Educational assessment is a process of collecting evidence and interpreting it to provide instructors with information regarding students' learning. However, the current design and scoring of most standardized educational tests are insufficient to serve this purpose. The limitation exists primarily due to the lack of cognitive information incorporated into traditional psychometric models. To date, some psychometricians have applied cognitive psychology principals to psychometric models of educational assessment data. Of these models, one of the most extensively researched and empirically supported is Tatsuoka's rule-space methodology (RSM). RSM can be used to validate a proposed cognitive model. A list of cognitive attributes, which describe what knowledge, strategies, and processing skills the TIMSS-R mathematics test measures, was developed with RSM by using the U.S. sample. Research using these cognitive attributes of the TIMSS items appears to adequately describe student performance for several other countries. In our current study, we intended to explore how a list of cognitive attributes expresses student performance in Taiwan. Three analyses, including calculation of classification rates, multiple regression analyses, and comparisons of attribute mastery probabilities across four booklets, were conducted. Successful classification rates ranged from 99.3% to 99.9% for four booklets, and R2 and adjusted R2 for each booklet were estimated using multiple regression analyses and ranged from 0.943 to 0.979. All ranges of mean attribute probabilities across booklets were less than 0.25, except for the Recognize patterns attribute (S6). Generally speaking, a list of cognitive attributes and the incidence matrix used as a proposed cognitive model in the current study represent the performance of Taiwanese eighth graders on the TIMSS-1999 mathematics tests very well. (Contains 6 tables.)