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This study investigated Turkish middle school students' proportional reasoning and provided a diagnostic assessment of their strengths and weaknesses on the ratio and proportion concepts. A proportional reasoning test with 22 multiple-choice items was developed from the context of the loglinear cognitive diagnosis model. The test was developed around four core cognitive skills (attributes) that required in solving middle school ratio and proportion problems. These skills included understanding ratios, directly, inversely, and nonproportional relationships. The test was applied to 282 seventh grade students, and the collected data were analyzed using the Mplus software. The analysis showed that approximately 62% of the students were able to recognize directly proportional relationships. Whereas, roughly 48% of them were able to recognize inversely proportional relationships. Moreover, while 25% of the students did not master any of the four cognitive skills, 39.1% mastered all four of these skills. In addition, many students had difficulty distinguishing proportional relationships from nonproportional relationships. Diagnostic feedbacks on the students' strengths and weaknesses were provided based on the findings.

The purpose of the present study was to analyze an international large-scale data set using a cognitive assessment approach. Although some researchers question the usefulness of international large-scale assessments (e.g., TIMSS), participating countries have continued to use the results from these large-scale assessments to improve their curricula and teaching methods. Despite the common reporting practice-single-score-in these large scale assessments gives useful insights about students' overall performances, they still lack diagnostic information. Cognitive diagnosis models (CDMs) were developed to provide more feedback on students' cognitive strengths and weaknesses. This study retrofitted the TIMSS 2011 eighth grade mathematics assessment by applying a specific CDM called the DINA (the deterministic, inputs, noisy, "and" gate) model to data from South Korea and Turkey. Results of the DINA model were used to make a detailed comparison between students of these two countries.

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