Dan Chazan and Deborah Ball
For the past several years, we have been developing and studying teaching practices through or own efforts to teach school mathematics Ball’s work has been at the elementary level, in third grade, and Chazan’s at the secondary level, grade ten and above, in Algebra I. In our teaching, we have been attempting, among other things, to create opportunities for classroom discussions of the kinds envisioned in the US National Council for Teachers of Mathematics Standards (NCTM, 1989, 1991) At the same time, we have been exploring the complexities of such practice. By using our
teaching as a site for research into, and as a source for formulating a critique of, what it takes to teach in the ways reformers promote, we have access to a particular ‘insider’ sense of the teacher’s purposes and reasoning, beyond that
which a researcher might have. [I]
This article originated with frustration at current math education discourse about the teacher’s role in discussion intensive teaching For instance, an exhortation simply to avoid ‘telling’ seems inadequate as a guide for practice on at least two levels First, it ignores the significance of context and as a result seems to underestimate the teacher ‘s role and suggests that teachers are not supposed to act, regardless of what is going on in the classroom What is a teacher to do when a discussion becomes an argument and flashes out of control, hurting feelings? What is a teacher to do when students reach a consensus, but their· conclusion is mathematically incorrect? Or what if a discussion focuses on a matter of little mathematical importance?