Psychological and Pedagogical Conditions of Functioning of a Hybrid Intellectual System of Teaching Mathematics in High School

Abstract

The article examines the characteristics of the psychological and pedagogical conditions required for the functioning of the hybrid intellectual system of teaching (HIST) mathematics in high school. The article describes such internal conditions related to the development and primary trial of the HIST as the methodological basis of the intellectual management of educational and cognitive activity of students in general and the research and project activities in particular, the identification of the personalized parameters of the high school students’ scientific potential which determines the teaching content, the development of such diagnostic tools that can take the students’ individual psychological characteristics into account and serve as a component of intellectual management in the mathematical modelling of research activities, the development of the procedures and the methods of creating individual educational routes that are based on the students’ types of thinking. These conditions determined the architecture and functions of the hybrid neural network. The trial experiment on the internal conditions of the functioning of HIST involved 711 high school students. The results of the trial study indicate a steady annual increase in the number of students in experimental groups who get high scores, which is connected with an in-depth study of mathematics within the framework of the student's educational and research activities aimed at acquiring complex mathematical knowledge with the help of a hybrid intellectual system. The obtained results confirmed the effectiveness of the intelligent management system of the students' research and project activities. It was found that the external conditions, i.e. the readiness of the participants of the research and project activities to use the HIST, is not unimportant for its successful implementation. Consequently, the effectiveness of the hybrid intelligent learning system is determined not only by the readiness of the teachers, but also by the motivational and technological readiness of high school students to carry out research and project activities in a hybrid learning environment.