Formal notations are diagrams: Evidence from a production task

Persistent perceptual grouping effects in the evaluation of simple arithmetic expressions

“…This does, however, blur the behavioral distinction between verbal and visual encoding in the present context. It also requires a relatively sophisticated mapping from the visual stimulus to the verbal code, since perceptual-grouping effects like those reported here can be induced with grouping cues not typically found in written or typeset arithmetic expressions (Landy & Goldstone, 2007a). On the other hand, there is evidence that, in some cases, a great deal of spatial information is preserved well in representations derived from language (Zwaan & Radvansky, 1998), so even if a verbal code were to replace a visuospatial code, it could still give rise to a representation that retained spacing information.…”

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Abstract Landy and Goldstone (2007a demonstrated that an explicit rule, operator precedence for simple arithmetic expressions, is enforced in part by perceptual processes like unit formation and attention. When perceptual grouping competes with operator precedence, errors increase.

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The Import of Knowledge Export: Connecting Findings and Theories of Transfer of Learning

“…Similarly, David Landy and colleagues have focused on the role of perceptual processes in understanding and interacting with mathematical formulas. For instance, in practice, the perceptual grouping of terms (i.e., which terms are closer together in space on the page) can interfere with and even trump groupings based on operator precedence (e.g., grouping by multiplication before grouping by addition; Landy & Goldstone, 2007a, 2007b. On the other hand, experience with mathematical formulas can lead to the automatic deployment of attention to operators with higher priority (Landy, Jones, & Goldstone, 2008).…”

How to make a good animation: A grounded cognition model of how visual representation design affects the construction of abstract physics knowledge

“…In fact, interference between perceptual features of representations and their represented abstract meaning has already been demonstrated through a series of studies by Landy and Goldstone on math calculation [39][40][41]. For example, they have shown that our understanding of the order of precedence in math calculation, which is nothing but a set of abstract rules, very likely shares much of the same brain system responsible for detecting visuo-spatial proximity.…”