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. In recent years, the problem of training a new generation of mathematics teachers who have fundamental mathematical knowledge in combination with formed methodological competence and fluency in digital technologies has become topical.  The purpose of the article is to present a scientifically based system for training future mathematics teachers, created at Donetsk National University, based on a comprehensive program for managing the project and heuristic activities of students for their productive work in a modern school. Methods. The study involved 125 people studying at Donetsk National University (65 students of the direction of training "Pedagogical education" (Profile: mathematics and computer science) – an experimental group, 60 people of the direction of training "Mathematics" – a control group). The effectiveness of a comprehensive program for managing students' project and heuristic activities was assessed according to three criteria: heuristic and didactic (HD); methodological and mathematical (MM); project and activity (PA). The meters selected: author's texts of control papers with heuristic tasks and computer testing systems (for HD and MM criteria), assignments for the development of author's educational projects using IT, students' term papers and theses (for PA criterion). To analyze the effectiveness of the complex program, the Student's t-test was used. Results. During the experiment, it was revealed that for each criterion, the average values of their indicators (in fractions of one) in the experimental group increased significantly. For the HD criterion, the level of heuristic skills formation among students of the experimental group increased from 0.51 to 0.65, for the MM criterion, the levels of mathematical and methodological competence formation increased from 0.67 to 0.753, for the PA criterion, the level of mastering the methods of project activities changed from 0.57 to 0.756. The empirical value of the statistics of the Student's criterion t = 2 (p &lt; 0,05) obtained in the assessment procedure proves that changes in the results of training are not random, which means that the proposed comprehensive program is more effective than the traditional one. Conclusions. The preparation of a future mathematics teacher based on a comprehensive program for managing the project and heuristic activities of students ensures the formation of heuristic and didactic, methodical and mathematical, project components of the teacher's professional activity, which are necessary for teaching schoolchildren of the Z generation.

The system of training a new generation of mathematics teachers based on project and heuristic activities