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Conditional inference and advanced mathematical study
journal contribution
posted on 2011-07-05, 10:24 authored by Matthew InglisMatthew Inglis, Adrian SimpsonMany 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.
History
School
- Science
Department
- Mathematics Education Centre
Citation
INGLIS, M. and SIMPSON, A., 2008. Conditional inference and advanced mathematical study. Educational Studies in Mathematics, 67 (3), pp. 187-204.Publisher
© SpringerVersion
- AM (Accepted Manuscript)
Publication date
2008Notes
The final publication is available at: www.springerlink.comISSN
0013-1954;1573-0816Publisher version
Language
- en
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