Teaching the Representations of Concepts in Calculus: The Case of the Intermediate Value Theorem

This paper offers instructional interventions designed to support undergraduate math students’ understanding of two forms of representations of Calculus concepts, mathematical language and graphs. We first discuss issues in students’ understanding of mathematical language and graphs related to Calculus concepts. Then, we describe tasks, which are situated in the context of the Intermediate Value Theorem, that are designed to promote students’ understanding of multiple quantifiers in mathematical statements, as well as outputs and points on graphs of functions in the Cartesian plane. We offer suggestions for instruction and include sample dialogue to illustrate how these tasks may be used in the classroom.