Argumentos variacionales en la comprensión de la concavidad en gráficas de funciones

Abstract

The purpose of this article is to report the meanings of concavity taking into accounts such situations that favor the study of change in the graph of functions, so that it is useful to the teaching community and the student body for understanding this knowledge. Using elements of the socio-epistemological theory of educational mathematics and a qualitative methodology, we build a series of phases beginning with the problematization of mathematical knowledge, followed by the design and implementation of learning situations and, finally, the socialization of the materials and reflections with the teaching group. The situation is implemented with six female students and some similarities are found between their arguments and the contributions of the mathematician Agnesi in relation to the explanation of the turning point from the perspective of the study of variation. This allows us to report six ways of interpreting concavity in functions and reinforces the results presented by other authors