Harnessing human perception and gesture to develop sharable expertise in algebra

Harnessing human perception and gesture to develop sharable expertise in algebra

Perception—how sensory information is selected or ignored—is a hallmark of expertise from chess grandmasters to sommeliers. Perception may also distinguish expertise in more abstract domains such as mathematics.

School algebra begins in the elementary grades and involves coordinating different representational systems including graphs, equations, and verbal descriptions to understand abstract concepts like linear function. A key challenge for teaching and learning is that any particular representation within a system is just one member of a set of algebraically equivalent but perceptually dissimilar representations. For example, the scale of the x-axis affects the perceptual steepness of a linear graph but not the function’s rate of change.

Human perception can be rapidly trained to perceive invariance across wide perceptual variability, but perceptual learning is largely unconscious, introducing two problems: perceptual expertise may be difficult to integrate with explicit knowledge and may confound rather than enhance teachers’ explanations. Growing evidence suggests kinesthetic action grounds abstract ideas, improves conceptualization, and increases gesturing—a critical modality for mathematics teaching and learning.

Our IUCRG project will recruit undergraduate education majors to experimentally test whether kinesthetic perceptual learning improves integration with conceptual knowledge and enhances the communicability of resulting perceptual expertise relative to non-kinesthetic perceptual learning. Data will include standard measures of perceptual and conceptual learning and novel measures of shareable expertise, such as gesture frequency and elementary student learning in response to undergraduate explanations.

This pilot is the first step towards understanding how means of gaining perceptual expertise influence the ability to share it.