# The Problems Of Teaching And Learning Algebra At The Senior Secondary Schools

## 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 two hundred and thirty-eight (238) students out of a population of two thousand four hundred (2400) students were used for the study. The responses from the instrument used in the study formed the basis for data analysis The study cited several literature and empirical studies. The quasi-experimental design was used for this study. Both descriptive and inferential statistics were used for the analyses of the data collected from the sampled students. The reliability of the two instruments AAT and ATQ were established with the use of the test-retest reliability estimate and the coefficients were found to be 0.87 and 0.89respectively which signified that the instruments were highly reliable. Five objectives and five research questions were set and five null hypotheses were propounded for the study. Basically, independent sample t-test statistic was used to test all the hypotheses since they are all two variables parametric data. It was observed that problem solving strategy had significant positive effect on studentsâ€™ attitude towards algebra as well as improved the performance of students; it was recommended that Mathematics teachers should be given all needed encouragement and motivation to use the problem-solving method in place of the conventional lecture method for better academic performance. Also, the study recommended that Teachers who had mastery of the subject (algebra) should be encouraged to teaching the rural areas. Finally, the study recommended that for studentsâ€™ attitude towards the learning of mathematics improves, well qualified teachers should be allowed to teach the subject mathematics.

## 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). Itâ€™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. Itâ€™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. Itâ€™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 arithmeticâ€™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 â€śalgorismâ€ť meaning â€ś the art of calculatingâ€ť 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 itâ€™s subdivisions retain itâ€™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. One way is the improvement of the teaching process by introduction of problem solving strategy in our class. Hence, the research â€śEffect of problem solving strategy on Attitude and performance in Algebra among senior secondary school students in Lagos stateâ€ť.

#### 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 teacherâ€™s professional growth and development.

The problem of this study is to analyze the impact of problem solving method on attitude and performance of secondary schools students in Lagos state, Nigeria. The major concern and important function of the School system is to improve the academic performance of students and produce a pool of skilled manpower that will help a nation grow and develop. Problem solving is at the core of learning in mathematics. Personal classroom experience with secondary school students in Nigeria and results of private and public examination show that most learners are yet to acquire the vital problem solving skills required for success in mathematics.

Mathematics is a subject that majority of the secondary school students are not interested in because of its nature and content (Ojonugwa, 2007). Algebra as one of the major component of mathematics at the senior secondary school is seen as abstractic in nature and cannot be understood by many students as such most questions on algebra are not attempted in the examination at all or fairly attended to, methodology of instruction is another factor that lead to poor performance in Algebra.. Despite several attempts by parents, stakeholders in education and the government of Nigeria to achieve the formulated objectives of mathematics, it seems that attempts are not yielding positive result in senior secondary schools in Lagos state hence, the basis for this dissertation effect of problem solving strategy on attitude and performance in algebra among senior secondary school students in Lagos state.

Hence, it is against this background that the researcher deems it necessary to investigate the effect of problem solving strategy on attitude and performance in Algebra among senior secondary school students in Lagos state Nigeria.

#### 1.3 Objectives of the Study

The main objective of this study was to investigate effects of problem solving strategy on attitude and performance in algebra among senior secondary school students in Apapa, Lagos State Nigeria, the other specific objectives are to:-

- Establish the attitude of student taught Algebra with problem solving strategy (EG) and those taught with conventional method (CG).
- Find out the difference between performance of student taught Algebra with problem solving strategy (EG) and those taught with conventional method (CG).
- Investigate the attitude of Male and Female students taught Algebra with problem solving strategy (EG).
- Find out difference in performance of male and female students taught Algebra with problem solving strategy (EG),
- Find out if students from Urban and Rural areas taught Algebra with problem solving strategy (EG) differs in performance.

