Online Diagnosis in Intelligent Computer-Based Mathematical Training

The ability of human teachers to diagnose student misconceptions and to adapt their teaching methods is a necessary prerequisite for direct support or individualising measures. Due to the high expenditure of time this is nearly impossible in practice. In computer-based mathematical training systems these diagnostic abilities were not available until the present day, because existing diagnostic systems were not fast or flexible enough.

This research proposes a new algorithm for online diagnosis in computer-based training systems in mathematical domains. It extends standard term rewriting by numerous new concepts to describe student behaviours and combines term rewriting techniques with dynamic programming. 

A possible implementation of a diagnostic module, called BUGFIX, is introduced. To demonstrate its abilities a bug library for fraction arithmetic was developed. In this domain BUGFIX is able to consider several billion different student calculations for one task, without a subjectively perceptible waiting period for the learner.