A Reification of a Strategy for Geometry Theorem Proving

This study addresses a novel technique to build a graphical user interface (GUI) for an intelligent tutoring system (ITS) to help students to learn geometry theorem proving with construction - one of the most challenging and creative parts of elementary geometry. Students’ task is not only to prove theorems, but also to construct missing points and/or segments to complete a proof (called auxiliary lines). The problem space of theorem proving with construction is generally huge, thus understanding a search strategy is a key issue for students to succeed in this domain. Two major challenges in building a GUI for an intelligent learning environment are (a) to build a theorem prover that is capable of construction, and (b) to establish a cognitive model of understanding a complex problem-solving strategy.