The Education of Perception

Abstract

Although the field of perceptual learning has mostly been concerned with low-to middle-level changes to perceptual systems due to experience, we consider high-level perceptual changes that accompany learning in science and mathematics. In science, we explore the transfer of a scientific principle (competitive specialization) across superficially dissimilar pedagogical simulations. We argue that transfer occurs when students develop perceptual interpretations of an initial simulation and simply continue to use the same interpretational bias when interacting with a second simulation. In arithmetic and algebraic reasoning, we find that proficiency in mathematics involves executing spatially explicit transformations to notational elements. People learn to attend mathematical operations in the order in which they should be executed, and the extent to which students employ their perceptual attention in this manner is positively correlated with their mathematical experience. For both science and mathematics, relatively sophisticated performance is achieved not by ignoring perceptual features in favor of deep conceptual features, but rather by adapting perceptual processing so as to conform with and support formally sanctioned responses. These ''rigged-up perceptual systems'' offer a promising approach to educational reform.

Persistent perceptual grouping effects in the evaluation of simple arithmetic expressions

“…The ability to use basic neural machinery in novel ways may be of critical importance. As Goldstone, Landy, and Son (2010) discussed, evolutionarily speaking, we have only recently begun evaluating arithmetic expressions. Our ability to coopt perceptual machinery that has served humanity well for millennia demonstrates the remarkably efficient adaptability of the human brain.…”

Learning to Think: Cognitive Mechanisms of Knowledge Transfer

“…ey organize the changes internal to the mind that are necessary to implement learning and transfer (cf. Goldstone et al, 2010;Novick, 1990). e second theme is that learning grows in "pieces" and thinking involves using those pieces in new combinations.…”

“…Such chains of reasoning are diffi cult to do in one's head, without the external memory and perceptual processing support of symbol systems (cf. Goldstone et al, 2010). Experts are certainly capable of chains of mental reasoning without external symbolic support.…”

“…Examples include symbolic algebra and other mathematical notation systems (e.g., calculus notation, probability and statistics notation), Cartesian graphing and other scientifi c visualization techniques, and computer programming languages, including the huge and growing number of end-user programming languages (e.g., functions in Excel or html). We create external symbols (including pictures and diagrams; see Hegarty & Stull, Chapter 31) to make abstract ideas more available to our brains' powerful perceptual processing and learning mechanisms (e.g., Goldstone, Landy, & Son, 2010;Koedinger & Anderson, 1990). ese forms make the abstract concrete and leverage thinking by allowing easier processing of the abstract ideas (e.g., Larkin & Simon, 1987).…”

Embodiment and Embodied Design

“…David Landy contrived an elegant experimental design which demonstrated that the colloquial notion of "manipulating symbols," such as "moving +2 across the equal sign so it becomes -2," is not just a metaphorical form of speech-in our "mind's eye" we literally move those symbols across the equal sign, so that we arrive later at our destination if the moving symbol must brave a counter current (Goldstone, Landy, & Son, 2009).…”