Resumen de Level-spanning proof-production strategies to enhance students’ understanding of the proof structure in school mathematics

Mikio Miyazaki, Taro Fujita, Koji Iwata, Keith Jones

• This study focused on improving students’ learning mathematical of proofs and proving by using combinations of proof strategies that span different levels of understanding of proof structure; we refer to these as ‘level-spanning proof-production strategies’. We analysed the level-specific proof-production strategies evident in the lessons and class tests of two Grade 8 classes (students aged 13–14). Our analysis revealed the level-spanning proof-production strategies by students and teachers that emerged during lessons to enhance the students’ understanding of the proof structure. The idea of combining strategies at different levels is not found in previous studies and can be applied outside of proof studies, provided that the students’ levels are well developed. It can be expected that the conscious use of these strategies by teachers in their proof teaching will enhance students’ ability to produce proofs according to their understanding of proof structures.