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# THE PROBLEMS OF TEACHING AND LEARNING ALGEBRA AT THE SENIOR SECONDARY SCHOOLS

## Content

**ABSTRACT**

This research was designed to identify the problems teachers and students encountered when teaching and learning algebra at the secondary school level.

A total of seventeen (17) mathematics teachers and one hundred (100) students randomly selected served as the subjects of this study.

The instrument used for this research were Algebra Diagnostic Test (ADT) for students and Questionnaire for teachers and students. The data collected were analyzed using the statistical package for social sciences (SPSS) which include simple percentages, the mean, standard deviation and analysis of variance (ANOVA).

The research questions were investigated and two null hypothesis were tested. The findings revealed that;.

i. There are significant problems encountered by teachers while teaching algebraic concepts that adversely affect students’ appreciation and achievement in algebra classes.

ii. There are significant problems encountered by students when learning algebraic concepts that lead to poor performance in mathematics and application to other subjects.

Based on these findings, appropriate recommendations were made and it was concluded that problems of teaching and learning algebraic concepts affect students achievement and performance in algebra test and mathematics in general.

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**Title page** **Pages**

Certification ii

Dedication iii

Acknowledgement iv

Table of content v

Abstract vi

**CHAPTER ONE- INTRODUCTION**

1.1 Background to the study. 1

1.2 Statement of the problem. 9

1.3 Purpose of the study. 10

1.4 Research Questions. 10

1.5 Research Hypothesis. 10

1.6 The Significance of the study. 11

1.7 Scope and Limitation of the study. 11

**CHAPTER TWO: A REVIEW OF RELATED **

** LITERATURE **

2.1 Introduction. 14

2.2 Problems of Teaching Algebra. 15

2.2.1 Professional Development and Mathematics 15

instruction of Teachers.

2.2.2 Limited Pedagogical Knowledge of Teachers. 16

2.2.3 Lack of Realization of the Effects of Students

Algebraic Thinking in effective Teaching. 17

2.2.4 Complexities in Coding Students Responses. 18

2.2.5 Limited content Knowledge base of Teacher. 18

2.2.6 Absence of Teaching Algebra as Modelling Tool. 19

2.3 Problems Students Encounter in Learning Algebra. 20

2.3.1 Isolation of Mathematical Ideas from Elementary

Algebra. 21

2.3.2 Nature of Learning Environment. 22

2.3.3 Misconception about the Use of

Letters and Symbols. 22

2.3.4 Nature of Algebraic Concepts. 23

2.3.5 Academic Procrastination among Students. 24

2.4 Research Finding on the Solution Strategies to

the problems of Teaching Algebra . 25

2.4.1 Improved Condition for professional and

Non-professional Mathematics Teacher. 25

2.4.2 Adequate Pedagogical Knowledge of Teachers. 26

2.4.3 Preference to the Effects of Students Algebraic

Thinking to Effective Teaching. 27

2.4.4 Devising projects for Coding Students Response. 28

2.4.5 Adequate Content Knowledge of Teachers. 29

2.4.6 Teaching of Algebra as a Modelling Tool . 30

2.5 Solution to the Problems of Learning

Algebra among Students. 31

2.5.1 Integrating Mathematical Ideas to Elementary

Algebra. 32

2.5.2 Fostering Positive Learning Environment. 32

2.5.3 Positive Concepts about Use of Letter and

Symbol In Algebra. 33

2.5.4 Reducing Abstraction Level in Algebra. 34

2.5.5 Counselling Students with Procrastinating Attitude. 35

2.6 The Dynamics of Problems of Teaching and

learning Algebra in the Secondary Schools. 36

**CHAPTER THREE: DESIGN AND METHODOLOGY**

3.1 Introduction. 43

3.2 Research Design. 44

3.3 Area of Study. 44

3.4 Population of the Study. 44

3.5 Sample and Sampling Technique. 45

3.6 Research Instruments. 46

3.7 Method of Data Collection. 47

3.8 Method of Data Analysis. 47

3.8.1 Scoring Algebra Diagnostic Test. 48

3.8.2 Statistical Treatment of the Data Analysis. 48

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**CHAPTER FOUR: DATA AND ANALYSIS**

