The Structure Properties of Rational Numbers Are Important Component of Mathematical Knowledge of Mathematics Teachers.
Keywords:
Group, ring, field, automorphism, ration number, fraction, fraction number, discreteness, densityAbstract
An outstanding German mathematician and educator F. Klein (1849 – 1925) devoted much effort to substantiate the ideas of the modernization of school mathematical education. In [1], he critically evaluated the situation with the teaching of mathematics at school. According to F. Klein and the successor to his ideas Dutch mathematician and popularizer of this science G. Freudenthal (1905 – 1990) it is absolutely unacceptable for a school to remain alien to all that constitutes the content of modern mathematics [2], [3]. Now a step forward in the teaching of elementary mathematics would be to study the problems of elementary mathematics from the standpoint of modern higher mathematics, in which are dominated by structural approaches.
References
F. Klein, Elementary mathematics from higher point of view. Part 1. Arithmetic. Algebra. Analysis, Moscow, 1933 (in Russian).
H. Freudenthal, Mathematics as a pedagogical problem, Prosveshchenie, Moscow, 1982 (in Russian).
H. Freudenthal, Mathematics as a pedagogical problem, Prosveshchenie, Moscow, 1983 (in Russian).
L. M. Vyvalnyuk, V. K. Grygorenko, S. S. Levishchenko Numerical systems, Vyshcha Shcola, Kyiv, 1988 (in Ukrainian).
