Dynamic Euclidean Geometry: pseudo-Toulmin modeling transformations and instrumental learning trajectories

Abstract

The present paper attempts to bridge the world of DGS technology with the world Euclid bequeathed to us in his Elements. Competence in the DGS environment depends on the competence of the cognitive analysis as students seek to decode their ideas using the tools provided by the software. The dynamic notions (e.g., dynamic point, dynamic segment, instrumental decoding, hybrid-dynamic objects, active/ “alive” representations etc.), are taken as given and form the specific /particular theoretical basis for the constructive processes. Dynamic Euclidean constructions will be considered using pseudo-Toulmin’ diagrams. These considerations provide a theoretical basis for the idea that, in order to solve a mathematical construction problem in Dynamic Euclidean Geometry, we have to build up the interdependencies of tools in various sequential steps (based on theorems and definitions and the competence in using tools) which can be linked to the level of our conceptualization. The central idea is the following: Do the tools of Dynamic Euclidean Geometry determine a new kind of Geometry? Is Dynamic Euclidean Geometry a new kind of geometry? Does it have its own axiomatic system or its own undefined terms? In the paper, the notion of an instrumental learning path/trajectory is introduced as the interdependence/intra-dependence between dynamic tools, diagrams and mathematical objects during an instrumental decoding process. Keywords: Dynamic geometry , Euclid “Elements”, instrumental learning trajectories, Dynamic Euclidean Geometry DOI: 10.7176/JEP/12-9-09 Publication date: March 31 st 2021