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Conditional inference and advanced mathematical study

Inglis, M.; Simpson, A.

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Authors

M. Inglis



Abstract

Many mathematicians and curriculum bodies have argued in favour of the theory of formal discipline: that studying advanced mathematics develops one’s ability to reason logically. In this paper we explore this view by directly comparing the inferences drawn from abstract conditional statements by advanced mathematics students and well-educated arts students. The mathematics students in the study were found to endorse fewer invalid conditional inferences than the arts students, but they did not endorse significantly more valid inferences. We establish that both groups tended to endorse more inferences which led to negated conclusions than inferences which led to affirmative conclusions (a phenomenon known as the negative conclusion effect). In contrast, however, we demonstrate that, unlike the arts students, the mathematics students did not exhibit the affirmative premise effect: the tendency to endorse more inferences with affirmative premises than with negated premises. We speculate that this latter result may be due to an increased ability for successful mathematics students to be able to ‘see through’ opaque representations. Overall, our data are consistent with a version of the formal discipline view. However, there are important caveats; in particular, we demonstrate that there is no simplistic relationship between the study of advanced mathematics and conditional inference behaviour.

Citation

Inglis, M., & Simpson, A. (2008). Conditional inference and advanced mathematical study. Educational Studies in Mathematics, 67(3), 187-204. https://doi.org/10.1007/s10649-007-9098-9

Journal Article Type Article
Publication Date Mar 1, 2008
Deposit Date Oct 28, 2010
Publicly Available Date Nov 22, 2010
Journal Educational Studies in Mathematics
Print ISSN 0013-1954
Electronic ISSN 1573-0816
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 67
Issue 3
Pages 187-204
DOI https://doi.org/10.1007/s10649-007-9098-9
Keywords Advanced mathematical thinking, Conditional inference, Logic, Reasoning, Representation systems, Theory of formal discipline,

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Accepted Journal Article (387 Kb)
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Copyright Statement
NOTICE: this is the author's version of a work that was accepted for publication in Educational studies in mathematics.





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