What is DG’s philosophy on teaching students to write proofs?
Discovering Geometry’s primary focus is getting students to work together to discover and discuss geometry concepts in a student-centered environment. In Discovering Geometry students are guided to discover on their own not only the basic vocabulary of geometry but even the construction techniques they are going to use to discover their own geometric properties. At the same time students are inductively discovering geometric properties we are carefully developing a full breadth of reasoning skills, both inductive and deductive. There is a heavy emphasis in Discovering Geometry on using higher order thinking as opposed to memorization and drill. In this investigative approach to geometry, reasoning, concepts, and skills are developed with two basic principles in the background – the research of the van Hieles (van Hiele Model) and the work of Michael de Villiers and others on purposes of proof. At the beginning of the course we assume a low level of geometric reasoning in students. (van