This study looks at how students embody their ideas about geometry conjectures and how those ideas travel within and between student groups. In one classroom of a Title 1 high school, students participated in a three-part program in which they: (1) played "The Hidden Village," a motion-capture video game where they assess the veracity of…

Proof, though central to mathematical practice, is rarely explored through the lens of embodiment because of the centrality of abstraction and generalization. We use the case of a high school geometry student to investigate two research questions: (1) How do embodied processes facilitate mathematical learning? (2) How can generalized mathematical…

Gestures have been shown to play a key role in mathematical reasoning and be an indicator that mathematical reasoning is "embodied" -- inexorably linked to action, perception, and the physical body. Theories of extended cognition accentuate looking beyond the body and mind of an individual, thus here we examine how gestural embodied…

Findings synthesized across five empirical laboratory- and classroom-based studies of high school and college students engaged in geometric reasoning and proof production during single- and multi-session investigations (346 participants overall) are presented. The findings converge on several design principles for computer technologies to support…

In this study, we devised research design that provides pre-service teachers to effectively experience embodied geometric thinking with the goal that it will impact teachers' instruction to students in their classrooms. Using a motion-capture video game and design tool, we offered opportunities for pre-service teachers to experience of performing…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

The Hidden Village (THV) is a motion-capture video game for investigating how physical movements foster mathematical thinking and proof practices based on principles of embodied cognition. Analysis of the interactions of students in an all-Limited English Proficiency Title 1 high school geometry classroom revealed ways simulated enactment and…

Research in mathematics education has established that gestures--spontaneous movements of the hand that accompany speech--are important for learning. In the present study, we examine how students use gestures to communicate with each other while proving geometric conjectures, arguing that this communication represents an example of extended…