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Philip Kellman, Everett Mettler, Carolyn Bufford; The Psychophysics of Algebra: Mathematics Perceptual Learning Interventions Produce Lasting Changes in the Perceptual Encoding of Mathematical Objects. Journal of Vision 2018;18(10):1073. doi: 10.1167/18.10.1073.
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© ARVO (1962-2015); The Authors (2016-present)
Perceptual learning (PL) refers to experience induced improvements in information extraction, including complex pattern recognition that is a hallmark of expertise. Perceptual learning interventions in mathematical domains produce substantial gains on tests of mathematical competence (e.g., Kellman, Massey & Son, 2010). Here we report direct evidence that such perceptual learning modules (PLMs) improve perceptual encoding of mathematical objects, measured psychophysically. In two experiments, accuracy and speed of college students' encoding of equations was assessed in a forced-choice, same-different task with brief exposures. Between a pretest and a delayed posttest, the experimental group completed an Algebraic Transformations PLM, comprised of interactive learning trials requiring mapping of equations across transformations. The aim of the PLM was to improve students' seeing of structure and relationships in algebra; previous research showed that it produced substantial improvements in middle school students' algebra performance. A control group received equal exposure to the same stimuli in a non-mathematical task. On a delayed posttest, the PLM group, but not the control group, showed reliably improved encoding of mathematical objects on the same-different task, even though that task depended solely on physical identity and required no mathematical interpretation. Perceptual learning interventions accelerate expertise in complex domains and produce measurable, durable changes in perceptual encoding.
Meeting abstract presented at VSS 2018
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