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This research will focus on algebraic expression in simplification subtopic. In algebraic expression chapter, there are many concepts that the students need to learn such as expansion, factorization, and simplification because by mastering these concepts, it can help them to have better understanding in algebraic expression. Therefore, a lot of effort needs to be put forth by the teachers and the students to make sure that they are heading towards good performance. They need to broaden their horizon and think in a very critical manner and in extraordinary ways in order to improve their understanding in algebraic expression chapter.
Mathematics education research basically has one of the major targets to promote students' understanding, especially for critical and creative thinking and problem solving situation. The understanding in algebraic expression is very important because the algebraic expression will be asked in the Malaysia examination. Besides that, the students need to learn this topic because it has correlation with other chapters. In addition, simplification is one method to simplify the questions given to the simplest form. The researcher had experienced during practicum in one of the famous boarding school in Klang. During the practicum session, the researcher realized that his students did not have good basic concept in algebraic expression, such as factorization, expansion and simplification. Therefore, the researcher decided to investigate the students' level of performance in simplification of algebraic expression. The researcher was really disheartened upon looking at the A's students in mathematics PMR students yet still did not know to solve the simplification question. Then, the researcher wishes to investigate the students' common errors in simplification of algebraic expression.
The need for thorough understanding of the structure of an algebraic expression when performing mathematical operation has been recognized by a number of authors in previous researches. According to Kirshner, (1989) suggests that the basic fundamental to competent performance in algebra is the ability of students to comprehend the syntactic structure of an algebraic expression. The students must have a good ability to show their competency for getting the good result especially in algebraic topic. In addition, Yerushalmy, (1992) stated that the researcher must know the students' ability in order to involve in mastering of algebraic rules in order to analyze the structure of expressions the students.
1.1 Background of the study
Mathematics education for secondary school was established in order to produce individuals who are both knowledgeable and skilled that can help in problem solving and critical thinking, towards a dynamic and progressive society. In addition, the mathematics subject also encourage the students to think deeply in order to solve the questions whether in class or in the examination paper. Students can develop the ability to think critically, creatively and to reason logically. Pupils are nurtured from early age with the skills to solve problems and communicate mathematically, to enable them to make effective decisions. Efforts are taken to ensure a society that assimilates mathematics into daily lives.
Algebra is the language of mathematics. Its opens doors to more advanced mathematical topic for those who master algebraic concept. It closes doors to college and to technology-based careers for those who do not. The language of mathematics means that it is allowed the teacher to learn new ways to explain to students the nature of mathematics, its interpretation as a language, and its notation.
1.2 Statement of Problem
The aim of ministry of education was explained in additional mathematics subject syllibus (2006):
"Additional Mathematics is an elective subject in secondary school, which cater to the need of pupils who are inclined towards Science and Technology. The content of additional mathematics syllabus covers most mathematical concepts namely algebra, geometry, calculus, trigonometry and statistic," (CDC, 2006)
Based on the aim of MOE, can be seen that the algebra component is important to produce workforce who are highly competent. In order to realize the government's intention, the mastery of algebra is needed from the very basic level.
The simplification of expression is chosen as an area of study for two reasons. First, the researcher wants to see student's common errors during cancelling the terms. Second, the researcher wants to see students' understanding and performances about the simplification process that involves many ways to solve it.
Kids need to have construction rule and basis in education, based on systematic mistake made by children so as to enable them to search for his social life (Erl Wanger, 1974). Without solid knowledge of basic in algebra, this causes many students to experience difficulties in solving related Mathematical problems. This is the same with the basic concept of algebra that needs to be mastered first by the students before they could apply them in problem solving. Algebraic Expression is an early topic in basic algebra at the secondary level, especially the lower secondary and needs to be fully mastered by students before advancing to the higher level.
Although in high shool, Algebraic Expression only involves basic algebra, but to master this topic is not an easy task, especially for students with low intelligence. This does not exclude students with moderate to high intelligence. They definitely need sufficient time as well to master them. This problem persists with the added factor of teachers having to teach continuously to finish up the syllabus according to the stipulated time without being able to give sufficient time for a student to master the topics taught, especially algebra.
Based on the statement of the problem, researcher is of the opinion that it is crucial for researcher to identify the level of mastery and mistakes of students in the topic of Algebraic Expression. Thus, researcher has decided in depth and and detail to study the level of understanding and mistake of students in schools for the simplification subtopic in the topic of Algebraic Expression. This specialization is very important to identify the level of understanding of the students itself in-depth and in detail.
