From conjecture generation by maintaining dragging to proof

TL;DR

This paper explores how maintaining dragging, as a physical or psychological tool, affects the connection between conjecture generation and proof in geometry, highlighting its impact on cognitive processes.

Contribution

It introduces a hypothesis on the influence of maintaining dragging's dual roles on the cognitive link between conjecturing and proving, supported by two illustrative examples.

Findings

Physical maintaining dragging may cause cognitive rupture between conjecture and proof.

Psychological maintaining dragging may promote cognitive unity in geometric reasoning.

The role of maintaining dragging influences the reasoning process in dynamic geometry environments.

Abstract

In this paper we propose a hypothesis about how different uses of maintaining dragging, either as a physical tool in a dynamic geometry environment or as a psychological tool for generating conjectures can influence subsequent processes of proving. Through two examples we support the hypothesis that using maintaining dragging as a physical tool may foster cognitive rupture between the conjecturing phase and the proof, while using it as a psychological tool may foster cognitive unity between them.