Geodesic
A Broader way Through Themas of Elementary School Mathematics, II
The Teaching of Mathematics, II (1999) no. 2, p. 81 .

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In this paper we start to analyze the first topics of the school arithmetic. To help the reader recognize the fundamental position and role of the system of natural numbers, a historical glance at the evolution of the number idea is given. Then, the block of numbers 1--10 is seen as a conceptual structure which dictates a series od didactical steps and procedures. As it is easy to observe, many textbooks contain rashly gathered groups of arithmetic problems without bringing before the mind of cognizing subject the effects of these steps. Since at this stage, numbers and operations as well as all their properties are perceptual entities and experiences, the role of drawings, from those showing a piece of reality to the schematic ones which condense the carrying meaning with an elegant simplicity, is particularly emphasized. A bad practice of ``proving'' the arithmetic rules by means of calculation of values of a few related numerical expressions is also criticized. Though, we have given the chief points only, we expect that the sketch of this block will reflect some good practice in a pragmatic way.
Classification : 00A35
Keywords: Didactical blocks of numbers, addition and subtraction schemes, rules of interchange and association of summands. 
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Milosav M. Marjanović. A Broader way Through Themas of Elementary School Mathematics, II. The Teaching of Mathematics, II (1999) no. 2, p. 81 . http://geodesic.mathdoc.fr/item/TM2_1999_II_2_a1/