Conditional inference and advanced mathematical study |
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| Authors: | Matthew Inglis Adrian Simpson |
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| Institution: | (1) Learning Sciences Research Institute, University of Nottingham, Nottingham, UK;(2) School of Education, University of Durham, Durham, UK |
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| 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.
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| Keywords: | Advanced mathematical thinking Conditional inference Logic Reasoning Representation systems Theory of formal discipline |
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