PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
Calculus students’ understanding of logical implication and its relationship to their understanding of calculus theorems
Page: 405
In undergraduate mathematics, deductive reasoning is an important skill in the learning of theoretical ideas. Deductive reasoning is primarily characterized by the concept of logical implication (inferring what follows from a given premise). This plays a role whenever mathematical theorems are applied, i.e. one must first check if a theorem’s hypothesis is satisfied and then make a correct inference. In Calculus, students must learn how to apply theorems. However, most undergraduates have not yet received extensive training in propositional logic. How do these students comprehend the notion of logical implication and how does it relate to their understanding of theorems? Results from a pilot study indicated that students struggled with the notion of logical implication in both symbolic and Calculus contexts. However, findings were inconclusive regarding the relationship between the two areas. Background on the current literature, results of the pilot study, and further avenues of inquiry are discussed.