Investigating problem-posing during math walks in informal learning spaces.

Informal mathematics learning has been far less studied than informal science learning - but youth can experience and learn about mathematics in their homes and communities. "Math walks" where students learn about how mathematics appears in the world around them, and have the opportunity to create their own math walk stops in their communities, can be a particularly powerful approach to informal mathematics learning. This study implemented an explanatory sequential mixed-method research design to investigate the impact of problem-posing activities in the math walks program on high school students' mathematical outcomes.

The Effect of Cognitive Relevance of Directed Actions on Mathematical Reasoning.

Theories of grounded and embodied cognition offer a range of accounts of how reasoning and body-based processes are related to each other. To advance theories of grounded and embodied cognition, we explore the cognitive relevance of particular body states to associated math concepts. We test competing models of action-cognition transduction to investigate the cognitive relevance of directed actions to students' mathematical reasoning in the area of geometry.

Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language.

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 occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities.