Designs for Environments That Invite and Sustain Mathematical Thinking

In this chapter we discuss a set of theoretical principles that guide our attempts to design environments that invite and sustain mathematical thinking (see Nemirovsky & Monk, chap. 6, this volume). The particular environments that we describe are intended for students from fifth grade to adult, and are organized around the Jasper Woodbury Problem Solving Series—a series of 12 videodisc- and CD ROM-based adventures that focus on areas such as rate (in the context of trip planning), statistics, geometry, and algebra (see Cognition and Technology Group at Vanderbilt [CTGV], 1997). However, the design principles that we discuss go beyond Jasper and apply to a wide variety of mathematical curricula.