Running Heading: DIF AND RSM FOR VALIDATION A Unified Approach that Combines Differential Item Functioning with the Rule-Space Method for Validating Cognitive Attributes for the TIMSS Mathematics Items

The main goal of the rule space method is to classify examinees into the closest ideal attribute mastery patterns and to assigned appropriate attribute mastery probabilities to them based on their item response patterns. The quality of pattern classification and probability assignment depends on the validity of the proposed attributes and the Qmatrix. The rule-space method provides the quality indices of classification, such as the classification rate and the D distance. The study was intended to apply the differential item functioning technique to further validate the attributes and the Q-matrix at the individual item-level. The results indicated that 5 items and 4 items out of 45 items did not exhibit DIF based on assigned attribute patterns and probabilities, respectively. This suggests that the proposed attributes and Q-matrix used in this study with RSM works well to map Taiwanese students into appropriate attribute mastery patterns and to assign appropriate attribute mastery probabilities to them. More discussion and conclusions were presented in the paper.