4.0 Introduction. 49

4.1 Analysis of the Demographic Information of the

Respondents (Teachers). 49

4.2 Analysis of the Items in the Teacher’s

Questionnaire . 51

4.5 Representation and analysis of Data According to

Research Hypothesis and Questions. 62

4.6 Analysis of the Demographic Information of the Respondents Students. 64

4.9 Representation and Analysis of Data According

to Research Hypothesis and Questions. 77

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**CHAPTER FIVE: DISCUSSION OF RESULT, IMPLICATION FOR EDUCATION AND RECOMMENDATION**

5.1 Discussion of Results. 80

5.2 Limitations. 82

5.3 Implications and Recommendation. 83

5.3.1 Science Teaching and Learning. 83

5.3 2 Education Policy Makers and Administrators . 86

5.3.3 Parents. 87

5.3.4 Future Research. 87

5.4 Conclusion. 88

**References**

**Questionnaire **

**Appendix **

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**CHAPTER ONE**

**INTRODUCTION**

**1.1 Background to the Study **

The place of mathematics in any enterprise is all encompassing and divergent in thought processes and logical reasoning. (Oshin, 1995). It’s usefulness and applications to other subject disciplines in the education system is undeniably feasible; as most of the algorithms, systematization, organization, interpretation and analysis in presentation of facts, points, generalizations and argument has helped to order the sequence of synthesized knowledge to producing comprehensive volumes of materials to be taught and learnt in these disciplines; some of which are sciences, commerce, economics, medicine, maritime, defence and vocations. (Olayinka & Omoegun 2006;Butter& Wren 1951 cited in Udeinya & Okobiah, 1991 and Sule, n.d).

Olayinka & Omoegun (2006) and Usman & Umeano (2006), submitted that mathematics is an indispensable tool for national development it helps to build the computational, manipulative, deductive and inductive thinking as well as problem solving skills of prospective individuals to function effectively within his ever dynamic world, through self discovery, development, worth and actualization. Mathematics is unique in diversities. It is resourceful in scientific industrial, technological social and vocational progress of any society. (Asikhia, 2010).

The teaching and learning of mathematics concepts has been ranked as one of the most important activities in the education system. It’s distinctive nature as enunciated by Piaget (1972) and Piaget &Garcia (1998) cited in Cooley, Martin, Vidakovic &Loch (2007) and Mashooque (2010) attest to the crucial placement of concepts learning and appreciation as well as utilization of mathematics ideas to solve problems and analyze concepts in other school subjects. They highlighted visualization, abstractness, hierarchy of concepts, problem solving and discovery nature of mathematics as the tremendous implication to the teaching and learning processes. In view of these, stakeholders (teachers, parents, educational planners and government) in educational planning and implementation have helped to structure the mathematics curriculum into concept sequence to be taught and learnt at all levels of Nigerian education system. (primary secondary and tertiary).

At the secondary schools, topics that make up the branches of mathematics, such as measuration, geometry, inequalities, statistics, functions, algebra among others have been structurally arranged and discussed in sequence, content, teaching activities and aids with respect to sub concepts, concept hierarchy, simplicity, difficult, technicality and applications (Macre, Kalejaiye, Chima, Garba, Ademosu, chairman, Smith and Head, 2001) so that mathematics idea would be taught in such a way that repetition for re-inforcement, understanding and appreciation of topics are made at each level but with elements of advancements in technicality and structure at higher classes in the secondary schools.

Algebra, as a branch of mathematics has been reckoned with as an important concept in mathematics. It is a generalized arithmetic which require the use of known and unknown quantities. (Osta and Laban, 2007). They further define algebra as that branch of mathematics in which situation of life are represented with a first degree equations where the unknown appear in both sides of the equal sign. In the same vein, Mashooque, (2010) disclosed that algebra uses symbols, letters and signs for generalizing arithmetic which have different meanings and interpretations in different situations. It’s usage and applications to effective acquisition of knowledge, skills and understanding the titbits of other concepts in mathematics (measuration, geometry, inequalities, indices, statistics etc) sciences, social sciences, maritime, medicine, defence and vocations among others: (Mashooque , 2010), attest to the crucial ordinal placement of this multidimensioned branch of mathematics in solving problems.

