The purpose of this research is to evaluate the application methodology of blended learning technology in mathematics education, with the views of teachers. In this study, the case study method, which is one of the qualitative research methods, was used. A total of 80 mathematics teachers working in various high schools in Nur Sultan city of Kazakhstan participated in the research. Research data were collected with a semi-structured interview form prepared by the researchers. As a result of the research, most of the mathematics teachers stated that the students' attitudes towards the mathematics lesson were negative. The majority of teachers participating in the research stated the combination of the superior features of face-to-face learning environments, diversity in learning and teaching methods, diversity in learning–teaching materials and increase in student success as the advantages of mathematics education in a blended learning environment. The majority of teachers participating in the research stated that the inadequacy of programmes suitable for blended learning, the deficiencies of software and hardware to be used in the course and the inability to use technology efficiently and effectively are the disadvantages of mathematics education in a blended learning environment. In-service training programmes should be organised to develop teachers' self-efficacy regarding blended learning environments and to ensure that they manage assessment and evaluation processes correctly. Keywords: Psychological and pedagogical foundations, preschool teachers, teacher competencies

This research aimed to form a technology for creating reasonable reasoning competence of mathematics students by solving open problems using the help of mathematics and technology, and the research was prepared for this purpose. The research was prepared and designed in the fall academic year of 2022–2023, and 256 students studying in the mathematics department in Kazakhstan participated in the research. An application dimension was prepared for the students participating in the research and they were allowed to participate in this application for 3 weeks. Immediately after the trainings to be given in the research were given, the data collection tool was applied to the participant groups and this information was obtained from them. Keywords: Mathematics, technology, reasoning, distance education;