Examining pre-service elementary mathematics teachers' proportional reasoning competencies through log-linear cognitive diagnostic model

This study aims to examine prospective middle school mathematics teachers' proportional reasoning competencies with the help of log-linear cognitive diagnosis models. More specifically, it was investigated whether there is a statistically significant difference in prospective teachers' proportional reasoning competencies with respect to gender, grade level, universities enrolled in, the regions of these universities, and university entrance examination scores. A descriptive survey model was used in the research. The proportional reasoning test used in this study was developed considering past research in the literature. The proportional reasoning test includes ratio and proportion problems for the following three competencies: understanding ratios, understanding proportions, and understanding nonproportional relationships. The data analysis showed that among 747 prospective teachers, 148 did not master any competency related to proportional reasoning. On the other hand, it was seen that 599 prospective teachers were competent in understanding ratios, 240 prospective teachers were competent in understanding ratios and in understanding proportions, and 110 prospective teachers were competent in all three competencies related to proportional reasoning. It was found that the prospective teachers had a good level of competence in understanding ratios and a lower level of competence in understanding ratios and nonproportional relationships. In addition, it was revealed that prospective teachers' proportional reasoning competencies did not differ according to gender. However, it differed according to year levels, the universities enrolled in, the regions of these universities, and university entrance examination scores. According to the analysis results based on the regions where the universities are located, a significant difference was found in the disfavor of the Eastern Anatolia Region for all three competencies related to proportional reasoning.