About the Teaching and Learning of Differentiability for Piecewise Functions in Science Degrees’ First-Year Calculus Courses

Abstract

In this work, we present an issue we have observed over the last several years in the first year ofSpanish science degrees’ (such as mathematics, physics or engineering) calculus courses. It is related to the studyof differentiability of piecewise one real variable real functions at a point. We have analyzed how students studythe differentiability of piecewise functions at a point, explaining the students’ work and reasoning and commentingabout the common misunderstandings we have found. Then, we have researched about how to help the studentsin their learning process related to this calculus concept, and we have also used several activities or ways to work:student meeting groups to talk about their worries and misunderstandings, mathematical definitions, explanationsand theory and also working out specific examples.