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**CHAPTER ONE**

**INTRODUCTION**

**Â Background to the Study**

The role that mathematics plays in every endeavor is multifaceted, both in terms of the thinking processes it stimulates and the line of reasoning it requires (Oshin, 2016). 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 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, marital arts, and so on. (Olayinka & Omoegun 2016;Butter& Wren 1951 referenced in Udeinya & Okobiah, 2019).

According to Olayinka and Omoegun (2016) and Usman and Umeano (2016), mathematics is an essential tool for national development. It helps to build the computational, manipulative, deductive and inductive thinking as well as problem-solving skills of prospective individuals, which allows them to function effectively within his ever-changing world. Actualization of one’s self, development of one’s worth, and self-actualization are all achieved through the study of mathematics. Mathematics is one of a kind due to its many facets. Any society’s scientific, industrial, technical, social, and vocational development may benefit from the use of this resource. (Asikhia, 2019). It has been determined that one of the most essential functions of the educational system is the dissemination of mathematical ideas together with their acquisition by students. Piaget (2017) and Piaget &Garcia (2004), which were cited in Cooley, Martin, Vidakovic &Loch (2017) and Mashooque (2020), attest to its distinctive nature, which demonstrates the critical placement of concept learning and appreciation, as well as the utilization of mathematics ideas to solve problems and analyze concepts in other school subjects. They focused on the nature of mathematics, namely how it can be seen, how abstract it can be, how ideas can be arranged in hierarchies, how it can be used to solve problems, and how it may lead to discoveries. This aspect of mathematics has a great In light of these considerations, those involved in the planning and implementation of education in Nigeriaâ€”including teachers, parents, educational planners, and the governmentâ€”have contributed to the organization of the mathematics curriculum into a concept sequence that can be taught and learned at all levels of the country’s education system. tertiary, secondary, and basic levels of education).

At the secondary schools, topics that make up the different branches of mathematics, 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, 2019). This is done so that the mathematics idea would be

Algebra, which is a sub-field of mathematics, is generally acknowledged to be one of the most essential ideas in mathematics. It is a generalized kind of mathematics that necessitates the use of both known and unidentified quantities. (Osta and Laban, 2017). They go on to describe algebra as the field of mathematics in which real-world scenarios are modeled using equations of the first degree, with the unknown variable appearing on both sides of the equal sign. This is the algebra that they are referring to. In the same line, Mashooque (2020) stated that algebra utilizes symbols, letters, and signs for the purpose of generalizing arithmetic. These components all have distinct connotations and interpretations depending on the context in which they are used. Its use and applications to the effective acquisition of knowledge, skills, and understanding the tidbits of other concepts in mathematics (measuration, geometry, inequalities, indices, statistics, etc.), sciences, social sciences, maritime, medicine, defense, and vocations, among others: (Mashooque, 2020), attest to the crucial ordinal placement of this multi dimension branch of mathematics in the process of problem solving.

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According to Diophantus and Al-Khawarzmi Mohammed Ibn Musa,(2009) the founder and consolidator of algebra, as cited in Oshin, (2016), algebra is one of the earliest mathematics inventions that evolved from arithmetic but became distinct from it after the development of equations and methods for reducing them. This discovery was made by Diophantus and Al-Khawarzmi Mohammed Ibn Musa. They proposed algebra as the scientific study of the process of substitution and cancellation. In this particular sub-field of mathematics, the goal is to find a solution to an equation using logical operations such as transposition and cancellation. In a similar vein, Oshin (2016) revealed that as time passes, the name Al-Khawarizmi was distorted into “algorism,” meaning ” the art of calculating,” which is now referred to as Arithmetic. This has helped in the revolutionized mathematical manipulation, thereby making long division rather simple for children. It has also served as a model for later writings in their applications of arithmetic and algebra to the distribution of inheritance and astronomical inventions. Because it is taught at such a wide variety of educational levels, algebra encompasses a broad range of subject matter, including concepts, forms, structures, and applications. (The National Council of Teachers of Mathematics, 1989, as referenced in Cooley, Martins, Vidakovic, and Loch 2017). In elementary schools, students learn the fundamentals of counting as well as basic equations including sum, difference, product, and division of numbers as well as word problems. This subject is often referred to as Arithmetic. Although there are differences in the idea sequence, classifications, complexity, and application of algebra in secondary and tertiary institutions, the subject is still referred to by its original name. Algebra’s subdivisions still keep their names. For example, in the senior secondary schools, algebra was separated into the subjects of equations (simple simultaneous and quadratic), set theory, inequality, and variation, each of which required a unique set of problem-solving strategies (Macrae, Kalejaiye, Chima, Garba, Ademosu, Channon 2019). All of these ideas are presented to students in senior secondary schools, where they are also taught and learned, in order to facilitate students’ competency in using the strategies presented therein to solve difficulties in other courses.

