The Partitioning and Fraction Schemes
As stated at the beginning of the first chapter, the basic hypothesis that guided our work is that children’s fraction schemes can emerge as accommodations in their numerical counting schemes. We explained our way of understanding this hypothesis as follows. The child constructs the new schemes by operating on novel material in situations that are not a part of the situations of the preceding schemes. The child uses operations of the preceding schemes in ways that are novel with respect to the situations of the schemes as well as operations that may not be a part of the operations of the preceding schemes. The new schemes that are produced solve situations that the preceding schemes did not solve, and they also serve purposes the preceding schemes did not serve. But the new schemes do not supersede the preceding schemes because they do not solve all of the situations the preceding schemes solved. They might solve situations similar to those solved by the preceding schemes in the context of the new situations, but the preceding schemes are still needed to solve their situations. Still, the new schemes can be regarded as reorganizations of the preceding schemes because operations of the preceding schemes emerge in a new organization and serve different purposes.
KeywordsFourth Grade Recursive Partitioning Partitioning Scheme Splitting Scheme Fraction Scheme
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