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Tracy Noble, Ricardo Nemirovsky, Tracey Wright, and Cornelia Tierney

In the SimCalc project and in the Mathematics of Change group at TERC, we are investigating how students from elementary through high school learn about the mathematics of change in multiple mathematical environments. As part of this research, we studied 5th-grade students doing mathematics-of-change activities from the Investigations curriculum (Russell, Tierney, Mokros, & Economopoulos, 1998) in multiple mathematical environments. This experience has led us to question the view that students connect experiences in different environments by recognizing a core mathematical structure that is common to all environments. We propose an alternative perspective on learning, in which students make mathematical environments into livedin spaces for themselves and connect environments through the development of family resemblances across their experiences.

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Ricardo Nemirovsky, Molly L. Kelton, and Bohdan Rhodehamel

Research in experimental and developmental psychology, cognitive science, and neuroscience suggests that tool fluency depends on the merging of perceptual and motor aspects of its use, an achievement we call perceptuomotor integration. We investigate the development of perceptuomotor integration and its role in mathematical thinking and learning. Just as expertise in playing a piano relies on the interanimation of finger movements and perceived sounds, we argue that mathematical expertise involves the systematic interpenetration of perceptual and motor aspects of playing mathematical instruments. Through 2 microethnographic case studies of visitors who engaged with an interactive mathematics exhibit in a science museum, we explore the real-time emergence of perceptuomotor integration and the ways in which it supports mathematical imagination.