Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking
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Warren and Cooper concluded that students' understanding of generalization relies on having adequate opportunities to generalize patterns; exposing students to visual growth patterns prepares them to construct algebraic expressions based on their internal mathematical authority.
“They concluded that students' understanding of generalization relies on having adequate opportunities to generalize patterns; that is, by exposing students to visual growth patterns, they will be prepared to construct algebraic expressions based on their internal mathematical authority.”
From Exercising Mathematical Authority: Three Cases of Preservice Teachers’ Algebraic Justifications (2019) · cites this paper as Warren & Cooper, 2008
Warren and Cooper found that although third-grade students were able to think functionally, they expressed visual patterns algebraically as a relationship between subsequent steps rather than between the term of the visual pattern and the step number.
“Warren and Cooper found that although third-grade students were able to think functionally, they expressed visual patterns algebraically as a relationship between subsequent steps rather than between the term of the visual pattern (i.e., the output) and the step number (i.e., the input).”
From Exercising Mathematical Authority: Three Cases of Preservice Teachers’ Algebraic Justifications (2019) · cites this paper as Warren & Cooper, 2008
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References 22 · Cited by 159
- Authors
- Warren, E., & Cooper, T.
- Affiliations
- Australian Catholic University (AU)
- Queensland University of Technology (AU)
- Corresponding author
- Warren, Elizabeth
- Venue
- Educational Studies in Mathematics
- Published
- 2007-09-21
- Volume
- 67
- Issue
- 2
- Pages
- 171-185
- ISSN
- 0013-1954 (ISSN-L)
- 1573-0816
- OpenAlex
- W2083596463
- Cited by
- 159
- References
- 22
- Citations by year
- 2026: 7 · 2025: 8 · 2024: 8 · 2023: 5 · 2022: 17 · 2021: 7 · 2020: 15 · 2019: 12 · 2018: 10 · 2017: 11 · 2016: 8 · 2015: 9 · 2014: 4 · 2013: 12 · 2012: 9
- FWCI
- 11.79
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Educational Studies in Mathematics (publishedVersion)
- QUT ePrints (Queensland University of Technology) (submittedVersion)
- Research Bank (Australian Catholic University) (submittedVersion)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Physical Sciences › Mathematics › Applied Mathematics › Mathematics Education and Pedagogy
- Physical Sciences › Computer Science › Computer Science Applications › Teaching and Learning Programming
- Keywords
- algebraic generalization, early algebra, teaching action, abstract thinking, algebraic expressions, teaching experiment, elementary school students
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