While proof, proving, and argumentation are recognized as core aspects of mathematics teaching and learning, they are not practiced in a culturally neutral way. What is counted as "proof" in the classroom, and even the meaning of the word "proof", may differ substantially depending on local traditions, national curriculum frameworks, and everyday language (e.g., Knipping, 2008; Miyakawa, 2017). Yet, these contextual aspects have often been overlooked in mathematics education research (Reid, 2015).

This project has been conducting international comparative research on curricula, textbooks, and lessons by using classroom data to gain a deeper understanding of how students and teachers engage in the practices of proof, proving, and argumentation, with the triplet model of ‘structure,’ ‘language,’ and ‘function’  (Miyakawa & Shinno, 2021) as a perspective for understanding the cultural specificity of teaching and learning of proof.

By shedding light on the diverse ways in which mathematical proof, proving, and argumentation are practiced in classrooms around the world, this project contributes to a deeper understanding of how mathematics education is culturally situated. Knowing about mathematics lessons in other countries is useful for understanding the implicit assumptions of mathematics lessons in your own country.

Consequently, we may be blind to some of the most significant features that characterize teaching in our own culture because we take them for granted as the way things are and ought to be. Cross-cultural comparison is a powerful way to unveil unnoticed but ubiquitous practices. (Stigler et al., 2000, p.88)

This project also provides insights that can inform more inclusive teaching approaches and foster international dialogue in mathematics education research.