Investigation of pre-service middle school mathematics teachers' statistical knowledge for teaching through problem posing tasks

This study was aimed to investigate the statistical knowledge for teaching of pre-service middle school mathematics teachers' through problem posing tasks. The case study method was used in the research. The study group consisted of 24 pre-service middle school mathematics teacher studying in the mathematics teaching program of a state university in Turkey. The data of the study were collected through the "Statistical Knowledge for Teaching Through Problem Posing Tasks" form developed by the researcher and semi-structured interviews. In the development of this form, the problem posing classification and model of statistical knowledge for teaching in the literature were used. The form prepared based on these two frameworks includes a total of 12 items, including 8 different problem situations and 4 sub-items. The problems constructed by the pre-service teachers were analyzed according to the problem evaluation criteria in the first stage. The problems in the solvable problem category were analyzed in the second stage according to the levels of statistical knowledge for teaching (awareness, emergence, competence, accomplished). The indicators for these levels were reconstructed in line with the problem posing tasks. The results obtained from the study showed that the problems constructed by the pre-service teachers' about statistics topics were mostly evaluated in the problem category and most of these problems were solvable problems. When the problems constructed by pre-service teachers' were analyzed according to the components of statistical knowledge for teaching, it was concluded that they were level of emerging in the key developmental understandings, knowledge of content and teaching; and the level of aware in the knowledge of content and students, curriculum knowledge and pedagogically powerful ideas. It was observed that the pre-service teachers were inadequate in strengthening students' statistical understanding and focused on constructing problems based on arithmetic operations. In general, it was concluded that pre-service middle school mathematics teachers' concentrated at lower levels in reflecting their statistical knowledge for teaching to the problems they constructed. According to the results of the research, it was suggested that different teaching practices should be included in order to improve pre-service teachers' statistical problem posing.