Diophantus and Al-Khawarzmi Mohammed Ibn Musa; founder and consolidator of algebra cited in Oshin, (1995) revealed that algebra is one of the earliest mathematics inventions that transited from arithmetic’s and got separated from it when equations and methods for reducing them were introduced. They proffered algebra as the science of transposition and cancellation. It is the branch of mathematics that involves the solution of equation by such device as transposition and cancellation. In the same vein, Oshin (1995) revealed that as time passes, Al-Khawarizmi name was distorted into “algorism” meaning “ the art of calculating” now referred to as Arithmetic, which has helped in the revolutionized mathematical manipulation, thereby making long division rather simple for children and served as a model for later writings in their applications of arithmetic and algebra to the distribution of inheritance and astronomical inventions.

Deductively, algebra is wide in concept, forms, structure and applications, since it is studied virtually at all levels of education. (NCTM, 1989 cited in Cooley, Martins, Vidakovic and Loch 2007). It is popularly known as Arithmetic in the primary schools, where pupils are taught the titbits and rudiments of counting, simple equations on sum, difference, product, divisions and word problems. Algebra with it’s subdivisions retain it’s name at the secondary and tertiary schools with dissimilarities in concept sequence, classifications, technicality and application. For instance, at the senior secondary schools, algebra was divided into equations (simple simultaneous and quadratic), set theory, inequality and variation with distinctive techniques for solving their problems (Macrae, Kalejaiye, Chima, Garba, Ademosu, Channon 2001). All these concepts are taught and learnt at the senior secondary schools to facilitating proficiency of students in applying the techniques therein to solve problems in other subjects.

Inspite the utilitarianism of algebra to the material world in developing skills in computation, manipulation, balancing and analyzing equations, logical reasoning, deductive thinking and problem solving in individual to adapting and functioning effectively in the technologically dynamic world, students in the secondary schools; especially those in the senior secondary Two (ss2) have not explored the resourcefulness of algebraic concepts, evident in their poor performance in not only algebraic sections of mathematics examination but also in mathematics in entirety and subjects like physics, chemistry, Economics etc. (Kucheman, 1981 cited in Mashooque, 2010). This development is traceably linked to the problems associated with teaching and learning algebraic concepts at the senior secondary schools.

Teaching and learning are tools for implementing educational policies and programmes. They constitute the basis for drawing out and developing the innate potentials of an individual to aiding usefulness to oneself and the society. Teaching; a process of making someone attend, observe, reason and think. (Akande, 2004) and learning; a relative permanent change in behaviour due to experience (Nwadinigwe, 2001) are two sides of a coin; as one complements the other in terms of effectiveness. The teaching and learning of mathematics concepts with algebra inclusive is beset with many problems; most of which have adversely affected the performance of students in mathematics examinations despite several viable efforts put in by stakeholders to ameliorate the appreciation achievement and utilization of mathematics concepts. (Okereke, 2005). Chimere, (2007) submitted that this ;pose grave danger to national development.

Teaching algebraic concepts has become evolving, multidimensional and divergent (Catherine, 2005). With the adventures in technological discoveries and mathematical inventions in algebraic simplification, expression, manipulation and problem solving, concepts in this encompassing branch of mathematics absorb complexities in forms, structures and algorithms that directly affect proficiency farewell of students in mathematics as whole and other subjects, many of which have advance the course of effective teaching. To this end, Catherine (2005) observed that these complexities have implications on the content and pedagogical knowledge of teachers in effectively communicating algebraic ideas to the understanding and appreciation of the students, and submitted that the adequacy or otherwise of content and pedagogical knowledge of teachers affect the achievement level of students in algebra classes.

But in most teaching and leaning encounters, it is revealed that teachers do the greater works by exposing titbits, algorithms and structures of algebra to students. Thereby, leaving him or her to nothing for self discovery, attitudes of appreciation, which invariably discourage curiosity for further learning. This affects the true essence of self development (Catherine and Vistro, 2005). Moreso, Udeinya & Okobiah (1991) highlighted poor methods of teaching, unqualified mathematics teachers, poor condition of service for teachers and apathy towards mathematics by the general public as some of the threat hampering mathematics growth and development. They and Okereke, (2005) opined that it is a common knowledge that many mathematics teachers, mathematicians and the general public are distressed about the state of general mathematics instruction in the country, inspite the pivotal role mathematics play as a key subject in the school curriculum.

