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.

Key features

Generating diagnoses during the runtime of the training system.

Available in less than 200 ms. 

Multiple incorrect rules within on diagnosis. No need to discover each incorrect rule singly. 

Efficient memory management by maximum structure sharing.


This web site is based on poster designed for the Conference at the Occasion of Dagstuhl's 10th Anniversary: Informatics - 10 Years Back, 10 Years Ahead. 

The diagnosis algorithm and the BUGFIX module is part of the Ph. D. thesis “Online Diagnose in intelligenten mathematischen Lehr-Lern-Systemen”, Fortschr.-Ber. VDI Reihe 10, Nr. 605, Düsseldorf: VDI Verlag 1999.