Dr. Alvarado-Martínez, Hugo

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.

This work aims to analyze the responses of a group of engineering students related to problems about tangents in a teaching learning process of derivative in a differential calculus course. The methodological design, oriented to a group of 161 students from two Chilean universities, considers different onto-semiotic configurations in problem-situations about tangents. The methodology implemented integrates information and communication technologies in differentiated activities, favoring the use of languages and progressive approach to the meaning of the derivative. The exploratory-type analysis was carried out applying some tools of the ontosemiotic Approach of mathematical knowledge and instruction. Difficulties were found in the concept of function and the Euclidean conception of the tangent line, which brings with it a weak interpretation of the derivative function and its geometric representation. It is concluded that the implementation of the geometric interpretation through information and communication technologies makes it possible to improve the teaching of the derivative.