#### 1.4 Research Questions

The study was guided by the following research questions:

- What is the difference between attitude of student taught Algebra with problem solving strategy (EG) and those taught with conventional method (CG)?.
- What is the difference between performance of student taught Algebra with problem solving strategy (EG) and those taught with conventional method (CG)?.
- Do Male and Female students taught Algebra with problem solving strategy (EG) differs in attitude?.
- Do Male and Female students taught Algebra with problem solving strategy (EG) differs in performance?
- Do students from Urban and Rural areas taught Algebra with problem solving strategy (EG) differs in performance?

#### 1.5 Null Hypotheses

The following research hypotheses were formulated based on the research questions raised and are the null hypothesis tested at 5% level of significance.

**HO1: **There is no significant difference between the attitude of student taught Algebra with problem solving strategy (EG) and those taught with conventional method (CG).

**HO2: **There is no significant difference between the average performance of student taught Algebra with problem solving strategy (EG) and those taught with conventional method (CG).

**HO3: **There is no significant difference between the attitude of male and female students taught Algebra with problem solving strategy (EG)

**HO4: **There is no significant difference between the average performance of male and female students taught Algebra with problem solving strategy (EG)

**HO5: **There is no significant difference between the average performance of students from urban and rural areas taught Algebra with problem solving strategy (EG)

#### 1.6 Significance of the Study

The study would provide adequate information on the importance of using problem solving method in solving Algebraic problems in mathematics. This study would contribute immensely by reducing the general mathematics phobia worrying students at post-basic level of education due to the use of ineffective instructional strategies by mathematics teachers

The findings of this research would reduce the distaste students and their teachers have towards teaching and learning algebra as a difficult area in mathematics. They would come to realized that with the application of suitable methods of teaching, algebra can be easily taught and learnt.

The study would also, provide teachers, curriculum and textbook developers with relevant materials that may be used to improve the teaching and learning algebra at SSS level. This study could also, help to provide empirical basis for improvement and modification of the methods of teaching mathematics which could be of special interest to curriculum planners, authors of textbooks and students. Such improvement and modification could also make parents to be happy to see that their children are passing mathematics for their future educational progress.

It is also hoped that the findings of the study would stimulate and promote further researches. Professional organizations in mathematics like Mathematical Association of Nigeria (MAN), curriculum development organizations like Nigeria Educational Research and Development Council (NERDC) and even individual mathematics educators will find the results worthy of discussion and dissemination to stimulate and promote further researches.

#### 1.7 Scope / Delimation 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.

The study is limited to only SSS II students in Lagos State; private ad junior secondary schools are not included in the study. However, the result of the research can be applied to those not included in the study as Algebra is taught from the primary school level of educational system in Nigeria to tertiary level.

Another limitation is in the numbers of schools used in the research. Four schools are used, two in the urban and two in the rural area which included two girlsâ€ź schools and two boysâ€ź schools

However, as delimitation, the study did not go into other causes of poor performance beyond the issue of teaching methods. The study did not also, treat other topics of mathematics such geometry, number and numeration and statistics as the study was only confined to algebraic aspect of mathematics.

#### 1.8 Basic Assumptions

- That the students in senior secondary school had learned the content of Algebra in mathematics as stipulated in the National curriculum by NERDC.
- The schools that will be chosen for the study have similar teaching and learning facilities and resources.
- All teachers who take these students who were sampled were trained and had good mastering of Algebraic content and have good teaching strategies

## Chapter Five

### Summary, Conclusion and Recommendations

#### 5.0 Introduction

This study was set to investigate the effect of problem solving instructional strategy on attitude and performance in algebra among secondary school students of Lagos State, Nigeria. The final chapter of this research work was dedicated to the following subheadings:

#### 5.1 Summary

This study assessed the problems of teaching and learning algebra at the senior secondary schools in Apapa L.G.A of Lagos State, Nigeria. The results of the data analyzed revealed that:

- Problem solving instructional method had an influence on studentsâ€ź attitude in algebra.
- Problem solving instructional method had a significant effect on studentsâ€ź performance in algebra.
- Male and female students do not differed significantly in their attitude scores when exposed to treatment of problem-solving strategy.
- The performance of male and female students did not differ significantly when exposed to the treatment of Problem-Solving Strategy.
- The higher the students level of attitude the higher their performance in Algebra and vice-verse.

