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Intuitive vs analytical thinking: four perspectives
Authors:Uri Leron and Orit Hazzan
Affiliation:(1) Department of Education in Technology and Science, Technion–Israel Institute of Technology, Haifa, Israel
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).
Contact Information Orit HazzanEmail:
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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