Mathematical science and the elementary teaching of mathematics

As for the intellectual development of a younger learner and his or her further education in mathematics it is necessary for him or her to acquire the mathematical knowledge permanently and with comprehension, that is to enable the pupil to get to know and understand the elementary structures mathematics is built of. The presentation of these structures must be. however, adequate to the learner’s experience and his so far acquired intellectual standard. The scientific system of the mathematical discipline (at the first grade at the basic school of the theoretical arithmetics and the computor sciences) must be, in cooperation with psychology, sociology and the pedagogics, transformed into a rational didactic system.