Statistics, which serves as a tool for other disciplines, is based on calculation of probabilities. Statistics enables researchers addressing probability and random events and making inferences from the data. Although probability is very important in real-life and various disciplines, some problems in learning this topic are observed in the literature. For example, Boyacioğlu (1996) found permutations and probability as two of the leading problematic topics for Turkish teachers and students (As cited in Sengul and Ekinozu, 2004). Boyacioğlu (1996) stated that 91% of the students and 84% of teachers have placed permutations and probability in the first place in which they have difficulty in learning and teaching, respectively. After reviewing the relevant literature in statistics education, we recognized that studies usually focused on understanding students’ performances and difficulties. Therefore, this study contributes to the statistics education literature by investigating preservice teachers’ (PSTs) performances and difficulties on statistics topics and by providing a diagnostic assessment on their strengths and weaknesses.

After reviewing the relevant literature and getting expert opinions on the statistical knowledge and reasoning skills that needed by mathematics teachers, we developed a Statistical Reasoning Skills Test (SRST), which consisted of five open-ended and 15 multiple choice items. The SRST administered to a total of 460 PSTs from four different universities in Turkey. The collected data will be analyzed using diagnostic classification models (DCMs; e.g., Rupp, Templin, & Henson, 2010). DCMs can be used in providing detailed cognitive feedback on participants’ strengths and weaknesses. Hence, by using DCMs, we will be able to provide diagnostic feedbacks on PSTs’ responses to the SRST items. Recently, some studies (e.g., Dogan, E., & Tatsuoka, K. 2008; Sen, S., & Arican, M., 2015) have compared the students’ performances in the international large-scale assessments (e.g., TIMSS, PISA, and PIRLS) by using DCMs. For instance, Dogan and Tatsuoka (2008) compared Turkish and American eighth-grade students’ mathematics performances on the TIMMS-R 1999. Their results suggested that Turkish students were weak in algebra, probability and statistics in comparison to their American peers. Similarly, Sen and Arican (2015) compared Turkish and Korean eighth-grade students’ performances on the TIMMS 2011. They observed that in comparison to Korean students, Turkish students did not perform well on the data and chance items. Although Korean students mastered almost all of the skills which were necessary to solve the problems, Turkish students had difficulties mastering some of these skills. 

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