No 4 (2021)

Geometry is one of the complex disciplines where many facts are interconnected. It is possible to develop the idea of facts interrelations through correlation using the duality principle. The duality principle is known in projective geometry, mathematical logic. This principle is clearly pronounced in one of the theorems of new triangle geometry. The traditional analytical geometry course does not study the facts of new triangle geometry. To reinforce many topics of the analytical geometry course, for example, “The distance between two points”, “The symmetrical form of the equation of a line”, “The angle between two lines”, it is reasonable to consider some facts from the new triangle geometry in the Cartesian coordinate system. Thus, an element of novelty is introduced to the reviewed material. The guidebooks on triangle geometry solve tasks through classical approaches or applying barycentric coordinates not using analytical geometry formulas. The paper proposes the constructing technique for the couples of exercises using the duality principle in the plane geometry teaching methods. Tasks are constructed for the Cartesian coordinate system as this allows demonstrating the duality of points in the drawings. In the composed exercises, two drawings are constructed in parallel columns. In different cases, the points can be the triangle-apexes, an orthocenter, or a height base. The initial triangle sides are located on the axes of coordinates, and their side lengths set up Pythagorean triple for better understanding the task-solving algorithm by the students. The symmetrical form of the equation of a line shows the necessity of analytical study since it is difficult to check the distance from the orthocenter to the orthotriangle sides in the drawings due to the small value. For many such information units, the aggregation relationships (whole-part) are set up, reflecting the geometric embedding of components.

Nowadays the number of foreign students entering various educational programs at Russian universities is actively growing. Multimedia technologies are actively used for their training along with traditional forms of work. This paper discusses the features of working with video material in physics lessons in a foreign language classroom. Such classes help to increase the motivation of students to acquire knowledge and successfully master the main course material. The authors focus their attention on a visual demonstration of the basic provisions of the general theory of relativity, for which the Oscar-winning film “Interstellar” by Christopher Nolan is chosen. The paper describes the main stages of the lesson such as preparatory, viewing and final, as well as their main aims. The authors offer different types of tasks and exercises that prepare students for watching a scientific and feature film on the topic under study, control their understanding and learning of theoretical information. The paper provides examples of the implementation of all types of speech activity while working on the selected topic. The authors demonstrate that this form of the lesson allows one to form not only communicative competence, such as the ability to answer questions and present the studied material, but also professional competence, such as the ability to solve tasks, formulate hypotheses, and scientifically argue one’s point of view. The proposed system of organizing the lesson proves the importance and efficiency of including video material in the process of studying physics. It is necessary to emphasize the practicality of the work that offers a well-planned lesson, which can be adapted to the level of a student (either a student of the pre-academic programs, bachelor’s or master’s). In addition, the presented types of tasks can form the basis for creating a similar lesson on any other topic.

Positive body image is a construct that has actively been formed in the last two decades. Its appearance in the psychological discourse was a kind of response to the spreading of the practice of studying the body image from the point of view of pathology in the context of clinical studies of the second half of the XX century. Currently, the world has accumulated some experience in studying a positive body image, which is especially relevant in the pandemic era. The paper analyzes contemporary foreign publications considering a positive body image published in English-language journals on developmental, clinical, and social psychology from 2001 to 2021. The research allows monitoring the transformation of the studied construct in the context of humanistic and positive psychology that considers the body image both through the concept of appearance and through such definition as body functionality. The emphasis on the functionality within the analysis of the embodiment problematics allowed shifting the focus of the psychologists’ attention from the strategies of object attitude to a body to the strategies of taking care of a body as a value. The authors highlight the key areas of studying a positive body image at the current stage of development of science: the characteristics of a structure and components of the phenomenon under the study; the search for the sociocultural, family, and individual-psychological factors influencing the formation of positive body image; the assessment of the efficiency of prevention and correction programs aimed at the promotion of healthy body image; the analysis of positive body image as a recourse of a personality in the pandemic epoch.