From Exploration to Proof Production

This chapter focuses on four topics: how exploration, especially hands-on exploration with concrete materials, is integrated into the teaching of proof in Taiwan; different ways of interpreting exploration; exploration’s intrinsic features and value in the context of proving; and a proposed conceptual model, the ‘EP-spectrum’, for the relationships amongst exploration, problem-solving, proving and proof in the classroom. Furthermore, the chapter raises some ideas requiring future research, such as the primary factors contributing to the progression from exploration to proof production and the integration of exploration into the context of proving.