Opportunity to learn about optimization problems provided by undergraduate calculus textbooks: A case study

Abstract

This study investigated opportunities to learn about optimization problems provided by undergraduate calculus textbooks. To accomplish this, we analyzed examples and practice problems from two calculus textbooks widely used in the teaching of calculus in the United States. Findings of this study indicate that a majority of the problems in both textbooks lack realistic and essential contexts, have matching or missing information, and require a low cognitive demand to solve. Setting up objective functions is either not necessary or it is straightforward for most problems in the two textbooks. In addition, both textbooks provide ample opportunities to interpret critical numbers and extrema in context. Overall, findings of this study suggest the existence of a relationship between known students’ difficulties with solving optimization problems and the opportunities to learn about optimization problems provided by calculus textbooks. Implications for several stakeholders, including calculus textbook authors and calculus instructors are discussed.