A Probabilistic Model for Diagnosing Misconceptions By The Pattern Classification Approach

This paper introduces a probabilistic approach to the classification and diagnosis of erroneous rules of operations that result from misconceptions (“bugs”) in a procedural domain of arithmetic. The model is different from the usual deterministic strategies common in the field of artificial intelligence because variability of response errors is explicitly treated through item response theory. As a concrete example, we analyze a dataset that reflects the use of erroneous rules of operation in problems of signed-number subtraction. The same approach, however, is applicable to the classification of several different groups of response patterns caused by a variety of different underlying misconceptions, different backgrounds of knowledge, or treatment.