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# DIFFICULTIES ENCOUNTERED BY SENIOR SECONDARY SCHOOL STUDENTS IN SOLVING ALGEBRAIC PROBLEMS

## Content

**ABSTRACT**

This research work examined the difficulties encountered by students in solving algebraic problems in Surulere Education District of Lagos State. The design used for the study was descriptive survey. Data was collected from a sample of one hundred and twenty students and fifteen mathematics teachers from four Senior Secondary Schools selected. The instrument used was questionnaires for students, questionnaires for teachers and diagnostic test for the students on algebra.

The main purpose of this study was to analyze the difficulties encountered by Senior Secondary School students in solving algebraic problems in senior secondary school and identify the difficulties that students encounter in solving algebraic problems, identify the various factors contributing to the difficulties faced by students while solving algebraic problems and to assess student’s level of performance in algebra.

The result of the diagnostic test revealed that the students performance was poor due to the difficulty in understanding symbols and special terms, poor understanding of use of order of operation, inability to interpret expression. Also from the questionnaire given to the teachers it was revealed that lack of qualified teachers, large number of students in a class made it difficult for students to solve algebraic problems. Conclusion was drawn and recommendation was made.

**TABLE OF CONTENTS**

**TITLE PAGES **

CERTIFICATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

TITLE CONTENTS vi

**CHAPTER ONE: INTRODUCTION**

1.1 BACKGROUND TO THE STUDY 1

1.2 STATEMENT OF THE PROBLEM 4

1.3 PURPOSE OF THE STUDY 5

1.4 RESEARCH QUESTIONS 6

1.5 SIGNIFICANCE OF THE STUDY 6

1.6 SCOPE AND LIMITATION OF THE STUDY 6

**CHAPTER TWO: REVIEWING THE LITERATURE**

2.1 INTRODUCTION 8

2.2 THE IMPORTANCE OF MATHEMATICS AND ALGEBRA

2.3 DIFFICULTIES STUDENTS ENCOUNTERED IN SOLVING 9

ALGEBRIC PROBLEMS

2.4 EFFECT OF PREREQUISITE KNOWLEDGE OF STUDENTS IN 14

ALGEBRA

2.5 POSSIBLE SOLUTIONS TO THE DIFFICULTIES 17

ENCOUNTERED BY THE STUDENTS IN SOLVING

ALGEBRAIC PROBLEMS

2.6 SUMMARY 19

**CHAPTER THREE: RESEARCH METHODOLOGY **

3.0 INTRODUCTION 21

3.1 THE DESIGN OF THE STUDY 21

3.2 AREA OF THE STUDY 21

3.3 POPULATION OF THE STUDY 21

3.4 SAMPLE AND SAMPLING TECHNIQUE 22

3.5 RESEARCH INSTRUMENTS 22

3.6 METHOD OF DATA COLLECTION 23

3.7 METHOD OF DATA ANALYSIS 23

**CHAPTER FOUR: DATA PRESENTATION AND ANALYSIS **

4.1 INTRODCUTION 24

4.2 PRESENTATION OF DATA 24

4.3 ANALYSIS OF DATA 33

4.4 MISTAKES MADE BY THE STUDENTS 34

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

5.0 INTRODUCTION 35

5.1 DISCUSSION 35

5.2 CONCLUSION 36

5.3 RECOMMENDATION 38

REFERENCES 39

APPENDIX 43

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** **

**CHAPTER ONE**

**INTRODUCTION**

**1.2 ****BACKGROUND TO THE STUDY **

Education is seen as the best means for developing the potentialities of young and adult learners so that they can in turn make meaningful contribution to the development of the society. Education in Nigeria is an instrument “par excellence” for effecting national development (National policy on Education, 2004). It is generally recognized that no society or nation can make only significant progress without relevant education.

According to Ivowi (2003), national development can only occur if there is a crop of human resources with sufficient knowledge and skills to interact with ideas and materials in order to produce the required result. The development of an individual started from his early childhood particularly at primary school (Owolabi, 1991).

Mathematics can be defined in various ways but according to the Oxford dictionary (1982) it is the “science of numbers”. Mathematics is also referred to as the acquisition of the ability by an individual to apply deductive and inductive, reasoning to real life situation.

Abiodun (1989) states that Mathematics is the core of all educational objective so to indulge people into functioning effectively and efficiently especially in an age of modern technology. It requires the person studying it to acquire the in depth knowledge of mathematics so that he or she can understand the theories of the subject.

Ames (1992) said that Mathematics enhances problem solving skills and analysis skills of students. It enables students to apply their skills to both familiar and unfamiliar situations.

