Purpose: The purpose of the current research was to study and use cognitive diagnostic models in estimating the psychometric properties of the published 8th grade mathematics questions of Tims 2019.

Research method: The research method of this study is quantitative-qualitative, which was carried out with the approach of retrofitting existing tests. The statistical population of this study was all Iranian, Korean and American eighth grade students participating in the 2019 TEAMS study. The size of Iranian students included 1,095,026 students from 23,895 schools, the size of South Korean students included 465,626 students from 3,006 schools, and the size of American students included 4,059,757 students from 48,557 schools. The sample of Iranian, Korean, and American eighth grade students participating in the TEAMS 2019 study is that through a two-stage cluster sampling method, 5980 Iranian eighth grade students from 220 schools with an average age of 14.1, 3861 Korean eighth grade students from 168 schools with an average age of 14.5 and 8698 American eighth grade students from 273 schools with a mean age of 14.2 were reported.

Findings: Using the qualitative method, 16 skills in four areas of content, knowledge, application and reasoning were identified and the Q matrix was compiled. Then, in the quantitative section, the fit of the three Dina, Dino, and G-Dina models was examined with the data obtained from the students' answers to the questions of the math section in blocks 1, 2, 3, and 5, and the G-Dina model had a somewhat better fit.