Faculty Publications


Developing Secondary Students’ Understanding of Proof through Constructing, Critiquing, and Revising Arguments

Document Type



critiquing arguments, geometry, justification, Reasoning-and-proving

Journal/Book/Conference Title

Investigations in Mathematics Learning


We examined high school geometry students’ written work on four proof tasks where they posed a conjecture, drafted an argument, provided written critiques, then revised their argument based on peer feedback. Students’ written work across the tasks was analyzed to determine whether the instructional sequence supported them in improving their arguments and attending to key aspects of proof (justifications, generality, clarity, structure). Claim-level analysis for each of the key aspects revealed minor changes between students’ draft and revised arguments with results varying by task. That said, students attended to the key aspects of proof through the critiques they provided each other with most critiques, if appropriately addressed, having the potential to help improve the draft argument. Students’ reflections also showed this process helped them think about the clarity and level of detail in their arguments. Implications for this study include the benefits of providing proof tasks that offer fewer supports for students, alongside multi-faceted analysis of their written arguments, in terms of providing insights into students’ current understanding of proof.


Department of Mathematics

Original Publication Date


DOI of published version