A model to analyze the complexity of calculus knowledge at the beginning of University course

Abstract

Our research focuses on the difficulties students encounter with the learning of calculus, considering that they have to cope with many more mathematical objects but also with new ways of reasoning – not only algebraic calculation, but also the practice of approximation, and a scaffolding way of using functions, limits, derivative, integrals, etc. to justify their answers. The semiotic facet of new objects, and the way to manage it, is also a source of great difficulties. In this article we establish that the model we built (Bloch & Gibel, 2011) is adequate to describe the work of University students who have to deal with the resolution of exercises about parametric curves and differential equations, even if this context is not an adidactical situation. In 2018, L2 students of Pau University were asked to solve little problems about limits, integral calculations or recurrence questions. They revealed difficulties to organize their knowledge and conclude about a limit, for instance. We give some examples of these troubles. We conclude for the necessity to implement adequate devices to help students better understand these 'new mathematics'. Calculus, students' understanding of mathematical signs and objects, reasoning processes, parametric curves, differential equations