Graduation Semester and Year

Spring 2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Dr. James A.M. Álvarez

Abstract

This study explores first-semester calculus students’ use of mathematical problem-solving strategies while working related rates of change problems in both an online homework format and a traditional pencil-paper format. We address two research questions: (1) How do students’ mathematical problem-solving strategies when working online homework on related rates of change problems compare with their problem-solving strategies when working paper-and-pencil homework related rates of change problems? (2) What influence does the ‘view an example’ feature in online homework have on a student’s problem-solving strategies when working an online RRC homework problem? Using scores on free-response midterm exam problems on related rates of change to select participants, we then conducted task-based interviews in which participants were asked to solve four (two paper-pencil and two online) related rates of change problems. Thematic analysis methods (Braun & Clarke, 2006) were used to analyze interview data recordings, transcriptions, and student work. In this setting, we identified more instances of problem-solving strategy use when participants engaged in the paper-pencil format related rates of change problems. In addition, instances of problem-solving strategy use by participants from the highest midterm score quartiles were higher than for those with scores in other quartiles represented. When participants used the ‘view an example’ online homework feature, fewer instances of problem-solving strategy use were identified. Four uses of the ‘view an example’ feature emerged from participant data: use to mimic, use to learn the process, use for sense-making, and non-use of the feature. The findings suggest that participants may be using features of online homework platforms on related rates of change problems in a manner that circumvents opportunities to engage in mathematical problem-solving.

Keywords

Problem-Solving, Related-Rates of Change, Calculus, Online Homework, View an Example, Traditional Homework

Disciplines

Educational Technology | Online and Distance Education | Other Mathematics

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