AN EVALUATION ON THE CHALLENGES OF TEACHING AND LEARNING ALGEBRA AMONG STUDENTS IN SECONDARY SCHOOLS
CHAPTER ONE
INTRODUCTION
1.1 Background to the Study
According to Oshin (2016), mathematics plays a variety of roles in every endeavor, both in terms of the thinking processes it stimulates and the line of reasoning it necessitates. It is undeniable that it can be used in the education system and applied to other subject areas; as systematization, organization, interpretation, and analysis in the presentation of facts, points, generalizations, and arguments have helped to arrange the sequence of synthesized knowledge, resulting in comprehensive volumes of materials that can be taught and learned in these disciplines, as the majority of algorithms do; Sciences, business, economics, medicine, marital arts, and other related fields are just a few examples. Olayinka and Omoegun (2016); Butter and Wren 1951, cited in Udeinya and Okobiah, 2019).
Mathematics, as stated by Olayinka and Omoegun (2016) and Usman and Umeano (2016), is a crucial instrument for national development. It aids in the development of prospective individuals’ computational, manipulative, deductive, and inductive thinking, as well as problem-solving abilities, which enable them to function effectively in his ever-changing world. The study of mathematics can lead to self-actualization, development of one’s worth, and all three of these goals. Math is unique because of its numerous features. Any general public’s logical, modern, specialized, social, and professional advancement might profit from the utilization of this asset. ( 2019 Asikhia). It has been determined that one of the educational system’s most important functions is to spread mathematical concepts and help students learn them. Piaget (2017) and Piaget &Garcia (2004), which were cited in Cooley, Martin, Vidakovic &Loch (2017) and Mashooque (2020), attest to its unique nature, demonstrating the importance of concept learning and appreciation, as well as the application of mathematical concepts to problem-solving and concept analysis in other subjects taught in schools. They focused on how mathematics 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 could lead to discoveries. Teachers, parents, educational planners, and the government in Nigeria have all 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 in light of these considerations. This aspect of mathematics has a great secondary, elementary, and tertiary education levels).
Measurement, geometry, inequalities, statistics, functions, and algebra, among other mathematics topics, have been structurally arranged and discussed in order, content, teaching activities, and aids with respect to sub concepts, concept hierarchy, simplicity, difficulty, technicality, and applications in secondary schools (Macre, Kalejaiye, Chima, Garba, Ademosu, chairman, Smith, and Head, 2019). This is done so that the mathematical concept of algebra, which is a subfield of mathematics and is generally regarded as one of the most fundamental concepts in mathematics, would be presented. It is a type of generalized mathematics that requires the use of known and unknown quantities. 2017) Osta and Laban They go on to define algebra as the branch of mathematics in which equations of the first degree are used to model real-world situations, with the unknown variable appearing on both sides of the equal sign. They are referring to this particular algebra. In the same vein, according to Mashooque (2020), algebra uses symbols, letters, and signs to generalize arithmetic. Depending on the context in which they are utilized, each of these components carries its own set of connotations and interpretations. Its application to the efficient acquisition of knowledge, skills, and an understanding of tidbits of other mathematical concepts (such as measurement, geometry, inequalities, indices, statistics, and so on), sciences, social sciences, maritime, medical, defense, and vocational fields, among other things: Mashooque, 2020), attest to the significance of this multidimensional mathematical branch’s ordinal placement in the process of problem solving.
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, according to Diophantus and Al-Khawarzmi Mohammed Ibn Musa, who is cited in Oshin (2016). Diophantus and Al-Khawarzmi Mohammed Ibn Musa made this discovery. They suggested that the scientific study of substitution and cancellation should be algebra. Using logical operations like transposition and cancellation, the objective of this particular subfield of mathematics is to find an equation’s solution. Similar to this, Oshin (2016) revealed that over time, the name Al-Khawarizmi became “algorism,” which means “the art of calculating” and is now called “arithmetic.” As a result of this, long division has become relatively simple for children thanks to the revolutionized mathematical manipulation. In addition, it served as a model for subsequent writings’ applications of algebra and arithmetic to the inheritance distribution and astronomical inventions. Algebra covers a wide range of topics because it is taught at such a wide range of educational levels, including concepts, structures, forms, and applications. According to Cooley, Martins, Vidakovic, and Loch (2017, citing the National Council of Teachers of Mathematics, 1989) In elementary school, students learn to solve word problems and basic equations like sum, difference, product, division, and division of numbers. Arithmetic is a common name for this subject. The subject is still referred to by its original name, despite differences in the idea sequence, classifications, complexity, and application of algebra in secondary and tertiary institutions. The subdivisions of algebra retain their names. According to Macrae, Kalejaiye, Chima, Garba, Ademosu, and Channon (2019), for instance, algebra was divided into the subjects of equations (simple simultaneous and quadratic), set theory, inequality, and variation in senior secondary schools. Each of these subjects required a distinct set of strategies for solving problems. All of these concepts are presented to students in senior secondary schools, where they are also taught and learned, to make it easier for them to be competent in using the strategies in these books to solve problems in other classes.
