MATHEMATICAL FOUNDATIONS OF TECHNOLOGICAL IMPLEMENTATION OF VYGOTSKY’S CONCEPT

Abstract

The paper presents a real mechanism for implementing the concept of L. Vygotsky about self-development and self-knowledge, as opposite to the method of just learning, which is currently implemented in developing education systems. Based on the qualitative features of the nature of object of knowledge and on mathematical relations, discovered by M. Arest, the authors analyze the essence of the process of logical reflection as a learning process. The authors propose to use the mathematically represented process of knowledge in society, as a tool to implement the concept of L. Vygotsky for the process of self-knowledge. The paper justifies the fact that interrelation between ontogenesis and phylogeny should not duplicate phylogeny in ontogenesis, but should correlate them, resulting in the development of the tools for getting knowledge. The authors argue that subject, according to the concept of L. Vygotsky, should understand appropriate mathematical relationships at cognitive levels in a similar way as mathematical knowledge in society evolved during the development of these relationships. In addition, the subject must itself develop logical mapping tools, instead of receive them in the finished form. A new look at intellectual development as a consistent development of mathematical relationships at the appropriate cognitive level, presented as a model of cognitive intelligence. The resulting model can represent the content of mathematics education as a structure of mathematical relationships that develops. According to the same principle, the authors propose to build a system of tasks, the complexity of which increases by switching from one mathematical relationship to another. This educational and developmental environment will create conditions for self-knowledge and selfdevelopment of pupils, because, while the nature of the content relationships will be provided by a teacher, the nature of the relationship itself the child should identify themselves.