Dale (2008) describes Mathematics as a base for all technologies. All innovations are by product of science and mathematics. It is applied in medicine, engineering, natural science, social science, physical science, technology, business and commerce. It is necessary in learning computer science, computers are to be found in banks, hospitals, universities etc. they are used by accountants, doctors, teachers, research scientists, students and many others, all these becomes a reality as a result of the importance of mathematics in all aspects of human life.

Butler (1960) describes mathematics as the bedrock of all human knowledge. This is because mathematics has been in the forefront of human endeavours to understand his environment and be able to aggregate all factors in it, to make life comfortable for him. Hence mathematics embraces many branches of science and highly required in many spheres of life regardless of the manner of level of application.

Kenku (1988) defines mathematics as the language of science. He further explains that mathematics could be better defined as the study of numbers, shapes, physical systems and their relationship.

Mathematics plays a major part in the human daily lives, it started with counting, by the primitive man, this led to computation argument and logical thinking followed. It is common knowledge that mathematics is allocated the greatest number of period in the secondary school’s timetable, however students perform least in it.

The objective of teaching mathematics in Senior Secondary school are:

1. To generate interest in mathematics and lay a solid foundation for everyday living.

2. To develop pupils computational skills.

3. Encourage creativity and provide necessary mathematical background for further education.

4. To develop ability to be accurate to a degree relevant to the problem at hand.

5. To develop ability to recognize problems and to solve them appropriately and relate to mathematical knowledge.,

6. To develop precise, logical and abstract thinking.

Don Small (2002) Identified high school preparation, placement, syllabus, content, face, attitude, lack of persistence, determination and pedagogy etc as the main factors that contribute to poor performance of student in mathematics.

Many children growing into the adulthood have developed negative attitude towards algebra (Brekke, 2001) students easily understand algebra and it is a source of consideration, confusion and negative attitudes among students.

According to Encarta premium (2006) He defined algebra as a branch of mathematics in which symbols (usually letters) reqpresents unknown numbers in mathematical equations algebra allows the basic operations of arithmetic’s, such as addition, subtraction, multiplication and division to be performed without using specific numbers. Mac Gregor (2004) listed the reasons why students should be helped to easily understand algebra and solve problems in it. Amongst which are:

First, algebra is a vital part of the general knowledge of numbers in a democratic society secondly, it is pre-requisite for further study of mathematics, thirdly it is a crucial component of mathematical literacy, fourthly it is an efficient way of solving certain types of problems, finally, it promotes generalizations, organized thinking and deductive reasoning which are keys to intellectual activities.

1.2 **STATEMENT OF THE PROBLEM **

Mathematics in Nigeria education is a core and compulsory subject, an important aspect of which is algebra. Although teachers often teach students this aspect of mathematics, researchers have shown that there is a low output in terms of students performance in algebra (Ignacio, 2006). This indicates that many students at SSS t level do not have a good grasp of the algebraic aspects of mathematics.

According to Edgeton (2000), the teaching of algebra is not allowed to grow out of direct experience and most algebraic ideas are simply handed over by the teacher than helping students to discover them.

According to Okello 2010 and Parker, (1999) most problems encountered by students include:

i. Teachers inability to teach the fundamentals of algebra i.e guides students to discover how generalizations in algebra are derived.

ii. The use of inappropriate methods in the teaching of algebra.

iii. Lack of motivation

iv. Lack of practice

v. Lazy students

vi. Poor use of resources. These problems need urgent attention and are likely to affect our national development if not handled adequately.

1.3 **PURPOSE OF THE STUDY **

The main purpose of this study is to investigate the difficulties encountered by S.S.I students in solving Algebraic problems in Surulere Local Education District of Lagos State, Nigeria.

The objectives of the study are to:

1. Identify the difficulties that students encounter in solving algebraic problem at S.S. I level.

2. Identify the various factors contributing to the difficulties faced by students while solving algebraic problems.

3. Assess student’s level of performance in algebra S.S.I level in the study population.

1.4 **RESEARCH QUESTIONS **

** **The following research questions were proposed for this study.

1. What are the problems encountered by students at SS1 level in solving algebraic problems?.

2. What factors give rise to these problems?

3. What is the level of performance of students in algebra in the study sample?

1.5 **SIGNIFICANCE OF THE STUDY **

This study will be particularly useful to senior secondary school mathematics teachers as it will give them insight into the problem faced by students at the immediate higher level, hence they will be better equipped to groom their students adequately.

It will be as well of benefit to curriculum developers in time tabling and other administrative process concerning this unique subject. It is also useful to S.S.S.I students so as to identify the solution in solving problems algebra in senior secondary school.

1.6 **SCOPE AND LIMITATION OF THE STUDY **

The Study covered Senior Secondary School selected from Surulere Local Government Education District of Lagos State.

The possible limitation to the study were financial and time constraints.

** **