Students in secondary schools, particularly those in senior secondary Two (ss2), have not explored the resourcefulness of algebraic concepts, which is evident in their poor performance. Despite the fact that algebra is helpful in developing individuals’ skills in computation, manipulation, balancing and analyzing equations, logical reasoning, deductive thinking, and problem solving for adapting and functioning effectively in the technologically dynamic world, students have not explored the resourcefulness of algebraic concepts. despite the fact that algebra helps students learn how to calculate, manipulate, balance, and analyze equations (Kucheman, 1981; Mashooque, 2020). This shift can be attributed to the difficulties associated with teaching and comprehending algebraic concepts in senior secondary schools.
Teaching and learning serve as the primary means by which educational policies and programs are implemented. They provide the framework for bringing out and developing an individual’s inherent potentials in order to aid in both the individual’s own usefulness and the individual’s usefulness to society. The act of getting another person to pay attention, notice, think, and reason can be referred to as teaching. (Nwadinigwe, 2019) Learning, which can be defined as “a somewhat permanent change in behavior owing to experience,” and experience are two sides of the same coin (Akande, 2017); In terms of their respective levels of efficacy, each complements the other. Numerous issues plague the teaching and learning of mathematical concepts, including algebra. The majority of these problems have hindered students’ ability to perform well on math tests. This is the case despite the fact that stakeholders have made numerous worthwhile efforts to enhance mathematical concept appreciation, achievement, and application. 2015 Okereke). Chimere (2017) says that this is a big threat to the country’s growth and development.
According to Catherine (2015), the teaching of algebraic concepts has become more dynamic, diverse, and multifaceted. The concepts that make up this all-encompassing subfield of mathematics encompass complexities in forms, structures, and algorithms. These complexities have a direct impact on students’ proficiency in mathematics and other subjects, and many of them have paved the way for more efficient instruction. Concepts in this all-encompassing branch of mathematics have become more complex as a result of technological discoveries and mathematical inventions in algebraic simplification, expression, manipulation, and problem solving. To this end, Catherine (2015) made the observation that these complexities have an effect on teachers’ content and pedagogical knowledge in terms of effectively communicating algebraic ideas to students so that they understand and appreciate them. She also claimed that teachers’ content and pedagogical knowledge has an effect on students’ achievement levels in algebra classes. Catherine (2015) also made the observation that these complexities have an effect on teachers’ content and pedagogical knowledge in terms of effectively conveying algebraic concepts to students for their understanding and appreciation.
However, it has been discovered that providing students with tidbits, algorithms, and structural aspects of algebra are the instructors’ primary responsibilities. The majority of interactions between teaching and learning are like this. As a result, he or she has few opportunities for self-discovery or appreciation, both of which typically impede pursuing further education. According to Catherine and Vistro (2015), this has an effect on the core of what it means to grow as a person. According to Moreso, Udeinya, and Okobiah (2019), some of the threats that are preventing the growth and development of mathematics include inadequate instructional methods, untrained mathematics teachers, poor conditions of service for teachers, and public apathy toward mathematics. According to Okereke (2015), many mathematicians, teachers, and the general public are concerned about the state of general mathematics instruction in the country. Despite the fact that mathematics is an essential component of the school curriculum, this is the case. According to Okereke, it is common knowledge that a lot of people are concerned about the state of general mathematics education in the country.
