To What Extent Can Teachers and Preservice Teachers Predict Students' Mathematical Thinking? A Qualitative Analysis

In studies over recent years, there has been an increasing interest in teachers' predicting middle school students' thinking processes. However, as far as we are aware, there are no studies examining students' thinking in terms of mathematical thinking components. This study primarily aimed to determine the mathematical thinking of middle school students. Therefore, the study examined how six mathematics teachers and 24 preservice mathematics teachers (from first to fourth grade) predicted the mathematical thinking of 96 middle school students. In this context, the predictions were categorized according to the sub-components of mathematical thinking: conjecturing, specializing, justifying and convincing, and generalizing. Regarding the "conjecturing," the teachers explained students' prediction of their mathematical thinking in more detail than preservice teachers. Regarding the "specializing," the study, both groups of teachers could not predict that the students could express different situations in their problem solutions. Within the scope of the "justifying and convincing," the preservice teachers had different perspectives on problem solving compared to the teachers. In regard to the "generalizing," teachers and preservice teachers made similar predictions but all groups from first to fourth grade lack experience for this component. It can be stated that preservice teachers' interaction with more students will be effective in predicting students' mathematical thinking. The same is true for teachers, as it is believed that greater experience will be beneficial.