Despite the fact that algebra is useful 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 the secondary schools, especially those in the senior secondary Two (ss2), have not explored the resourcefulness of algebraic concepts, which is evident in their poor performance. In spite of the fact that algebra is useful in developing skills in computation, manipulation, balancing and analyzing equations (Kucheman, 1981 cited in Mashooque, 2020). This transformation may be traced back to the difficulties that are involved with the instruction of and the understanding of algebraic ideas in senior secondary schools.

The implementation of educational policies and programs relies on teaching and learning as its primary instruments. They provide the framework for bringing out and developing the inherent potentials of a person in order to help in one’s own usefulness and the usefulness of the individual to society. Teaching may be defined as the process of influencing another person to pay attention, notice, reason, and think. (Akande, 2017) learning, which may be defined as “a somewhat permanent change in behavior owing to experience” (Nwadinigwe, 2019), and experience are two sides of the same coin; each one complements the other in terms of their respective levels of efficacy. The teaching and learning of mathematical concepts, including algebra, is plagued with many problems. The majority of these issues have had a negative impact on the performance of students in mathematics examinations. This is the case despite the fact that numerous viable efforts have been put in by stakeholders to improve the appreciation, achievement, and utilization of mathematical concepts. (Okereke, 2015). According to Chimere (2017), this poses a significant threat to the growth and development of the country.

The instruction of algebraic ideas has grown more dynamic, multi-faceted, and diversified (Catherine, 2015). Concepts in this all-encompassing branch of mathematics absorb complexities in forms, structures, and algorithms that directly affect the proficiency farewell of students in mathematics as a whole and other subjects, many of which have advance the course of effective teaching. With the advent of technological discoveries and mathematical inventions in algebraic simplification, expression, manipulation, and problem solving, concepts in this all-encompassing branch of mathematics absorb complexities in forms, structures, and algorithms. To this end, Catherine (2015) 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 she submitted that the adequacy or otherwise of content and pedagogical knowledge of teachers affect the achievement level of students in algebra classes. In addition, Catherine (2015) 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.

However, it is discovered that instructors perform the bigger tasks by providing tidbits, algorithms, and structural aspects of algebra to their pupils. This is the case in the majority of teaching and learning interactions. Consequently, this leaves him or her with little opportunity for self-discovery or attitudes of appreciation, both of which generally inhibit a quest for future study. This has an impact on the core of what it means to grow oneself (Catherine and Vistro, 2015). Moreso, Udeinya, and Okobiah (2019) noted inadequate methods of instruction, untrained mathematics teachers, bad conditions of service for teachers, and indifference towards mathematics by the general public as some of the threats that are holding back the growth and development of mathematics. Okereke (2015) expressed the opinion that it is common knowledge that many mathematics teachers, mathematicians, and the general public are distressed about the state of general mathematics instruction in the country. This is despite the pivotal role that mathematics play as a key subject in the school curriculum. Okereke’s opinion was that it is a well-known fact that many people are distressed about the state of general mathematics instruction in the country.

