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An international comparison using a diagnostic testing model: Turkish students’ profile of mathematical skills on TIMSS-R

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This study illustrates how a diagnostic testing model can be used to make detailed comparisons between student populations participating in international assessments. The performance of Turkish students on the TIMSS-R mathematics test was reanalyzed with a diagnostic testing model called the Rule Space Model. First, mathematical and cognitive skills (‘attributes’) measured by the test were determined. One hundred sixty-two items were coded in terms of their attribute involvement, creating an incidence matrix—the Q-matrix. Using the Q-matrix and the student response data, each student’s attribute mastery profile was determined. Mean attribute mastery levels of Turkish students were computed and compared to those of their American peers. It was shown that Turkish students were weak in algebra and probability/statistics. They also demonstrated poor profiles in skills such as applying rules in algebra, approximation/estimation, solving open-ended problems, recognizing patterns and relationships, and quantitative reading.

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  1. BUGSHELL classified each student according to their mastery on each attribute. However, composite attributes were created to reduce the number of knowledge states and hence produce more manageable and interpretable results.


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This study has been supported by the National Science Foundation (REC NO. 0126064).

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Correspondence to Enis Dogan.

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Dogan, E., Tatsuoka, K. An international comparison using a diagnostic testing model: Turkish students’ profile of mathematical skills on TIMSS-R. Educ Stud Math 68, 263–272 (2008).

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