#### 5.2 Conclusion

Based on the result of the hypothesis, the following conclusions can be deduced:

Problem solving instructional on method has a positive effect on the academic performance scores on algebraic concept of mathematics. Students and teachers from rural areas should be encouraged and motivated more by exposing them to more problems solving strategy as students performance in algebra was affected by school location.

However, gender was not found to be a factor as problem solving instructional method in this study carried both sexes along. The poor performance of Nigerian students in mathematics examinations portrayed danger for a country in quest of technological advancement. Hence, all hands must be on deck to make the

acquisition of mathematics knowledge possible for all students for the benefit of all. The finding of this research work has further established the fact that acceptable methods of instruction are capable of changing studentsâ€ź performance and attitude towards algebra.

#### 5.3 Recommendations

Based on the outcome of this study, the following recommendations are hereby put forward.

- Mathematics teachers should be given all needed encouragement and motivation to use the problem solving method in place of the conventional lecture method for better academic performance.
- Teachers who have mastery of algebra should be used in the teaching of algebra.
- Studentsâ€ź attitude towards the learning of algebra can be improved by using teachers who are well qualified in the mathematics as a subject in general.
- Teachers should develop cordial, friendly and caring relationship with their students in order to improve the teaching and learning process in Mathematics.
- Positive attitude towards learning and performing well in algebra are necessary ingredients in senior secondary school Mathematics education. There is need for teachers, parents and any other education stakeholder to enhance these positive attitudes.
- Efforts should be made to ensure does not hinder learning and/or performance in algebra among students. Teachers, parents and siblings of the students should encourage both the female and male learners to equally embrace mathematics generally.
- The un favourable attitude should be curtailed professionally and early enough before students utterly give up in learning and/or performance of mathematics.
- The recommendations of algebraic textbooks for use in schools should be taken very seriously and should be based on nothing other than the text satisfying the features of a good algebraic textbook that will secure studentsâ€ź interest in learning algebra.
- Problem solving instructional strategy should be used in teaching algebra at both primary and secondary levels of education.
- Efforts made at carrying out researches should not be allowed to waste away. Research result should be made to reach the implementation of the findings to be able to achieve the desired results.
- Authors of algebraic textbooks should include the instructional strategy at which each topic should be taught in their textbooks.
- Mathematics teachers should take turns in attending workshops and seminars and each person on return should expose others in the school to the knowledge they acquired during the training.

#### 5.4 Suggestions for Further Studies.

The study is by no means exhaustive. Further studies can be carried out especially on:

- Similar study on effect of problem solving instructional method on studentsâ€ź interest and performance in geometry and other aspects of mathematics could be carried out.
- This study could be replicated in other parts of Nigeria.
- The study was restricted to government owned schools; it could be also be extended to private and organizational owned schools.

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## Frequently Asked Questions

### What are the difficulties in learning algebra?

**Difficulties in learning algebra can be seen from how students work on algebra problems. students’ difficulties. As Result, there should be a study that explain what difficulties are experienced when students learn algebra in Junior High School Students.**

### Is algebra hard to learn in the early grades?

**Algebra is an important domain that first studied at the junior high school. This domain will be useful in obtaining the concept of another domain. However, learning algebra in the early grades has some challenges for students. This study aims to describe students â€™ difficulties when learning algebra in the early grade.**

### What is the problem of mathematics instruction and learning in Nigeria?

**In essence Obodo (2000), lamented the poor state of mathematics instruction in Nigeria and averred that the problem of quality of mathematics instruction and learning are from diverse sources. The teacher has been accused to be responsible for the low quality of student performance in our secondary schools.**

### What are the results of the algebra achievement test?

**The Algebra Achievement Test were developed by the researchers to collect the data. According to the findings of the study, 6th grade elementary students have low performance in solving declarative, procedural, and conditional problems in the field of algebra.Â **