Although it can be argued that constructivist epistemologies have been around for a long time (Mousley, 1993; von Glasersfeld, 1983), perhaps the first time the international mathematics education research community was directly confronted with the claims of radical constructivism was at the 11th annual conference of the International Group for the Psychology of Mathematics Education (PME), held in Montreal in 1987. At that conference, the level of understanding of what radical constructivism might mean ranged from high, for those who were presenting keynote addresses (Kilpatrick, 1987; Sinclair, 1987), to almost nothing for many in the audience. The terminology was new, and it took time to bridge the gulf between those who were actively debating and researching constructivist ideas and those who had been researching and debating issues in other areas. Participants at that 1987 Montreal Conference could not miss the intensity of . feeling among those debating facets of radical constructivism. Like anythmg new, there seemed to be an aura about the word, and with retrospect, it is not surprising that over the past ten years, the major tenets of "radical constructivism" have defined an important, albeit sometimes unconscious, epistemological framework for' many mathematics education researchers. At the same time, other kinds of constructivism have been posited, to the extent that Phillips (1995) was able to assert that "constructivism has many sects" (p. 1), each of which harbours some distrust of its rivals. In' the 1990s curriculum frameworks for school mathematics and teacher education programs have increasingly carried specific references to radical and other varieties of constructivism. One often hears expressions such as the "constructivist classroom" and the "constructivist teacher" (Bosse, 1995). But what do such expressions really mean? And, when such words flow from the lips or pens of researchers, have the researchers thought about the implications of their utterances,' both with respect to the research framework within which they are operating, and from the perspective of the teachers and schools with whom they are working?
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