Integrating computer algebra systems as an instructional aid in an introductory differential calculus course

Mathematicians in general claim that the Computer Algebra Systems (CAS) provide an excellent tool for illustrating calculus concepts. They caution, however, against heavy dependency on the CAS for all computational purposes without the mastery of the procedures involved. Very little empirical research exists to support these claims. The research that does exist uses CAS for all computational purposes and primarily focuses on integral calculus. This study examined the effect of using one of the CAS, Mathematica, as an instructional tool in enhancing the conceptual knowledge and problem solving abilities of students in a differential calculus course.; The research questions examined in this study were: (a) does the use of the CAB as an instructional tool enhance students' conceptual understanding of differential calculus, and (b) is there a difference in students' abilities to find critical numbers, inflection points, and relative extrema if the CAS is used as an instructional tool?; Topics of differential calculus were introduced by the traditional lecture method to both the control and experimental groups comprised of students enrolled in two sections of the Business and Life Sciences I course. Mathematics was used by the students of the experimental group to reinforce and illustrate the concepts developed by the traditional method. The experimental group was able to solve homework problems analytically, graphically, and numerically, whereas, the control group had to solve those problems using analytical methods only. A content analysis was conducted using the qualitative data obtained from students' explanations of the derivative of a function. The quantitative data, the students' test scores, were analyzed using ANCOVA. The ACT math subscores were used as the covariate.; The results showed that students in the experimental group scored statistically significantly higher than students in the control group on both the conceptual and the computational parts of the examination. The qualitative analysis results revealed that, compared to the control group, a higher percentage of students in the experimental group had a better understanding of the derivative. Based on the results of this study, integrating the CAS with the traditional method of teaching has the potential to affect calculus instruction positively.