Examining mathematics questions with a cognitive diagnostic model: Q-Matrix study

The College Entrance Examination (CEE) is a curriculum-orientated performance examination administered to fifth-grade primary school students who wish to study at Maarif Colleges in Northern Cyprus, where the medium of instruction is English. This study was conducted to determine the psychometric characteristics of the CEE mathematics test administered to 1,833 fifth-grade primary school students in 2021. To achieve the purpose of the study, a cognitive diagnostic model, namely DINA, was used. The theoretical infrastructure of the DINA model is easy and strong compared to other models. The Q-matrix was constructed for 23 mathematics questions and 15 attributes were determined based on expert opinions. The results of the study showed that the mean values of the parameters g and s were 0.25 and 0.13, respectively. The mean of the δ values of the fifth-grade students was high (0.73). Skill patterns showed that 13% of fifth-grade students possessed all the attributes included in CEE. The construction of the Q-matrix is a very important stage in the use of CDMs. The cognitive attributes and the Q-matrix were determined by expert opinion in this study. The (1-s) values indicated the validity of the Q-matrix. For all of the items, 1-s values appeared to be quite high. This showed that the attainments and item-attainment relationship were done as accurately as possible. These results can be interpreted as the validity of the Q- matrix. The results of the study showed that the DINA model provides a detailed conclusion about students’ attributes.