A Support System for Solving Problems of Two-Triangle Congruence Using ‘Backward Chaining’

Abstract

We developed a system called DELTA that supports the students' use of backward chaining (BC) to prove the congruence of two triangles. DELTA is designed as an interactive learning environment and supports the use of BC by providing hints and a function to automatically check the proofs inputted by the students. DELTA also has coloring, marking, and highlighting functions to support students' attempts to prove the congruence of two triangles. We evaluated the efficacy of DELTA with 36 students in the second grade of a junior high school in Japan. We found that (1) the mean number of problems, which the experimental group (EG) completely solved, was statistically higher than that of the control group on the post-test; (2) the EG effectively used the BC strategy to solve problems; and (3) the students' attempt to use both the forward chaining strategy and the BC strategy led to solving the problems completely.