Theoretical Foundations of the Historical and Cultural Component of School Mathematics Education

У статті з’ясовано теоретичні засади культурно-історичної складової сучасної математичної освіти. Трактується поняття освітньої парадигми з боку філософії та педагогіки. Здійснено класифікацію освітніх парадигм. Висвітлено особливості гуманізації та гуманітаризації освіти. Схарактеризовано складові культурно-історичної компоненти математичної освіти. Зроблено аналіз підручників шкільного курсу математики, який чітко показує рівень застосування культурно-історичної компоненти в даний час. Уточнено компоненти, змістовні складові й цілі культурно-історичної складової, зроблено огляд літератури, запропоновано аналіз рівня застосування в навчальному процесі з математики культурно-історичної складової математичної освіти.This article describes the theoretical foundations of cultural and historical part of modern mathematics education. The concept of educational paradigm of the philosophy and pedagogy is interpreted. Classification of educational paradigms is made. Humanization and liberalization of education are described. Components of cultural and historical components of mathematics education are characterized. Analysis of the scientific work of researchers who determine what educational principles and humanization reform covering all educational sectors at different stages of the didactic process and are important landmarks of modern didactics is made. The analysis of school textbooks in mathematics that clearly shows the level of use of cultural and historical components now is made. The substantive components and goals of cultural and historical constituent are described, the review of literature is made, the analysis of the proposed use in teaching mathematics cultural and historical component of mathematics education. The cultural approach is considered as a set of methodological techniques that provide analysis of education, in terms of cultural concepts such as culture, cultural patterns, norms and values, cultural activities and interests. The key components of mathematics education: theoretical, practical, technological, cultural and historical are examined. These components perform specific functions and tasks and are interconnected. The basic elements that make up all paradigms are the following: understanding of the system of knowledge necessary to a person; understanding the type of culture and means of human development in the process of mastering the subject; principles of coding and transmission of information; public awareness of the importance of education; awareness of the cultural development of a person; the role of education in society; understanding of the character and place of the teacher as a carrier of knowledge and culture in the educational process; image and place of the child in the structures of education and training