A perceptual account of symbolic reasoning

Landy, David; Allen, Colin; Zednik, Carlos

doi:10.3389/fpsyg.2014.00275

Cited by 48 publications

(44 citation statements)

References 53 publications

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“…Mathematics is too recent a cultural development for humans to have evolved mathematics-specific neural resources. Human mathematical abilities will need to rely on evolutionarily older capacities, recycled for new purposes (Anderson, 2015; Dehaene & Cohen, 2007; Landy, Allen, & Zednik, 2014). Could our perceptual systems be one of those recycled resources?…”

Section: Introductionmentioning

confidence: 99%

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

2016

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Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system—in particular, object-based attention—is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions—but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

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Section: Introductionmentioning

confidence: 99%

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

2016

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“…Applying proximity to typed symbols may also be quite natural to many readers, given that adjacent letters in words written in, for example, the modern English alphabet are typically more closely spaced than adjacent letters in different words. Although we used proximity exclusively in the experiments presented below, other principles of perceptual organization can also be applied (although perhaps less naturally) to the grouping of symbols in arithmetic expressions (Landy, Allen, & Zednik, 2014). Though the Gestalt principles are traditionally considered in the context of organization of visual or auditory scenes, even early Gestalt theorists saw the same principles as widely applicable to general problem solving (see, e.g., Ohlsson, 1984).…”

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confidence: 99%

Persistent perceptual grouping effects in the evaluation of simple arithmetic expressions

Rivera

Garrigan

2016

Mem Cogn

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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. We replicated this result (Exp. 1) and investigated whether perceptual grouping effects persist when the visual stimulus is presented briefly and then masked (Exp. 2) and when verbal recoding is encouraged through vocal expression (Exp. 3). We found that perceptual-grouping effects persisted in the masking condition, suggesting that the mental representations of arithmetic expressions retain visuospatial characteristics. Similarly, verbalization of the expressions did not eliminate perceptualgrouping effects, suggesting that participants were not verbally recoding. In sum, the persistent effects of unit formation and spatial attention emphasize the importance of perceptual processing in the development of human expertise in this domain.

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“…Landy and Goldstone (2007) showed that features such as similarity or connectedness affect performance in algebraic problems. Although Landy et al (2014) interpret these results with respect to the SNA, they may also be understood with reference to general rules of perception, that is, the Gestalt law of proximity (Wertheimer, 1923) and other domain-general factors. Namely, performance in such calculation tasks can be modulated by perceptual factors (influencing visual grouping of the stimuli presented) that affect performance in classical tasks assessing cognitive control (e.g., executive attention tasks).…”

Section: Visual Groupingmentioning

confidence: 99%

Bringing Back the Balance: Domain-General Processes Are Also Important in Numerical Cognition

et al. 2017

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A perceptual account of symbolic reasoning

Cited by 48 publications

References 53 publications

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

Mastering algebra retrains the visual system to perceive hierarchical structure in equations

Persistent perceptual grouping effects in the evaluation of simple arithmetic expressions

Bringing Back the Balance: Domain-General Processes Are Also Important in Numerical Cognition

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