Formulating a conjecture through an identification of robust invariants with a dynamic geometry system

Abstract

Conjecturing has been considered to inspire the need for proof, enhance the understanding of proofs, and construct a valid proof. This study describes students’ processes of formulating a Euclidean geometry conjecture in the form of a conditional statement through constructing a geometric figure and using measuring and dragging modalities of a dynamic geometry system (DGS). To accomplish this aim, we adapted the existing conjecturing model by Baccaglini-Frank and Mariotti ([2010]. Generating conjectures in dynamic geometry: The maintaining dragging model. International Journal of Computers for Mathematical Learning, 15(3), 225–253. https://doi.org/10.1007/s10758-010-9169-3) and used it to analyse students’ conjecturing processes. Our participants were prospective mathematics teachers (PMTs) during their first year at an Indonesian university, but the findings can be useful for secondary school students in other countries. We selected and categorized episodes from task-based interviews with eight PMTs a week after a teaching intervention. We interpreted their identification of robust invariants during constructing, dragging, and measuring. Our findings indicated that the adapted model was appropriate to describe PMTs’ processes of conjecturing, which emerged through an exploration that involved robust invariants. We found that PMTs determined these invariants as premises or conclusion of the conjecture by observing the measure of parts of the constructed figure during dragging. The findings indicated that the measuring and dragging modalities of DGS supported PMTs in conjecturing.