A lens for exploring which dimensions contribute to a justification’s proofiness

Abstract

This study extends the investigation of students’ conceptions of what makes a written justification a proof by introducing a novel theoretical lens—the proofiness lens. Under a proofiness lens a justification is conceptualized as occurring in a multi-dimensional space with each dimension influencing the extent to which that justification is considered a proof. In this work, we target a single potential dimension, the proof-to-procedure continuum, although, other dimensions emerged from students’ work. Our data allows us to explore how sensitive students are to the proof-to-procedure dimension of proofiness. Additionally, all students in our study were attentive to writing style as an emergent dimension. We demonstrate that the proofiness lens and its associated methodology shed light on which dimensions of proofs students attend to and why.