**ABSTRACT **

The purpose of this study was to determine secondary school mathematics teachers’ conceptions about linear and quadratic equations. Six research questions and four null hypotheses guided this study. The study was conducted in Ika education zone of Delta-state. The sample was 124 secondary school mathematics teachers. Instrument for Data collection was a questionnaire titled linear and quadratic equation questionnaire (LQEQ). Descriptive analysis involving means and standard deviations were used to answer the research questions while Analysis of variance (ANOVA) and t-test were used to test the null hypotheses at 0.05 level of significance. The results showed that mathematics teachers have various conceptions about linear and quadratic equations and that mathematics teachers’ conception can influence their action in the classroom. The study also revealed that gender and teaching experience have a great influence in the teaching and learning of linear and quadratic equations. The result showed that there is significant difference between male and female mathematics teachers in their conception about linear and quadratic equations. Again, that there is significant difference between experienced and inexperienced mathematics teachers in their conceptions about linear and quadratic equations.

**TABLE OF CONTENTS**

Title page i

Table of Contents ii

**CHAPTER ONE: INTRODUCTION **

Background of the Study 1

Statement of the Problem 10

Purpose of the Study 11

Significant of the Study 11

Scope of the Study 13

Research Questions 13

Hypotheses 14

**CHAPTER TWO: LITERATURE REVIEW 15**

**Conceptual Framework** 16

Concept of Equation 16

Concept of Gender 31

Concept of Teaching Experience 34

Teachers’ Mathematical Conceptions 34

**Other Related Sub-Themes 36**

Mathematics and its Importance 36

Problems of Teaching and Learning Mathematics 39

**Theoretical Framework** 40

The Cognitive theory of learning 40

Constructivist theory of Learning 41

**Empirical Studies** 42

Teachers’ conceptions about teaching and learning of mathematics 42

Teachers’ conceptions about equations 44

Teacher’ conceptions as determined by teaching experience 46

Teachers’conceptions as determined by gender 47

**Summary of Literatures** 49

**CHAPTER THREE: RESEARCH METHOD**

Research Design 51

Area of the Study 51

Population of the Study 51

Sample and Sampling Techniques 52

Instrument for Data Collection 52

Validation of the Instruments 52

Trial Testing 53

Reliability of the Instrument 53

Method of Data Collection 53

Method of Data Analysis 53

**CHAPTER FOUR: RESULTS **

Research Question 1 54

Research Question 2 56

Research Question 3 57

Research Question 4 58

Research Question 5 58

Research Question 6 59

Hypothesis 1 60

Hypothesis 2 60

Hypothesis 3 61

Hypothesis 4 61

Summary of Finding 62

**CHAPTER FIVE: DISCUSSION, CONCLUSION AND SUMMARY **

Discussion of the Finding 63

Conclusion 66

Implication of the Finding of the Study 67

Limitations 67

Recommendations 68

Suggestions for Further Studies 68

Summary of the Study 69

**REFERENCES **71

**APPENDIX**

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**CHAPTER ONE**

**INTRODUCTION **

**Background to the Study **

Mathematics is one of the core subjects that is taught in Nigerian secondary schools. It is the science that deals with the logic of shape, quantity and arrangement. It also deals with logical reasoning and quantitative calculation (Attah and Guwam, 2014). Mathematics holds the potency of making individuals relate its knowledge to everyday problems being encountered by individuals in the society. This is why mathematics is an important subject in the education of a child. With the knowledge of mathematics, the child can easily actualize some of the educational objectives and will be able to function well in the society. This is why the schools mathematics curriculum formulated most of these stated objectives,which can be actualized through the mathematics teachers.

The teacher being at the centre of the entire education at all levels is the most potent instrument for ensuring the fullest possible development of the student. The mathematics teachers play a vital role in the teaching and learning of the students and also help to expose the learners to numerous possibilities, which can be explored to deal with individual and group problems. This is why they are the initiator of creativity (Ugwuda, 2014). The mathematics teachers actualize the above goals through the school mathematics curriculum.

The mathematics curriculum is a set of planned learning experiences which are taught in schools, directed and evaluated by the mathematics teachers to attain specified goals with recommended materials (Attah and Guwam, 2014). The mathematics curriculum is an official document stating educational aims, goals and objectives for a particular subject in the school system. Thus, the curriculum specifies what should be taught, why it should be taught, how it should be taught and to whom it should be taught (Ughamadu, 2006). This document is further broken down to syllabus, scheme of work, unit of lesson and lesson plan. The mathematics teachers prepare the lesson plan for teaching a particular topic from the scheme of work in which equationsis included. For effective teaching and learning the mathematics teachers use the scheme of work. This scheme of work is usually a guide in planning what is to be done per week over a term, and for the three terms in an academic year in school. The various topics are stipulated for student learning in the scheme of work, including equations, which are taught in second term in SS II class.

In mathematics, equations are statements that show that two algebraic expressions are equal in value. For example, 6x – 4 = 2x – 1 with an unknown x value. This equation is only true when x has a particularknown numerical value. In mathematics, letters of the alphabet are used, to stand for numbers e.g. 8 + p. Any letter can be used. For example 8 + a would be just as good as 8 + p. Capital letters are not used, only small letters are used. When using a letter instead of a number, the letter can stand for any number in general. When letters and numbers are used together in this way the mathematics is called algebra.

The word algebra comes from a book written by Mohammed Musa al Khnowarizmi- around AD836. The title of the book was Al-jabrwa’IMuqabalah. The statement y + 3 = 14 is called an algebraic expression, which means an unknown number y plus 3 equal or make 14. The number that the letter stands for should make the sentence true. To solve an equation means to find the real number value of the unknown that makes the equation true. The two most common equations taught at secondary school are linear equations and quadratic equations, (Macra et al, 2007).