The article discusses the current technology of three-dimensional modeling and prospects for its implementation in the structure of the modern system of professional training of IT specialists according to the concepts of sustainable development. The problems have been actualized and the methodology for three-dimensional modeling and printing has been proposed by using modern software, in particular, the features of using the basic core of geometric design and software preparation of the model for printing have been presented. An algorithm for the formation of practical skills of students in hardware preparation and calibration of 3D printers, the adjustment of the main technological parameters of work, preparation for the manufacture of a spatial model has been proposed. The developed algorithm promotes to the formation of practical skills of modeling and printing three-dimensional objects in future IT-specialists of vocational education, contributes to the formation of their professional competencies. In turn, this contributes to the formation of professional competencies among future IT specialists and creates the need for systematic improvement of knowledge and their creative implementation in practice with a more efficient use of IT technologies, which is the basis in solving the problems of sustainable development of society.

The investigation deals with designing and developing of intellectual system of movies recommendations  based on the collaborative filtering using the Python software environment. In particular, the approaches (Content-based approach, Collaborative filtering, Hybrid models) in recommendatory system construction with the help of neural networks have been analyzed. It has been established that it is difficult to implement and learn the Content-based approach and it strongly depends on the subject area. Collaborative filtering is more simple in implementation, training, it is universal, but it has a flaw in the form of a «cold-start». Accordingly, the collaborative filtering has been chosen for the design and development of the intellectual system of movies recommendations. While designing a system of recommendations based on collaborative filtering, the Naive Recommendations, Recommendations based on average ratings of similar users, Recommendations based on average user ratings and similarity matrix have been described; their algorithm and their implementation using the Python software environment have been demonstrated. As a result the intellectual system of recommendations has been realized and it can offer a movie to the user according to his/her preferences.

The article deals with the effectiveness of testing as a method of pedagogical control of the professional knowledge of future specialists with higher education. The purpose of the article is to describe the advantages and disadvantages of mass control technologies, the reasons of weak development of pedagogical testing in domestic practice, to give recommendations for a partial solving the problems with the introduction of pedagogical testing. Methods. The authors implement the purpose with the help of such methods as analysis, comparison, generalization, systematization, testing. The results. The authors state that with the paradigm shift in education the main role in controlling the student’s knowledge was shifted to testing, which gave us the possibility to reduce a teacher’s workload and reduce the time for the process of knowledge control itself, as well as to activate the process of self-control among students. The authors emphasize that due to the modern requirements for professional knowledge of future specialists with higher education, they must have an advanced level of information culture and skills to work with printed and electronic source of information, systematize and interpret the professional information which they have obtained during the reading task. There is a description of two insights as for the advantages and disadvantages of mass control technologies in the article. The reasons of weak development of pedagogical testing in domestic practice have been also described. The recommendations for a partial solving the problems with the introduction of pedagogical testing have been given. Conclusions. The article deals with a method of problem solving of education management efficiency. It’s considered as a minimization of time to achieve the advanced level of success in a particular topic. In addition, the mathematical description of the success function and the function of time-consuming have been given in the article. Due to these, a method of minimizing training time for proving the required level of success has been obtained. The article suggests also a description of the applying of a given model for the education structure adaptive management, which saves the substantial time and teacher’s workload without losing the quality of learning material. The authors make an attempt to define the reasons for the absence of testing at the Ukrainian educational services market.