PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Best Paper Award: Guiding reinvention of conventional tools of mathematical logic: Students’ reasoning about mathematical disjunctions
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Motivated by the observation that formal logic answers questions students have not yet asked, we conducted an exploratory teaching experiment with undergraduate students intended to guide their reinvention of truth-functional definitions for basic logical connectives. We intend to bridge the gap between reasoning and logic by inviting students to ask and answer questions that motivate logic as an objective science. We present categories of student strategies for assessing truth-values for mathematical disjunctions. Students’ reasoning heavily reflected content-specific and pragmatic factors in ways inconsistent with the norms and conventions of mathematical, formalized logic. Despite this, all student groups reinvented the standard truth-functional definition for non-quantified disjunctions once they began reasoning about logic by attending to logical connectives and by comparing their interpretations across various disjunctions. Students struggled to develop generalizable tools for assessing quantified disjunctions because they explored sets of examples in context-dependent ways.