instruments
3.6 Reliability of Instrument
3.7 Data Collection Procedure
3.8 Data Analysis
Chapter Four - Analysis of Results and Discussion
4.1 Analysis of Data
4.2 Hypothesis I
4.3 Hypothesis II
Chapter Five - Summary, Conclusion and Recommendation
5.1 Summary
5.2 Conclusion
5.3 Recommendation

Appendix I
Appendix II
ABSTRACT

This study was designed to find out the effects of problem solving on students achievement in Mathematics in Ibadan North East Local Government. The research was conducted with the use of Mathematics achievement test.
The research devoted chapter one of the study to give detail background, purpose, statement of research problems, research questions, hypothesis, significance and definition of certain terms for easy understanding of the work.
The second chapter is used in reviewing on the study. It therefore brings out the opinion of various authors on Mathematics and problem solving method.
Chapter three deals with the research design and procedure. The population used in selected from Ibadan North East Local Government Area. Sixty students randomly selected in three Secondary Schools used for the study.
The fourth chapter deals with the result obtained through analysis of the figures obtained form the test. In addition, the hypothesis generated were tested using of t-test statistics at 0.05 level of significance.
From hypothesis I, it is observed that there is no significant difference between the performance of students who are exposed to problem-solving method and teaching method.
In hypothesis II there is significance difference btween the performance fo student who are taught using problem-solving method and lecture method.
In conclusion, chapter five contains a summary of the investigation discuttion of the research findings and the recommendations.

CHAPTER ONE
INTRODUCTION

1.1 BACKGROUND TO THE STUDY
Mathematics is very important and actually started before the council era. Also the role is essential in the lives of peoople. Is the fact that people’s ability to reason distinguishes them from other animals. Our forefathers started by counting 5s, 9s etc. and a way of easy remembrance, they usually use charcoal for making lines on the wall. One line to them means one, while two lines means two and so on. Besides, they also make contributions in either 5 days interval and 9 days intervals and for easy counting they use either fingers or stone.
Moreover, mothers taught the female ones how to count the number of yams to be prepared for the family and amny other informal ways of teaching. As a way of advancement in counting, they started counting in 100s meaning half of a tag and so on. People in the civilized world agitate for innovations on schools mathematics curriculum. They are restless about how mathematics should be taught due to the importance to mankind and the native as an support of the evolution of modern programmes include:
1. The innovations and launching of early satellites depend on expert applications of fluid dynamics to which calculus is the basic fundamental.
2. Development of supersonic flight.
3. Recent researcher in geophysics, discovery of deep ocean current.
4. New achievement in mechanic engineering on automatic radar communications depend heavily on the work of analysis and apply mathematics.
Mathematics is also used for social science as well. There are occasions to deal with large masses of data obtained by sampling through the tehory of probability and statistical influences. There is also mathematics in sociology in which mathematical methods and techniques are appplied to pupulation and socials studies concerning individual and community as a whole.
Objectives of mathematics are stated below
1. To generate interest in mathematics and to provide solid foundation for every living.
2. To develop the logical and concrete thinking of the students.
3. To develop and inculcate the numeracy knowledge of the student.
4. To develop the ability to make relevant judgement through discrimination of values.
5. To foster the desire and ability to be accurate to a degree relevant to the problem at hand.

The objectives of mathematics in junior and senior secondary schools are stated below
1. Development of intellectual curiosity.
2. Development of aesthetic appreciation and expression.
3. Development of intellectual independent.
4. Development of the ability to distinguish between relevant and irrelevant data.
5. Communication of taught through symbolic expression and graphs.
6. Development of the ability to make relevant judgement through the discrimination of values and so on.
The West African Examinatin Council (WAEC) also stated that the objectives of mathematics that may assume the objectives of the secondary or post primary school because the body deals directly with post secondary schools such objectives are as follows:
1. To develop computational skills
2. To foster the desire and ability to be accurate to a degree relevant to the problem at hand.
3. To provide a solid foundation for every living.
4. To develop precise logical and abstract thinking.
5. To develop the necessary mathematical background for further education.

