Gestures are associated with powerful forms of mathematical understanding. However, determining the causative role of gestures has been more elusive. In the present study, we inhibit students' gestures by restraining their hands, and examine how this impacts their problem-solving when presented with geometric conjectures to prove. We find no…

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…

We explore whether "directed actions"--body movements that learners are instructed to formulate--enhance mathematical reasoning during proof production. Evidence is mounting that sensorimotor activity can activate neural systems, which can in turn alter and induce cognitive states (Nathan, 2014). New interventions are using…

Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts…

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 mathematics thinking not apparent in their speech, and analyzing gestures after proof production can contribute significantly to our…

Grounded and embodied cognition (GEC) serves as a framework to investigate mathematical reasoning for proof (reasoning that is logical, operative, and general), insight (gist), and intuition (snap judgment). Geometry is the branch of mathematics concerned with generalizable properties of shape and space. Mathematics experts (N = 46) and nonexperts…

Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is "embodied" -- inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building…

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…

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This…

The role of the body, particularly gesture, in supporting mathematical reasoning is an emerging area of research in mathematics education. In the present study, we examine undergraduate students providing a justification for a task about a system of alternating gears, which involves concepts of number relating to even/odd patterns. Some…

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…

The role of reasoning and proof in mathematics is undeniably crucial, and yet research in mathematics education has repeatedly indicated that students struggle with proof production. Our research shows that proof activities can be illuminated by considering action and gesture as a modality for crucial aspects of mathematical communication. We…