Date of Graduation
2016
Document Type
Dissertation
Degree Type
PhD
College
Eberly College of Arts and Sciences
Department
Mathematics
Committee Chair
Vicki L Sealey
Committee Co-Chair
Marjorie Darrah
Committee Member
Harvey Diamond
Committee Member
Nicole Engelke Infante
Committee Member
Scott A Myers
Abstract
The purpose of this dissertation is to examine how students define and think about the tangent line in first semester calculus and investigate the influence of these ways of thinking on their understandings of the derivative. Students' conceptions of the tangent line were explored through four primary tasks: defining and constructing tangent lines, sketching the derivative, and graphically interpreting the formal symbolic definition of the derivative. The first two tasks were designed to access students' knowledge of tangent lines, and the second two tasks drew upon their ability to apply this knowledge and connect the tangent line to the derivative. In this dissertation, I describe students' responses in terms of overlap or lack of overlap with how the tangent line and derivative are formally defined. The Tangent Line Framework of this dissertation and the Derivative Framework developed by Zandieh (2000) were used to structure this knowledge. The frameworks present a diagrammatic way to illustrate the understandings evidenced by the students and graphically contrast these for the concepts of tangent line and derivative. The results of this analysis revealed ways in which students' concept images of the tangent line and derivative relate.
Recommended Citation
Vincent, Brittany, "First Semester Calculus Students' Concept Definitions and Concept Images of the Tangent Line and How These Relate to Students' Understandings of the Derivative" (2016). Graduate Theses, Dissertations, and Problem Reports. 6876.
https://researchrepository.wvu.edu/etd/6876