On the part of students, Michele and Assude in their project work opined that algebra is a crucial domain as regard the relationship students develop with mathematics. This shows that algebra is fundamental to students competence in mathematics ideas, structures and problems solving. Thus, it is an important concept that serves as a tool for analyzing other concepts in mathematics Algebra also play a crucial role in facilitating students proficiencies in other subjects like physics, chemistry, economics etc because calculations, use of equation and expressions that are algebraic in nature are absorbed by authors of the subjects to expound, analyse and solve concepts in these subjects. (Sule, n.d).

But, the state of affairs in the performance scale of student in mathematics and other subjects like physics, chemistry, economics etc is at a low ebb. Mashooque (2010) identified poor understanding of algebra fundamental of students in the use of symbols, letter and signs, misconceptions in algebraic processes and poor attitude towards problems solving as some of the factors inhibiting students appreciation and proficiencies in algebraic processes. Asikhia (2010) submitted that these anomalies emanated from the learning difficulties and challenges students encounter in the teaching and learning process, which have implication to students functionality and adaptation in other subject as well as their future career.

In Sule, (n.d) project work on the relationship between attitude and problem solving in mathematics of secondary students in Kogi state stated that algebra concepts can be used to solve a multitude of problems arising form diverse academic field, such as physics, chemistry, Economics, Sociology, Astronomy and statistics. By implication, poor academic performance in these field could be linked to deficiency of students in interpreting, analyzing, balancing and solving algebraic expressions arising from numerous problems they encountered in learning algebra concepts.

**1.2 Statement of the Problem**

Inspite the utilitarian nature of algebra in facilitating potency in students to understand and apply basic concepts like equations, inequalities, set theories, variation, problem solving techniques to interpret, analyse and solve problems in other branch of mathematics as well as other school subjects like physics, chemistry, economics etc for better functionality and adaptation of their rudiments and structural patterns for improved performance, students have not been able to explore the usefulness of algebra to better their proficiency in these subjects due to the difficulties encountered by teachers and students in the teaching and learning of algebra concepts. The students incessant poor performance in examination is posing threat to their educational and teacher’s professional growth and development.

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**1.3 Purpose of the Study**

The main purpose of this study is to identify the problems of teaching and learning algebraic concepts at the senior secondary school Two (SS 2) by undertaking a diagnostic test analysis of selected mathematics teachers and students in Apapa Local Government Area of Lagos State Secondary Schools.

**1.4 Research Question**

In this study, the following research questions were raised:

i. What are the problems teachers encountered while teaching algebraic concepts, that adversely affect students’ appreciation and achievements in algebra classes?

ii. What are the problems students encountered while learning algebraic concepts that lead to poor performance in mathematics and application to other subjects.

**1.5 Research Hypothesis**

The following hypothesis stated below would be tested in this study.

**HoI**: There are no significant problems encountered by teachers while teaching algebraic concepts that adversely affects student’s appreciation and achievement in algebra classes.

**HoII:** There are no significant problems encountered by student’s while learning algebraic concepts that lead to poor performance in mathematics and applications to other subjects.

**1.6 The Significant of the Study**

This study is significant because it would help to provide valuable information to acquaint.

i. Teachers on problems of teaching algebra at the senior secondary schools and model for improved instruction.

ii. Students on problem of learning algebraic expressions and model for improved appreciation and performance in mathematics as well as application to other subjects.

**1.7 Scope and Limitation of the Study**

Considering the broad nature of algebraic concepts taught and learnt at different levels of education with their antecedent problems, massiveness in the number of mathematics teachers and students at these schools, limited time frame, space and resources, this research study intend to focus on studying the problems of teaching and learning algebraic concepts among selected mathematics teachers and SSS2 students in Apapa Local Government Area of Lagos State Secondary Schools.