Redesigning Proofs Without Words for secondary level mathematics

This study seeks to capitalize on the pedagogical potential of visual proof documents called Proof Without Words (PWWs) to advance proof learning in secondary mathematics. The data is drawn from design-based research (DBR), in which a PWW document was iteratively redesigned to lead students to generate more detailed and rigorous proof attempts. The gap-filling theoretical framework for proofs in mathematics education was used to evaluate students’ written proof products when working on initial vs. redesigned PWW versions. The results reveal a substantial positive effect of the PWW redesigned version on the quality of students’ products. They suggest the potentiality of five proposed PWW design principles in promoting secondary students’ proficiency in proof-related activities.