The DOI matches its Crossref record; 90 of the 90 references it cites were found in a registry or an index.
An integrated theory of whole number and fractions development
Open accessAbstract
This article proposes an integrated theory of acquisition of knowledge about whole numbers and fractions. Although whole numbers and fractions differ in many ways that influence their development, an important commonality is the centrality of knowledge of numerical magnitudes in overall understanding. The present findings with 11- and 13-year-olds indicate that, as with whole numbers, accuracy of fraction magnitude representations is closely related to both fractions arithmetic proficiency and overall mathematics achievement test scores, that fraction magnitude representations account for substantial variance in mathematics achievement test scores beyond that explained by fraction arithmetic proficiency, and that developing effective strategies plays a key role in improved knowledge of fractions. Theoretical and instructional implications are discussed.
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Cites
A Handbook of Child Psychology
(1932) · Nature · doi:10.1038/130331a0 · Cited by 10,101
National Council of Teachers of Mathematics
(1979) · The Mathematics Teacher · doi:10.5951/mt.72.8.0637 · Cited by 8,499
Ericsson (1993) · doi:10.1037/0033-295x.87.3.215 · Cited by 4,539
Adding It Up: Helping Children Learn Mathematics
Kilpatrick, J., Swafford, J. O., & Findell, B. R. (2013) · DSpace Biblioteca Universidad de Talca (Universidad de Talca) · Cited by 4,081
Second Handbook of Research on Mathematics Teaching and Learning.
Lester, F. (2007) · Cited by 3,090
The mental representation of parity and number magnitude.
Dehaene, S., Bossini, S., & Giraux, P. (1993) · Journal of Experimental Psychology General · doi:10.1037//0096-3445.122.3.371 · Cited by 2,630
Advances in Instructional Psychology
(2019) · Routledge eBooks · doi:10.4324/9781315864341 · Cited by 2,532
Feigenson, L., Dehaene, S., & Spelke, E. (2004) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2004.05.002 · Cited by 2,466
Time required for Judgements of Numerical Inequality
MOYER, R. S., & LANDAUER, T. K. (1967) · Nature · doi:10.1038/2151519a0 · Cited by 2,068
The Number Sense: How the Mind Creates Mathematics.
Hersh, R., & Dehaene, S. (1998) · The American Mathematical Monthly · doi:10.2307/2589308 · Cited by 2,052
Cited by
Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014) · Journal of Experimental Child Psychology · doi:10.1016/j.jecp.2014.01.013 · Cited by 448
Self-citationDevelopmental and individual differences in understanding of fractions.
Siegler, R. S., & Pyke, A. A. (2013) · Developmental Psychology · doi:10.1037/a0031200 · Cited by 305
Self-citationWhy is learning fraction and decimal arithmetic so difficult?
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015) · Developmental Review · doi:10.1016/j.dr.2015.07.008 · Cited by 266
Self-citationKiili, K., Moeller, K., & Ninaus, M. (2018) · Computers & Education · doi:10.1016/j.compedu.2018.01.012 · Cited by 119
Crosnoe, R., & Benner, A. D. (2015) · Handbook of Child Psychology and Developmental Science · doi:10.1002/9781118963418.childpsy407 · Cited by 73
Metadata
- Authors
- Siegler, R. S., Thompson, C. A., & Schneider, M.
- Venue
- Cognitive Psychology
- Publisher
- Elsevier BV
- Published
- 2011-06
- Volume
- 62
- Issue
- 4
- Pages
- 273-296
- ISSN
- 0010-0285 (ISSN-L)
- OpenAlex
- W2016438993
- Cited by
- 706
- References
- 90
- FWCI
- 21.98
- Type
- journal article
- Language
- en
- Open access
- green
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