During a clinical investigation carried out by Akinloye(1986) on some students understanding of mathematics a students in answering an intreview question answer sharply “Mathematics is the most difficult subject taught by wicked teacher” the above statement are the belief and views of many students about mathematics and those teaching it. Even in the tertiary institutions, mathmatics generally rerquire logical thinking. As a result, the effects of student poor performance in mathematics could be their inability to solve mathematics activities in the classroom environment.
May (1974) described problem solving as a complex mental process involving visualization, imagination, manipulation, abstraction and the association of ideas. In teaching problem-solving, teacher must analyze closely all the stteps required in the process so that they can reach the students.
The poor achievement in problem-solving is due to inappropriate studying habit of students, not because they do not have the mental ability to do well in problem-solving but because of poor study
techniques and habit.
1.2 Purpose of the Study
This study was designed to determine the effects of problem-solving method on student’s
achievement in mathematics. More essentially, the knowledge of problem-solving method can assist both the teachers and students to find solution to word problem and apply them to similar situation.
1.3 Significance of the Study
This project (i.e. The effect of problem-solving method on students achievement in mathematics) is important to various peoople such as students, teachers, government and the society at large. Its important to a nation cannot be overemphasized as written earlier in this study especially taking iinto consideration the present scientific and technological situation of our country when compared with the developed countries. It would enable students to see the important of this study as a way of thinking logically to satisfy their sense of curiosity.
The result of the research would be a great importance to tteachers and educational planners. It will also afford the teachers the opportunity to know different methods of teaching mathematics and to make the teachers to guide their students in solving the problem(s) and that the teaching of mathematics is entirely different from other fields of specialization.
This technique allows learners to learn form their successes and failures and culminate into real comprehension of facts since permits the learners to participate in their learning. It also guides and stimulates the learners into discovering the solutions to certain problems.
Equally, it is hoped that the study will be benefit to eduational planners in the training and selection of mathematics teachers and to encourage the teachers to have more interest towards the educational achievement of their students.
1.4 Research Questions/Hypothesis
(a) Hypothesis
The hypothesis generated for this study are stated below.
1. There is no significant difference between the performance of student who are taught using problem-solving method in mathematics and those who use professional methods.
2. There is no significant difference between the performance of students who are taught using lecture methods in mathematical problems.
(b) Research Questions
On the basis of the identified problem the following research questions are raised. they are:
1. What problem solving suitable for teaching and learning of mathematics?
2. Is there any thing to be considered before using problem-solving method?
1.5 Scope of the Study
This project focuses mainly on the effects of problem solving methods on students’ achievement in mathematics.
Three secondary Schools were chosen and all the data for the research are colected froom the fonfinement of the arrea of study. Thus, three secondary schools were randomly selected froom Secondary Schools in Ibadan North East Local Government Area of Oyo State. Other researcher can replicate the study.
1.6 Definition of Terms
Effects: It is operationally defined as the result or outcome of an event. That is, it’s the results or outcome of problem-solving method on students’ achievement in mathematics. It can also be defined as the result; what is found after something has being done. That is, after the application of the problem-solving method on students’ achievement in mathematics what is found out is called effects.
Problem-solving: Problem is a difficult matter which has to be examined (in a difficult question). While solving is a way of finding out of a difficulty (i.e fo find the answer t a problem). This requires the ability to reason and demand active thinking on getting solutions to problems.
Achievement: It is a successful coompletion of an activity.
Teaching: This is an art. It is essentially a system of interactions involving the teacher, the learner and the learning task (i.e material). It is also a way where teacher is using to help a person to learn unknown something.

