Steffe L. P. & Glasersfeld E. von (1985) Helping children to conceive of number. Recherches en Didactique des Mathématiques 6: 269–303.
Helping children to conceive of number.
Recherches en Didactique des Mathématiques 6: 269–303.
Number is presented as a uniting operation that can have collections of sensory items as material and a unit of units as the result. One thesis of the paper is that children who have constructed this uniting operation have not necessarily constructed number sequences. Problem situations are suggested for such children that might encourage the internalization of counting and the concomitant construction of the iterable unit of one. Situations are then suggested in which the child can use the number sequence that is based on the iterable unit of one to construct other iterable units and their corresponding number sequences. A second thesis of the paper is that for children who are yet to construct the uniting operation, counting is a sensory-motor scheme that should be coordinated with spatial, finger, and auditory patterns. Problem situations are suggested for these coordinations. While a teacher cannot give a child the uniting operation, the suggested situations can encourage its construction by the child.
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