Mathematics subject in lower secondary level

本文是一篇英国留学生课程论文,是关于马来西亚初中水平的数学学科调查分析!

 

这个是一篇关于研究马来西亚数初中水平的数学学科相关研究主题的文献综述.这篇综述简短谈及马来西亚的教育,在初中水平的数学学科以及学生在代数表达式上的成绩表现.从这篇综述来看,它会产生一个结果使得这个研究主题更清晰用更大的战略蓝图去强调开展这项研究的重要性.

This chapter presents a literature review on major components of this research as well as related topic. The review will be briefly on education in Malaysia, mathematics subject in lower secondary level and also on students' level of performance in simplification of algebraic expression. From the review, it will lead to conclusion that will relate the components of the topics to make it clearer as a bigger picture and to stress the importance of conducting this research.

 

These aims of research are to investigate the students' level of performance in simplification of algebraic expression among form four students at Sekolah Menengah Teknik Shah Alam, Selangor. Besides that, this research will be conducted to identify the common errors that were made by the students in the test of algebraic expression simplification. In addition, the research also wants to see the relationship of students' performance among gender, their PMR examination grade and the grades of test in algebraic expression simplification.

 

2.1 Mathematics Concepts（数学概念）

It is admittedly difficult to determine the level of understanding or mastery of a certain concept. So is the case in this case study which involves the level of mastery of basic concepts of Mathematics for the simplification subtopic in the topic of Algebraic Expression. However, it can be evaluated by looking at the concept of understanding and common mistakes made by students in solving Mathematical problems.

 

Based on the concept of comprehension, students must understand the concept of Mathematics, which is following the steps correctly in solving Mathematical problems. Rubric should be the basis for the solving of Mathematics (Skemp, 1971). The concept of understanding is totally different than knowledge. Understanding is an ability to apply while looking for ways to achieve the targeted goals. Skemps also differentiates between 3 types of understanding, namely instrumental, understanding of relationship and logical understanding.

 

Based on Skemp's statement, it can be observed that in solving Mathematical problems, it requires the right steps. This can be related to the working which is undeniably the most important thing in solving Mathematical-related problems. The right and systematic working can definitely provide the accurate answer or solution as what the question requires.

 

Most Mathematical psychologists agree that the concept of Mathematics is hard to define (Skemp, 1971). Mathematical concepts can be divided to primary and secondary concepts. The primary concept is formed using senses and the induction method, which is to abstract through observation of similar features.

 

What is needed is the sources of conceptual and technical knowledge related as well as tehnical support in understanding the solving process. (Schoenfeld,1985). Students were found to use wrong concept of solve due to errors in understanding a certain concept. Understanding Mathematics requires building a clear basic concept and prediction of a certain concept being made easy should it be done hierarchically.

 

Cognitive psychologist are of the opinion that there exists differences between conceptual knowledge and procedural knowledge, and yet both have critical and mutually beneficial relationship. Solid conceptual knowledge will foster learning, reduce usage of confusing procedures, making them to remember the appropriate procedures to be used and improving the quality of performing a certain problem-solving.

 

A model of solution involving 4 phases, namely understanding problem, plannin solution, doing solution and checking the answers produced is being proposed (Polya, 1957). The first phase requires students to read, understand and decide what is required of the question. The second phase requires the relation between fact and the data thus planning for steps to solve. Students conduct solving by doing calculation and finally checking the answers produced to ensure that the question is solved correctly along with the answer.

 

Hiebert (1997) said that students need to master certain concepts in Mathematics where inside contain rules, procedures and principles of simple Mathematics. They also need to learn on how to use those procedures and principles to enable them to solve the Mathematical problems. However, students who managed to achieve high result in Mathematics still failed to use the knowledge and skills of Mathematics into other situations or subjects. (Schoenfeld, 1985). This shows that the understanding of concepts is very vital to achieve excellent result in true meaning.