THE PROBLEMS OF TEACHING AND LEARNING ALGEBRA AT THE SENIOR SECONDARY SCHOOLS
ABSTRACT
The purpose of this study was to identify the difficulties that teachers and students encountered when teaching and learning algebra in secondary school.
The subjects of this study were seventeen (17) mathematics teachers and one hundred (100) randomly selected students.
The Algebra Diagnostic Test (ADT) for students and a Questionnaire for teachers and students were used in this study. The collected data was analyzed with the statistical package for social sciences (SPSS), which includes simple percentages, the mean, standard deviation, and analysis of variance (ANOVA).
Two null hypotheses were tested after the research questions were investigated. According to the findings;
i. There are significant issues that teachers face when teaching algebraic concepts, which have a negative impact on students’ appreciation and achievement in algebra classes.
ii. Significant difficulties are encountered by students when learning algebraic concepts, resulting in poor performance in mathematics and application to other subjects.
Based on these findings, appropriate recommendations were made, and it was concluded that issues with teaching and learning algebraic concepts have an impact on students’ achievement and performance in algebra tests and mathematics in general.
INTRODUCTION
1.1 The Study’s Background
Mathematics has an all-encompassing and divergent role in thought processes and logical reasoning in any enterprise. (Oshin, 1995) Its usefulness and applications to other subject disciplines in the education system are undeniably feasible; as most of the algorithms, systematization, organization, interpretation, and analysis in
presentation of facts, points, generalizations, and argument have helped to order the sequence of synthesized knowledge to producing comprehensive volumes of materials to be taught and learned in these disciplines; some of which are sciences, commerce, economics, medicine, and marit. (Olayinka and Omoegun 2006; Butter and Wren 1951, as cited in Udeinya and Okobiah, 1991; Sule, n.d.)
According to Olayinka and Omoegun (2006) and Usman and Umeano (2006), mathematics is an indispensable tool for national development because it helps to develop prospective individuals’ computational, manipulative, deductive and inductive thinking,
as well as problem solving skills, allowing them to function effectively in his ever-changing world through self-discovery, development, worth, and actualization. Mathematics is diverse in many ways. It is useful in any society’s scientific, industrial, technological, social, and vocational progress. (Asikhia, 2010)
One of the most important activities in the educational system is the teaching and learning of mathematical concepts. Its distinct nature, as articulated by Piaget (1972) and Piaget &Garcia (1998), as cited in Cooley, Martin, Vidakovic & Loch (2007) and Mashooque (2010), attests to the critical placement of concept learning and appreciation, as well as the application of mathematics ideas to solve problems and analyze concepts in other school subjects.
They emphasized mathematics’ visualization, abstractness, hierarchy of concepts, problem solving, and discovery nature as having a huge impact on the teaching and learning processes. In light of this, stakeholders in educational planning and implementation (teachers, parents, educational planners, and government) have helped to structure the mathematics curriculum into concept sequences to be taught and learned at all levels of the Nigerian education system (primary secondary and tertiary).
At secondary schools, topics such as measurement, geometry, inequalities, statistics, functions, and algebra, among others, have been structurally arranged and discussed in sequence, content, teaching activities, and aids with respect to sub concepts, concept hierarchy, simplicity, difficulty, technicality, and applications (Macre, Kalejaiye, Chima, Garba, Ademosu, chairman, Smith, and Head, 2001).
Algebra, as a branch of mathematics, has long been regarded as an important concept in the field. It is a type of generalized arithmetic that necessitates the use of both known and unknown quantities. 2007 (Osta and Laban). They go on to define algebra as the branch of mathematics in which real-world situations are represented by first-degree equations with the unknown appearing on both sides of the equal sign.
Similarly, Mashooque (2010) revealed that algebra uses symbols, letters, and signs to generalize arithmetic, which have different meanings and interpretations in different situations.