CHAPTER TWO
2.0 Literature Review
At any time in our lives when we take decisions, we often make use of mathematics without realizing it. One of the tools that we do not normally give taught, in this our everyday use of mathematics is the system of number we use. In this chapter we shall take cognizance of the review of related literature on the effects of problem solving method on students’ achievement in mathematics. This review of literature will be done under the following subheadings:
i. Definition of mathematics
ii The nature of mathematics
iii The nature of problem-solving
iv Other methods of Teaching
v Researches in problem solving strategies
vi The ideas in teaching problem-solving
vii Appraisal of related literature review
2.1 Definition of Mathematics
Mathematics as a term is capable of many definitions by different authors. It could means “the mother of sciences (i.e all sciences subjects). In one of its frequent meaning “is the study of numbers and the size of spaces; (Oxford Dictionary).
According to Adegunly defines mathematics as a summary tool used by all scientists in their ssearch for clear understanding of physical world. According to Fakuade (i979) defines mathematics served as a tool for use in the sequences, in industries and technicall and in some other respects.
According to Encyclopedia World Dictionary (1979) “Mathematics is the average of a set of possible values of a variable, the value wrghted by the probabilities associated with these value”.
According to Sikiru (1990), Mathematics is art of science that deals with calculatin of number and finding solution to questions. It can be describe as an essential of life for mans day-today activities revolve round the use of numerate subjects.
According to Allen and Umwin (1979) Mathematics is the science of numbers and shapes and of the link between them, they stressed further that mathematics is the logical development of fundamental abstract idea giving substances through words, number and symbols.
Finally, mathematics is the science of size and numbers (of which arithmetic, algebra, trigonometry, geometry, are branches). Mathematics is the logical development of fundamental abstract idea, given substance through words, numbers and symbols (Hornby 1974).

2.2 The Nature of Mathematics
The nature and structure of the subject can be use to separate problem solving in mathematics by consider them (i.e by considered the nature and structure of the subject). By the time we are trying to study the problem solving in mathematics, the nature and structure are peculiar. Characterisitics of the subject that must be examined.
Mathematics is problem solving subject by itself. Mathematics according to Gegues Hierarchical learning of instruction, he believes that the learning of a concept or skill depends upon the learning of the pre-requisite concepts or skills.
According to Moon (1971) is hierarchical sequential and its nature is made up of patterns. It is hierarchical because it is a learning process that proceeds from simple to complete and of often involving the combination or integration of simple skills to produce more complex skills.

2.3 The Nature of Problem-Solving
Problem-solving techniques comprises of identifying and choosing mathematical problems which grow out of the experiences of individual learners. Problem solving has been identified by scholars as one of the basic objectives of science education in general and that of mathematics in particular.
Adams et al (1977) claimed that ultimately all goeals in mathematics point towards problem-solving skills and understanding are gained to enable people solved problems encountered in the world outside the classroom. Opportunity ofr flexibility of behaviour is an essential of problem solving in the classroom. If the teachedr gives the solution immediately, the time necessary for the students’ understanding of the problem is too short.
Problem solving techniues allows learners to learner form their successes and failures and culminates into real comprehension of facts since it permits the learners to participate in their learning. It tends to forced students to arrange and classify facts or data. This techniques also guide and stimulate the learners into discovering the solutions to certain problems which arise in their course of study by themselves and to encourage the learners to reason and judgement in order to arrive at a reasonable solution to their problem.

