An investigation of the results of a change in calculus instruction at the University of Arizona

The results of the change in Calculus instruction at the University of Arizona in 1991, 1992, and 1993 were examined using three complementary methods. A survey of students (45) who took calculus during this period was administered, and analyzed for attitudinal differences between those who took traditional and those who took reform calculus. There were no statistically significant differences in reported attitude. Volunteers (14) were solicited from those who had been freshmen during the change to participate in interviews. These interviews included students taught by each method, and were analyzed by using concept maps to determine if there is a difference in retained knowledge. Although consortium (reform) students showed slightly improved retention, the differences were not statistically significant. University computerized grade records were used to determine if there was a difference between students who took consortium calculus and those who took the traditional course. Both retention and grades in subsequent calculus-dependent mathematics, science, and engineering courses were examined. A pattern of comparisons emerged which showed that consortium students somewhat outperformed traditional students. The patterns were indicative of better teaching and cannot be directly attributed to the materials. There is good evidence that the consortium students were not at a disadvantage in subsequent course work. This research should be of interest to teachers of calculus, and those involved in calculus reform. The techniques and computer programs for analysis of large data sets for performance differences in subsequent (dependent) course work can be useful for comparing different instructors, procedures, or materials in large institutions