THE ROLE OF ERROR ANALYSIS, DIAGNOSTIC GRADING PROCEDURES, AND STUDENT REFLECTION IN FIRST SEMESTER CALCULUS LEARNING (EPISTEMOLOGY, METACOGNITION, INQUIRY)
The present study is an integrative study designed to explore the nature of student difficulties within the context of a first semester college calculus course. The techniques of error analysis were used to identify and categorize the student difficulties. Insights gained from this categorization served as the basis for the design and development of calculus grader preparation materials implemented with a subgroup of undergraduate calculus graders. These grader preparation materials emphasized grader diagnosis of student difficulties and student reflection on errors and process. Current preparation procedures served as the control on the basis of which comparisons and evaluations were made. Questions regarding the relationship between these materials, the grading environment established by their implementation, and the factors of SEX, COLLEGE, student reflection, and calculus achievement, were investigated. Achievement scores as measured by calculus unit tests and a calculus final examination were collected on all subjects. A reflection attitude scale was administered to all students and graders participating in the study. Univariate analyses of variance of the unit test scores and the final examiniation revealed a significant effect of COLLEGE on the first and second try for Unit 4 and the final examination. A significant SEX x GRADING FORMAT interaction, indicating a more positive influence of the treatment grading format for men than for women, was found on the second try for Unit 4. The effect of GRADING FORMAT fell just short of significance on the final examination, suggesting the possibility that the effect is cumulative. A multivariate analysis of co-variance indicated a significant main effect for COLLEGE. A log-linear analysis of the distractor choices on the 40-item multiple choice final examination indicated several significant main effects and interactions on several of the items. Results of the analysis performed on a grader reflection attitude scale suggest that a difference in attitude, commitment, and use of the constructive grading procedures existed between the treatment and control graders. Hypotheses and questions suitable for future research in the areas of error analysis, teacher training, and student reflection are generated.
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