2.4 Other Methods of Teachng
In mathematics, many methods of teaching can be accepted in teaching particular topic. Any of these methods used by the mathematics teachers indicates the type os behaviour he wants to bring out form his students in learning condition.
Basically, thee are numerous of methods of teachng with different author. According to Obanya (1986), methods of teaching are the systematic procedure by which the set objectives of teacher are realized through passing information to his/her students.
More also, SAN (Science Teacher Association of Ngeria) 1970, defines methods of teaching techniques are adopted by the teachers. STAN said that the learner should make teaching and learning of mathematics thorough for the students would dictate the methods that the teacher adopts. They involve the combination of all things a teacher does to convey this message successfully to his students during the course of teaching students.
Teaching methods are the procedure by which a teacher are attempts to dispense information to his/her students. They involve a combination of all things or activities a tacher performs in order to maximize the students understanding of the lesson with the minimum of strains on the part of the students.
Generally, methods of teaching can be seeing as the strategies, method and system adopted by the mathematics teacher in order to enhance a proper understanding.
There are crucial factors need to be considered by mathematics teacher in choosing a particular methods to be use in teaching mathematics. They are:
a. Their educational background and the age of the students.
b. The needs and interest of the students
c. Individual differences of the students.
d. Objectives of the teacher.
e. Objectives of the subject (i.e of that particular topics i mathematics.
f. Type of instructional materials that available, some of the teaching methods usually used by the teacher are hereby stated and discuss below:
(i) Project Method: This is the method in which student or a group of students are given project (i.e specific topic) to write something on; with the teacher standing-by
(i.e Supervisor) to guide and correct that student when necessary or when needed. The teacher needs to guide them (i.e the student) from the beginning to the end.
According to Ajila (1992) defines “Project method as a type of method in which student learn through independent activity through under the guidance of a teacher”. This type of method enables the students to have new experience when they are searching for a main topic approved by their
Supervisor.
(ii) Lecture Method: This is a teaching method in which facts or principles are presented orally to a group of people (i.e learners) who take notes, have little or not participation is discussion. It is usually adopted at Seminars or among adult learners. Laecturing method is also a teacher-centers method. Lecturing method is used to train learners the art of listening and writing, also more ground (i.e more topics) can be covered by the teacher. Plus method emphasize on teaching than learning in the sense that the learner will be passive rather than active in the class and they can (i.e learners can not be accessed adequately and teachers canot access their method of teaching.
(iii) Discussion Method: This is the method which based on the principle that, the ideas of many people are better in addressing issues and finding solutions to problem. It is a child-centered method. /The discussion may be carried out when the teacher prepares questions for the lesson while some other questions are spontaneous based on how he regulates the activities of that discussion and learners encourage to contribute. Examples are: Debate, small group discussion etc for this method (i.e
discussion method) be effective, it must have a structuring device that is a topic either in form of question or a statement. This method enhances communication skills in learners (i.e students) as they engage in oral arguments I their collective efforts to resolve some issues; and it liberates them from the clws of dgmatism and build each of them to have self-confidence in themselves.
(iv) Group Method: This involves breaking the class into manageable units of say 5 or 10 learners per group while the teacher moves round to guide the activities of each group. This method helps the students to work together, learn froom each other and accept the contributions of others.
(v) Demonstration Method: This method is a teacher-centered method. The teacher to show clearly how some exercise should be done uses this method and the learner will just merely looked at the process which other teacher is showing them. This method help the students to tackle other
questions pertaining to that process, and give room for the question when necessary.

