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

ABSTRACT

This study is on the problems of teaching and learning algebra at the senior secondary schools. The total population for the study is 200 staff of selected secondary schools in Uyo. The researcher used questionnaires as the instrument for the data collection. Descriptive Survey research design was adopted for this study. A total of 133 respondents made up principals, vice principals adm, mathematics teachers and junior staff were used for the study. The data collected were presented in tables and analyzed using simple percentages and frequencies

 CHAPTER ONE

INTRODUCTION

• Background of 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 its subdivisions retain its 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 student’s incessant poor performance in examination is posing threat to their educational and teacher’s professional growth and development.

• OBJECTIVE OF THE STUDY

The objectives of the study are;

1. To ascertain the problem encounter by teachers in teaching of algebra in senior secondary schools
2. To ascertain the relationship between algebra teachers and students
3. To ascertain the problems teachers encountered while teaching algebraic concepts, that adversely affect students’ appreciation and achievements in algebra classes
   • RESEARCH HYPOTHESES

For the successful completion of the study, the following research hypotheses were formulated by the researcher;

H₀:   there is no the relationship between algebra teachers and students

H₁: there is the relationship between algebra teachers and students.

H₀²: there are no the problems teachers encountered while teaching algebraic concepts, that adversely affect students’ appreciation and achievements in algebra classes

H₂: there are the problems teachers encountered while teaching algebraic concepts, that adversely affect students’ appreciation and achievements in algebra classes

• SIGNIFICANCE OF THE STUDY

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

1. Teachers on problems of teaching algebra at the senior secondary schools and model for improved instruction.
2. Students on problem of learning algebraic expressions and model for improved appreciation and performance in mathematics as well as application to other subjects.

• SCOPE AND LIMITATION OF THE STUDY

The scope of the study covers the problems of teaching and learning algebra at the senior secondary schools. The researcher encounters some constrain which limited the scope of the study;

1. a) AVAILABILITY OF RESEARCH MATERIAL: The research material available to the researcher is insufficient, thereby limiting the study
2. b) TIME: The time frame allocated to the study does not enhance wider coverage as the researcher has to combine other academic activities and examinations with the study.

1.7 DEFINITION OF TERMS

LEARNING: Learning is the process of acquiring new, or modifying existing, knowledge, behaviors, skills, values, or preferences. The ability to learn is possessed by humans, animals, and some machines; there is also evidence for some kind of learning in some plants

TEACHING: Teaching is an instruction or delivering a particular skill or subject or something that someone tells you to do. For Teaching in this case may refer to showing or explaining to a student how to do something. Learn more in: Active Learning with Technology Tools in the Blended/Hybrid Classes.

ALGEBRA: Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics

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