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Euclid's Random Walk: Developmental Changes in the Use of Simulation for Geometric Reasoning
Author(s) -
Hart Yuval,
Mahadevan L.,
Dillon Moira R.
Publication year - 2022
Publication title -
cognitive science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.498
H-Index - 114
eISSN - 1551-6709
pISSN - 0364-0213
DOI - 10.1111/cogs.13070
Subject(s) - euclidean geometry , non euclidean geometry , visual reasoning , task (project management) , axiom , extrapolation , foundations of geometry , spatial intelligence , differential geometry , mathematics , computer science , cognitive psychology , artificial intelligence , psychology , geometry , projective geometry , statistics , management , economics
Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human's intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans' intuitive reasoning about Euclidean geometry. One‐hundred‐twenty‐five 7‐ to 12‐year‐old children and 30 adults completed a localization task in which they visually extrapolated missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even young children's visual extrapolations, only older children and adults reasoned about triangles in ways that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry may thus emerge when children abandon incorrect, axiomatic‐based reasoning strategies and come to reason using mental simulations of visual extrapolations.