Problems about teaching-learning of differential of a function

摘要

A study in Coahuila shows that Bachelors and Masters students do have not much understanding of the concept of differentials and are confused about the concepts of differentials, derivatives and tangent of a function. We have done a detailed study of the didactic obstacles of the concept of differentials, the form in which the concept is treated in classrooms and the difficulties students face in understanding that it is possible to consider the variation of linear functions instead of the variation of the function in certain neighborhood of a point, since this is different for each point. We designed Worksheets for the construction of the concept of differentials with the help of technology, using GeoGebra for functions of one real variable and Matlab for functions of two real variables. They start by working on the visualizations, then questions, theoretical and practical problems, and finally lead to the formalization.