In their project work, students Michele and Assude came to the conclusion that algebra is an important subject area in reference to the connection that students establish with mathematics. This was stated by the students. This demonstrates that students’ proficiency in mathematical concepts, structures, and problem-solving need algebra as a foundational subject. As a result, it is an essential notion that may be used as a framework for the investigation of several other mathematical topics. Calculations, the use of equations and expressions that are algebraic in nature are absorbed by authors of the subjects to expound, analyze, and solve concepts in these subjects; therefore, algebra plays an important role in facilitating students’ proficiency in other subjects such as physics, chemistry, economics, etc.

However, the current state of things in the performance scale of students in mathematics and other disciplines like physics, chemistry, economics, and other such topics is at a low ebb. Mashooque (2020) identified students’ poor understanding of algebra fundamentals in the use of symbols, letters, and signs, students’ misconceptions in algebraic processes, and students’ poor attitude toward problem-solving as some of the factors inhibiting students’ appreciation and proficiency in algebraic processes. Other factors included students’ misconceptions in algebraic processes and students’ poor attitude toward problem-solving. According to Asikhia (2017), these anomalies originated from the learning difficulties and challenges that students encounter in the course of the teaching and learning process. These difficulties and challenges have implications for students’ functionality and adaptation in other subjects, in addition to their future careers. According to Asikhia (2017)’s project work on the relationship between attitude and problem solving in mathematics of secondary students in Kogi state, it was found that algebra concepts can be used to solve a multitude of problems arising from a variety of academic fields, including physics, chemistry, economics, sociology, astronomy, and statistics. The research was conducted by Kogi state secondary school students. Poor academic performance in these fields could be linked to a deficiency of students in interpreting, analyzing, balancing, and solving algebraic expressions as a result of the numerous problems they encountered while learning algebra concepts. This is implied by the fact that poor academic performance is linked to poor academic performance in these fields.

**Statement of the Problem**

Despite the fact that algebra helps students understand and apply fundamental concepts such as equations, inequalities, set theories, variation, and 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, students have not been able to adapt their fundamentals and structural patterns to improve their performance. This is due to the fact that students have not been taught algebra’s utilitarian nature, which enables students to understand (Mashooque, 2020). The persistently low performance of the pupils in examinations poses a danger to the continued growth and development of both their education and their teachers’ professional careers.

**Â Objective of the Study**

The main objective of the study is the challenges of teaching and learning algebra among students in secondary schools. The specific objectives is as follows:

i.Â Â Â Â Â Â Â Â Â To examine students challenges in learning algebraic equations.

ii.Â Â Â Â Â Â Â To find out if lack of instructional material influences the teaching and learning of Â algebraic equations.

iii.Â Â Â Â Â To find out measures to undertake in mitigating the challenges in the teaching and learning of algebraic equations.

**Research Question**

In this study, the following research questions were raised:

i.Â Â Â Â Â Â Â Â Â What are the Â challenges students face in learning algebraic equations?

ii.Â Â Â Â Â Â Â Does lack of instructional material influences the teaching and learning of Â algebraic equations?

iii.Â Â Â Â Â What are the measures to undertake in mitigating the challenges in the teaching and learning of algebraic equations?

**Â Significance of the Study**

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

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

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

The study will be significant as it will be significant to the academic community as it will contribute to the existingÂ literature.

**Â Scope of the Study**

Considering the broad nature of algebraic conceptsÂ Â 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.

**Â Â Limitation of the study**

Like in every human endeavour, the researchers encountered slight constraints while carrying out the study. Insufficient funds tend to impede the efficiency of the researcher in sourcing for the relevant materials, literature, or information and in the process of data collection (internet, questionnaire, and interview),Â which is why the researcher resorted to a moderate choice of sample size. More so,Â the researcher will simultaneously engage in this study with other academic work. As a result, the amount of time spent on research will be reduced.

**Â Â Definition of terms**

**Teaching :Â **the occupation, profession, or work of a teacher.

**Learning:**the acquisition of knowledge or skills through study, experience, or being taught.

**Challenges:Â **a call to someone to participate in a competitive situation or fight to decide who is superior in terms of ability or strength.

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