PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Calculus students’ deductive reasoning and strategies when working with abstract propositions and calculustheorems
Page: 608
In undergraduate mathematics, deductive reasoning is an important skill for learning theoretical ideas and is primarily characterized by the concept of logical implication. This plays roles whenever theorems are applied, i.e., one must first check if a theorem’s hypotheses are satisfied and then make correct inferences. In calculus, students must learn how to apply theorems. However, most undergraduates have not received instruction in propositional logic. How do these students comprehend the abstract notion of logical implication and how do they reason conditionally with calculus theorems? Results from our study indicated that students struggled with notions of logical implication in abstract contexts, but performed better when working in calculus contexts. Strategies students used (successfully and unsuccessfully) were characterized. Findings indicate that some students use “example generating” strategies to successfully determine the validity of calculus implications. Background on current literature, results of our study, further avenues of inquiry, and instructional implications are discussed.