Trends Index

Some Concluding Comments

In this paper we have pointed to the major move by mathematics education researchers in the 1980s away from statistical and developmental research paradigms that characterised much of mathematics educations research carried out in the 1960s and 1970s. Philosophical, anthropological, sociological and critical research approaches, involving the analysis of qualitative rather than quantitative data, were more widely adopted. Increasingly, the aim was to gain a holistic understanding of the sub-cultures within which mathematics teaching and learning occur. It is our belief that these more qualitative research paradigms need to be adopted by Southeast Asian mathematics education researchers.

Another message carried by this paper, is that the mathematics education research of the last two decades has made it abundantly clear that mechanistic and prescriptive approaches to mathematics curriculum development and assessment, often accompanied by tightly controlled national curriculum and assessment practices, and employing behaviourist language (such as outcomes and competency-based learning) do not work. They fail because many teachers teach for the lowest common denominator, so that the skills prescribed in the curriculum, and the skills they know will be tested, are taught to all students in their classrooms, irrespective of whether the mathematics being presented is culturally or cognitively appropriate for the learners.

Such an approach inevitably produces a majority of school leavers who feel they cannot do mathematics, and have developed an attitude that mathematics is an "out-there," reified body of knowledge that is useful only for very intelligent people in certain professions.

Despite Bishop's (1988) distinction between Mathematics (capital M) and mathematics (small m), we have argued that the teaching and learning of mathematics must always be culture- and value-laden. In particular, after drawing attention to the increasingly widespread use of the distance mode in mathematics education programs, we argued that claims by reputable bodies that quality mathematics materials produced for mathematics programs at one institution can be translated, virtually intact, to other places without compromising the quality of the educational experiences of learners, are regrettable. To support this argument, we made four points, and these are as pertinent to Southeast Asian educators as they are to educators in other parts of the world:

1. Philosophical and mathematical developments in the twentieth century, especially as it is represented in the writings of Wittgenstein, Lakatos, and Gödel, indicate that while Mathematics does not exist "out-there" (in the Platonist sense) as an absolute form of knowledge, it does exist as a socially constructed body of knowledge. In that sense, it can be regarded as part of what Evers and Walker (1983) called the "seamless web of knowledge." While, the agreements represented by the existence of Mathematics (capital M) tend to overshadow the practice of mathematics (small m) in many societies, mathematics education cannot avoid, and should not try to avoid, being heavily influenced by cultural forms.

2. The history of mathematics education indicates that a form of colonialism has always operated, and still operates, whereby representatives of "higher" cultures have believed it to be their duty to pass on Mathematics (capital M) to developing nations. This colonialism has been made possible by the willingness of the "higher" cultures to pass on their knowledge, and the desire of the developing nations to receive it.

3. The practice of colonialism in mathematics education, be this conscious or unconscious, has resulted in the downgrading of local forms of mathematics, and a consequent acceptance of rote teaching and learning of Mathematics.

4. Mathematics curricula should be localised to the extent that mathematics education around the world can be enriched by the variety of local mathematical forms that are part of the learners' personal worlds.

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South-East Asia

Trends Index