Integrating Intuition The Role Of Concept Image And Concept Definition For Students' Learning Of Integral Calculus

In this paper we analyze students' conceptual learning regarding the notion of the definite integral. By means of a comprehensive questionnaire, students' concept image and concept definition, as mentioned ill the model by Tall and Vinner (1981), were ascertained as well as the corresponding problem solving competence. Participants in this study were 24 students in grade 12 of a German secondary school. The results indicate that definitions play a marginal role ill Students' learning whereby intuition inherent ill concept images dominates the conceptual learning. Based on these subjective convictions, intended and realised knowledge may deviate from each other and might cause difficulties for students.