Growth of mathematical knowledge for teaching – the case of long division

Overview & Synopsis

When university mathematicians teach mathematics courses for non-mathematicians, there may be a discrepancy between the mathematics they aim to teach and the mathematics their students aim to learn. In this paper, I analyze a lesson on long division taught by a mathematics Ph.D. student, where the learners were in-service elementary school teachers. Taking a Commognitive approach, I describe some crucial differences in the teachers' and the mathematician's discourse on mathematics and on teaching, which created opportunities for mutual learning. Uncovering the affordances and limitations of this teaching/learning situation is expected to help mathematicians become more effective teachers of non-mathematicians in general, and of pre-service and in-service teachers in particular.