Introduction

Reasoning and proving (R&P) are central to learning mathematics with understanding (e.g., Hanna and de Villiers, 2012 ; Schoenfeld, 2011 ) and are seen as essential to learning mathematics in secondary school. The importance of R&P in school education is also reflected in policy documents such as the PISA 2022 mathematics framework ( OECD, 2022 ), the new National Curriculum in Slovakia ( MinEdu, 2023 ), Norway ( Ministry of Education and Research, 2019 ), the Czech Republic ( MŠMT, 2023 ), Italy ( MIUR, 2010 , 2025 ), Türkiye ( MoNE, 2024a , 2024b ), or in the United States ( NCTM, 2009 ). Indeed, mathematicians often see reasoning as the core activity in mathematics education. At the same time, recent international literature reviews (e.g., Mariotti et al., 2018 ; Stylianides et al., 2017 ) have shown that proof has been challenging to learn and teach, and moreover to integrate R&P as an essential component of mathematics education. Studies report that teachers tend to focus on procedural skills that are easier to teach and assess ( Harel & Rabin, 2010 ).