Alcock_RCME_2009_mathematicians.pdf (255.96 kB)
Mathematicians' perspectives on the teaching and learning of proof
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.
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School
- Science
Department
- Mathematics Education Centre
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. 63-92Publisher
© American Mathematical Society, copublished with CBMS and in cooperation with the Mathematical Association of AmericaVersion
- AM (Accepted Manuscript)
Publication date
2010Notes
This is a chapter from a book and is available here with permission from the American Mathematical Society.ISBN
9780821849965Book series
CBMS Issues in Mathematics Education;Volume 16Language
- en
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