Development of Instrumental and Methodological Support for the Assessment of Students ' Knowledge in Mathematics in the Framework of Hybrid Intelligent Learning Environment

Abstract

The article is devoted to the development of an integrated complex of knowledge base and artifi-cial intelligence tools for assessing students' knowledge in mathematics within the framework of a hybrid intellectual learning environment. In accordance with the structural diagrams of mod-els of intellectual assessment of knowledge and creative potential of schoolchildren in mathe-matics, the structure of the corresponding knowledge base is formalized. The knowledge base is developed within the framework of data mining methods to create a module for monitoring and assessing knowledge in mathematics. As a methodological basis for the development of a knowledge base, the idea of V.P. Bespalko about the representation of the possible structure of human activity in the form of suc-cessive levels of assimilation, reflecting the development of the student's experience in a given subject in the learning process. The levels of assimilation (student, typical, heuristic, research) are determined through the ability to solve problems of the corresponding type. A formalized in-dicator of a student's achievement of a particular level of assimilation of educational material (level of training) is the coefficient of assimilation; assessment of the assimilation of material on a specific topic or section is provided for both at each of the above levels, and in general. The examples of the formation of a knowledge base for assessing the skills and abilities of schoolchildren in algebra are considered. To model the educational process, we propose methods for solving clustering, dimen-sionality reduction and classification problems based on machine learning and artificial neural networks. The foundations for the development of integrated complexes of knowledge bases and artificial intelligence tools to ensure the educational process are presented. The results obtained are aimed at creating methods that provide the processes of operational learning, control and assessment of knowledge, competencies and procedures, the level of formation of subject and professional competencies of students in the information and educational intellectual environment.