A comparison of problem-solving abilities between reform calculus students and traditional calculus students

The purpose of this study was to evaluate the effects of CCH calculus instruction on problem solving achievement with the students enrolled in CCH sections as the experimental group and students enrolled in traditional curriculum sections as the control group. The major objective of the study was to determine whether the CCH or the traditional calculus students demonstrate greater problem solving achievement. Related objectives were to determine the specific strategies being used by the students who demonstrate better problem solving abilities, and what components of the students' problem solving procedures are consistent with demonstrated strengths or weaknesses in problem solving. The study was conducted with thirty-one students in the control group, receiving traditional instruction, and forty-one students in the experimental group, receiving CCH instruction. Each group worked the same five posttest problems as part of their final exam. The groups' performance on these problems was compared using a linear regression model, at the $\alpha$ =.05 significance level, with the postscore as the dependent variable, the prescore as the predictor variable and the instructional curriculum as the independent variable. It was shown that calculus students who received traditional instruction performed significantly better on a problem solving posttest than calculus students who received CCH instruction. Using the Mann-Whitney Rank Test, it was shown that calculus students who received traditional instruction used significantly more problem solving techniques on an applied maximum/minimum problem than calculus students who received CCH instruction. From the results of the Fisher Exact Test for 2 x 2 Tables, it was shown that the course completion rate, with a letter grade of "C" or better, was not significantly different for the two groups. Recommendations for further research were outlined. One recommendation was the inclusion of an interview component so that the researcher can ask subjects to provide a discussion of calculus concepts and their solutions to problems. A second recommendation was to track the success of students from the two instructional groups in subsequent mathematics and mathematics related courses.