Calculus Students' Deductive Reasoning and Strategies when Working with Abstract Propositions and Calculus Theorems. Issue 2 (7th February 2021)

• Record Type: Journal Article
• Authors: Case, Joshua; Speer, Natasha
• Is Part Of: PRIMUS. Volume 31:Issue 2(2021)
• Page Start: 184
• Page End: 201
• Publication Date: 2021-02-07
• Subjects: Student thinking -- logic -- implication -- calculus -- theorems -- conditionals; Mathematics -- Study and teaching (Higher) -- Periodicals; 510.711
• DOI: 10.1080/10511970.2019.1660931
• Languages: English
• ISSNs: 1051-1970

Abstract

Abstract : In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students must learn to work with such statements; however, most have not studied propositional logic. How do these students comprehend the abstract notion of logical implication, and how do they reason conditionally with calculus theorems? Study results indicate that students struggle with logical implication in abstract contexts, but perform better when working in calculus contexts. Findings indicate that some students use "example generating" strategies to successfully determine the validity of calculus implications. We discuss ways instructors might support students' use of such strategies, as well as further avenues of inquiry.