In this study, we illustrated an application of the confirmatory mixture IRT model for multidimensional tests. We aimed to examine the differences in student performance by domains with a confirmatory mixture IRT modeling approach. A three-dimensional and three-class model was analyzed by assuming content domains as dimensions and cognitive domains as item groups. We estimated the item performance differences among the students through structural parameters. There were 463 students from Turkey and 880 students from Canada who participated in the TIMSS 2015 4th-grade mathematics assessment. Results for Turkey indicated, students in Class 2 had better performance in knowing and reasoning compared to those in Classes 1 and 3. Students in Class 2 and Class 3 were similar in applying math concepts compared to students in Class 1. For the Canadian sample, students in Class 2 had better performance in knowing, applying, and reasoning compared to those in Class 1 and 3. Also, Class 3 students were better at applying domain than Class 1. Also, mean values were obtained for all content domains in the two countries. Confirmatory mixture IRT modeling approaches appear to differentiate students' mathematics competencies.