A real-time coaching environment for triangle congruence proofs

Abstract

This paper describes a real-time system that coaches students in developing high school geometry proofs. The program consists of an expert that creates the proof solution and the coach that helps the student develop a proof. The expert is described elsewhere. The tutor consists of three parts: a student model module, the coach, and the interface. The student model keeps track of the student's progress through the geometry concepts and guides the coach if remediation is required. The coach manages the environment by responding to the student's questions and by posing problems and doing example solutions. The interface establishes communication between student and coach through the use of four windows. Two windows are used for text and two for graphics. The interface also handles the graphical dialogue, allowing the student to propose problems for the program to solve. The system is designed and implemented to provide students with a hands-on environment for real-time proof generation.