Chapter 10: Expressiveness and Mathematics Learning

How do multiple representations come together and participate in mathematics learning and insight? This is the broad question that we explore in this chapter. We observed the activities of students in an environment of multiple representations. The primary phenomenon that we examine here is how aspects of these multiple representations became incorporated into streams of bodily activity, exhibiting features of expression. As Noble, Nemirovsky, Wright, and Tierney (2001) note, there appears to be a general view “that students connect experiences in different environments by recognizing a core mathematical structure that is common to all environments” (p. 85). These authors challenge this view and instead “propose an alternative perspective on learning, in which students make mathematical environments into lived-in spaces for themselves and connect environments through the development of family resemblances across their experiences” (p. 85). In this chapter, we examine a related but different research question: not how different lived-in spaces interrelate through family resemblances, but how different representations simultaneously intermingle within a certain lived-in space. The representations we consider include a force sensor, a car moving along a track (its acceleration depending on the force applied to the sensor), and a real-time graph of force/acceleration versus time on a computer and projector screen.