Chapter 16: 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 in the model by Tall and Vinner (1981), were ascertained as well as the corresponding problem solving competence. Participants in this study were 24students in grade 12 of a German secondary school. The results indicate that definitions play a marginal role in students’ learning whereby intuition inherent in concept images dominates the conceptual learning. Based on these subjective convictions,intended and realised knowledge may deviatefrom eachother and mightcause difficulties for students.