Web-based interactive module with multiple representations for learning geometry theorem proving

Some researchers have successfully utilized multiple representation theories in the learning of certain mathematical subjects. However, the analysis of geometry proof problems from the perspective of multiple representations was rarely discussed in the past. This study attempts to use five representations in computer-assisted environment for learning geometry proofs: problem statement, static figure, dynamic geometry figure, formal proof, and proof tree. The environment is called MR Geo (Multiple Representations for Geometry theorem proving). An empirical experiment was done to evaluate the effects of using MR Geo. The findings are very encouraging. In MR Geo, students at the middle proficiency level interacted most frequently with the proof tree representation. The results of questionnaires demonstrated that students found MR Geo help them better understand the problems. Proof tree was also helpful to students in improving the summary and inference aspects in their comprehension of proofs.