Alcock_RCME_2009_mathematicians.pdf (255.96 kB)
Download file

Mathematicians' perspectives on the teaching and learning of proof

Download (255.96 kB)
chapter
posted on 14.10.2011, 13:53 by Lara AlcockLara Alcock
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.

History

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. 63-92

Publisher

© American Mathematical Society, copublished with CBMS and in cooperation with the Mathematical Association of America

Version

AM (Accepted Manuscript)

Publication date

2010

Notes

This is a chapter from a book and is available here with permission from the American Mathematical Society.

ISBN

9780821849965

Book series

CBMS Issues in Mathematics Education;Volume 16

Language

en

Usage metrics

Categories

Keywords

Exports