Abstract
One of the main tasks of the modern education system is to train teachers who are creative, capable of critical thinking, and equipped with research skills. In this context, the issue of forming research activity becomes especially relevant. This article identifies teaching methods and tools necessary for developing the research activity of future mathematics teachers and proposes a methodology for solving research-based problems in the process of teaching differential and integral calculus, illustrated with specific examples. The aim of the study is to determine the methodological foundations for forming the research activity of future mathematics teachers through problem-solving. The objectives of the study are to explore methodological aspects of developing research activity among future mathematics teachers in pedagogical universities and to develop content-based and methodological recommendations for the use of research problems in teaching differential and integral calculus. The effectiveness of the methodological recommendations proposed in the study was experimentally confirmed during the training of future mathematics teachers at the South Kazakhstan Pedagogical University named after U. Zhanibekov and the South Kazakhstan University named after M. Auezov. The scientific significance of the study lies in its contribution to the development of research activity among future mathematics teachers in the process of learning mathematical disciplines at the university level, as