An important result of the preparation of the future teacher of mathematics is the formed professional competences. The process of formation should be carried out systematically, starting from the first year. While studying at the university, the foundations of modern mathematical knowledge should be laid, the need for professional self-development and self-education should be formed. The purpose of the study: the development of tools that contribute to the formation and development of professional competencies of students, future teachers of mathematics, in the study of mathematical disciplines. The study analyzed the professional competencies of a mathematics teacher, the components of mathematical culture and established their relationship. The competencies that can be formed during the first year of study are defined. Identified the need to convert standard mathematical problems. Based on the research, a technology for creating special complex problems based on standard mathematical problems has been developed. Tasks consist of two parts: subject (mathematical) and professionally-oriented. Tasks can be used to form subject and professional competencies, diagnose their formation. The article presents the requirements for them, types and examples of tasks. The result of the assignments from the point of view of the formation of subject and professional competences is described.

With the development of civilization, the environment takes an increasing place in our lives. Analysis of the current state of environmental education of students in the University allows to make a conclusion about the need for a comprehensive approach to the problems of formation of ecological culture of future teachers. One of the directions is the integration of mathematics and ecology. Environmental knowledge can be generated when the study of mathematics through the solution of tasks with environmental content. This article presents mathematical tasks with environmental contents of the different sections of mathematics. Jobs can be used in the process of teaching mathematics students of a direction "Pedagogical education".

The professional training of subject teachers should be aimed at developing professional competencies that will allow them to be successful in their field, to be professionals, ready for change, and be able to adapt to various situations. A significant element of professional training at a university is pedagogical practice, during which the student performs the subject teacher functions. However, students in practice often face such difficulties as organizing their activities and the activities of students in the lesson, allocating time to the lesson stages and observing the time schedule, selecting didactic materials, evaluating outcomes of students’ activities, solving unexpected pedagogical situations, and others. Particular attention should be paid to the psychological readiness of the future mathematics teacher to work at school. Therefore, it is essential to prepare students methodically and psychologically for the implementation of primary professional activities in teaching practice. This can make it feasible to carry out methodological practice, which is a transitional stage between educational and industrial practice. The issue of organizing methodological practice is currently new. Based on the literature analysis and the experience of organizing and managing practices, the paper proposes a model of methodological practice, which is aimed at applying active teaching methods to prepare future mathematics teachers for the main activity in teaching practice, namely, preparing and conducting lessons. The model includes seven stages with tasks, describing active learning methods and student activities.

Профессиональная компетентность студента начинает формироваться в течение его обучения в вузе и затем совершенствуется только в процессе его профессиональной деятельности. Важную роль в процессе профессиональной подготовки обучающихся играют интегративные взаимодействия на разных уровнях. С их помощью можно эффективнее и на качественно новом уровне решать задачи профессионального образования и развития студентов. Анализ научно-методической литературы показал, что в процессе обучения будущего педагога принцип интеграции не реализуется в полной мере. Недостаточно разработано методическое сопровождение процесса профессиональной подготовки учителя математики с применением интегративного подхода. Однако полноценное развитие и формирование профессиональной компетентности будущего педагога возможно только во взаимосвязи различных предметов, изучаемых в вузе. Целью исследования является определение методов, форм и средств обучения, которые могут способствовать профессиональной подготовке будущего учителя-предметника, построенной на основе принципа интегративности. В статье рассматривается вопрос о формировании профессиональной компетентности будущего учителя математики с точки зрения интегративного подхода, выявлен его системообразующий характер. Представлены разработанные материалы и задания для формирования профессиональных компетенций через применение принципа интегративности в обучении будущих учителей математики; описан опыт их применения.Ключевые слова: интегративный курс по математике, интегративный подход в обучении, интеграция знаний, интегрированные задания, профессиональная компетентность учителя математики, технология интегрированного обучения