A diagnostic comparison of Spanish and Turkish middle school students’ proportional reasoning

Abstract

This small-scale comparative study investigated Spanish and Turkish middle school students’ mastery of four core cognitive skills required for proportional reasoning using the log-linear cognitive diagnosis model. We compared students in the two samples for their proportional reasoning and provided a diagnostic assessment of their strengths and weaknesses. The study included 314 Spanish eighth grade and 282 Turkish seventh grade students. The students were administered a proportional reasoning test with 22 multiple-choice items. We found significant differences between the two samples in two of the cognitive skills. While the Spanish sample were better at understanding nonproportional relationships, the Turkish sample were better at understanding the concept of ratio. Furthermore, while the Spanish sample had a more dispersed distribution of students among different attribute profiles, the Turkish sample mostly consisted of either low-performing or high-performing students. To better understand the similarities and differences between the two samples, we compared students’ performance on some specific test items. The study shows how cognitive diagnostic models, which are not widely used in small-scale comparative studies, can be very useful in revealing similarities and differences between two samples that cannot be detected by traditional psychometric models.