’This is crazy. Differences of differences!’ On the flow of ideas in a mathematical conversation. (English)

Zaslavsky, Orit, 23. Conference of the International Group for the Psychology of Mathematics Education (PME-23). Vol. 4. ,. 217-224 (1999).

This paper describes the flow of a mathematical conversation in a high school mathematics classroom. The analysis attempts to elucidate how the discussion of a particular mathematical problem is inherently open-ended and to describe the complexity in managing the wide range of ideas and choices emerging from the interactions among students and the teacher. A major implication of our analysis is that whether an idea turns out to be mathematically correct is only one piece of what contributes to making it valuable and inspiring. Another implication is that the teacher’s mathematical expertise plays out throughout multiple ongoing dilemmas that go much beyond the classic dichotomy between “telling vs. letting them discover it”.