Resumen de Didactic Engineering in the Study of the Sense of Variation of Functions: Preliminary Analysis

Noé Oswaldo Cabañas Ramírez, Edgardo Locia Espinoza, Armando Morales Carballo

• This paper shows the results of the epistemological and didactical analysis of the sense of variation of functions. Specifically, on the conceptions of growth and decay in a function that underlie the demonstrations of the theorem that links the sign of ??’ with the sense of variation of ??. The epistemological approach covered the years 1795 to 1912. It was identified that the conceptions of Fourier, Lagrange and Cauchy about growth and decay differ from the conception in the formal current definition; however, the posed procedures and definitions provide elements that foster reconstruction processes of the definitions and properties of increasing and decreasing functions.

  It is important to highlight that the current definition of growth and decay has a solid foundation on the definition made by Osgood in 1912. The didactical analysis identified that the current text books inherit some of the limitations and inconsistencies of the definitions found on the epistemological approach. The conflicting issues enhance the starting point for the development of a didactic engineering for the treatment of the sense of variation of a function at a preuniversity level.