If I consider the philosophical views of mathematics as presented in the literature then what considerations should be made by a theorist in curriculum development in mathematics? Jere Confrey (1981) emphasised that
If the curriculum theorist accepts a curriculum change theory of knowledge in mathematics, then the question is what are the
implications for the first task in curriculum design: the determination of content. This can be answered at two levels:
The basic tenet is that what one teaches ought to reflect the theory of knowledge which one thinks is appropriate and adequate for that discipline. This means that one ought to select content which
Chapter: Four: Review of the Literature on Beliefs 63
accurately portrays the particular discipline involved. For mathematics, it means that mathematics ought to be portrayed evolving, growing and changing, not as static immutable truths.
An analysis of particular concepts in the discipline yields a variety of ways of conceiving a particular concept, as well as a variety of ways in which those concepts develop. Therefore, the curriculum theorist must also consider alternative conceptions of particular concepts to assess their appropriateness for inclusion as content. (p. 249)
Analysis of KBSR documents left me with no doubt that the nature of mathematics and how teachers' (both pre-service and in-service) instructional practices were affected by their conceptions of mathematics had either not been on the curriculum developers' agenda or they did not heed its importance. The failure to address the issue of teachers' conceptions of mathematics affecting their instructional practice could be explained by the curriculum
developers not being aware of the discourse or their not seeing the relevance or importance of such a discourse on mathematics teaching and learning. This gap in the curriculum developers' agenda suggested that they had worked on an "inherited and unexamined philosophical dogma that mathematical truth should possess absolute certainty" which is contradicted by
mathematicians whose "actual experience in mathematical work offers uncertainty in plenty"
(Hersh, 1986, p17, original emphasis).
A close examination of the KBSR document showed that it placed great emphasis on the pedagogic elements and physical arrangements of the classroom. I could not find any particular philosophical change in the way mathematics was perceived. While the change in the pedagogy called for a more active and experiential based learning, the content supported a competence view of mathematics and a didactic pedagogy. This was in sharp contrast to the view of mathematics reflected in documents such as The Cockcroft Report (DES, 1982) and the Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989). The view of mathematics permeating these official documents was one where learners were engaged in purposeful activities that grew out of problem situations, requiring reasoning and creative
Chapter: Four: Review of the Literature on Beliefs 64
thinking, gathering and analysing information, discovering and communicating ideas and testing those ideas through critical reflection and argument. This view of mathematics was in sharp contrast to that gleaned from the ICBSR where mastery of concepts and procedures was the ultimate goal of instruction. The conflict in the pedagogy and the mathematics content was also seen in the British National Curriculum. According to Burton (1992) the pedagogic practice in the Non-statutory Guidance to the National Curriculum called for a "broader, more questioning, pupil-driven curriculum" (p. 163) while the National Curriculum was about content delivery and externalised evaluation. Furthermore Burton maintained that even if one did not make a value judgement about the kind of experiences that engaged learners in their classrooms, the philosophy of mathematics drove the choices that were made in the syllabus and assessment. "After all, again in terms of efficiency, if you want to know who has learnt a particular what, perhaps the quickest and the cleanest way to find out is to administer a test"
(Burton, 1993, p.48).
In my opinion Malaysian teachers' and students' view of mathematics was what D'Ambrosio described as academic mathematics and this was consistent with what Thompson (1992) found among the general "educated masses" in the U.S.A. According to Thompson (1992), for the
"educated masses"
mathematics is a discipline characterized by accurate results and infallible procedures, whose basic elements are arithmetic operations, algebraic procedures, and geometric terms and theorems. (p.127)
More importantly I believe that Malaysians in general see primary mathematics as simple and therefore there is little need to worry about preparing teachers to teach primary mathematics.
Bergeron and Herscovics (1990) criticised such a view because
Cognitive psychology today recognizes that higher mental processes are involved in the learning of early arithmetic, that is, the acquisition of the fundamental conceptual schemes of number and additive structures (p. 31).
Chapter: Four: Review of the Literature on Beliefs 65
This "simplicity belief" (Burton, 1988) encouraged teachers to teach mathematics as a subject building it up from simple to complex. According to Ball (1990b) this doomed mathematics teaching to dull routines which meant that children spent "endless hours in school reciting sums in unison to memorise them" (Bergeron and Herscovics, 1990, P. 31). Ball (1990b) said that the situation described by Bergeron and Hercovics is a view with which we are so familiar. Despite the KBSR's intention to change these kinds of experience, I suspect that such a change will be difficult to achieve.
What reasons do I have for such a view? My observations showed that ten years after the introduction of KBSR, the mathematics that Malaysian teachers offered their primary pupils contrasted strongly with the views mathematicians and philosophers of mathematics had of mathematics as presented in Section 4.4.1.1. Moreover, at the philosophical level, the ICBSR document on mathematics teaching and learning contains the same conflict between content and pedagogic elements. If there is no change in the presentation of the ICBSR mathematics, it is more than likely that Malaysian mathematics teachers, lecturers and pre-service teachers will still hold onto the view of mathematics held by Malaysians in general, namely of
instrumentality.