Constructing Facilitative Teaching
This chapter synthesizes ideas from the earlier chapters to illuminate what is known about teaching that supports students' construction of mathematics knowledge and what questions remain to be investigated. Although the authors of several chapters have offered insights on such teaching from their chosen theoretical and methodological positions, my goal is to use their work to synthesize an emergent view of teaching that is consonant with a constructivist view of learning, and make connections among the views provided by the authors to create a more complete description. In doing so, we see that there are points at which these lines of work overlap —where researchers may be looking at similar phenomena from quite different points of view. These points of overlap offer the opportunity to explore the interconnections between quite different theoretical orientations, to reveal the instances where differing points of view and inconclusive evidence remain, and to articulate current points of contention and debate. Because the theoretical orientations taken by the authors lead them to focus on quite different aspects of facilitative teaching, some of the most interesting and productive lines of work for the future may occur at these points of overlap.