Intuitive vs Analytical Thinking: Four Perspectives

This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives—mathematics, mathematics education, cognitive psychology, and evolutionary psychology—each offering a different view on mathematical thinkin...

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Bibliographic Details
Published in:Educational studies in mathematics 2009-07, Vol.71 (3), p.263-278
Main Authors: Leron, Uri, Hazzan, Orit
Format: Article
Language:English
Subjects:
Algebra
Cognitive Processes
Cognitive Psychology
Education
Error Correction
Evolutionary psychology
Human nature
Humans
Logical theorems
Mathematical theorems
Mathematics
Mathematics Education
Mathematics Instruction
Mind
Misconceptions
Reasoning
Social evolution
Statistics
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Summary:This article is an attempt to place mathematical thinking in the context of more general theories of human cognition. We describe and compare four perspectives—mathematics, mathematics education, cognitive psychology, and evolutionary psychology—each offering a different view on mathematical thinking and learning and, in particular, on the source of mathematical errors and on ways of dealing with them in the classroom. The four perspectives represent four levels of explanation, and we see them not as competing but as complementing each other. In the classroom or in research data, all four perspectives may be observed. They may differentially account for the behavior of different students on the same task, the same student in different stages of development, or even the same student in different stages of working on a complex task. We first introduce each of the perspectives by reviewing its basic ideas and research base. We then show each perspective at work, by applying it to the analysis of typical mathematical misconceptions. Our illustrations are based on two tasks: one from statistics (taken from the psychological research literature) and one from abstract algebra (based on our own research).
ISSN:0013-1954
1573-0816
DOI:10.1007/s10649-008-9175-8