What We Say and How We Do: Action, Gesture, and Language in Proving

In this Brief Report, we share the main findings from our line of research into embodied cognition and proof activities. First, attending to students' gestures during proving activities can reveal aspects of mathematical thinking not apparent in their speech, and analyzing gestures after proof production can contribute significantly to our understanding of students' proving practices, particularly when attending to dynamic gestures depicting relationships that are difficult to communicate verbally. Second, directing students to produce physical actions before asking them to construct a mathematical proof has the potential to influence their subsequent reasoning in useful ways, as long as the directed actions have a relationship with the proof content that is clearly meaningful to the students. We discuss implications for assessment practices and teacher education, and we suggest directions for future research into embodied mathematical proof practices.

Contributor Notes

Caroline (Caro) Williams-Pierce, Department of Educational Theory & Practice, University at Albany, SUNY, ED 114B, 1400 Washington Avenue, Albany, NY 12222; cwilliamspierce@albany.edu

Elizabeth L. Pier, Department of Educational Psychology, University of Wisconsin–Madison, 1025 W. Johnson St., Madison, WI 53706; epier@wisc.edu

Candace Walkington, Department of Teaching and Learning, Southern Methodist University, P.O. Box 750455, Dallas, TX 7527; cwalkington@smu.edu

Rebecca Boncoddo, Department of Psychological Science, Central Connecticut State University, 1615 Stanley Street, New Britain, CT 06050; boncoddo@ccsu.edu

Virginia Clinton, Department of Educational Foundations and Research, University of North Dakota, 231 Centennial Dr., Grand Forks, ND 58202; virginia.clinton@und.edu

Martha W. Alibali, Department of Psychology, University of Wisconsin–Madison, 1202 W. Johnson St., Madison, WI 53706; martha.alibali@wisc.edu

Mitchell J. Nathan, Department of Educational Psychology, University of Wisconsin–Madison, 1025 W. Johnson St., Madison, WI 53706; mnathan@wisc.edu

(Corresponding author is Williams-Pierce cwilliamspierce@albany.edu)(Corresponding author is Pier epier@wisc.edu)(Corresponding author is Walkington cwalkington@smu.edu)(Corresponding author is Boncoddo boncoddo@ccsu.edu)(Corresponding author is Clinton virginia.clinton@und.edu)(Corresponding author is Alibali martha.alibali@wisc.edu)(Corresponding author is Nathan mnathan@wisc.edu)
Journal for Research in Mathematics Education

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