A Qualitative Document Analysis of Quantitative and Covariational Reasoning Opportunities Provided by Calculus Textbooks: The Case of Related Rates Problems Related rates problems: Calculus textbook research

Abstract

With a focus on related rates problems, the current study reports on quantitative and covariational reasoning opportunities provided by five widely used calculus textbooks in the United States. There are three major results from this study. First, quantitative reasoning opportunities are plentiful, while covariational reasoning opportunities are scarce in all the textbooks, respectively. Second, there is a severe shortage of related rates problems that require more than recalling geometric formulas to mathematize. Third, opportunities promoting the use of diagrams to support students’ quantitative reasoning when solving related rates problems are minimal in practice problems provided in the five textbooks. Overall, the textbooks provide limited opportunities to engage in covariational reasoning when working with related rates problems. Implications for instruction are discussed.