• Cognitive Unity
• Conjecture
• Dynamic Geometry Environment
• Figural Concepts
• Logical Hierarchy
• Maintaining Dragging
• MD-model
• Proof
• Pseudo-objects

This thesis is a replication study of Anna Baccaglini-Frank’s doctoral thesis, where the cognitive processes that emerge in solving open problems in a Dynamic Geometry Environment are described and the Maintaining Dragging model is theorized.
This study aims at exploring the validity of the model after years and in new educational contexts. In addition, the comparison between the conjecturing and proving processes, only briefly investigated in Baccaglini-Frank’s work, is thoroughly examined. We also focus on the phenomena that unexpectedly emerged during the investigation, we advance a working definition of length of a proof (or argumentation) and propose an artifact on logical hierarchy. In the thesis the MD-model is applied and integrated with other constructs such as Cognitive Unity to compare conjecturing and proving, and the Theory of Figural Concepts to analyze some phenomena in terms of the interaction between figural and theoretical elements.
The results of our work confirm the validity of the MD-model; moreover, we describe conjecturing processes that are centered on unforeseen uses of maintaining dragging and on interesting dialectics between conceptual and figural elements. From a didactic point of view, the study offers ideas for the creation of resources with the aim of promoting the resolution of open problems and working on the formulation of conjectures and their proofs.