CLASSIFICATION PROBLEMS IN THE PROCESS OF MATHEMATICAL TRAINING OF FUTURE PRIMARY SCHOOL TEACHERS

This article deals with the possibilities of using classification problems in the process of mathematical training of future primary school teachers. Particular attention is paid to the solution of classification problems on the set of natural numbers. The set of natural numbers makes it possible to formulate a variety of classification problems. These are problems on dichotomy, problems on division into a given number of infinite classes, and problems on division into infinitely many finite classes. Special attention is paid to the problem of partitioning into infinitely many infinite classes. The paper gives different ways of solving this problem. There is a solution based on the digital notation of a natural number. There is a solution based on the idea that all natural numbers containing the same number of multipliers 2 in their decomposition into prime factors should be classified into one class (of course, the case of zero occurrence should not be omitted). The multiplier 2 can be replaced by any other prime multiplier. Finally, the solution of this problem is given, based on the preliminary establishment of a one-to-one correspondence between the set of natural numbers and the set of points of the coordinate plane, first with natural coordinates and then with integral coordinates. All the problems considered in the article are of different levels of complexity, which gives the teacher an opportunity to build a lesson where students can not only show the presence of relevant knowledge, but also show their confidence.