More than just the basic derivation formula: The impact of prior knowledge on the acquisition of knowledge about the concept of derivative

Based on process-object theories, knowledge about mathematical concepts can be viewed as having an operational and a structural aspect. Ideally, structural knowledge should build on operational knowledge. However, some students are not able to acquire enough operational knowledge and only acquire a pseudostructural conception of a mathematical concept (see Sfard, 1992). In this study with 144 grade 10 students from Germany we examine the effects of different areas of prior knowledge on the acquisition of knowledge about the concept of derivative. We found evidence that substantial knowledge about the concept of function, the concept of slopes of linear functions, and mathematical symbols is necessary to acquire mathematical knowledge about the concept of derivative that goes beyond a pseudostructural conception.