Toward a Working Model of Constructivist Teaching: A Reaction to Simon

We start this discussion of article by Martin A. Simon with two major conjectures that we will try to substantiate. The first is that there is a kind of teaching that can legitimately be called The second is that Simon's model of teaching his prospective elementary school teachers, if modified, would fit our understanding of constructivist teaching, even though his basic premise is that constructivism does not tell us how to teach mathematics (Simon, 1995). The issue concerning whether constructivism tells us how to teach mathematics resides in how constructivism is understood. One way to understand constructivism is in terms of basic tenets like knowledge is not passively received but is actively built up by cognizing subject, and the function of cognition is adaptive and serves in organization of experiential world rather than in discovery of ontological reality (von Glasersfeld, 1989, p. 162). These basic tenets are orienting, but as indicated by Simon, they do not stipulate a particular model of teaching mathematics. Neither do they tell us how to do family therapy or how to provide psychiatric counseling. People who engage in these types of human activities, however, can use basic tenets of constructivism in building models of realities of those with whom they interact. If a teacher formulates a model of children's mathematical knowledge, including its construction, we claim that model is an important part of teacher's understanding of constructivism. Similarly, if teacher formulates a model of how she makes sense of children's mathematical knowledge, including its construction, this would be a constructivist model of teaching. It, too, would be an important part of teacher' s meaning for constructivism. Regarding teacher as a learner in activity of teaching is essential in our understanding of constructivist teaching, and it is a basic aspect of Simon's model of teaching as well.