Learners' difficulties in applying correct interpretations of mathematical concepts

Results of an interview study on basic ideas of the derivative and the integral

Abstract

Empirical findings indicate that high school students are often aware of correct interpretations of the concept of derivative and integral (e.g. derivative as tangent slope or integral as area under a curve). At the same time, the students are not able to apply these interpretations (successfully) in corresponding tasks. In order to explain this discrepancy between knowledge and application of the interpretations, three case studies from an interview study with learners in the qualification phase are presented. The results show a fragmentary understanding of the interpretations, an interpretation limited to specific contexts and a lack of basic knowledge as possible explanations.