Date of Award

12-1993

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Dr. Christian R. Hirsch

Second Advisor

Dr. James Flanders

Third Advisor

Dr. Gerald Sievers

Fourth Advisor

Dr. Gary Chartrand

Abstract

The purposes of this study were to: (a) explicate the nature of symbol sense, (b) determine the differential effects of two computer algebra system (CAS) environments on students' development of symbol sense, (c) explore differences in symbol sense among students using a CAS and students not using a CAS, and (d) examine students' achievement in calculus with and without the use of a CAS.

Six sections of first-semester calculus at Western Michigan University during the 1992-93 academic year were used in the study. The investigator taught two CAS sections both semesters (n = 41, 34 Fall and n = 35, 34 Winter). Each semester a different professor who was recognized by students and the university for excellence in teaching taught a third comparison section (n = 39 and n = 36). The CAS sections used investigator-developed laboratory materials for MAPLE and THEORIST. The comparison sections followed a traditional lecture/discussion format which included the use of graphics calculators. Data were gathered from pre- and post-treatment administration of an investigator-developed test of symbol sense, from departmental comprehensive final exams, from a laboratory practical, and from 5 video-taped interviews with 4 students from each section.

Quantitative data were analyzed with the pretest as a covariate. The results indicated no significant differences among treatment groups on any of the criterion measures with the exception of a significant difference in favor of the comparison section over the THEORIST section on the Fall comprehensive final exam (p < .04).

The interviews suggested that the CAS students more frequently identified patterns and standard forms, while the traditional students were better able to modify standard procedures. The CAS students used comparative information not presented within the problem to guide judgments and strategy-making more often than the comparison students. For the THEORIST sections, this information was typically graphical in nature. The CAS students more often purposefully used the symbolic transformations of calculus than did the comparison students.

It was concluded that the manner of symbolic manipulation may not be a factor in students' development of symbol sense and that a laboratory approach to calculus may aid in students' broader development of symbol sense.

Comments

Fifth Advisor: Dr. Bert Waits

Access Setting

Dissertation-Open Access

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