Introducir el concepto de función afín y lineal a partir de una tarea abierta en un entorno tecnológico

Abstract

The study focuses on analyzing how the mathematical work of eighth grade students (13 and 14 years old) develops in relation to linear and affine functions when faced with an open-ended task in a technological environment. The Mathematical Workspace Theory is used to study what students do. The research methodology responds to the phases of Didactic Engineering, which in its preliminary phase a curricular analysis is carried out that allows the design of the contextualized open task. In the first instance, students are faced with a task about the quotation of event rooms, which can be solved arithmetically. In the second instance, a collective discussion is carried out with the results obtained by the students, which allows the construction of the concepts of linear and affine function, which were implicit in the task. The results show a transition from an individual arithmetic mathematical work to a collective functional work guided by the teacher in charge and the role of the task in the platform to allow collective mathematical work.