Supporting middle school mathematics teachers' pedagogical ways in their teachings based on hypothetical learning trajectories

The purpose of this study is to enable the elementary school mathematics teachers to make progress in the pedagogical ways that they can use in the teaching process designed in accordance with the expected learning trajectories. In this study, conducted as participatory action research, it was aimed that two junior high school math teachers and the researcher would improve their teaching practices by working in collaboration. That is, it was aimed to enable the math teachers to make progress in pedagogical ways. The research was completed in 10 weeks. The expected learning trajectories for the sixth grade algebra learning areas were planned and put into practice by the teachers. The focus was centred on the pedagogical ways used in teachers' teaching practices. Preliminary discussions with the teachers, instructional videos and the researcher's field notes were used as data sources in this research. It was shown that with professional development activities applied in this research, the teachers displayed a major change and development in knowledge and skills they use in their teaching practices. Such changes and developments took place within the context of the use of student ideas, educational ways based on classroom discussions, the use of demonstrations and the knowledge of mathematical instruction. Recommendations are offered with respect to the findings of this study carried out to enable teachers' professional development and for similar studies that can be carried out in the future. Keywords: Hypothetical learning trajectory, Middle school mathematics teachers,Algebra, Pedagogical ways.