Constructing mathematical proofs is a fundamental yet challenging skill in secondary school geometry. While technology has been used to scaffold different aspects of the proving process, existing approaches often separate inquiry and conjecturing from formal proof or focus on structural and technical assistance without addressing students' initial…

The paper argues that there is a need for new approaches to teaching proof with newly-available technology. It contributes to filling this need by opening a discussion on digital proof assistants, programs that allow one to do mathematics with the aid of a computer, construct proofs, and check their correctness. The paper starts by exploring such…

This paper highlights the pedagogical importance of gaps in mathematical proofs to foster students' learning of proofs. We use the notion of 'gap-filling' (Perry & Sternberg, 1986) from literary theory to analyze a task based on a Proof Without Words, which epitomizes the notion of gaps. We demonstrate how students fill in gaps in this…

When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

In this paper, we propose a potential interactional explanation of tertiary-to-secondary (dis)continuity: that of authority relations. Using secondary mathematics teachers' proof validations across two contexts, we suggest that secondary teachers' conceptions of authority shape their capacity to reconcile their positions as former mathematics…