Characterization of sub-fields of derivative problems in engineering textbooks

This paper aims to characterize the subfields of problems emerging from problem-situations of the derivative in university textbooks proposed for the training of civil and commercial engineers. Thirteen textbooks used for the teaching of the derivative in the syllabi of different Chilean universities were qualitatively analyzed. The notion of epistemic configuration of the onto-semiotic approach to mathematical knowledge and education was used for this purpose. It is observed that a complex approach to the derivative is adopted in the textbooks considered. A total of 21 subfields of problems appear, although not all the textbooks extensively use subfields of derivative problems. The findings of this research establish relevant guidelines for the design of a specific didactic proposal to learn the construction of the derivative in engineering courses.