A PROPOSAL FOR A FRACTAL -BASED ‘DYNAMIC’ PROGRAM: THE PYTHAGOREAN TREE STRUCTURE GENERATED THROUGH ‘INSTRUMENTAL’ SCHEMATA – International Journal of Research in Education Humanities and Commerce

A PROPOSAL FOR A FRACTAL -BASED ‘DYNAMIC’ PROGRAM: THE PYTHAGOREAN TREE STRUCTURE GENERATED THROUGH ‘INSTRUMENTAL’ SCHEMATA

Author: Stavroula Patsiomitou

ABSTRACT

This document primarily investigates the structure of the Pythagorean Tree, integrating my previous research and writings with earlier insights and contemporary ideas related to its fractal nature, which is produced through instrumental schemata. To illustrate the concept of instrumental schemata, I will present the example of Generator tools that can be created within dynamic geometry software environments. I will briefly discuss the van Hiele theory, which is crucial for classifying students based on their understanding and interpretation of geometric figures. In one section, I will investigate a fresh perspective on the Pythagorean tree, concentrating on the figures that arise when one carefully observes the empty spaces formed between the branches of the tree. Finally, I will delineate the essential elements of an innovative Fractal-based Dynamic Program (FDP) that I designed, developed and implemented. I will propose its effective implementation, as it has the potential to serve as an informal curriculum centered on the principles of transformation geometry and fractals for educational projects. It is anticipated that educators will regard the incorporation of fractal geometry into the standard curriculum as a beneficial didactic and pedagogic framework for fostering students’ curiosity and demonstrating the dynamic character of the field.

Keywords: Fractal, Pythagorean Tree, Dynamic Geometry Software, van Hiele Geometric Thinking Levels, Transformation Geometry, Instrumental social schema

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