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Formal notations are diagrams: Evidence from a production task
| Citations: | 12 - 3 self |
BibTeX
@MISC{L_formalnotations,
author = {Dav I D L and Robert L. Goldstone},
title = {Formal notations are diagrams: Evidence from a production task},
year = {}
}
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Abstract
Although a general sense of the magnitude, quantity, or numerosity of objects is common in both untrained people and animals, the abilities to deal exactly with large quantities and to reason precisely in complex but well-specified situations—to behave formally, that is—are skills unique to people trained in symbolic notations. These symbolic notations typically employ complex, hierarchically embedded structures, which all extant analyses assume are constructed by concatenative, rule-based processes. The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that some of the same cognitive resources involved in representing spatial relations and proximities are also involved in representing symbolic notations—in short, that formal notations are a kind of diagram. We examined self-generated productions in the domains of handwritten arithmetic expressions and typewritten statements in a formal logic. In both tasks, we found substantial evidence for spatial representational schemes even in these highly symbolic domains. It is clear that mathematical equations written in modern notation are, in general, visual forms and that they share some properties with diagrammatic or imagistic displays. Equations and mathematical expressions are often set off from the main text, use nonstandard characters and shapes, and deviate substantially from linear symbol placement. Furthermore, evidence indicates that at least some mathematical processing is sensitive to the particular visual form of its presentation notation (Cambell, 1999; McNeil & Alibali, 2004, 2005). Despite these facts, notational mathematical representation is typically considered sentential and is placed in opposition to diagrammatic representations in fields as diverse as education
Keyphrases
formal notation production task symbolic notation linear symbol placement behavioral measure substantial evidence spatial relation mathematical expression mcneil alibali particular visual form untrained people main text naturalistic task spatial representational scheme diagrammatic representation typewritten statement rule-based process self-generated production symbolic domain modern notation general sense mathematical equation imagistic display cognitive resource well-specified situation notational mathematical representation large quantity mathematical processing handwritten arithmetic expression presentation notation visual form formal logic nonstandard character primary goal embedded structure
