To understand the difficulties that many students have with comprehension of mathematics, we must determine the cognitive functioning underlying the diversity of mathematical processes. What are the cognitive systems that are required to give access to mathematical objects? Are these systems common to all processes of knowledge or, on the…

Listening to students in productive ways seems to be at the core of teaching practices aligned with the basic tenets of the constructivist world view. We present a definition for productive ways of listening, discuss the challenges involved in implementing it, and propose a way to support the "decentering" needed to learning to listen for teacher…

Examines the role that memory plays in the understanding of mathematics. Areas discussed include: retention research; memory and teaching; structure and organization in memory; and transformations in memory. Relevant research and implications for instruction are addressed. (JN)