EFFECTS OF CONCEPT-BASED INSTRUCTION ON STUDENTS' CONCEPTUAL UNDERSTANDING AND PROCEDURAL KNOWLEDGE OF CALCULUS

Abstract

ABSTRACT An original study, involving 305 college-level calculus students and 8 instructors, and its replication study, conducted at the same university and involving 303 college-level calculus students and 8 instructors, investigated the effects of instructional environment (concept-based vs. procedure-based) on students' conceptual understanding and procedural knowledge of calculus. Multiple achievement measures were used to determine the degree to which students from different instructional environments had mastered the concepts and the procedures inherent to first semester calculus. Achievement measures included two skills examinations designed to evaluate procedural competence and a midterm examination and a final examination both designed to evaluate procedural skills as well as conceptual understanding. The learning environment resulted in no significant differences in the students' abilities to employ procedural skills, as measured by the skills examinations. The students enrolled in the concept-based learning environment scored significantly higher than the students enrolled in the procedure-based learning environment on assessments that measured conceptual understanding as well as procedural skills (p < .001). The results of the replication study are consistent with the results of the original study, increasing the generalizability of the results. These results provide post-secondary level evidence that concept-based instructional programs can effectively foster the development of student understanding without sacrificing skill proficiency.