A quantitative and covariational reasoning investigation of students’ interpretations of partial derivatives in different contexts

Abstract

This paper extends work in the areas of quantitative reasoning and covariational reasoning at the undergraduate level. Task-based interviews were used to examine third-semester calculus students’ reasoning about partial derivatives in five tasks, two of which are situated in a mathematics context. The other three tasks are situated in real-world contexts (i.e. weight, revenue, and mortgage). There are three main findings from this study. First, interpreting quantities representing partial derivatives in real-world contexts was problematic for most of the students. Second, students’ interpretations of partial derivatives were not consistent across tasks. Third, all the students engaged in several levels of covariational reasoning when interpreting quantities representing partial derivatives in the context of weight, revenue, and mortgage. Implications for calculus instruction and directions for future research are included.

KEYWORDS:

• Quantitative reasoning
• covariational reasoning
• partial derivatives
• rates of change
• calculus

Acknowledgments

I extend sincere thanks to the reviewers for the RUME 2020 conference for their insightful feedback on a previous draft of this paper that appeared in Mkhatshwa (2020b).

Disclosure statement

No potential conflict of interest was reported by the author.