By N. A. Sanin
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How this second split might occur highlights the essentiality of both fragmenting and segmenting in making a split. Distribution and Simultaneity We have to always operate on something, and this “something” in Confrey’s analysis of splitting is a unit of some kind. At the point of the second split, I find it necessary to introduce a new operation of distribution because it is quite unlikely that anyone can simultaneously split each of n things into n parts (Steffe 1994b, p. 21). Rather, 10 We focus on breaking into n equal parts because of our interest in partitioning.
Stolzenberg’s view is compatible with an assumption I make in our work with children, but it is not identical. ” “To invent” implies the production of something unknown by the use of ingenuity or imagination. An invention certainly falls within the scope of what is meant by a construction, but the latter term implies conceptual productions within or as a result of interactions that I would not want to call inventions. Although any construction implies the production of a novelty, I would hesitate to call, for example, an association between two contiguous perceptual items (Guthrie 1942), an invention if for no other reason than many such associations are formed without forethought and sometimes even without the awareness of the associating individual.
Moreover, Kerslake (1986) found that 13 and 14-year old students in England had a good idea of fractions as part of a whole, which is compatible with Washburne’s findings concerning “nongrouping fractions,” but only a fragile 1 A “nongrouping” fraction did not involve a composite part of a unit. For example, the children were asked “A pint is what part of a quart”? ” A “grouping” fraction did involve a composite part of a unit. For example, when showing children a picture of three piles of five pennies each, they were asked what part of the pennies were in each pile.