Date of Award

Fall 2001

Project Type

Dissertation

Program or Major

Mathematics Education

Degree Name

Doctor of Philosophy

First Advisor

Karen Graham

Abstract

The purpose of this study was to investigate the manner by which students enrolled in an integrated Calculus/Physics course use their understanding of physics to inform their conceptualizations of calculus concepts. This study utilized a multiple case study design with analysis by and across cases. The cases represent eight first year students in the College of Engineering and Physical Sciences at the University of New Hampshire who enrolled in an integrated calculus/physics program. Data was gathered in a three-part process: (1) Semi-structured task-based interviews, (2) Participant-observation in the calculus/physics course, and (3) Obtaining copies of students' in-class notes, in-class activities, homework assignments, and examinations.

A series of tasks designed to elicit information about students' conceptualizations of average rate of change, derivative, integral, and the Fundamental Theorem of Calculus were developed and pilot-tested by the researcher. To further corroborate the information gathered through the interview tasks, the students' examination, homework assignments, and in-class activities were reviewed. A description of each students' concept image was developed by analyzing the students' responses to interview tasks and triangulated with student-produced concept maps, observation of students in class, and students' homework, performance on examinations, and class work. A second layer of analysis resulted in the emergence of a classification scheme that describes how the students use physics to inform their conceptualization of calculus concepts, if at all. Finally, by searching individual student descriptions for patterns and similarities, a general description for the interactions between concept image and classification was proposed.

The results from this research investigation suggest that students frequently use physics concepts to construct meaningful conceptualizations of average rate of change. However, the students less frequently draw upon physics concepts to inform their conceptualizations of derivative and integral. The results from this research investigation also suggest that the students participating in this study possess richer conceptualizations of calculus concepts that what has previously been reported in the literature.

Hypotheses and questions for further investigation of students' uses of physics concepts to inform their conceptualizations of calculus concepts are generated. Implications for teaching practice and curriculum development are suggested and discussed.

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