Perceptual Learning Modules in Mathematics: Enhancing Students’ Pattern Recognition, Structure Extraction, and Fluency
Version of Record online: 30 OCT 2009
Copyright © 2009 Cognitive Science Society, Inc.
Topics in Cognitive Science
Volume 2, Issue 2, pages 285–305, April 2010
How to Cite
Kellman, P. J., Massey, C. M. and Son, J. Y. (2010), Perceptual Learning Modules in Mathematics: Enhancing Students’ Pattern Recognition, Structure Extraction, and Fluency. Topics in Cognitive Science, 2: 285–305. doi: 10.1111/j.1756-8765.2009.01053.x
- Issue online: 5 APR 2010
- Version of Record online: 30 OCT 2009
- Received 6 March 2009; received in revised form 18 August 2009; accepted 20 August 2009
- Perceptual learning;
- Pattern recognition;
- Learning technology;
- Mathematics learning;
- Mathematics instruction
Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students’ abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning.