Date of Award

1994

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Educational Theory, Policy, and Practice

First Advisor

David Kirshner

Abstract

The purpose of this study is to examine the effects of the Computer-Intensive Algebra (CIA) and traditional algebra (TA) curricula on students' understanding of the function concept. CIA was developed recently in an effort to address some of the deficiencies in TA, namely, its over-emphasis of procedural skills and lack of attention to concepts and problem solving (Fey, 1992; Kieran, 1990). The major features of this innovative curriculum are (a) a problem solving approach based on the modelling and exploration of realistic problem situations, (b) an emphasis on conceptual knowledge, and (c) the extensive use of technology. This study hypothesizes that CIA students develop a richer understanding of functions than their TA counterparts while achieving at least the same level of procedural skill. A theoretical framework is proposed which describes a conceptual knowledge of functions in terms of the following components: (a) modelling a real-world situation using functions, (b) interpreting a function in terms of a realistic situation, (c) translating between different representations of functions, and (d) reifying functions. The subjects were university students enrolled in a College Algebra course. One section of this course was taught following the CIA curriculum and compared to the traditional sections. Instruments included pre and post tests on functions, attitude measures, researcher questionnaires, and the departmental final examination. Qualitative data were also collected via two sets of interviews conducted with students from each of the two curricula. The results indicated that the CIA students achieved a better overall understanding of functions and were better in the individual components of modelling, interpreting, and translating. No significant differences were found for reifying, which emerged as the most difficult in the function model for both groups. The data from the final examination were less definitive making it difficult to draw any definite conclusions about skill development. Other findings of interest were that the CIA students showed significant improvements in their attitudes and levels of anxiety toward mathematics. Also, the CIA class was rated as more interesting by the students and achieved a much higher percentage of students successfully completing the course.

Pages

357

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