RUME_2014_LogicPredicts_final.pdf (200.37 kB)
Download fileThe ability to reject invalid logical inferences predicts proof comprehension and mathematics performance
conference contribution
posted on 2014-05-13, 12:10 authored by Lara AlcockLara Alcock, Toby Bailey, Matthew InglisMatthew Inglis, Pamela DochertyIn this paper we report a study designed to investigate the impact of logical reasoning ability on
proof comprehension. Undergraduates beginning their study of proof-based mathematics were
asked to complete a conditional reasoning task that involved deciding whether a stated
conclusion follows necessarily from a statement of the form “if p then q”; they were then asked
to read a previously unseen proof and to complete an associated comprehension test. To
investigate the broader impact of their conditional reasoning skills, we also constructed a
composite measure of the participants’ performance in their mathematics courses. Analyses
revealed that the ability to reject invalid denial-of-the-antecedent and affirmation-of-theconsequent
inferences predicted both proof comprehension and course performance, but the
ability to endorse valid modus tollens inferences did not. This result adds to a growing body of
research indicating that success in advanced mathematics does not require a normatively correct
material interpretation of conditional statements.
History
School
- Science
Department
- Mathematics Education Centre
Citation
ALCOCK, L. ... et al, 2014. The ability to reject invalid logical inferences predicts proof comprehension and mathematics performance. Presented at: 17th Conference on Research in Undergraduate Mathematics Education, Denver, CO, USA, 27th February - 1st March 2014.Publisher
Special Interest Group of the Mathematical Association of American on Research in Undergraduate Mathematics Education (SIGMAA on RUME)Version
- AM (Accepted Manuscript)
Publication date
2014Notes
This is a conference paper.Language
- en