Development of Variational Thinking for the Teaching of Preliminary Notions of Calculus. A Class Experience in Basic Education

Abstract

Background: This work incorporates results that help to understand how to favour the development of variational thinking and language in students of middle school education. Objective: to relate variational thinking with some preliminary notions of calculus. Design: a sequence of activities is presented to analyse variational aspects of the function concept and the results of its implementation. Setting and participants: the experience takes place in a middle and high school education institution with a sample of 40 students attending the 9 th grade. Data collection and analysis: a didactic sequence (DS) was elaborated from the results of a diagnostic test and applied to the students' group. The information collected from the application of the DS was submitted to an inductive analysis. Results: we focused our attention on the way in which the study variation processes allowed students to build meaningful approaches to understanding and using functions as models of change situations. Conclusions: despite the institutional limitations and the difficulties of the students, the development and emergence of variational arguments is observed in young people, based on previous knowledge that they relate to experiences of daily life.