One presents the methodology implemented for a problem relating to the construction, which the children and girls do, of the polynomial representation of numerals written in the Decimal System of Numeration (SDN). Being this representation, in his form ostensive, it forms of condensation of big numerals, the fundamental intention of the study was to describe and to characterize the strategies that the children and girls implement when there is requested them a situation solves problem. This approximation is done by base in the follow-up and description of the strategies that children and girls develop between 9 and 11 years faced the resolution of situations of this type. To obtain this intention a situation designed and applied to itself problem that he considered to be the elements that do part of a polynomial in base 10, demanding of the participants reading and writing of different numerical representations. With the information of 22 children and girls of degrees 4°, 5° and 6° of basic education in Popayán, Colombia, it was possible to identify the set of used and organized into a hierarchy strategies, which constitute a new contribution in the aim to explain the form like he constructs the polynomial representation of numbers written in the SDN.
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