Teoretyczne i dydaktyczne aspekty nauczania o największym wspólnym dzielniku i najmniejszej wspólnej wielokrotności w zbiorze liczb naturalnych

Abstract

This article contains a collection of didactic ideas concerning teaching the elementary arithmetic. Although they are firmly based on abstract mathematics, they can be realized at different levels of teaching school mathematics. The source of these didactic propositions is the fact that using the set of natural numbers and suitable relations it is possible to construct the models of structures which are called lattices. In this paper we consider the two models of lattices: the lattice of natural numbers with the divisibility relation and the lattice of hereditary sets with the inclusion relation. These lattices are abstract models describing the theoretical foundations of the intuitive process of teaching the greatest common divisor and the least common multiple in the school mathematics. The properties of these lattices inspire considerations of interesting mathematical problems using the elementary notions of the school mathematics. In this paper the didactic propositions are directed to the work with pupils who are interested in mathematics and who will probably choose mathematics as a subject of their studies