Integration of knowledge while mathematical courses studying by prospective teachers of Mathematics

The paper focuses on the main directions of integration in modern education. The basis for the examples and conclusions were fundamental studies in the field of Philosophy, Pedagogy and Mathematics. Integration as a general methodological concept in the context of the paper is more concerned with the integration of knowledge in the content of the school course of Mathematics in order to recognize and operate on them in various academic disciplines and the surrounding life. As examples of integration the author gives various concepts from different branches of mathematics (straight line, proportion, symmetry), methods of solving equations and inequalities (functional-graphic, coordinate-vector along with traditional methods), methods of proving identities and inequalities (geometric methods in Algebra and algebraic methods in Geometry). The study of mathematical content in the classroom at school should be a systematic and multifaceted process for the teacher to establish and disclose the links between different concepts, their properties, as well as methods of applying knowledge in a variety of situations. In mathematical courses and the course of Mathematics teaching methods the author offers to pay special attention to prospective teachers’ ability development to consider mathematical objects from different sides, thereby establishing links between different sections of Mathematics. Various special courses (or elective courses) on relevant subjects are also an important part of prospective teachers’ professional training, which can be purposefully used to expand inter-subject relations. In addition, the subject of term and final papers can also be made up taking into account different interpretations of mathematical concepts and methods. The author also pays great attention to the organization of such work with students. Only free knowledge enables the teacher to form students’ solid educational results at the level of knowledge and educational activities for the purpose of their further use in professional activities and in everyday life.