Students Michele and Assude came to the conclusion in their project work that algebra is an important subject in terms of how students connect with mathematics. The students mentioned this. This demonstrates that algebra must be a foundational subject for students to be proficient in mathematical concepts, structures, and problem-solving. As a result, it is a crucial idea that can serve as a framework for studying a number of other mathematical subjects. The authors of the subjects use algebraic calculations, equations, and expressions to explain, analyze, and resolve concepts in these subjects; As a result, algebra helps students become more proficient in other subjects like physics, chemistry, economics, and so on.
However, the performance scale for students studying mathematics, physics, chemistry, economics, and other related subjects is currently at a low ebb. According to Mashooque (2020), some of the factors that hinder students’ appreciation and proficiency in algebraic processes include students’ misconceptions about algebraic processes, their poor attitude toward problem-solving, and their poor understanding of algebraic fundamentals in the use of symbols, letters, and signs. The students’ poor attitude toward problem-solving and their misconceptions of algebraic processes were two additional factors. These anomalies, according to Asikhia (2017), resulted from the difficulties and learning difficulties that students encounter during the teaching and learning process. Students’ future careers as well as their ability to function and adapt in other subjects will be affected by these difficulties and challenges. Algebra concepts can be used to solve a wide range of problems in a variety of academic fields, including physics, chemistry, economics, sociology, astronomy, and statistics, as demonstrated by Asikhia (2017)’s project work on the relationship between attitude and problem solving in mathematics among secondary students in Kogi State. Students at a secondary school in Kogi state carried out the research. Students’ inability to interpret, analyze, balance, and solve algebraic expressions as a result of the numerous difficulties they encountered while learning algebra concepts may be linked to poor academic performance in these fields. The fact that poor academic performance is correlated with poor academic performance in these fields suggests this.
1.2 Statement of the Issue Despite the fact that algebra teaches students fundamental concepts like equations, inequalities, set theories, variation, and problem-solving techniques for interpreting, analyzing, and resolving problems in other areas of mathematics as well as in other school subjects like physics, chemistry, and economics, among others, students have not been able to adapt their fundamentals and structural patterns to improve their performance. This is because students have not been taught that algebra is utilitarian, which makes it easier for them to understand (Mashooque, 2020). Both the students’ education and their teachers’ professional careers are in jeopardy as a result of the students’ consistently poor exam performance.
1.3 The Purpose of the Study The primary objective of the study is to investigate the difficulties that students in secondary schools face when learning and teaching algebra. The following are the specific goals:
i. To investigate the difficulties students encounter when learning algebraic equations.
ii. to determine whether the teaching and learning of algebraic equations is affected by a lack of instructional materials.
iii. to determine the measures that can be taken to reduce the difficulties associated with teaching and learning algebraic equations.
1.4 Research Question The following research questions were posed for this study:
i. What obstacles do students encounter when learning algebraic equations?
ii. Does a lack of instructional materials affect how algebraic equations are taught and learned?
iii. How can the difficulties encountered in teaching and learning algebraic equations be mitigated?
1.5 Importance of the Study This research is important because it could help educate people with useful information.
Teachers on the challenges of teaching algebra in senior secondary schools and as a model for better instruction.
Students on the difficulty of learning algebraic expressions and a model for enhancing their appreciation of mathematics, their performance, and their ability to apply it to other subjects.
The study will be significant because it will add to the existing literature and will be significant to the academic community.
1.6 Extent of the Review
Taking into account the wide idea of arithmetical ideas instructed and learnt at various degrees of training with their precursor issues, enormity in the quantity of math educators and understudies at these schools, restricted time span, space and assets, this exploration review expect to zero in on concentrating on the issues of instructing and learning logarithmic ideas among chose science educators and SSS2 understudies in Apapa Nearby Government Area of Lagos State Optional Schools.
1.7 The study’s limitations As with any human endeavor, the researchers were limited in some way during the course of their research. The researcher chose a moderate sample size because insufficient funds typically hinder the researcher’s ability to find relevant materials, literature, or information and to collect data (via the internet, questionnaire, and interview). Plus, the researcher will be working on other academic projects at the same time on this study. As a consequence of this, less time will be spent on research.
1.8 Terms used in the field of education: the work, profession, or occupation of a teacher.
Learning: the process of gaining knowledge or skills through instruction, experience, or study.
Challenges: a request to take part in a competition or fight to determine who has more strength or ability than the other person.
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