Computer Algebra Systems (CAS), a powerful mathematical software currently available on hand held calculators, is becoming increasingly available to assist secondary students learn school mathematics. This study investigates how two teachers taught introductory differential calculus to their Year 11 classes using multiple representations in a CAS-supported curriculum. This thesis aims to explore the impact of the teaching on students’ understanding of the concept of derivative. / Understanding of the concept of derivative was gauged using an innovative Differentiation Competency Framework that was developed to describe understanding of the concept of derivative. It consists of eighteen competencies for formulation and interpretation of derivatives with, and without, translation between different representations. It clarified the objectives of the curriculum, purpose for using particular CAS activities, and also guided the construction of individual test items on the Differentiation Competency Test that enabled individual and class learning about the concept of derivative to be identified. / The Framework also helped identify each teacher’s privileging characteristics and facilitated analysis of the learning in relation to the teaching. / This study found that using multiple representations was important in developing understanding of the concept of derivative but that the graphical and the symbolic representations were the most useful and important to emphasize and link. / Analysis of the teaching actions showed that the teachers used CAS in ways that were consistent with their teaching approach and preferred use of representations and that a conceptual teaching method and student-centred style supported understanding of the concept of derivative. / Teaching is directly linked to learning and each class developed a different understanding of the concept of derivative that related to the combined effect of their teacher’s privileging characteristics: calculus content, teaching approach, and use of CAS. This study also shows that if a CAS-supported curriculum is to be successfully implemented, it needs to acquire institutional status including a corresponding change in assessment to legitimize new teaching practices.

The purposes of this study were (a) to develop, implement, and evaluate a computer-oriented instructional program for introductory calculus students, and (b) to explore the association between a computer-oriented calculus instructional program, a non-computer-oriented calculus instructional program, student achievement on three selected calculus topics, and student attitude toward mathematics. An experimental study was conducted with two groups of introductory calculus students during the Spring Semester, 1989. The computer-oriented group consisted of 32 students who were taught using microcomputer calculus software for in-class presentations and homework assignments. The noncomputer-oriented group consisted of 40 students who were taught in a traditional setting with no microcomputer intervention. Each of three experimenter-developed achievement examinations was administered in a pretest/posttest format with the pretest scores being used both as a covariate and in determining the two levels of student prior knowledge of the topic. For attitude toward mathematics, the Aiken-Dreger Revised Math Attitude Scale was administered in a pretest/ posttest format with the pretest scores being used as a covariate. Students were also administered the MAA Calculus Readiness Test to determine two levels of calculus prerequisite skill mastery. An ANCOVA for achievement and attitude toward mathematics was performed by treatment, level, and interaction of treatment and level. Using a .05 level of significance, there was no significant difference in treatments, levels of prior knowledge of topic, nor interaction when achievement was measured by each of the three achievement examination posttests. Furthermore, there was no significant difference between treatments, levels of student prerequisite skill mastery, and interaction when attitude toward mathematics was measured, at the .05 level of significance. It was concluded that the use of the microcomputer in introductory calculus instruction does not significantly effect either student achievement in calculus or student attitude toward mathematics.