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Mathematics Curricula and Culture

This paper was presented at an "International Seminar on Mathematical Science" held in Malaysia. While both writers have worked, over many years now, with mathematics teachers and tertiary mathematics educators in Southeast Asia, we are the first to admit that, of course, we do not understand local forces as fully as many others present at the Seminar, who have grown up and worked for many years in this part of the world. In an attempt to make the paper more obviously relevant, and to challenge those present at the Seminar (and those not present but who subsequently read the paper), we shall make some generalisations about our understandings of the forces influencing mathematics educators in Southeast Asia, and comment on the extent to which the present situation is consonant with international trends in mathematics education research.

At the outset we recognise the dangers of what we are now doing. It is often unwise for outsiders to comment on what others are doing, and this is especially true of education in this part of the world, where there are deeply embedded cultural, social, and religious values that impinge on what happens in schools. We recognise too, that the nations of Southeast Asia are all different, that they have their own education traditions, and that quality summaries of mathematics education research in Southeast Asia already exist (see, for example, Liau Tet Loke, Sim Jin Tang, & Marinas, 1990). Even so, it can be useful to hear the views of outsiders who have some knowledge of the sensitivities of which they need to take account.

Are mathematics curricula in Southeast Asian nations of the "mathematics for all" variety, or are they more suited to the needs of a minority of students? In most parts of Southeast Asia, as in most parts of the world today, the locally constructed versions of mathematics and the internationally recognised formal Mathematics impinge on the thinking of individuals. For example, the system of Hindu-Arabic numerals is used in schools throughout this region, and facilitates a level of commonality across cultures in mathematical knowledge (Stigler & Baranes, 1988, p. 259).

However, to be blunt, it seems to us that school mathematics in most Southeast Asian nations is based on centralised curricula, frequent pencil-and-paper testing of students, and rather formal textbooks. Behaviourist approaches are commonly adopted, and Benjamin Bloom's (1956) Taxonomy of Educational Objective: Cognitive Domain continues to exert a powerful influence over curriculum and test developers. Multiple-choice tests continue to enjoy a certain mystique, despite the fact that from a mathematical point of view they are invalid because practising mathematicians rarely have to choose one correct answer from four or five given possibilities.

Is there evidence of colonialist thinking in School Mathematics in Southeast Asia? The history of mathematics education in Commonwealth countries suggests that there was always a tendency among educators in the colonies to mimic what was happening in school mathematics in England (Clements, Grimison & Ellerton, 1989, pp. 50-78), and we suspect that the same tendency is everpresent in Southeast Asian nations, where curriculum developments in the United States, the United States, and even Australia and New Zealand are studied, and often more or less reproduced. Often the rhetoric (of curricula having been developed which take into account local and national needs and sensitivities) does not match the reality of prescribed curricula. There is even a move towards the definition and adoption of internationalised mathematics curricula (Oldham, 1989).

History provides an excellent example of what we talking about: those attempting to explain why the payment-by-results system (Dear, 1975) was introduced into the Australian colonies in the 1860s need not look far beyond the fact that the system was introduced in England just before its introduction in Australia - it should also be observed that the same system was adopted later in the nineteenth century in many British Commonwealth colonies including India, Ceylon, East Africa and Malaya (Watson, 1982). More recently, which of the Asian nations represented at this Seminar did not introduce a version of the "New Math(s)" in the late 1960s or 1970s? Of course, around that time every Australian state and territory introduced its version of the New Maths - we had to be seen to be keeping up with the rest of the world. Yet, we did this despite the fact that New Math(s) was meeting with only limited success in those countries where it had been originally introduced (Moon, 1986).

Clearly, a form of colonialism has been shaping the curricula, assessment policies and indeed the perceived raison d'etre of school mathematics in many countries around the world, including the nations of Southeast Asia. Such thinking should not be thought of as having been confined to countries politically regarded as colonies, or to the nineteenth or early twentieth century: rather, it was evident in the relationship between many developing countries and so-called "advanced" nations, such as the United States of America, the United Kingdom, and the former United Soviet Socialist Republic. It can be argued that despite the best intentions of all concerned, the employment of mathematics education consultants from "advanced" countries, by UNESCO, the World Bank, and other similar organisations, for the purpose of advising on mathematics curricula in developing countries has nurtured, developed and maintained colonialist attitudes and policies in school mathematics.

Considerations such as these led Clements et al. (1989) to deplore the tendency among Australian mathematics educators to mimic developments in school mathematics in England. That this tendency still existed was apparent throughout the 1980s, when the Cockcroft Report and national assessment and curriculum ideas emanating from the United Kingdom had a major impact on the thinking of educators in all Australian states. Clements et al. (1989) attributed this tendency, in Australia and elsewhere, to what they called the "colonialist" forces operating among those who seek to define the practices and scope of school mathematics in many countries. They defined "colonialism" as "an attitude of mind accepted by both the leaders and representatives of the colonising power and by those who are colonised, that what goes on "at home" should also take place in the colonies," and added that while this acceptance is sometimes a conscious act, "more often it is unconscious - people behave in a colonialist way simply because that is the way they have learnt to behave (Clements et al., 1989, p. 72). We wonder whether a similar attitude of mind permeates those responsible for mathematics education in Southeast Asia nations.

