A comparison study of students from two calculus sequences on their achievement in calculus-dependent courses

This study compared traditional calculus students and Calculus & Mathematica students on their achievement in courses which require calculus as a prerequisite. The first part of the study involved quantitative analyses of grades in calculus-dependent courses. The second part of the study was a qualitative analysis of six students in an introductory engineering: mechanics course. Task-based interviews were conducted over a ten-week period to investigate conceptual and procedural understanding of calculus and ability to apply that knowledge of calculus to engineering mechanics problems. The theoretical framework was based on the theory that active learning with a conceptual focus can enhance the decontextualization of knowledge, which can promote transfer.;Results from the quantitative analysis show a significant difference in a differential equations course favoring traditional students, and a significant difference in the first of a calculus-based physics sequence favoring the Calculus & Mathematica students. Other significant differences, favoring the top third of Calculus & Mathematica students, were found in the introductory physics courses and an engineering mechanics course. Results from the qualitative analysis showed that Calculus & Mathematica students were more likely to approach problems from a conceptual viewpoint of calculus knowledge whereas traditional students were more likely to approach problems procedurally. Students who had generalized and abstracted their understanding of the derivative and integral were better able to apply their calculus knowledge to engineering mechanics problems.