Center of Research, Evaluation, Accreditation and Quality Assurance of Higher EducationEducational Measurement and Evaluation Studies2476-2865103220210120Application of Cognitive Diagnostic Models (CDM) Study of the Differential Item Functioning of TIMSS Eighth Grade Mathematics 2007 Among Females and MalesApplication of Cognitive Diagnostic Models (CDM) Study of the Differential Item Functioning of TIMSS Eighth Grade Mathematics 2007 Among Females and Males73624439810.22034/emes.2021.244398FAAsgharMinaiAssociate Professor of Assessment and Measurement (Psychometrics), Allameh Tabataba’i University, Tehran, Iran0000-0002-2875-7449JalilYounesiAssociate Professor of Assessment and Measurement (Psychometrics), Allameh Tabataba’i University, Tehran, IranBehroozKazemi DanaPh.D. Student of Assessment and Measurement (Psychometrics), University of Tahran, Tehran, IranJournal Article20210614Investigation of the bias and Differential Item Functioning of important tests like mathematics between different groups has appealed to many researchers in education; most of them, however, have examined mathematics as a general structure. Attempts were made in this research to make use of the capabilities of Cognitive Diagnosis Models (CDMs) for precise and more detailed investigation of the Differential Item Functioning in the mathematics test of the eighth grade (third grade of guidance school) (T. 2007), and also for investigation of the effects of the questions with Differential Item Functioning on students’ performance. The statistical population of the study is the same as the eighth grade statistical population in the 2007 TIMSS math test, which was conducted in the academic year 2006-2007. In the academic year in question, 1,475,368 third grade middle school students were studying in 29,956 classes. The sample of the present study was a part of the Iranian third year middle school students participating in the 2007 TIMSS, whose number is equal to 1137. For analyzing the data and responding to the research questions, the non-compensative model DINA, with the two parameters of guessing and slipping, was used. First, the q matrix was set using required attributes of the questions. Then, the data were fitted to the model, and the parameters were estimated for the two female and male groups. The Differential Item Functioning was then examined using the Wald test. The results demonstrated that of the 44 investigated questions, 26 were anchoring questions, and 18 (40%) were ones with DIF, where 12 out of the 18 questions with DIF had linear DIF, and 6 had nonlinear DIF. Of the 18 questions with Differential Item Functioning, 7 had Differential Item Functioning in favor of the female students who had achieved mastery over the attributes necessary for responding correctly to the questions, and 10 in favor of the male ones. One question here had Differential Item Functioning in favor of neither the group of females nor the group of males who had achieved mastery over the attributes necessary for responding correctly to the questions. Furthermore, of the 18 questions with DIF, 9 have Differential Item Functioning in favor of the female students who have not achieved mastery over the attributes necessary for responding correctly to the questions, and 7 in favor of the male ones, and 2 questions have Differential Item Functioning in favor of neither the group of females nor the group of males who have achieved mastery over the attributes necessary for responding correctly to the questions. It can be concluded that The Wald test is enabled in the Framework Cognitive Diagnosis Models (CDMs). In addition to the test linear DIF and nonlinear DIF To be used in identifying differential function in mastery and non -mastery Persons in attributes It is suggested by these results and those of the research in the area that question format can decrease or increase gender difference; test developers; therefore, should try to make the questions so that gender differences is minimized. By identifying the factors effective on gender differences, instructors, teachers, and educational policy-makers in the country will be able to design and formulate novel, creative curricula or improve current ones to make the educational environment and system of the country flourishing and rich.Investigation of the bias and Differential Item Functioning of important tests like mathematics between different groups has appealed to many researchers in education; most of them, however, have examined mathematics as a general structure. Attempts were made in this research to make use of the capabilities of Cognitive Diagnosis Models (CDMs) for precise and more detailed investigation of the Differential Item Functioning in the mathematics test of the eighth grade (third grade of guidance school) (T. 2007), and also for investigation of the effects of the questions with Differential Item Functioning on students’ performance. The statistical population of the study is the same as the eighth grade statistical population in the 2007 TIMSS math test, which was conducted in the academic year 2006-2007. In the academic year in question, 1,475,368 third grade middle school students were studying in 29,956 classes. The sample of the present study was a part of the Iranian third year middle school students participating in the 2007 TIMSS, whose number is equal to 1137. For analyzing the data and responding to the research questions, the non-compensative model DINA, with the two parameters of guessing and slipping, was used. First, the q matrix was set using required attributes of the questions. Then, the data were fitted to the model, and the parameters were estimated for the two female and male groups. The Differential Item Functioning was then examined using the Wald test. The results demonstrated that of the 44 investigated questions, 26 were anchoring questions, and 18 (40%) were ones with DIF, where 12 out of the 18 questions with DIF had linear DIF, and 6 had nonlinear DIF. Of the 18 questions with Differential Item Functioning, 7 had Differential Item Functioning in favor of the female students who had achieved mastery over the attributes necessary for responding correctly to the questions, and 10 in favor of the male ones. One question here had Differential Item Functioning in favor of neither the group of females nor the group of males who had achieved mastery over the attributes necessary for responding correctly to the questions. Furthermore, of the 18 questions with DIF, 9 have Differential Item Functioning in favor of the female students who have not achieved mastery over the attributes necessary for responding correctly to the questions, and 7 in favor of the male ones, and 2 questions have Differential Item Functioning in favor of neither the group of females nor the group of males who have achieved mastery over the attributes necessary for responding correctly to the questions. It can be concluded that The Wald test is enabled in the Framework Cognitive Diagnosis Models (CDMs). In addition to the test linear DIF and nonlinear DIF To be used in identifying differential function in mastery and non -mastery Persons in attributes It is suggested by these results and those of the research in the area that question format can decrease or increase gender difference; test developers; therefore, should try to make the questions so that gender differences is minimized. By identifying the factors effective on gender differences, instructors, teachers, and educational policy-makers in the country will be able to design and formulate novel, creative curricula or improve current ones to make the educational environment and system of the country flourishing and rich.https://jresearch.sanjesh.org/article_244398_5a9a02f97a9ffda7d57b2fc4c702cacf.pdf