Early algebra and mathematical generalization
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Previous research has identified criteria for analyzing elementary school students' generalization of functional thinking problems, including the form of the underlying mathematical function, the variables mentioned, the types of arithmetic computation used, the use of symbolic-algebraic notation, and the meanings of the components of the written expression.
“Carraher et al. (2008), for instance, emphasize: (a) the form of the underlying mathematical function, which could relate both variables involved in the task or only one of them; (b) the variables mentioned; (c) the types of arithmetic computation used; (d) the use or otherwise of symbolic-algebraic notation; and (e) the meanings of the components of the written expression.”
From Generalizations of third and fifth graders within a functional approach to early algebra (2021) · cites this paper as Carraher et al., 2008
These students' prior mathematical experiences seem to have influenced how they attend to and relate covarying quantities, and how they perceive general rules.
“As in reports by other authors (e.g., Carraher et al., 2008), however, these students' prior mathematical experiences seem to have influenced how they attend to and relate covarying quantities, and how they perceive general rules.”
From Generalizations of third and fifth graders within a functional approach to early algebra (2021) · cites this paper as Carraher et al., 2008
The citation lists haven’t been fetched yet
References 53 · Cited by 243
- Authors
- Carraher, D. W., Martinez, M. V., & Schliemann, A. D.
- Affiliations
- Tufts University (US)
- ORCID
- Carraher, David W.
- Venue
- ZDM
- Published
- 2007-11-27
- Volume
- 40
- Issue
- 1
- Pages
- 3-22
- ISSN
- 1615-679X (ISSN-L)
- 1863-9690
- 1863-9704
- OpenAlex
- W2148081659
- Cited by
- 243
- References
- 53
- Citations by year
- 2026: 9 · 2025: 13 · 2024: 19 · 2023: 15 · 2022: 31 · 2021: 30 · 2020: 14 · 2019: 18 · 2018: 13 · 2017: 19 · 2016: 12 · 2015: 9 · 2014: 5 · 2013: 9 · 2012: 12
- FWCI
- 14.73
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- ZDM (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Physical Sciences › Mathematics › Theoretical Computer Science › History and Theory of Mathematics
- Keywords
- early algebra, mathematical generalization, linear functions, patterns, functions, recursive sequences, empirical generalization, theoretical generalization, third grade, geometric figures, closed-form expressions, conjecture
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