Mathematics teacher educators' philosophies of mathematics education and reflections of their philosophies on the teaching environment

Mathematics and philosophy are the two eyes of the mind. It is quite difficult to influence the reality of information without one or the other. Education, on the other hand, offers individuals the ability to use these two important disciplines. In this context, the purpose of this study is to determine the philosophies of mathematics teacher trainers and the reflections of these philosophies on learning environments. In this context, a multi-method research approach was used in the study. The participants of the study are 11 lecturers working in the departments of mathematics education at the faculties of education at state universities in Turkey and selection of the participants was determined by the theoretical sampling as a purposeful sampling method. The data of the study were collected through a scale, semi-structured interviews and classroom observations. Two-stage analysis method was used in the analysis of the data. In this context, constant comparative method was used in the first stage, and in this way, the theoretical infrastructure of the mathematics education philosophies of the academic staff was revealed. In the second stage, content analysis method was used and the findings obtained in this way were analyzed together with the findings obtained from the Education Beliefs Scale, whose sub-dimensions are educational philosophies developed by Yılmaz, Altınkurt and Çokluk (2011). Results of all analyses revealed that mathematics teacher trainers' mathematics education philosophies were categorized into four different groups: progressive mathematics educators, existentialist mathematics educators, pragmatist mathematics educators, and humanist mathematics educators. Then, the lessons of the teacher trainers falling into these four different categories were observed, video-recorded and analyzed. As a result of the study, the theoretical structure of mathematics education philosophies of mathematics education trainers in Turkey was revealed with a model. It was determined that mathematics and education philosophies created the basis for teaching mathematics in this model. While the educational philosophies of the instructors differ based on individual and society, their mathematical philosophies are divided into subjective and objective knowledge. The reflections of these philosophies on the teaching environment were been different. While the first group of progressive mathematics educators structured the knowledge in the lessons, the existentialist mathematics educators of the second group highlighted the student in the teaching process. While the third group of pragmatist mathematics educators associated the information that will be useful for students with their daily lives, the fourth group of humanist mathematics educators designed learning environments based on respect and love. As a result of the study, it is recommended that mathematics educators develop their philosophical competencies and develop mathematics teaching programs that they will be aware of. Researchers are suggested to investigate the relationship between the causes of philosophical approaches of mathematics educators, culture, etc. In addition, it is thought that the current study will make an important contribution to the literature in terms of presenting a theoretical framework that can be used in future studies on the philosophy of mathematics education.