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THE PROBLEM OF DEFINITION OF THE PURPOSES AND CONTENT OF THE SUBJECT “MATHEMATICS” FOR STUDENTS OF HUMANITARIAN DEGREE PROGRAMMES // Tomsk State Pedagogical University Bulletin. 2012. Issue 2 (117). P. 175-179

In the article there is an attempt to designate and solve the following problems: 1) the analysis of the conceptual bases of teaching methods of mathematics to students of humanitarian degree programmes, 2) understanding of current issues related to the introduction of the federal state educational standards of the third generation.

Keywords: subject “Mathematics” for students of humanitarian degree programmes, the federal state educational standard of the third generation, mentality

METHOD OF REFLEXIVE LEARNING TO SOLVE MATHEMATICAL PROBLEMS // Tomsk State Pedagogical University Bulletin. 2020. Issue 6 (212). P. 92-98

Introduction. The method of teaching mathematics has a long history, which reflects all the success of teachers in creating a system of mathematical education both in Russia and in the world. Despite the fact that this system has been functioning for a long time and has produced outstanding results, mathematical subjects are currently the most difficult subjects for students both at school and at University. This leads to the fact that there are extreme points of view calling for the exclusion of the subject «Mathematics» from school and University courses due to its difficulty and low student performance. The solution to this problem in the modern world can be the use of psychologically-oriented learning concepts, one of which is the theory of reflexive learning. This article presents one of the aspects of applying this theory to the practice of mathematical education, namely reflexive learning to solve mathematical problems. The purpose of the article is to develop a methodology for teaching a «generalized algorithm» for solving mathematical problems based on stimulating reflexive mechanisms of activity. Materials and methods. The research material is the work of domestic and foreign authors devoted to the problems of teaching methods for solving problems and the psychology of reflexive learning. Their ideas allowed us to apply the theory of reflexive learning to teaching students to consciously regulate their own mathematical activities. Reflexive skills are the basis of the ability to intellectual self-regulation, and, consequently, a condition for productive intellectual mathematical activity. Results and discussion. The authors see the possibility of stimulating students’ cognitive activity based on reflection of their thought processes as one of the ways to solve psychological and methodological difficulties in learning to solve mathematical problems. The method of teaching problem solving involves teaching students to consciously perform four main stages. Formation of skills to analyze the problem, the solution to this problem, proper design of the idea of solving the problem and verifying the implemented solution is based on the mental experience of the student with the use of reflective learning strategies. Conclusion. As a result of reflexive learning to solve mathematical problems, students will develop a «generalized ability» to solve mathematical problems.

Keywords: reflexive learning, self-regulation training, reflexive strategies, mathematical problems, methods of teaching mathematics