On the meaning and content of school mathematical education (methodological analysis)

The author analyzes the situation and crisis in mathematical education, and outlines the ways to overcome this crisis. The loss of the meaning of mathematical education by schoolchildren and attempts to resume this meaning are discussed. The author, relying on his own research on the origin of mathematics and the experience of teaching it, characterizes the meaning of modern mathematical education: this is an important historical phenomenon, one of the first types of ancient science, mathematics is a language of mathematical schemes and models used in physics and a number of other scientific disciplines, it is a kind of creativity and thinking (mathematical) that a person can join. Three interpretations of the content of mathematical education are analyzed: knowledge, meta-subject and reflexive, as ways of thinking. The author offers another reflexive reconstruction of situations, activities and thinking that led to the formation and development of mathematics. An example of such a reconstruction is given. Other factors determining the features of the content of modern mathematical education are also discussed, namely, ideas about different types of personality and the trajectories of their development, the principle of cultural conformity, the attitude to diversity and variability of content. In conclusion, the author raises the question of the nature of a new type of mathematics textbook and gives an example, however, from the field of humanities, of a successful textbook on cultural studies written by him.