Math in Motion: Investigating the relationship between formal mathematics and body action

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The aim of this proposal is to investigate new approaches to nurture and cultivate the mathematical imagination of all students. Mathematics as a science to imagine-with is not incompatible with memorizing the multiplication tables, number facts, or shortcuts to operate fractions, but it changes what these memories are part of. It is about imagiining space and time: shapes, patterns, or trajectories; it is about envisioning houw things could be; it is about discriminating the finite and infinite, the discrete from the continuous, and dthe possible from the impossible. The main conjecture of this proposal is that cultivating mathematical imagination is deeply related to enriching bodily action/perception. The research we propose intends to investigate this thesis through a series of studies with high school students and pre-service teachers.