2.5 Researchers in Problem-Solving Strategies
Research conducted in the past and presently in the teaching of mathematics. In mathematics problem-solving could lead to better cognition, this suggested b Gague (1965), Popoola (1977), Falemu (1997) and Stinner (1954).
This problem-solving desined for solving both worded and unworded problem in mathematics. According to Polysa (1973) identified four stages in problems solving. The are:
stage1: Understanding the problem. The mathematics teacher(s) should ensure that the students comprehend the problem very well.
stage 2: Devising a plan to solve the problem. The teacher helps the students to gather relevant thought so as to help them in devising a plan. And help the students in analyszing and establish a relationship between the different variables in the proble. The teacher allows the student to represent the unknown(s) with letters or symbol and help them in formulating hypothesis and consequently plan a solution.
stage3: carrying out the plan. This stage, the students perform the necesary calculations and operation to arrive at the answer.
stage 4: Looking back. When they arrrive at a solution, the teacher should encourage the studens to go through the process of solving the problem and guide them to check how correct the answer is. The following sequences suggested for problem-solving techniques in mathematics.
Step : Identifying the Problem
The teacher will place the problem before the students in the class, and the learner should be able to identify out of their experience. Teacher should help providing students with sources of iformation that could help them in identifying the problem and guide the students.
Step 2: Defining and delimiting the problem
The learner should read the prblem first in order to comprehend, after that he should then re-read it with a view to find out what he is expected to do. The problem should be interested and pin point some facts from that question.
Step 3: Collection of Data and other Evidence
The students should gather together the relevant data or facts and other evidence form that problem.
Step 4: Proposing Hypothesis
The students are expected to plan alternative mathematical behaviours that can be utilized in solving the problem. The students should formulate the hypothesis for solving the problem.
Step 5: Trying out the Hypothesis
This is the stage for students to calculate3 that is, try out their plan or hypothesis which they are propose in step 4. The unknown in the problem should carry out the operations and perform the necessary calculation.
Step 6: Verification
Here, the student test for the acceptance rejection of the solution by checking the reasonableness of the solution obtained by seeing how it fits the condition of the problem.
Summarizing, the students should be encourage fo find solutin to problems by themselves so that learning becomes more meaningful to them. This is the one of akins and objectives of problem solving method.
2.6 The Ideals in Teaching Problem Solving
This ideals in teaching problem solving can also called the role of the mathematics teacher in
problem solving.
According to Chauchan (1985) put forward some useful suggestions whichcan help mathematics teachers in problem solving.
1. Moderate motivation of the learners. That is the students, to be motivated moderately by the teachers.
2. Encourage Divergent thinking in learners/students. The teacher should be encourage divergent thinking in their students by encouraging the to tackle mathematics problem in a variety of ways.
3. The problem should be prresented as a whole.
4. The level of difficulty of the problem. Mathematics teacher should neither presented too easy nor too difficult mathematical problem to their students.
5. Practice on the part of the students and so on.

2.7 Appraisal of Related Literature
The literature review on the effect of problem solving onstudens achievement in mathematics can be reviewed by taking a proper appraisal of the literature review which has borrowed words.
The following can be identified as the summaries of the review work.
- Problem-solving under this review enable the teaching and learning process to be effective
- It analyses many methods of teaching which we can use to tackle the problem in
mathematics
- It helps the students and the teacher to understand the simple ways or strategies to be used in other to solve the problem and check for the answer.
- Problem-solving helop the teacher to encourage divergent thinking of the students.
- It make the teaching of Mathmatics to be productive and effective.
- It helps the students to have slef confidence and make them to be able to tackle some problems in mathematics and come out with correct solution to that problems(s).

CHAPTER THREE
3.0 Research Methodology
This chapter focuses attention on the research method and procedures used by the researcher in colecting data for analyzing and it was discussed under the following headings:
1. Research Design
2. Population
3. Sample and Sampling Techniques
4. Research Instruments
5. Validation of Instruments’
6. Data Collection Procedure
7. Data Analysis
3.1 Research Design
This is a descriptive research design, the research was designed to investigate the effects of problem solving on studens achievement in Mathematics at Ibadan North East Local Government Area. The schools involved were insisted personally by the researcher. The experimental group was aught
using problem-solving method. the control group was taught using conventional method. Schoo X was exposed to lecturing method while school Y was exposed to conventional method.

3.2 Population
The study population comprises of Senior Secondary One (SS 1) in three selected Secondary Schools out of ten to twenty secondary schools in the local government.

3.3 Sample and Sampling Techniques
the sample for this research study is made up of twenty students randomly selected in each school (due to constraint of time and finacne) with an average of ten students inscience class, five students in Arts class and five studens in commercial class making a total of 60 studens in the three selected secondary schools.
On the basis of udgmental sampling procedure, therefore, the following secondary schools were sampled for the study.
S/N School No of Students Selected in SS 1
X Renascent High School, Agugu Ibadan 20
Y Lagelu Grammar School, Agugu Ibadan 20
Z Loyola College Ibadan 20
Total 60

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