Investigating the 8th-grade Afghan students’ mathematics status and skills using the cognitive diagnostic model

Abstract

Cognitive diagnostic models (CDMs) are multidimensional multivariate verification flow models with complex structure. In this research, these models were used to investigate the status of eighth grade high school students in mathematics using the TIMMS questionnaire. The cognitive diagnostic test based on 13 attributes including 32 questions was conducted on a sample of 274 students who were selected based on the multi-stage cluster sampling method among the students of Firuzkoh city. IRT and RESMA models were used to determine the psychometric properties of the questions. Data analysis using DINA and DINO models in cognitive diagnostic modeling of mathematics showed that 13 attributes explain the mathematical performance of eighth-grade students. The result shows that Afghan students have a weak mastery level in most attributes compared to 45 other countries (the countries that were included in the TIMMS questionnaire) also general results show that the examinees perform better in the field of numbers (0.49), while they perform worse in data and chance (0.12). Moreover, there exists some difference in estimating item parameters under the DINA and DINO models, such as Item 3 and Item 27. One possible explanation is that the DINA model is completely compensatory while the DINO model is fully non-compensatory. Similar to the results under the DINA model, the SEs of guessing parameters are lower than those of slipping parameters under the DINO model.