Using Clustering in a Cognitive Tutor to Identify Mathematical Misconceptions

Abstract: We have implemented an Intelligent Tutoring System (ITS) prototype for teaching multi-column addition and subtraction to children aged 5-10, using a digitalized version of the Montessori bank game exercises. An Intelligent Tutoring System is a piece of software that teaches a certain subject to its users, and that typically uses artificial intelligence related algorithms to personalize the educational process. Our Intelligent Tutoring System focuses on collecting erroneous input from the user and analyzing it using an experimental clustering algorithm in order to find common misconceptions. The system is based on the assumption that if there is a lot of user errors that are similar, they might correspond to a misconception. To find which errors are “similar”, we use clustering. An ITS like this could support teaching by making the students become aware of their misconceptions, so that they can overcome them. Normally, ITS use bug libraries to systematize misconception handling. A bug library is a collection containing information about possible errors, that can be used to help identify these errors when encountered. Creating bug libraries takes a lot of effort, and if they could be avoided, a typical ITS implementation would take considerably less time. While we found that we could identify some misconceptions of a computer player, the clustering approach needs to be generalized further in order to enable effective application on humans. We conclude that if this approach were to be explored more in detail, it could prove to be a viable alternative to the bug library.