Its application and use in the effective acquisition of knowledge, skills, and understanding of titbits of other concepts in mathematics (measuration, geometry, inequalities, indices, statistics, and so on), sciences, social sciences, maritime, medicine, defense, and vocations, among others: (Mashooque, 2010), attest to the critical ordinal placement of this multidimensional branch of mathematics in problem solving.
Al-Khawarzmi and Diophantus According to Oshin (1995), Mohammed Ibn Musa, the founder and consolidator of algebra, algebra is one of the earliest mathematics inventions that transited from arithmetic and became separated from it when equations and methods for reducing them were introduced.
Algebra was proposed as the science of transposition and cancellation. It is the branch of mathematics concerned with the solution of equations using devices such as transposition and cancellation.
In the same vein, Oshin (1995) revealed that as time passed, Al-name Khawarizmi’s was distorted into “algorism,” which means “the art of calculating” and is 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.
Algebra is broad in concept, forms, structure, and applications deductively because it is studied at virtually all levels of education. Cooley, Martins, Vidakovic, and Loch (2007) cite NCTM (1989). In primary schools, it is commonly referred to as Arithmetic, and students are taught the fundamentals of counting, simple equations on sum, difference, product, divisions, and word problems. Algebra and its subdivisions keep their names in secondary and tertiary schools despite differences in concept sequence, classifications, technicality, and application.
For example, in senior secondary schools, algebra was divided into equations (simple simultaneous and quadratic), set theory, inequality, and variation, each with its own set of problem-solving techniques (Macrae, Kalejaiye, Chima, Garba, Ademosu, Channon 2001). All of these concepts are taught and learned in senior secondary schools to help students become proficient in applying the techniques learned to solve problems in other subjects.
Despite the material world’s utilitarianism of algebra in developing skills in computation, manipulation, balancing and analyzing equations, logical reasoning, deductive thinking, and problem solving in individuals to adapting and functioning effectively in the technologically dynamic world, students in secondary schools,
particularly those in senior secondary Two (ss2), have not explored the resourcefulness of algebraic concepts, as evidenced by their poor performance (Kucheman, 1981 cited in Mashooque, 2010). This development can be traced back to issues with teaching and learning algebraic concepts in senior secondary schools.
Teaching and learning are tools for putting educational policies and programs into action. They serve as the foundation for bringing out and developing an individual’s innate potentials in order to make oneself and society more useful.
Teaching is the process of getting someone to pay attention, observe, reason, and think. (Akande, 2004) as well as learning; a relatively permanent change in behavior as a result of experience (Nwadinigwe, 2001) are two sides of the same coin in terms of effectiveness; one complements the other.
The teaching and learning of mathematics concepts, including algebra, is plagued by numerous issues, the majority of which have negatively impacted student performance in mathematics examinations despite several viable efforts made by stakeholders to improve the appreciation achievement and utilization of mathematics concepts. (Okereke, 2005) According to Chimere (2007), this poses a serious threat to national development.
The teaching of algebraic concepts has evolved into a multidimensional, divergent, and evolving process (Catherine, 2005). With the advancements in technological discoveries and mathematical inventions in algebraic simplification, expression, manipulation, and problem solving, concepts in this broad branch of mathematics absorb complexities in forms, structures, and algorithms that directly affect students’ proficiency in mathematics as a whole and other subjects, many of which have advanced the course of effective teaching.
To that end, Catherine (2005) asserted that these complexities have implications for teachers’ content and pedagogical knowledge in effectively communicating algebraic ideas to students’ understanding and appreciation, and that the adequacy or otherwise of teachers’ content and pedagogical knowledge affects students’ achievement level in algebra classes.
However, in most teaching and learning encounters, it is revealed that teachers do the greater work by exposing students to algebraic tidbits, algorithms, and structures. As a result, he or she is left with nothing for self-discovery, and attitudes of appreciation, which invariably discourage curiosity for further learning. This has an impact on the true essence of self-development (Catherine and Vistro, 2005).
Moreso, Udeinya, and Okobiah (1991) identified poor teaching methods, unqualified mathematics teachers, poor teacher working conditions, and general public apathy toward mathematics as some of the threats impeding mathematics growth and development.
