The paper states that the current conditions in which the education system is located, and the rapid development of IT require constant improvement of methodological materials, taking into account the full capacity of the current software. Examples of programs necessary for preparation of methodological materials for high-quality classes are given. The purpose of the paper was to identify the Wolfram Mathematica didactic potential when conducting classes in the disciplines of the geometric and graphic profile at a technical high educational institution. In this paper has been performed analysis of literature sources both domestic and foreign ones on the Wolfram Mathematica system application in science and teaching of various disciplines. It has been shown that the program use scope is very wide, in fact, it is comprehensive and requires additional and in-depth study. Examples of Wolfram Mathematica using in mathematics, physics, chemistry, geometry, robotics, virology, and the humanities are given. In the paper have been provided examples for pedagogical design of simulation models for an electronic course on descriptive geometry in the Moodle system. An example of code written in the Wolfram Mathematica is provided. Interactive models developed during the design are presented, which allow the user to change the constructed curves and surfaces’ parameters. Have been defined some functional capabilities of the system, and has been revealed the Wolfram Mathematica didactic potential for teaching geometric and graphic disciplines. Have been considered other authors’ similar models, which can be used in the educational process to increase the clarity of the material presented in the classroom. In conclusion it is pointed out that interactive visualization in the "Descriptive Geometry" discipline, together with classical working practices, significantly enriches the content of geometric education.

The present paper presents the results of an analysis of the functioning principles of contemporary CAD systems and of their capabilities for modern process modelling. Requirements to process modelling software have been set forth. Physical processes during cutting of metals have been considered. The selection of Delphi programming environment has been substantiated. An interface, an algorithm and a program code for part machining modelling software has been developed for an all-purpose thread-cutting lathe with 3D graph involvement in OpenGL. A description of the software work and its specifications have been provided. Ways have been defined for further improvement and development of the developed software, as well as its promising application fields.

The paper states that the current conditions in which the education system is located, and the rapid development of IT require constant improvement of methodological materials, taking into account the full capacity of the current software. Examples of programs necessary for preparation of methodological materials for high-quality classes are given. The purpose of the paper was to identify the Wolfram Mathematica didactic potential when conducting classes in the disciplines of the geometric and graphic profile at a technical high educational institution. In this paper has been performed analysis of literature sources both domestic and foreign ones on the Wolfram Mathematica system application in science and teaching of various disciplines. It has been shown that the program use scope is very wide, in fact, it is comprehensive and requires additional and in-depth study. Examples of Wolfram Mathematica using in mathematics, physics, chemistry, geometry, robotics, virology, and the humanities are given. In the paper have been provided examples for pedagogical design of simulation models for an electronic course on descriptive geometry in the Moodle system. An example of code written in the Wolfram Mathematica is provided. Interactive models developed during the design are presented, which allow the user to change the constructed curves and surfaces’ parameters. Have been defined some functional capabilities of the system, and has been revealed the Wolfram Mathematica didactic potential for teaching geometric and graphic disciplines. Have been considered other authors’ similar models, which can be used in the educational process to increase the clarity of the material presented in the classroom. In conclusion it is pointed out that interactive visualization in the "Descriptive Geometry" discipline, together with classical working practices, significantly enriches the content of geometric education.

The possibilities of Wolfram Mathematica (WM), which is a package of symbolic mathematics, are endless. In this paper are investigated the possibilities of WM software product contextualization in the process of geometric-graphic teaching of students; is considered the experience for using a set of WM computational algorithms in teaching practice. The source codes and output data of our own WOLFRAM projects are offered, which are illustrative, in the form of interactive graphs, visualization of the solution for one of DG course’s basic problems on construction of points A, B, C and D, given by coordinates in space; construction a plane of general position passing through points A, B and C; determining positions of these points and the constructed plane in space; and also on determining the point D belonging to this plane. Have been presented examples of several of the existing WOLFRAM projects in the form of interactive graphs used in teaching. The study of applied issues and the ability to translate a professional problem into mathematical language, working in WM, provides a student with an opportunity to assimilate the necessary competencies. Interactive visualization of solving DG problems, which can be carried out using WM, together with traditional problem solving, enriches the content of geometric education, introduces new opportunities in organization of the educational process, allows stimulate, maintain and increase students' interest in studying the discipline and further research in the area of DG. However, the ability to work in WM cannot replace the fundamental knowledge obtained by students of a technical high educational institute from the traditional course, but only complements the DG course by WM acquaintance.

Introduction. For the last thirty years, UNESCO has been repeatedly raising questions of accessibility and quality of education for every child, teen, and adult by implementing the “Education for All” program. The new concept of education proposed by UNESCO aims at transforming people’s lives and formulates the following sustainable development goal “To provide inclusive and equitable quality education and create lifelong learning opportunities for all. One strategy for achieving this goal is to use and develop information and communication technology (ICT) to strengthen education systems, knowledge dissemination, access to information, and quality and effective learning. The aim of the work is to increase the efficiency of students’ learning of geometrical and graphic disciplines by developing a pilot electronic course in LMS Moodle and special software implementing elements of individualization of the learning process. Materials and methods. Theoretical research methods included generalization of scientific and pedagogical literature on formation of spatial thinking. Empirical research methods included testing, interviewing, and questioning using Google forms. Mathematical methods of research included algorithmizing and programming. Python 3.9 language and PyCharm development environment were used for writing the trainer program. The OpenCV, Matplotlib and Keras libraries, Microsoft PowerPoint, Microsoft Visio and CAD Compass-3D were used to create methodological materials Results. The software simulator for developing spatial thinking of engineering students studying “Descriptive Geometry” discipline has been developed in three versions. Conclusion. The ideas about the level of spatial thinking of modern students are supplemented. The original programs for the implementation of the elements of individualization of the educational process in the discipline of “Descriptive geometry” and algorithms of its work were developed and introduced into the scientific turnover, as well as the proposed pedagogical conditions of their use. Practical significance lies in the creation of learning and teaching methods and program basic elements for the use of end-to-end digital technology in the learning process.