A diagnostic model for large-scale assessment was applied to TIMSS data to compare mathematics performance of eighth graders from three countries--the US, Singapore, and Israel. Compared were attribute mastery probabilities for content, skills and cognitive processes underlying students' performance on the 1999 TIMSS-R mathematics test. Also compared were the proportions of students from the three samples in each of eight hierarchically ordered clusters of knowledge states. The results indicated significant differences in favour of the Singaporean sample on most attributes underlying the test. The results were discussed in light of the cultural context of education in the respective countries.