Chapter 2
MATHEMATIC EDUCATION
(Pendidikan Matematika)
1. Philosophy of Mathematics Education
Philosophy of mathematics education covers the review of some central problems of mathematics education: its ideology, its foundation and its aim. It also serves a more insight into the nature of its aspects: the nature of mathematics, the value of mathematics, the nature of student, the nature of learning, the nature of teaching of mathematics, the nature of teaching learning resources, the nature of assessment, the nature of school mathematics, the nature of students’ learn mathematics. In order to have a clear picture of the role of the study of philosophy of mathematics and its relationship to activities, it may be discussed about the nature of human resources development and the nature of lesson study in mathematics education.
2. 2. The Nature of Mathematics and School Mathematics
Mathematics ideas comprise thinking framed by markers in both time and space. However, any two individuals construct time and space differently, which present difficulties for people sharing how they see things. Further, mathematical thinking is continuous and evolutionary, whereas conventional mathematics ideas are often treated as though they have certain static qualities. The task for both teacher and students is to weave these together. We are again face with the problem of oscillating between seeing mathematics extra-discursively and seeing it as a product of human activity (Brown, T, 1994).
3. The Value of Mathematics In the contemporary times, the mathematical backbone of its value has been extensively investigated and proven over the past ten years. According to Dr. Robert S. Hartman’s, value is a phenomena or concept, and the value of anything is determined by the extent to which it meets the intent of its meaning. Hartman (1945) indicated that the value of mathematics has four dimensions: the value of its meaning, the value of its uniqueness, the value of its purpose, and the value of its function. Further, he suggested that these four “Dimensions of Value” are always referred to as the following concepts: intrinsic value, extrinsic value, and systemic value. The bare intrinsic and inherent essence of mathematical object is a greater, developed intensity of immediacy. Mathematical object is genuinely independent either of consciousness or of other things; something for itself. In and for itself belongs to the Absolute alone, mathematical object can be perceived as the developed result of its nature and as a system of internal relations in which it is independent of external relations.
4. The Nature of Students
Understanding the nature and characteristics of young adolescent development can focus effort in meeting the needs of these students. The National Middle School Association (USA, 1995) identified the nature of students in term of their intellectual, social, physical, emotional and psychological, and moral. Young adolescent learners are curious, motivated to achieve when challenged and capable of problem-solving and complex thinking. There is an intense need to belong and be accepted by their peers while finding their own place in the world. They are engaged in forming and questioning their own identities on many levels. The students may mature at different rates and experience rapid and irregular growth, with bodily changes causing awkward and uncoordinated movements. In term of emotional and psychologicalaspect, they are vulnerable and self-conscious, and often experience unpredictable mood swings. While in the case of moral, they are idealistic and want to have an impact on making the world a better place.
3. The Aim of Mathematics Education
Philosophically, the aims of mathematics education stretch from the movement of back to basic of arithmetics teaching, certification, transfer of knowledge, creativity, up to develop students understanding. Once upon a time, a mathematics teacher delivered his notion that the objective of his mathematical lesson was to use better mathematical, more advance terminology and to grasp a certain concept of mathematics. Other teacher claimed that the objective of his mathematical lesson was to achieve notions stated in the syllabi. While others may state that his aim was to get true knowledge of mathematics. So the purpose of mathematics education should be enable students to realize, understand, judge, utilize and sometimes also perform the application of mathematics in society, in particular to situations which are of significance to their private, social and professional lives (Niss, 1983, in Ernest, 1991).
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