Teaching practices promoting meta-level learning in work on exploration-requiring proving tasks

Abstract

In this study, we explore teaching practices promoting students’ learning to prove in a context where students work on exploration-requiring proving tasks. In these tasks, the goal is to provide an argument for the validity of a mathematical statement, and students are not given a particular procedure to follow. We propose a theoretical framing describing the students’ and teacher’s actions. Learning to prove in mathematics involves endorsing some meta-level rules that have been established historically and is an example of meta-level learning. We analyze two classroom episodes to show how the theoretical framing can be used in analysis and what the teaching practices can be.