Abstract — Recently, it is required to develop a Web-Based-CAI system to be able to learn efficiently due to the spread of Internet. However, since the order of giving a chain of decision frame does not change, without relation to whether a student of the CAI system can solve a given problem or not, he/she has also to learn the parts in his/her element. Therefore, he/she cannot learn efficiently. Therefore, the authors propose a new instruction program and a new student model that improved the existent overlay model. The new model is easy to create the teaching materials, and it is able to grasp where the student's weak parts in detail are. This paper clarifies by concrete examples how this system grasps where are the student's we...