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Impact of Maple™ on the Design, Instruction and Performance in an Undergraduate Physics Mathematical Methods Course

by

Alan P. Runge

A DISSERTATION

Presented to the Faculty of

The Graduate College at the University of Nebraska

In Partial Fulfillment of Requirements

For the Degree of Doctor of Philosophy

Major: Interdepartmental Area of Administration, Curriculum and Instruction

Under the Supervision of Professor David W. Brooks

Lincoln, Nebraska

July, 1997

Chapter/Section Links:

  • Abstract
  • Table of Contents & List of Figures and Tables
  • Chapter 1: Introduction
  • Chapter 2: Procedure
  • Chapter 3: Study Outcomes
  • Chapter 4: Relation of Outcomes to the Literature
  • Notes
  • References
  • Appendix A: Research Protocol Forms
  • Appendix B: IRB Consent Forms
  • Appendix C: Hierarchical Coding Scheme
  • Appendix D: Examples of Maple Materials and Examinations
  • Appendix E: Listing of Maple Commands Explained and Used in Class

    • ABSTRACT

    IMPACT OF MAPLE™ ON THE DESIGN, INSTRUCTION AND PERFORMANCE IN AN UNDERGRADUATE PHYSICS MATHEMATICAL METHODS COURSE

    Alan Paul Runge, Ph.D.

    University of Nebraska, 1997

    Advisor: David W. Brooks

    A traditional undergraduate physics course on mathematical methods has been redesigned to incorporate the use of Maple™, a computer algebra program, during all aspects of the course. Topics covered were: complex number theory; series approximations; matrix theory; partial differentiation; vector algebra; and vector calculus. Five undergraduate students were enrolled, from sophomore to senior in academic class standing. A qualitative case study methodology was used to describe the changes in the course design resulting from the incorporation of Maple™ and their impact on the instruction of the course, and to determine the effects on the studentsí learning and development of problem solving skills in physics using Maple™ as a problem solving tool. The impact of using Maple™ on the number and types of interactions is presented. The entire semester long course was included in this study. Each class session is described in detail. Examples of the Maple™ materials used are given.

    The use of the Maple™ program was allowed on all homework and exams with each student having their own computer during class. Constraints were made so that the assessment emphasis remained on the mathematics and the conceptual understanding of the problem solving methods. All of the students demonstrated some level of proficiency in using Maple to solve the assigned problems. Strategies for effectively using Maple were presented and were individualized by the students. The students reported positive and negative impacts of using Maple™. All of the students satisfactorily completed the course requirements, receiving final course grades from B to A+. All of them continued to voluntarily use Maple™ during the following semester.

    Instructional methods used included various lecture techniques without Maple™ assistance, lectures and demonstrations using only Maple™, and student tasks assigned in class worked with the aid of Maple™. Maple™ was used in one of these aspects in all but 3, out of 45, class periods. The use of Maple™ constituted about half of the overall class time.