The effects of writing in an applied calculus course: An analysis of performance and errors

This research study investigated the performance on a departmental final of students who wrote about their errors and misconceptions in complete sentences using correct mathematical terminology compared to students who did not write in complete sentences about their errors and misconceptions. The subjects in this study were primarily freshmen in six fall semester sections of Applied Calculus at a major university. The researcher taught the experimental and first control sections, while the four other sections were taught by four full-time faculty members. The statistical data was gathered from the departmental common final which had been given to all sections simultaneously. The experimental group was required to correct problems by identifying the errors made, describing the appropriate procedure to solve the problem using correct mathematical terminology, vocabulary, and complete sentences, and by providing a complete corrected solution with verification. The first control group's only requirement was to provide a complete corrected solution with verification. The remaining four sections of Applied Calculus, the second control group, had no requirements for correcting mistakes on their examinations. Both quantitative and qualitative methodologies were employed to analyze and describe the achievements of the students. For the quantitative analysis, the performance of the students was evaluated using the Wilcoxon rank sum test on the final scores from the departmental common final. From the statistical analyses, the experimental group performed on average significantly better than the second control group on the departmental common final. The experimental group also performed on average significantly better than the first control group on the departmental common final. There is statistical evidence the students in the first control group performed on average better than the second control on the departmental final. The qualitative portion of the study indicated the students in the experimental group who did through and complete error analyses did not repeat their conceptual errors on the final. The experimental and first control groups' test correction analyses indicated those who had conceptual errors on the final had a pattern of either incomplete or incorrect error analyses.