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Title: Referential and syntactic approaches to proving: case studies from a transition-to-proof course
Authors: Alcock, Lara
Weber, Keith
Issue Date: 2010
Publisher: © American Mathematical Society, copublished with CBMS and in cooperation with the Mathematical Association of America
Citation: ALCOCK, L. and WEBER, K., 2010. Referential and syntactic approaches to proving: case studies from a transition-to-proof course. IN: Hitt, F., Holton, D. and Thompson, P. (eds). Research in Collegiate Mathematics Education VII, pp. 93-114
Series/Report no.: CBMS Issues in Mathematics Education;Volume 16
Abstract: The goal of this paper is to increase our understanding of different approaches to proving in advanced mathematics. We present two case studies from an interview-based investigation in which students were asked to complete proof-related tasks. The first student consistently took what we call a referential approach toward these tasks, examining examples of the objects to which the mathematical statements referred, and using these to guide reasoning. The second consistently took what we call a syntactic approach toward these tasks, working logically with definitions and proof structures without reference to examples. Both students made substantial progress on each of the tasks, but they exhibited different strengths and experienced different difficulties. In this paper we: demonstrate consistency in these students' approaches across a range of tasks, examine the different strengths and difficulties associated with their approaches to proving, and consider the pedagogical issues raised by these apparent student preferences for reasoning in certain ways.
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/2134/8945
ISBN: 9780821849965
Appears in Collections:Book Chapters (Mathematics Education Centre)

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