The lecture deals with helping different pupils understand one of humankind greatest achievements, namely, the positional scale of notation, the decimal one, in particular. Children have individual peculiarities of information perception (through signs, images, action, emotional impression etc.). Considering them helps teacher prevent pupils’ mistakes in fulfilling operations with whole numbers and decimal fractions. A unique, psychologically justified approach to teaching decimal scale of notation is presented by Leo Tolstoy in his book “Arithmetic’. From this lecture, you will learn about special features of Tolstoy’s approach, his methodology and ways of using it in his own lessons. The possibilities of realizing Tolstoy’s ideas in modern school are analyzed here as well. You will also learn what kind of abacus and in which way Tolstoy used in teaching decimal notation; how his pupils got a table of categories and used it in fulfilling operations with whole numbers; why he considered it important for his pupils to learn about the Roman and Slavic notation; which role teaching positional notation as opposed to decimal notation played in his methodology.