Abstract: This paper used rule space model for identifying cognitive errors in students'problem solving. This model linked cognitive psychology, item response theory and the algebraic theory of databases. It mapped subjects'binary response patterns into a set of ordered pairs in Cartesian product space. Then the Mahalanobis distance of a student's position in the rule space to the positions representing the erroneous rules was computed. The students'error patterns were classified with Bayes decision rule. In the research, based on the responses of 644 middle school students to 30 mathematical items, it was identified that 86% of the students could be classified into 18 cognitive error patterns.

Key words: item response theory, problem solving, rule space model