Examining the problem posing skills of secondary school mathematics teachers regarding data processing learning field

The aim of this research is to examine the problems that secondary school mathematics teachers have posed for different problem posing cases in data processing learning field. As the problems that the teachers pose in the study were examined deeply, the case study method based on the qualitative research approach was used. Participants of the study consist of 7 secondary school mathematics teachers working in a state secondary school. Participants were selected with convenience sampling method. As the data collection tool, the Problem Posing Test (PPT) developed by the researchers was used as the measurement tool. The framework of Stoyanova and Ellerton (1996) which was created as the combination of free, semi-structured and structured problem setting strategies was to construct problem setting cases in PPT. For the validity and reliability of the study, three different expert opinions were taken on the problem cases and the pilot application was made before implementation. In accordance with the pilot application and expert opinions, PPT consisting of a total of 12 problems, four problems in each of free, semi-structured and structured problem-posing category, were prepared. In the first stage of data collection process, teachers were asked to pose problems related to different cases. In order to provide data diversity in the research, written explanations, interviewing, observation and document analysis about the problems were used. Semi-structured interviews were carried out individually, and three teachers' behaviors of problem-posing in data processing learning field were observed in the classroom. In the analysis of the data, descriptive and content analysis methods were used from qualitative data analysis techniques. In this context, the research findings have been subjected to descriptive analysis since those were evaluated according to the theoretical framework of Silver and Cai (2005). In addition, free problem-poses cases were analyzed according to the theoretical framework of information, practice and reasoning categories reported in Trends in International Mathematics and Science Study [TIMSS] (2011). In addition, content analysis was performed because the problems that were established by the teachers were analyzed according to the codes generated in the research process. While analyzing the problems in terms of content, draft codes were revealed and then the codes repeating in these draft codes were combined under four categories as conceptual, contextual, language-expression and cognitive skill. As a result of the study, it was determined that majority of teachers were able to pose solvable problems in the category of free and all of them in the category of semi-structured and structured. As a result of the content analysis, it was determined that some of the teachers made conceptual mistakes like posing a problem including imperfect knowledge, misusing the line chart, misunderstanding the starting point on the chart, failing to adjust data ranges equally and situating angles without establishing a centre point on the pie chart while forming a sentence for a mathematics problem. In the category of contextual, it was observed that some of the teachers storified their problems by associating them with their daily life, whereas some of them posed problems which required an operation. It was seen that some of the teachers did not pay much attention to language-expression and made mistakes like forming a complex problem text, incomprehensibility, linguistic mistakes and absence of a noun phrase. Another result of the study is that the teachers usually posed problems at the level of knowledge and applications that could be encountered in school books. There is a very limited number of teachers who can pose problems that require reasoning and these problems can be faced by students frequently. Considering these results; some suggestions have been made to develop the problem posing skills of the teachers in the study.