Introduction. In modern conditions, the practice-oriented training of rescue engineers, whose professional activities are associated with high-risk situations, is being updated. The purpose of the study is to describe the implementation of the author's methodology of practical-oriented training in mathematics of future specialists in fire and technosphere safety and experimental verification of efficiency. Materials and methods. The experimental training was attended by 685 students of the Donetsk Institute of the State Fire Service (Russian Federation), studying in the specialty "Fire safety" and the areas of training "Technosphere safety" (321 students in experimental groups, 347 in control groups). Methods of mathematical statistics: Wilcoxon signed-rank test, Fisher's exact test, Chi square test, Student's t-test. Results. The methodology of practice-oriented teaching mathematics to future rescue engineers has been developed. Mathematical training of students based on a practice-oriented approach ensures the formation of students' practice-oriented skills and mathematical modeling skills in the field of civil protection, as well as the development of personal qualities of a rescuer. Practice-oriented learning technologies are used: integration of educational and future professional activities of students, educational and practice-oriented research activities. Practice-oriented teaching methods are used (imitation of the practical activities of rescue engineers, "rapid response" and practice-oriented visualization of mathematical objects). The implementation of the developed teaching methodology contributes to the effective formation of practice-oriented mathematical competence among students (T = 0.32, α = 0.05). Conclusions. The implementation of practical-oriented training in mathematics of future specialists methodology in fire and technosphere safety contributes to increasing the level of development of practical-oriented mathematical competence due to the formation of personal qualities of the rescue engineer and his value orientations, knowledge of mathematical and practical-oriented knowledge, skills and methods of activity in mathematical and computer modeling.
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