According to Clements et al. (1989, p. 72), one of the most important factors that has contributed to the development and maintenance of colonialist thinking in mathematics education has been the largely unthinking acceptance of the idea that mathematics is a culture-free discipline; that is to say, it has been assumed that mathematics is, and should be, the same wherever it is studied. This kind of thinking has been particularly evident among those responsible for writing reports to bodies responsible for maintaining an overview of educational policy in different countries. For example, Lord Briggs (1987), in a report to the Commonwealth Secretariat in London, stated that it is arguable that mathematics might be particularly suitable to Commonwealth cooperation because "there is no practical requirement and the cultural dependence is less than with other subjects" (Briggs, 1987, p. 27). Similarly, some notes prepared for the Commonwealth Secretariat in 1986 state, in a section entitled "Foreign teaching material and cultural appropriateness," that there is virtually no danger of straight science, mathematics, or technology courses, that have been developed in one country, being culturally offensive in another" (see Ellerton and Clements, 1989b, p. 4). We believe that such notions fly in the face of recent anthropological and mathematics education research in which the culture-free idea of mathematics is specifically repudiated (see, for example, Joseph, 1992).

The idea of externally prescribed mathematics curriculum is, we would contend, not supported by the mathematical, the philosophical, and the historical frameworks that we have outlined. If, mathematics is, indeed, socially constructed then students' efforts to construct mathematics, in order to solve real-life problems, should not be straightjacketed by a rigid, externally prescribed curriculum backed up by a tightly administered external examination system. History suggests that such systems have developed as a result of colonialist thinking, and have produced only a small proportion of adults who recognise and make use of the power of mathematics.

We sincerely ask you to consider whether this is the case in your own country, and if it is, then to ask whether anything can be done to change the situation.

Should Southeast Asian nations have national mathematics curricula? Mellin-Olsen's (1987) arguments raise the thorny issue of the extent to which curriculum decision-making processes should be decentralised. And this issue is not confined to Southeast Asian nations, for as Mellin-Olsen (1987, p. 123) argues, such matters are pertinent in the United States and Europe (and we would add, in Australia, too). As previously stated, in the mid-1980s a national curriculum was introduced in the United Kingdom (Noss, 1989), and in the United States of America major standards document have been prepared by leading mathematics educators (Crosswhite et al., 1989; National Council of Teachers of Mathematics Commission on Standards for School Mathematics, 1989)

It is intriguing that moves towards a national curriculum in Australia (Baxter & Brinkworth, 1989) follow hard upon similar moves in the United Kingdom and the United States of America. The arguments that moved the politicians in 1901, when the Australian colonies were federated into one nation, to make the organisation of education the responsibility of the various state governments, and not the federal government, would appear to have been abandoned. Just as, in the 1960s, each Australian state moved to incorporate the ideas of the "New Math(s)" into its school mathematics programs, the notions of national curriculum and assessment are now being imported from abroad. Once again colonialist thinking seems to be rearing its ugly head in the context of Australian education, for the arguments now being advanced for a national mathematics curriculum would appear to be no more valid, or persuasive, than were arguments offered in support of the "New Math(s)" , "Cuisenaire rods," and other large-scale but ill-fated mathematics curriculum changes that were imported at various times throughout this century

Interestingly (and, from our own perspective, fortunately), this move to establish a national curriculum (including a national curriculum in mathematics) in Australia was defeated in July this year (1993), by a vote of 5 to 4 at a meeting of the State and Territory ministers of education. Australian mathematicians and mathematics educators had led the opposition to the introduction of the proposed national curriculum, and some believe it was their opposition which was instrumental in precipitating a majority of ministers to make the surprise decision.

Those supporting a national curriculum in Australia spoke of national accountability, the need for uniform reporting to parents about their children's mathematical progress, the need to provide clear guidelines to teachers, and the need to keep up with moves to internationalise the curricula of schools. The rhetoric was strong. The major argument, though, was economic: Australia, in the depths of a recession, could not afford the expense of each individual state paying for its own curriculum development. This, it was claimed would inevitably result in unnecessary and expensive duplication. In a similar vein, Swift (1986), in some notes prepared for the Commonwealth Secretariat in 1986, stated, in a section entitled "Foreign teaching material and cultural appropriateness," that there is virtually no danger of straight science, mathematics, or technology courses, which have been developed in one country being culturally offensive in another, and that "in these fields particularly, one would argue that it is grossly wasteful to think in terms of preparing course material that has already been well-prepared at immense expense."

This raises a number of issues concerning Southeast Asian mathematics education. What are the advantages and disadvantages of national mathematics curricula which have been developed and prescribed in Southeast Asian nations? Should basically the same mathematics be taught to groups from very different cultural heritages, but living within the same nation? Do the answers to these questions depend on the level of mathematics education being considered - that is to say, are the answers different for elementary and secondary school mathematics education?

Politics Conclusion and References

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