The Study of Teaching for Mathematics Learning: Views Through Two Lenses

This article uses several studies to illustrate the concepts and methods of process-product and mediating process research on mathematics teaching. An integration of these two perspectives suggests that, if all learners in a class are to benefit, instruction must clarify the nature of mathematical reasoning. This may be accomplished by development work on challenging problems, or by more- and less-able students working together on such problems in small groups. In both situations, however, students should be pressed to focus on the substance rather than the form of the mathematics being learned, and ultimately, to perform strategic and heuristic activities on their own.