An investigation of middle school mathematics teachers' evaluations of skill-based questions in terms of mathematical competencies

In this study, middle school mathematics teachers' solutions to skill-based mathematics questions and their evaluations in interviews were examined in terms of mathematical competencies. Mathematical competence demands are considered as communication, strategy development, mathematization, representation, use of symbols, operations and formal language, and reasoning and argument development, and the aim of mathematics teaching is to put knowledge and skills to work when necessary through the development of mathematical competencies. The participants of the study were 13 mathematics teachers working in public and private secondary schools affiliated to the Ministry of National Education and the participants were determined by snowball sampling method. The data collection process was carried out in the second semester of the 2021-2022 academic year. The method of the study is a case study from qualitative research methods and it is important to use various data collection tools to make an in-depth examination. In this direction, semi-structured interviews were conducted with each participant after the mathematics teachers solved 12 questions in the mathematics test of the High School Transition System numerical section booklet determined by the researchers. In the semi-structured interviews, it is aimed to determine how the teachers reveal their mathematical competencies with questions about six mathematical competencies for the LGS questions they solved. Mathematics teachers' question solutions and interview protocols were analyzed within the framework of mathematical competencies. When the mathematics teachers' solutions to the questions were analyzed, it was seen that different solution methods indicated different levels in terms of mathematical competencies. In the solution methods in which strategy development, representation and reasoning, and argument development competencies were activated at high levels, mathematization and using symbols, operations, and formal language competencies were activated at lower levels. However, in some solution methods, it was seen that the competence of using symbols, operations and formal language was prioritized by performing operations that included outcomes that were not included in the mathematics curriculum. When the evaluations made by the teachers in the interviews in the context of mathematical competencies were analyzed, it was revealed that mathematical competencies were evaluated at a lower level than the activated level. It was observed that teachers had difficulty in evaluating the actions they performed during the solution process and accordingly, the competencies of strategy development, mathematization, representation and reasoning, and argument development, especially communication, were evaluated at lower levels than the activated level. In line with the results of the study, it is recommended that in-service trainings on mathematical competencies be organized for mathematics teachers to improve their ability to analyze mathematical tasks in the context of mathematical competencies.