1.3 Research Objective
This study will find the level of students' performance together with the type of mistakes made by the students in simplification process.
1.4 Research Question
This study will attempt to answer the following questions:
What is the students' level of performances in the topic of simplification for algebraic expression using the TAES?
Is there any significant difference between male and female students' in their performances of simplification of algebraic expression?
Is there any significant difference between students' Mathematic grade in PMR Examination on and their performance in simplification?
What are the common errors made by students' during simplification process?
1.5 Significant of Study
This research is an effort towards contributing the information on simplification in algebraic expression among the students and the attention that needs to be given during the learning and teaching process. Result from this study is hoped to give a picture and contribution on simplification method in improving the level of knowledge of students on this topic. It is also hoped that the result of this research to be able to help students identifying the types of mistakes they commonly commit especially in the topic of Algebraic Expression. Besides that, teachers take initiatives to explain to the students on the basic concepts or method to learn simplification in algebraic expression. In addition, through this research, it is hoped that it could give valuable guides for the purpose of reference of all parties involved in the implementation of Mathematics education, such as the Ministry of Education Malaysia, Curriculum Development Center, and National Education Department, teachers, parents and educators.
This research will be conducted to clarify the reasons why students make errors in the simplification process in examination. Besides that, the factors that lead to the students' make errors happen will be investigated based on the students' level of performance on the simplification process. By identifying students' level of performance in simplification, the researcher also will know at what level are students' performance having misunderstanding based on simplification method that they used and the main sources that contribute the students to have misunderstanding in simplification. This is very important because the actions can be taken by the teachers in early stage to control this problems from become more serious.
If action not be taken in early stage, they will have difficulties to understand deeper concept since they already have misunderstanding in a basic concept. This is because the simplification process is related to many subtopics in Mathematics and Additional Mathematics subjects. Thus, they will not obtain good result even because they did not realize that they have misunderstanding of certain concept. Hopefully, from the result of this research, it can be a guideline and help the researcher to make an investigation at the other field soon.
1.6 Limitation of Study
This research was done among the form four students in Sekolah Menengah Teknik Shah Alam, Selangor. The limitation was the school is quite far from the UiTM Shah Alam. The researcher needs to spend a lot of time to collect the data and to run the interview sessions. The data collection might not be legit enough as the time was too short for the researcher to conduct the observation and collect the questionnaires from the students.
The number of respondents would also be one of the limitations for this study. Out of all the students in Sekolah Menengah Teknik Shah Alam, Selangor, only 32 students would be the sample for this study. Besides, another limitation was the study was only done in one school. Therefore, the finding of this study was varying from the study done in other school in Malaysia as this study focused only on students in Sekolah Menengah Teknik Shah Alam.
1.7 Definition of Terms
The following terms are widely use throughout this study.
Simplification (Oxford Dictionary)
Simplification is known as to make it simple or simpler, to reduce the equation or expression to the simplest form and to reduce to basic essentials and to diminish in scope or complexity. The simplification of expressions is the process of cancelling out of terms or unknowns that contain in the expression.
According to Ma and Klinger, (2000) in their studied focus on the factors of mathematics which include students' gender, age, ethnicity, their family socioeconomic status and school characteristic. In this research, the researcher focus on the students' level performance in simplification of algebraic toward students' gender and result in Test in Algebraic Expression Simplification (TAES).
Algebraic Expression (Merriam-Webster online)
An algebraic expression is made up of the signs and symbols of algebra. These symbols include the Arabic numerals, literal numbers, the sign of operation and so forth. Such an expression represents one number or one quantity. In mathematics syllabus, algebraic expression contains many concepts and method such as factorization, expansion and simplification method. The researcher was focused on simplification method in order to investigate the students' level of performance and the common mistakes done by the students in this subtopic.
This chapter covers aspects needed for the research already conducted. The mastery of basic concepts of Mathematics at the lower secondary level is very important for a student and influence the level of achievement of the student himself. Problems faced with the rise of many mistakes commonly made by students in the subtopic of simplification for the topic of Algebraic Expression, and the weaknesses of a student in mastering this basic algebra topic. The importance of this research is to provide guidelines for all parties including Malaysian Ministry of Education, State Education Department, teachers as well as students in overcoming the problems faced by considering the findings to be received. The limitation of study is that it only covers basic concepts of Mathematics with specialization on the Algebraic Expression topic for the subtopic of simplification and involve case study of a number of Form 4 students in Sekolah Menengah Teknik Shah Alam, Selangor.