Ontwikkeling in verandering : ontwikkeling van wiskundige bekwaamheid van leerlingen met betrekking tot het concept afgeleide

Learning of mathematics Secondary school students have difficulty applying their mathematical knowledge to other school subjects. This problem has already been reported long ago for the concept of derivative. Students often do not relate their knowledge and skills learnt in mathematics lessons and, for example, physics or economics. The central question in my research is how students’ knowledge of the derivative concept develops. To this aim, ten students are followed two years from grade 10 to grade 12. Each half year I determined students’ knowledge about this topic and how students relate different school subjects. It seems that, shortly after a topic has been introduced in the classroom, students’ knowledge is often limited and fragmentary. Relations between school subjects, but also relations between concepts taught in one subject, are almost absent. After repetition and extension of the subject matter knowledge becomes more coherent. A certain period is needed between the moment of introduction of concepts in math classes, and the moment students use these concepts in a proficient way. Some students finally relate knowledge from different school subjects. For these students similarities in notations, visualisations and words act as bridges for creating relations between different school subjects. Teachers should mention such relations between school subjects more explicitly and give students opportunities to work on tasks to construct these relations personally. This should not be done occasionally, but requires a curriculum over a longer period in which concepts are repeated and extended.