Problem identification skills of secondary school mathematics teachers: An investigation in terms of mathematical errors and minconceptions

The purpose of this study is to examine middle school mathematics teachers' problem identification skills regarding the root cause of an erroneous student answer. To this end, a case study design based on qualitative approach was used. For the study, 20 middle school mathematics teachers with different professional experiences working in different regions of Turkey were interviewed. Teachers were asked open-ended questions about fraction and set concepts in order to determine how they defined these concepts and how they explained the student's way of thinking in the scenario, whether they could express the student's answer as a misconception, and how they expressed the reasons (epistemological, pedagogical and psychological) that led to this misconception as a problem identifier. The data were analyzed by content analysis. Descriptive statistics as well as quotations from the teachers' responses were also used for presenting the finding. The findings of the study on the fraction part showed that teachers were not as aware of the division, ratio, measurement and operator meanings of fractions as the part-whole meaning. It was also observed that teachers had difficulty in explaining student thinking about the fraction question and expressing this way of thinking as a misconception. The findings also revealed that some teachers accepted the incorrect student answer as correct and therefore could not identify the problem in the student answer. The findings of the study on the set concept show that teachers defined the concept of set based on elements with common properties and used examples of sets consisting of elements with common properties. It was revealed that they had difficulty in explaining the student's way of thinking and identifying the problem situation in student responses that contained misconceptions about the set concept. The fact that some of the teachers had similar misconceptions about both fractions and sets as the students, even though they assumed the role of a problem identifier, showed that their content knowledge was not sufficient. As a result, this study shows that the teachers were not able to identify the root causes of erroneous student responses at the level of an expert problem identifier, but rather addressed errors and misconceptions with a practitioner approach. This situation reveals that teachers should be competent in having an expert perspective in addressing and eliminating student difficulties, misconceptions and errors encountered.