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Exploring Student Adaptability to Various Conceptions of Difference in Calculus
Shive, Jude
Shive, Jude
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Calculus—Study and teaching, Mathematics—Study and teaching (Higher), Concept learning—Mathematics, Problem solving—Study and teaching (Higher), Mathematics—Philosophy
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Abstract
This honors thesis investigates how undergraduate students understand and adapt to multiple conceptions of subtraction within calculus contexts. Drawing on prior research identifying four models of subtraction—magnitude, takeaway-values, takeaway-segments, and translation—the study examines how precalculus and elementary education students represent differences across number line and function-based tasks. Using surveys and exploratory teaching interviews, the research analyzes how students interpret subtraction in increasingly complex mathematical settings, including difference quotients, function transformations, and area comparisons. Findings reveal that students most often rely on a takeaway-values conception rooted in early mathematical instruction, even when other models are more appropriate, and frequently adjust rather than fully switch representations. The study highlights a tension between procedural memorization and conceptual understanding, showing that students struggle to connect symbolic expressions with graphical meaning in calculus. Ultimately, the thesis argues for more flexible, multi-representational teaching approaches to subtraction in order to support deeper understanding of foundational calculus concepts.