Constructive combinatorics in elementary school mathematics

The paper describes in detail a class of educational problems from an elementary school course of mathematics and computer science. This course has been implemented over the past decades by a team led by Academician of the RAS A.L. Semenov. In the problems, it is necessary to find, build, or list all objects that satisfy a certain system of conditions. The student conducts these activities in a visual world of basic objects of discrete mathematics and computer science: strings (finite sequences of symbols), bags (multisets), tables, trees, and statements containing quantifiers. The connections of these problems with problems in computational combinatorics (counting the number of options), with search problems in the theory of computational complexity, with “big ideas”, and general cognitive strategies for their formation in education are considered. The content of education in our approach is more adequate to the context of the modern world.