ABSTRACT
The question, “What do we mean by mathematical learning?” which lies at the heart of any discussion of mathematical learning, was not explicitly mentioned in the Learning Discussion Group. The answer depends on what we mean by “doing mathematics” and is culturally dependent, with different times and places yielding a variety of norms; recitation of Euclid, practical use of sextant, bookkeeping, and computer modelling of statistical functions. “Doing mathematics” in a late 20th-century technological society has involved a shift from earlier emphases on the rote learning of standard procedures. This is rooted in several interconnected phenomena. First, there is a need to be able to handle the new technology. In addition, the rapidly changing nature of novel systems requires flexibility and adaptability in workers and consumers. Moreover, developments in epistemology over the last half-century call into question the effectiveness of purely procedural learning. In the multicultural arena afforded by ICME-6, we quickly become alert to cultural differences. Two examples serve to indicate the huge potential variations in perceptions of “learning mathematics” in the contemporary world.
In some subcultures children have unrestricted access to microcomputers and calculators at school and at home and computers are used in most parental occupations. Whereas in other subcultures neither pupils, parents, or teachers use or ever expect to use such devices.
Many eastern cultures place a fundamental importance on the community, while most western societies emphasize the individual. Constructivism, with its central notion of individuals as agents in their own learning fits more easily with the latter that with the former.
