An investigation of elementary mathematics teachers' knowledge about open-ended questions

The aim of this study is to examine secondary school mathematics teachers' knowledge of open-ended questions. In this direction, phenomenographic research method was used. For the research, a two-stage questionnaire was applied to 40 secondary school mathematics teachers in different regions of Turkey. With the questionnaire questions, it was aimed to determine how the secondary school mathematics teachers defined the open-ended question, what kind of open-ended questions they prepared when open- ended questions were requested, and whether they chose the open-ended questions correctly among the prepared questions. While the data were analyzed through content analysis, descriptive statistics were also used. The findings of the study indicated that the teachers focused on the answer, form, function and solution process of the question while defining the open-ended question; also revealed that they used non-mathematical terms when describing the open-ended question and had particular difficulties in defining the mathematical open-ended question. Findings related to the examples presented by the teachers show that the teachers evaluate the questions with variable correct answers as open-ended, and do not present questions with infinitely correct answers. However, it was also observed that some teachers considered closed-ended questions as open-ended. In addition, some teachers had particular difficulties in presenting examples of mathematical open-ended questions. It was also observed that the participants did not have a comprehensive conceptualization of what an open-ended question was, which led to difficulties in determining whether some questions were open-ended. This study hence shows that teachers need a conceptualization of the open-ended question. For this, it should be noted that there is a need for both advanced research and purposeful professional development programs for teachers.