Calculus students' quantitative reasoning in the context of solving related rates of change problems

Despite the increasing amount of research on students' quantitative reasoning at the secondary level, research on students' quantitative reasoning at the undergraduate level is scarce. The present study used task-based interviews to examine 16 high-performing undergraduate calculus student...

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Published inMathematical thinking and learning Vol. 22; no. 2; pp. 139 - 161
Main Author Mkhatshwa, Thembinkosi P.
Format Journal Article
LanguageEnglish
Published Philadelphia Routledge 02.04.2020
Taylor & Francis Ltd
Subjects
Calculus
College Mathematics
Context
Differentiation
Geometry
Individualized Instruction
Logical Thinking
Problem Solving
Qualitative analysis
Quotients
Reasoning
Students
Undergraduate Students
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Summary:Despite the increasing amount of research on students' quantitative reasoning at the secondary level, research on students' quantitative reasoning at the undergraduate level is scarce. The present study used task-based interviews to examine 16 high-performing undergraduate calculus students' quantitative reasoning in the context of solving three related rates of change problems-two geometric and one non-geometric. A qualitative analysis of verbal responses and work written by the students when solving the three problems revealed that 15 students created and used diagrams to support their quantitative reasoning in the geometric problems, and that the creation of these diagrams helped the students to solve the two problems. In addition, seven students exhibited lack of facility with the product or quotient rule of differentiation. We argue that the use of diagrams in calculus instruction at the undergraduate level could play an important role in supporting students' quantitative reasoning in topics that require students to make sense of relationships between quantities such as related rates of change problems. Furthermore, we argue that helping students develop greater facility with rules of differentiation such as the product or quotient rule could increase students' success in many calculus application problems, including related rates of change problems. Directions for future research are included.
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ISSN:1098-6065
1532-7833
DOI:10.1080/10986065.2019.1658055