Symbols and the Bifurcation Between Procedural and Conceptual Thinking

Canadian Journal of Science, Mathematics and Technology Education - Tập 1 - Trang 81-104 - 2001
David Tall1, Eddie Gray1, Maselan Bin Ali1, Lillie Crowley1, Phil DeMarois1, Mercedes McGowen1, Demetra Pitta1, Marcia Pinto1, Michael Thomas1, Yudariah Yusof1
1University of Warwick, UK

Tóm tắt

Symbols occupy a pivotal position between processes to be carried out and concepts to be thought about. They allow us both to do mathematical problems and to think about mathematical relationships. In this article we consider the discontinuities that occur in the learning path taken by different students, leading to a divergence between conceptual and procedural thinking. Evidence will be given from several different contexts in the development of symbols through arithmetic, algebra, and calculus, then on to the formalism of axiomatic mathematics. This evidence is taken from a number of research studies recently conducted for doctoral dissertations at the University of Warwick by students from the United States, Malaysia, Cyprus, and Brazil, with data collected in the United States, Malaysia, and the United Kingdom. All the studies form part of a broad investigation into why some students succeed, while others fail.

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Thông tin xuất bản

Canadian Journal of Science, Mathematics and Technology Education

Tập 1

81-104

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