2.1 What is mathematics all about? The assignment brief suggests two viewpoints: (1) Mathematics is a given body of knowledge and standard procedures that has to be covered or
(2) Mathematics is an interconnected body of ideas and reasoning processes
2.2 The first viewpoint considers mathematics as a discipline consisting of rigid compartments of knowledge with set techniques and routine algorithms. The second viewpoint suggests that mathematics is made up of interlinking ideas to be developed through experimenting and investigation.
2.3 From a teaching and learning point of view, one’s conception of the nature of mathematics is considered to have a profound impact on one’s teaching practice. According to Hersh (1986), the issue is not “What is the best way to teach but, What is mathematics really all about?” (Grouws, 1992, page 127).
2.4 The perception of the nature of mathematics not only influences how the subject is taught, but also has implications on how mathematics education for school is defined. Indeed, Ernest (1991) states that the view of the nature of mathematics together with the social and political contexts are seen as the key factors affecting curriculum planning (Ernest, 1991, page 125).
2. Literature Review
3.5 Lerman (1990) has identified two contrasting themes concerning the nature of mathematics, namely the absolutist and fallibilist views. According to him, they correspond to the two competing schools of thought in the philosophy of mathematics suggested by Lakatos (1978): Euclidean and Quasi-empirical. The former considers mathematics to be based on a body of unchallengeable truths whilst the latter sees mathematical knowledge a result of a discovery process involving conjectures, hypotheses and refutations.
3.6 Ernest (1996) explained that absolutism considers mathematics to be timeless and a priori knowledge. In his view, teachers who hold...