By Leslie P. Steffe
Children’s Fractional Knowledge elegantly tracks the development of information, either through kids studying new equipment of reasoning and through the researchers learning their tools. The ebook demanding situations the generally held trust that children’s entire quantity wisdom is a distraction from their studying of fractions through positing that their fractional studying comprises reorganizing—not easily utilizing or development upon—their complete quantity wisdom. This speculation is defined intimately utilizing examples of tangible grade-schoolers drawing close difficulties in fractions together with the schemes they build to narrate elements to a complete, to provide a fragment as a a number of of a unit half, to remodel a fragment right into a commensurate fraction, or to mix fractions multiplicatively or additively.
These case reports supply a novel trip into children’s arithmetic adventure, which regularly varies enormously from that of adults. furthermore, the authors’ descriptive phrases mirror children’s quantitative operations, instead of grownup mathematical words rooted in suggestions that don't reflect—and which within the lecture room may also suppress—youngsters’ studying experiences.
Highlights of the coverage:
- Toward a formula of a arithmetic of living rather than being
- Operations that produce numerical counting schemes
- Case reports: children’s part-whole, partitive, iterative, and different fraction schemes
- Using the generalized quantity series to supply fraction schemes
- Redefining college mathematics
This clean standpoint is of instant value to researchers in arithmetic schooling. With the up-close lens onto mathematical improvement present in Children’s Fractional Knowledge, readers can paintings towards growing more advantageous tools for bettering younger inexperienced persons’ quantitative reasoning skills.
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Extra resources for Children’s Fractional Knowledge
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.