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Exploring Conceptual Structures in Numerical Knowledge
Başlık:
Exploring Conceptual Structures in Numerical Knowledge
Yazar:
Murphy, April Dawn, author.
ISBN:
9780438082717
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (133 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Timothy T. Rogers Committee members: Martha Alibali; Edward Hubbard; Chuck Kalish; Percival Matthews.
Özet:
How are conceptual structures learned and mapped onto the appropriate symbolic expressions in mathematical knowledge? Can children's difficulty in understanding fractions be explained and helped by focusing on reshaping knowledge structures, rather than assessing performance by more traditional measures? In this dissertation, I present 4 studies that address the measurement of numerical symbols as knowledge structures that account for individual differences in representation and the malleability of these structures as an means of assessing conceptual change. The first study uses a novel experimental framework to explore knowledge of single-digit integers, showing that the structure of even well-learned mathematical concepts differs critically between mathematics experts and educated but non-expert adults. The second and third studies use this framework to build on prior research involving ratio magnitude processing, under the postulate that children's difficulty understanding symbolic fractions arises from ineffective mapping from meaning (i.e., magnitude) to the symbolic expression. I hypothesized that (1) educated adults familiar with simple fractions should show similar representational structures whether assessed with symbolic or non-symbolic ratios, (2) children should show very different structures for symbolic and non-symbolic ratios, and (3) patterns of both children's and adults' structures should look similar for non-symbolic ratios, but different for symbolic ratios. In the fourth study, I explore how a task aimed at helping children learn to map non-symbolic ratio magnitudes onto their symbolic form may lead to measurable conceptual changes that reflect how learning shapes knowledge. The results indicated that both children and adults rapidly and easy perceive magnitude relations among non-symbolic ratios, and children who successfully learned a brief training task involving form-to-meaning mappings provided promising evidence in demonstrating appreciable change in their underlying knowledge of symbolic ratio magnitude. The results conclude with a discussion of limitations and directions for future research.
Notlar:
School code: 0262
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(695323.1) | 695323-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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