Meaning of the derivative as a rate of change through a graphic argumentation. A case with Chilean students

From the socio-epistemology perspective, the teaching of the derivative is problematized due to the lack of reference frameworks that give variational meanings to the derivative and allow its construction by means of graphical arguments. The objective of this research was to analyze the construction of meanings of the derivative, as a rate of change, that Chilean students developed through a graphic argumentation in a specific situation of variation. In order to respond to the stated objective, a qualitative methodology was used, consisting of a case study, where a situation of variation was designed with the purpose of promoting the analysis of temperature changes in specific everyday life phenomena. This design was applied to ten Chilean high school students interested in studying engineering. As a result of the research, it was obtained that the participants, through a graphic argumentation, understood the slope of a straight line as a rate of change of temperature regarding time. It was concluded that this research provides elements for the construction of frames of reference that signify the derivative, as a rate of change, in situations of variation, valuing the graphic arguments and functional justifications that emerged from the students.