TY - JOUR
T1 - Undergraduates’ Example Use in Proof Construction
T2 - Purposes and Effectiveness
AU - Alcock, Lara
AU - Weber, Keith
N1 - Publisher Copyright: © 2010, © 2010 by The Research Council on Mathematics Learning. All rights reserved.
PY - 2010
Y1 - 2010
N2 - In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully constructing proofs, and that these purposes are consistent with those described by mathematicians. We then examine other cases in which students used examples ineffectively. We note that in these cases, the purposes for which the students attempted to use examples are again appropriate, but the implementation of their strategies is inadequate in one of two specific ways. On this basis we identify points that should be borne in mind by a university teacher who wishes to teach students to use examples effectively in proof-based mathematics courses.
AB - In this paper, we present data from an exploratory study that aimed to investigate the ways in which, and the extent to which, undergraduates enrolled in a transition-to-proof course considered examples in their attempted proof constructions. We illustrate how some undergraduates can and do use examples for specific purposes while successfully constructing proofs, and that these purposes are consistent with those described by mathematicians. We then examine other cases in which students used examples ineffectively. We note that in these cases, the purposes for which the students attempted to use examples are again appropriate, but the implementation of their strategies is inadequate in one of two specific ways. On this basis we identify points that should be borne in mind by a university teacher who wishes to teach students to use examples effectively in proof-based mathematics courses.
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U2 - https://doi.org/10.1080/24727466.2010.11790298
DO - https://doi.org/10.1080/24727466.2010.11790298
M3 - Article
SN - 1947-7503
VL - 3
SP - 1
EP - 22
JO - Investigations in Mathematics Learning
JF - Investigations in Mathematics Learning
IS - 1
ER -