Emerging Perspectives on Gesture and Embodiment in Mathematics

Edited by:
Laurie D. Edwards, St. Mary's College of California
Francesca Ferrara, Università di Torino, Italy
Deborah Moore-Russo, SUNY, University at Buffalo

A volume in the series: Cognition, Equity & Society: International Perspectives. Editor(s): Bharath Sriraman, University of Montana. Lyn English, Queensland University of Technology.

Published 2014

The purpose of the book is to establish a common language for, and understanding of, embodiment as it applies to mathematical thinking, and to link mathematics education research to recent work in gesture studies, cognitive linguistics and the theory of embodied cognition. Just as in past decades, mathematics education experienced a "turn to the social" in which socio-cultural factors were explored, in recent years there has been a nascent "turn to the body." An increasing number of researchers and theorists in mathematics education have become interested in the fact that, although mathematics may be socially constructed, this construction is not arbitrary or unconstrained, but rather is rooted in, and shaped by, the body. All those who engage with mathematics, whether at an elementary or advanced level, share the same basic biological and cognitive capabilities, as well as certain common physical experiences that come with being humans living in a material world. In addition, the doing and communicating of mathematics is never a purely intellectual activity: it involves a wide range of bodily actions, from committing inscriptions to paper or whiteboard, to speaking, listening, gesturing and gazing. This volume will present recent research on gesture and mathematics, within a framework that addresses several levels of mathematical development. The chapters will begin with contributions that examine early mathematical and proto-mathematical knowledge, for example, the conservation of volume and counting. The role of gesture in teaching and learning arithmetic procedures will be addressed. Core concepts and tools from secondary level mathematics will be investigated, including algebra, functions and graphing. And finally, research into the embodied understanding of advanced topics in geometry and calculus will be presented.

The overall goal for the volume is to acknowledge the multimodal nature of mathematical knowing, and to contribute to the creation of a model of the interactions and mutual influences of bodily motion, spatial thinking, gesture, speech and external inscriptions on mathematical thinking, communication and learning. The intended audience is researchers and theorists in mathematics education as well as graduate students in the field.

CONTENTS
Introduction, Deborah Moore-Russo, Laurie D. Edwards, Francesca Ferrara. 1. Embodiment, modalities and mathematical affordances, Laurie D. Edwards & Ornella Robutti. Section I. Gestures and embodiment in early mathematics 2. Embodied knowledge in the development of conservation of quantity: Evidence from gesture, Martha Alibali, Breckie Church & Sotaro Kita. 3. Gesture’s role in learning arithmetic, Susan Goldin-Meadow, Steven Jacobs, & Susan Levine. Section II. Gestures and embodiment in school mathematics 4. Analytic-structural functions of gestures in mathematical argumentation processes, Ferdinando Arzarello & Cristina Sabena. 5. An exploratory study of multi-modalities in the mathematics classroom: Enrica’s explanation of an experience, Francesca Ferrara, Ornella Robutti & Laurie D. Edwards. 6. The gestures of blind mathematics learners, Lulu Healy & Solange Hassan Ahmad Ali Fernandes. Section III. Gestures and embodiment in university mathematics 7. Embodied cognition across dimensions of gesture: Considering teachers’ responses to three-dimensional tasks, Deborah Moore-Russo & Janine Viglietti. 8. The role of conscious gesture mimicry in mathematical learning, Caroline Yoon, Michael Thomas & Tommy Dreyfus. 9. Re-conceiving modeling: An embodied cognition view of modeling, George Sweeney & Chris Rasmussen. 10. More than mere handwaving: Gesture and embodiment in expert mathematical proof, Tyler Marghetis, Laurie D. Edwards & Rafael Núñez. 11. Blending across modalities in mathematical discourse, Nathaniel Smith.