Cycles of understanding about the concepts of function and variation

Authors: Verónica Vargas Alejo, Aarón Víctor Reyes Rodríguez, César Cristóbal Escalante

Abstract : In this paper we analyze the relationship between the conceptual tools
(representations) used by students enrolled in a college tourism program, to
model a situation about cost of sending packages, and the cycles of understanding
that the students develop about the concepts of step function, function, and
variation. Based on the perspective of Models and Modeling, the questions that
guide the discussion are: What kind of representations did first semester students
use to describe and analyze problematic situations where the underlying model
is a step function? To what extent did the representations support the development
of different cycles of understanding of the concepts of function and variation?
The results show multiple representations that students construct, analyze, modify,
and refine. The representations helped to acquire meaning of mathematical
concepts as function and variation.

Key words: Understanding cycles, functions, step functions, modeling and variation.