Pre-service Teachers' Beliefs and Expectations toward Students' Mathematical Proof

This study elaborates on pre-service teachers' beliefs and expectations toward students' mathematical proof. This is a qualitative case study using semi-structured interviews. The research participants were three 8-12 grade pre-service teachers in the Bachelor of Mathematics Education program at a university in Indonesia. The research instruments were an interview guide including four mathematics questions and several hypothetical arguments created following Stylianides' (2009) sophistication levels of reasoning. Participants defined proof as a tool to verify and explain the validity of a statement, as well as communicate and systematize mathematics. Their criteria for proof seemed relevant to a within-cluster definition of proof as described by Czocher and Weber (2020). Participants accepted demonstrations and generic arguments as proof, rationales and empirical arguments as non-proof, and others as incorrect proof. Finally, participants expected that proof is difficult for secondary students but is doable for some topics and students with some backgrounds.