A research object is a process of professional preparation of future teachers of physics and mathematics specialities; the subject of research is pedagogical terms of forming of mathematical competence of future teachers of physics and mathematics specialities by facilities of educational-playing technologies; research aim: to ground theoretically and experimentally check efficiency of pedagogical terms of forming of mathematical competence of future teachers of physics and mathematics specialities by facilities of educational-playing technologies; for the decision of the set forth tasks in research drawn on the complex of correlated theoretical and empiric methods of pedagogical research: theoretical: study, analysis and generalization of scientific literature for an acquaintance with the state of the investigated problem; systematization, comparison, generalization of the obtained theoretical data; empiric: supervision, questionnaire, method of independent estimations for diagnostics of level of forming of mathematical competence, pedagogical experiment - for verification of efficiency of pedagogical terms of forming of mathematical competence of future teachers of physics and mathematics specialities by facilities of educational-playing technologies; methods of mathematical statistics - for treatment of experimental work performances; a scientific novelty and theoretical value of research consist in that essence of "mathematical competence of future teachers of physics and mathematics specialities" is first exposed, that reveals in a presence thorough mathematical knowledge, abilities, skills and understanding of their importance, ability to apply ability in educational and professional activity, ability to decide physical and mathematical tasks and problems, to proof motivation to perfection of professional qualities; determined and scientifically granted the structure of outlined construct (motivational, substantial, operational, value-reflexive components) and pedagogical terms of forming of mathematical competence of future teachers of physics and mathematics specialities (actualization of positive motivation of students, use of didactics games during teaching of physics and mathematics disciplines, realization of project activity); the criteria of formed of mathematical competence of future teachers of physics and mathematics specialities (motivational, substantial, operational, value-reflexive) and their indexes are reasonable; characterized levels of forming of mathematical competence of future teachers of physics and mathematics specialities (high, sufficient, middle, low); a concept "project activity" and "method of projects" is specified; further development was purchased by the uses of didactics games during teaching of фізико-математичних disciplines, realization of project activity in the process of preparation of future teachers of physics and mathematics specialities for the effective forming of mathematical competence.
