Advanced Geometry Tutor: An intelligent tutor that teaches proof-writing with construction

Two problem solving strategies, forward chaining and backward chaining, were compared to see how they affect students' learning of geometry theorem proving with construction. In order to determine which strategy accelerates learning the most, an intelligent tutoring system, the Advanced Geometry Tutor, was developed that can teach either strategy while controlling all other instructional variable. 52 students were randomly assigned to one of the two strategies. Although computational modeling suggests an advantage for backwards chaining, especially on construction problems, the result shows that (1) the students who learned forward chaining showed better performance on proof-writing, especially on the proofs with construction, than those who learned backward chaining, (2) both forward and backward chaining conditions wrote wrong proofs equally frequently, and (3) the major reason for the difficulty in applying backward chaining appears to lie in the assertion of premises as unjustified propositions (i.e., subgoaling).