Developing Basic Principles of Calculus and Motion in Lower Secondary Education

The use of carefully selected contexts can help students in providing meaning, purpose, and relevancy to mathematical concepts and skills. Moreover, contexts can show the relevance of mathematics and support students in building mathematical knowledge on their intuitions and inventions. This use of contexts—from science—is illustrated with three cases on teaching and learning basic principles of calculus. Each case explores the potential of contexts involving modeling activities where motion plays an important role. The aim is to ground the concepts in students’ understanding of everyday-life motion. A central design heuristic for these activities is the emergent modeling principle. According to this heuristic, when working in a learning situation students develop and connect representations, whereby these representations ideally begin as informal context-based models before developing into generalized mathematical models. In this approach, the calculus concepts and skills develop in a dialectic relationship with context-based ideas and intuitions from the physics of motion. The importance of meaningful connections between calculus and physics is further grounded in (theoretical) ideas exploring the potential of inquiry-based learning, sensory-motor experiences, and embodied cognition. As a conclusion, we will argue that the connections with—and interactions within—meaningful contexts are fundamental for meaningful mathematics education