According to them and Okereke (2005), despite the pivotal role mathematics plays as a key subject in the school curriculum, many mathematics teachers, mathematicians, and the general public are concerned about the state of general mathematics instruction in the country.
In their project work, students Michele and Assude stated that algebra is a critical domain in terms of the relationship students develop with mathematics. This demonstrates the importance of algebra in students’ understanding of mathematical concepts, structures, and problem solving. As a result, it is an important concept that can be used to analyze other concepts in mathematics.
Algebra also plays an important role in facilitating students’ proficiency in other subjects such as physics, chemistry, economics, and so on, because authors of these subjects absorb calculations, use of algebraic equations, and expressions to expound, analyze, and solve concepts in these subjects. Sule (n.d.)
However, student performance in mathematics and other subjects such as physics, chemistry, economics, and so on is at a low ebb. Mashooque (2010) identified poor algebra fundamental understanding of students in the use of symbols, letters, and signs, misconceptions in algebraic processes,
and a poor attitude toward problem solving as some of the factors impeding students’ appreciation and proficiency in algebraic processes. According to Asikhia (2010), these anomalies resulted from the learning difficulties and challenges that students face during the teaching and learning process, which have an impact on students’ functionality and adaptation in other subjects as well as their future career.
Sule (n.d.) stated in her project work on the relationship between attitude and problem solving in mathematics of secondary students in Kogi state that algebra concepts can be used to solve a wide range of problems arising from various academic fields such as physics, chemistry, Economics, Sociology, Astronomy, and statistics.
Poor academic performance in these fields may be linked to students’ deficiencies in interpreting, analyzing, balancing, and solving algebraic expressions as a result of the numerous problems they encountered while learning algebra concepts.
1.2 Problem Description
Despite algebra’s utilitarian nature in facilitating students’ ability to understand and apply basic concepts such as equations, inequalities, set theories, variation, problem solving techniques to interpret, analyze, and solve problems
in other branches of mathematics as well as other school subjects such as physics, chemistry, economics, and so on for better functionality and adaptation of their rudiments and structural patterns for improved performance, students have not been able to do so. The students’ consistent poor performance in examinations endangers their educational and professional growth and development.
1.3 The Study’s Purpose
The primary goal of this research is to identify issues with teaching and learning algebraic concepts at senior secondary school Two (SS 2) by conducting a diagnostic test analysis of selected mathematics teachers and students in Apapa Local Government Area of Lagos State Secondary Schools.
1.4 Research Issues
The following research questions were raised in this study:
i. What are the issues that teachers have encountered while teaching algebraic concepts that have a negative impact on students’ appreciation and achievement in algebra classes?
ii. What problems did students encounter while learning algebraic concepts that resulted in poor mathematics performance and application to other subjects?
1.5 Research Proposal
In this study, the following hypothesis would be tested:
HoI: There are no significant issues that teachers face when teaching algebraic concepts that have a negative impact on students’ appreciation and achievement in algebra classes.
HoII: There are no significant issues that students face while learning algebraic concepts that lead to poor performance in mathematics or applications to other subjects.
1.6 The Study’s Importance
This study is significant because it will aid in providing useful information to acquaint.
i. Teachers on the difficulties of teaching algebra in senior secondary schools, as well as a model for improved instruction.
ii. Students working on the problem of learning algebraic expressions and developing a model for improved appreciation and performance in mathematics, as well as application to other subjects.
1.7 Study Scope and Limitations
Given the broad nature of algebraic concepts taught and learned at various levels of education, as well as their antecedent problems, the large number of mathematics teachers and students at these schools, as well as the limited time frame, space, and resources, this research study intends 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 School.
Do You Have New or Fresh Topic? Send Us Your Topic
INSTRUCTIONS AFTER PAYMENT
- 1.Your Full name
- 2. Your Active Email Address
- 3. Your Phone Number
- 4. Amount Paid
- 5. Project Topic
- 6. Location you made payment from