Date of Award

8-2026

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Marsh, Dalton

Abstract

Related-rates problems are a standard yet persistently difficult topic in first-semester calculus. Research increasingly recommends dynamic visualization tools such as GeoGebra, but direct comparisons of static and dynamic representations in related-rates settings remain scarce. This qualitative study examines how representation type shapes the quality of students' reasoning and their perceived experience during related-rates problem solving. Six mathematics students who had completed Calculus —a group of four undergraduates and a pair of graduate students—completed a static sliding-ladder task and a dynamic airplane-and-camera task supported by an interactive GeoGebra applet, followed by an interview. Findings indicate that the two representations supported reasoning in complementary rather than competing ways: the static diagram helped students organize the situation and recognize its structure, while the dynamic applet made motion and covariation directly observable. Students perceived the static task as easier but the dynamic task as more useful for understanding an unfamiliar situation, suggesting dynamic tools are most valuable when situations are unfamiliar.

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