Alcock_weber_RCME_2009_cases.pdf (208.09 kB)
Referential and syntactic approaches to proving: case studies from a transition-to-proof course
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.
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- Mathematics Education Centre
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. 93-114Publisher
© 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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