Mental mechanism of synthesis in the learning of the Sierpinski triangle as a totality
Abstract
Fractal geometry constitutes a field of study that integrates several concepts of school mathematics, among them, perimeter, area, self-similarity, iteration, succession, functions and infinity. Thus, the fractal Sierpinski triangle is chosen with the aim of proposing a cognitive model for its learning. Based on the APOS theory (action, process, object and scheme), mental structures and mechanisms that can be constructed by high school students who develop a sequence of written activities are described. The empirical results report that the fractal under study is built as a totality from a mental mechanism that has been called synthesis, a mechanism that could open new development opportunities for the APOS theory.
Keywords
Educational Mathematics, Sierpinski triangle, APOS theory, Totality, Synthesis mechanismReferences
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