Fractals in the teaching-learning of the dynamic conception of the concept of limit of a sequence: a didactic proposal for students of the Bachillerato General Unificado (BGU)

Abstract

The objective of the present research was to design didactic tasks for the teaching-learning of the dynamic conception of the concept of limit of a sequence for students of Bachillerato General Unificado (BGU) through the use of fractals. The research is based on the Piagetian construct called Genetic Decomposition (GD) and on the Action-Process-Object-Object-Scheme (APOE) theory; it also considers the difficulties associated with the teaching and learning process of the concept of limit, as well as the numerical and symbolic representation systems. It has a qualitative approach, a descriptive level of depth. The final product of this work was a set of tasks framed in the constructs and mechanism of APOE theory that allow BGU students to deduce in terms of the limit of a sequence the dimensions of fractals such as the Set of Cantor, Koch's Snowflake, Carpet and Sierpinski's Triangle.