Date of Award

1-2026

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School

College of Science and Mathematics

Department/Program

Mathematics

Thesis Sponsor/Dissertation Chair/Project Chair

Steven Greenstein

Committee Member

Jonathan Cutler

Committee Member

Eileen Fernandez

Abstract

Students often struggle to connect the conceptual meaning of the derivative with the symbolic structures of Leibniz (dy/dx) notation. Although symbol sense has been described as the coordination of mathematical concepts, signs, and objects, little is known about how instruction can purposefully support students in developing symbol sense for the derivative. This study addresses this gap by designing and examining a learning approach aimed at helping students construct the relational structures underlying derivative notation. Using design research methodology, the study engaged intact algebra, precalculus and calculus classes in a suburban New Jersey high school across iterative cycles of design, implementation, and analysis. The instructional activities centered on embodied experiences in creating tangent lines, supported by semiotic theory to analyze students’ sense-making. A semiotic epistemological triangle was introduced as an analytic tool for identifying connections students formed among geometric representations, the concept of instantaneous rate of change, and particularly Leibniz notation. Findings indicate that the approach effectively supported students’ development of symbol sense for the derivative and that the semiotic triangle offers a productive framework for making this development observable. Implications for curriculum design, classroom practice, and future research are discussed.

File Format

PDF

Download

Included in

Mathematics Commons

Share

COinS