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Cited by 105Mathematics Education and Teaching TechniquesMathematics Education and PedagogyMathematics Education and Programs

Middle school students' understanding of core algebraic concepts: Equivalence & Variable1

Knuth, Eric J., Alibali, Martha W., McNeil, Nicole M., Weinberg, Aaron, Stephens, Ana C.·2005·Zentralblatt für Didaktik der Mathematik
DOI 10.1007/bf02655899
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Integrity signals

Registry

Crossref · 10.1007/bf02655899

Cites

10 of 10 references verified0 citation errors · 0 not checkable

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Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Arithmetic is the foundation of algebra teaching despite the differences between arithmetic and algebra.

    “Therefore, it is obvious that arithmetic constitutes the basis of algebra teaching despite the differences resulting from the natures of arithmetic and algebra (Herscovics & Linchevski, 1994;Kieran, 1981;Knuth, Alibali, McNeil, Weinmberg & Stephens, 2005;Knuth, Stephens, McNeil & Alibali, 2006).”

    From Relational thinking: The bridge between arithmetic and algebra (2017) · cites this paper as Knuth, Alibali, McNeil, Weinmberg & Stephens, 2005

  • The results from session 1 and the first part of session 2 support the findings of previous studies [21] on the evidence of the use of relational thinking (although limited), even when not directly addressed in teaching.

    “The results from session 1 and the first part of session 2 support the findings of previous studies [21] on the evidence of the use of relational thinking (although limited), even when not directly addressed in teaching”

    From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [21]

  • In this study we detected relational thinking in even younger students than those considered by [21].

    “In this study we detected it in even younger students than those considered by [21].”

    From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [21]

  • Relational thinking develops naturally based on arithmetic learning experiences.

    “suggesting that it develops naturally based on arithmetic learning experiences.”

    From Third Grade Students’ Use of Relational Thinking (2021) · cites this paper as [21]

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Authors
Knuth, E. J., Alibali, M. W., McNeil, N. M., Weinberg, A., & Stephens, A. C.
Affiliations
University of Wisconsin–Madison (US)
ORCID
Venue
Zentralblatt für Didaktik der Mathematik
Publisher
Springer Science and Business Media LLC
Published
2005-02
Volume
37
Issue
1
Pages
68-76
ISSN
1615-679X (ISSN-L)
DOI
10.1007/bf02655899
OpenAlex
W4253934365
Cited by
105
References
10
Citations by year
2026: 10 · 2025: 10 · 2024: 9 · 2023: 5 · 2022: 15 · 2021: 14 · 2020: 4 · 2019: 6 · 2018: 3 · 2017: 2 · 2016: 1 · 2015: 4 · 2014: 4 · 2013: 3 · 2012: 4
FWCI
12.77
Type
journal article
Language
en
Open access
closed
Licence
www.springer.com/tdm (tdm)
Locations
ZDM (publishedVersion)
Topics
  • Social Sciences › Education › Mathematics Education and Teaching Techniques
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
  • Physical Sciences › Mathematics › Modeling and Simulation › Mathematics Education and Programs
Keywords
algebraic thinking, equivalence, variables, junior high school students, student understanding, problem-solving strategies, justification of solutions

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