Children’s Fractional Knowledge pp 49-74 | Cite as

# Articulation of the Reorganization Hypothesis

## Abstract

When fractions are introduced in school mathematics, they are usually introduced in the context of continuous quantity. Number sequences are essentially excluded because, as quantitative schemes, they are thought to be relevant only in discrete quantitative situations. Even though I developed number sequences in Chap. 3 in the context of discrete quantity, I can see no principled reason to keep them separate from continuous quantity. Reserving number sequences for discrete quantity stands in opposition to the concept of the real number line in higher mathematics, and, in this chapter, I argue that it also stands in opposition to the development of quantitative schemes. In articulating the reorganization hypothesis, I establish that a composite unit of specific numerosity can be used to make a split in the way that Confrey (1994) explained. This involves more than simply indicating the possibility of transferring the operations involved in compounding discrete units together to splitting continuous units. I do a deeper developmental analysis of children’s quantitative schemes in which I explore whether the operations that produce discrete quantity and the operations that produce continuous quantity can be regarded as unifying quantitative operations. If so, these quantitative operations would justify the reorganization hypothesis.

### Keywords

Clay Assure Assimilation### References

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