Modernization of the education system and the emergence of innovative learning technologies can improve the educational process. The use of augmented reality technology improves the learning of individual students, their motivation, as well as helps in organizing teamwork, group cooperation. As the topic of augmented reality in education is quite new and little studied for STEM education, the study reviews publications on this topic, describes the concept of augmented reality, the analysis of augmented reality technologies is carried out, which are adapted to the teaching of natural and mathematical disciplines. The role of STEM approach with augmented reality in the educational process is determined. An example of the use of augmented reality as part of a robotics project is given.

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The specialized training influence to the choice of further direction of study is considered in the work. The assumption that early involvement of students in the study of natural and mathematical disciplines, in particular mathematics is given. It will stimulate young people to get STEM education in future. The essential element in future professional choice, development and formation is the issue of motivation for learning. It is important that modern students are gradually losing their incentive to study. Almost a third of those who choose the appropriate study profile have contradictions between professional self-determination and the availability of the necessary knowledge for the profession, between choosing a higher education institution and being able to enter in it. The contradiction requires purposeful formation of a conscious choice of future activities. The conducted research has shown that the basis of the motivational component of the choice of STEM-learning is studying of natural and mathematical disciplines by modern teaching technologies and organizing of additional lessons system based on the projected teaching methods. It satisfies the growing needs for intelligence, knowledge, motivational beliefs to understand the specifics of the future profession.

The paper deals with issues of the metric geometry basics. In particular, the concept of rectilinear placement of points is considered, based on the axioms of the distance between two points of metric space. This approach allows forming a modern view of the property of straightness in the pupils. This paper analyzes the content of existing mathematics textbooks for general educational institutions to acquaintance of pupils with the elements of metric geometry. The first part of the paper provides information about the rectilinear placement of points; it can be used in Geometry lessons in the 7th – 9th grades. Set of linear functions are considered as examples of points of metric space. The similar work was done in the second part of the work for geometric material of the 10th – 11th grades. In addition, some simple examples of metric spaces that may be accessible to pupils of the relevant classes are discussed. The purpose of the work is gradually introduction of pupils to the elements of non-Euclidean geometries, to form a generalized notion of the distance between the points and rectilinear of their placement. The work can be used for Mathematics teaching at school and for retraining of teachers of Mathematics.

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