The work is devoted to the consideration of improving the quality of teaching students the discipline “Numerical methods” through the development of the cognitive component of computational thinking based on blended learning. The article presents a methodology for the formation of computational thinking of mathematics students, based on the visualization of algorithmic design schemes and the activation of the cognitive independence of students. The characteristic of computational thinking is given, the content and structure of computational thinking are shown. It is argued that a student with such a mind is able to manifest himself in his professional field in the best possible way. The results of the application of the technique are described. To determine the level of development of the cognitive component of computational thinking, a diagnostic model has been developed based on measuring the content, operational and motivational components. It is shown that the proposed method of developing computational thinking of students, taking into account the individual characteristics of students’ thinking, meaningfully based on the theoretical and practical aspects of studying the discipline, increases the effectiveness of learning the course “Numerical methods”. The materials of the article are of practical value for teachers of mathematical disciplines who use information and telecommunication technologies in their professional activities.

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Problem relevance. Due to the multi-departmental concepts and the different content of educational programs of schools and universities, a serious problem arises of the succession and continuity of the education system along the “vertical” in general and subject teaching in particular. Another didactic problem is the need to ensure interdisciplinary connections of basic courses in the traditional disciplinary model of the educational process for more effective and expedient formation of certain student’s competencies sets. In this regard, it is of interest to create new organizational and meaningful approaches to training specialists without a significant restructuring of the traditional educational process.The purpose of the article is to substantiate a collaborative model of subject training of students in a school-university cluster of disciplines, which ensures the succession and continuity of education at school and university.Methodological basis. On the example of three disciplines “Programming”, “Computanional Methods”, “Information Technologies in Education”, a cluster model of teaching schoolchildren and students in the direction of training “Mathematics and Computer Science” has been designed and implemented. A feature of the considered school-university cluster of disciplines is a unified methodological base of target, meaningful and didactic elements that form and develop the calculative-algorithmic component of the computational thinking of students. The basis of the means and methods of teaching in the cluster is made up of cognitive techniques and a platform of “computational and algorithmic primitives” — solving elementary task template. A recursive approach is used in the methods of cluster subject teaching of schoolchildren and students.Results and Conclusions. The model of the created disciplinary cluster “Programming — Computanional Methods — Information Technologies in Education” contributes to the formation and development of the calculative-algorithmic component of the computational thinking of schoolchildren and students, and also forms their assigned groups of competencies. The school-university cluster of disciplines ensures real succession and continuity of school and university education, without unnecessary, sometimes artificial, labor-intensive additional organizational and methodological means and techniques. The approach under consideration can be used to create clusters of disciplines in various educational areas, allowing their meaningful collaboration and forming given competencies sets and schoolchildren’s and student’s cognitive abilities.

Problem and goal . The issues of criteria-based evaluation of the student's educational results remain relevant for the modern theory and practice of education. As a rule, measures to monitor educational results and resources in educational institutions are carried out by expert, manual, non-automated methods. In accordance with the directions of digital transformation of education, it is necessary to create a technological assessment system that meets the requirements of modern society, subject to automation and intellectualization. The purpose of the work is to substantiate a new model of criteria-based assessment of the quality of the educational result, based on the mathematical methods of the theory of clustering and pattern recognition and allowing to automate the procedures for assessing the quality of educational objects, resources, educational and personal achievements of students. Methodology. The quality of an educational result or resource is determined by criteria indicators, which can be represented as features of the evaluated object using the information vector. By clustering the set of acceptable objects into three classes - with low, medium and high quality - it is possible to evaluate an object by its belonging to one of these classes. Clustering is carried out on the basis of a mining algorithm, the metric of city blocks is taken as a measure of the similarity of objects. Results. A program has been developed that consists of a source data module, a clustering module, and a recognition and training module. The model results of the program correlate with traditional rating assessments, in which the quality of the object is determined by a point scale. The obtained test results confirm the validity of the recognition algorithm and the correctness of the software product. Conclusion. Thus, the proposed model based on clustering and the recognition method showed the possibility of automated assessment of the quality of educational results of trainees and educational resources.

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