Non-formal mechanisms in mathematical cognitive development: The case of arithmetic

Cognition
David W BraithwaiteDavid Landy

Abstract

The idea that cognitive development involves a shift towards abstraction has a long history in psychology. One incarnation of this idea holds that development in the domain of mathematics involves a shift from non-formal mechanisms to formal rules and axioms. Contrary to this view, the present study provides evidence that reliance on non-formal mechanisms may actually increase with age. Participants - Dutch primary school children - evaluated three-term arithmetic expressions in which violation of formally correct order of evaluation led to errors, termed foil errors. Participants solved the problems as part of their regular mathematics practice through an online study platform, and data were collected from over 50,000 children representing approximately 10% of all primary schools in the Netherlands, suggesting that the results have high external validity. Foil errors were more common for problems in which formally lower-priority sub-expressions were spaced close together, and also for problems in which such sub-expressions were relatively easy to calculate. We interpret these effects as resulting from reliance on two non-formal mechanisms, perceptual grouping and opportunistic selection, to determine order of evaluation. Criti...Continue Reading

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Citations

Jul 13, 2016·Topics in Cognitive Science·Robert L Goldstone, Gary Lupyan
Feb 10, 2017·Cognitive Research: Principles and Implications·Tyler MarghetisRobert L Goldstone
Apr 16, 2019·Frontiers in Psychology·Jung Yeon ParkWim Van Den Noortgate
Mar 2, 2018·Journal of Intelligence·Abe D HofmanHan L J Van der Maas
Nov 22, 2016·Topics in Cognitive Science·Han L J van der Maas, Enkhbold Nyamsuren

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