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Title: Mathematicians' perspectives on the teaching and learning of proof
Authors: Alcock, Lara
Issue Date: 2010
Publisher: © American Mathematical Society, copublished with CBMS and in cooperation with the Mathematical Association of America
Citation: ALCOCK, L., 2010. Mathematicians' perspectives on the teaching and learning of proof. IN: Hitt, F., Holton, D. and Thompson, P. (eds). Research in Collegiate Mathematics Education VII, pp. 63-92
Series/Report no.: CBMS Issues in Mathematics Education;Volume 16
Abstract: This paper reports on an exploratory study of mathematicians' views on the teaching and learning that occurs in a course designed to introduce students to mathematical reasoning and proof. Based on a sequence of interviews with five mathematicians experienced in teaching the course, I identify four modes of thinking that these professors indicate are used by successful provers. I term these instantiation, structural thinking, creative thinking and critical thinking. Through the mathematicians' comments, I explain these modes and highlight ways in which students sometimes fail to use them effectively. I then discuss teaching strategies described by the participants, relating these to the four modes of thinking. I argue that teaching aimed at improving structural thinking tends to dominate, and that courses that introduce proof, regardless of classroom organization, should address all four modes in a balanced and integrated way.
Description: This is a chapter from a book and is available here with permission from the American Mathematical Society.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/8946
ISBN: 9780821849965
Appears in Collections:Book Chapters (Mathematics Education Centre)

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