Intuitive vs analytical thinking: four perspectives |
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| Authors: | Uri Leron and Orit Hazzan |
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| Institution: | (1) Department of Education in Technology and Science, Technion–Israel Institute of Technology, Haifa, Israel |
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| Abstract: | 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).
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| Keywords: | Mathematics education Cognitive psychology Evolutionary psychology Mathematical errors Rationality debate Dual process theory Medical diagnosis problem Bayesian thinking Base-rate neglect Group theory Lagrange's theorem |
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