Acquiring a concept and its subconcepts: Insights into the relevance of prerequisites for learning

Learning prerequisites play a significant role for achievement in mathematics. So far, the effect of such prerequisites throughout a whole teaching unit for a mathematical concept and its subconcepts has received little attention. For this reason, the present study examines the effects of learning prerequisites on achievement during a teaching unit on the concept of derivative implemented in 15 mathematics classrooms. For this, we administered a pretest, midterm tests, and posttest. The results highlight that prior knowledge, cognitive abilities, and subject-specific interest are key predictors for the overall concept. However, their effects on the subconcepts are more nuanced, with some predictors showing no influence for some subconcepts. This supports the knowledge-is-power hypothesis while revealing differential impacts at the subconcept.