Conjecturing in dynamic geometry: A model for conjecture-generation through maintaining dragging

Abstract

The purpose of this research is to study aspects of the impact of Dynamic Geometry Systems (DGS) in the process of producing conjectures in Euclidean geometry. Previous research has identified and classified a set of dragging schemes spontaneously used by students. Building on these findings, the study focuses on cognitive processes that arise in correspondence to particular dragging modalities in Cabri. Specifically, we have conceived a model describing what seems to occur during a process of conjecture-generation that involves the use of a particular dragging modality, described in the literature as dummy locus dragging. In order to accomplish this goal, we preliminarily introduced participants to specific dragging modalities, re-elaborated with a didactic aim from those present in the literature. In particular dummy locus dragging was re-elaborated into what we introduced as maintaining dragging (MD). This study aimed at developing and testing our model of conjecture-generation through MD by analyzing dynamic explorations of open problems in a DGS. The general experimental design was articulated in two phases, an introductory lesson on dragging modalities and interview sessions in which students were asked to solve conjecturing-open problems. Subjects were high school students in Italian "licei scientifici", a total of 31. Data collected included: audio and video recordings, screenshots of the students' explorations, transcriptions of the task-based interviews, and the students' work on paper that was produced during the interviews. The study shows appropriateness of the model, which we refer to as the MD-conjecturing Model. Furthermore the study shed light onto a relationship between abductive processes and use of MD, and motivated the introduction of the notion of instrumented abduction. The study has implications for the design of activities based on the use of maintaining dragging with the educational objective of introducing students to conjecturing and proving in geometry.