The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index.
Generalization of patterns: the tension between algebraic thinking and algebraic notation
Overview
Integrity signals
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Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“These results were somewhat different from those of Zazkis and Liljedahl (2002) who reported that their elementary preservice teachers had difficulty expressing generalizations of visual numerical patterns using algebraic notation.”
From Prospective elementary teachers use of representation to reason algebraically (2009) · cites this paper as Zazkis and Liljedahl (2002)
Citations
Cites
Fehr, H. F. (1948) · The Mathematics Teacher · doi:10.5951/mt.41.6.0270 · Cited by 646
When Good Teaching Leads to Bad Results: The Disasters of 'Well-Taught' Mathematics Courses
Schoenfeld, A. H. (1988) · Educational Psychologist · doi:10.1207/s15326985ep2302_5 · Cited by 624
Expressing Generality and Roots of Algebra
Mason, J. (1996) · Approaches to Algebra · doi:10.1007/978-94-009-1732-3_5 · Cited by 388
Signs and meanings in students' emergent algebraic thinking: A semiotic analysis
Radford, L. (2000) · Educational Studies in Mathematics · doi:10.1023/a:1017530828058 · Cited by 255
Finding and using patterns in linear generalising problems
Stacey, K. (1989) · Educational Studies in Mathematics · doi:10.1007/bf00579460 · Cited by 255
The development of algebra: Confronting historical and psychological perspectives
Sfard, A. (1995) · The Journal of Mathematical Behavior · doi:10.1016/0732-3123(95)90022-5 · Cited by 213
Teaching and Learning a New Algebra
(1999) · Mathematics Classrooms That Promote Understanding · doi:10.4324/9781410602619-16 · Cited by 170
An Initiation into Algebraic Culture through Generalization Activities
Lee, L. (1996) · Springer eBooks · doi:10.1007/978-94-009-1732-3_6 · Cited by 135
The General, the Abstract, and the Generic in Advanced Mathematics
Harel, G., & Tall, D. O. (1991) · for the learning of mathematics · Cited by 125
Divisibility and Multiplicative Structure of Natural Numbers: Preservice Teachers' Understanding
Zazkis, R., & Campbell, S. R. (1996) · Journal for Research in Mathematics Education · doi:10.5951/jresematheduc.27.5.0540 · Cited by 118
Self-citation
Research works printed but not linked: 5
- Iwasaki, H. and Yamaguchi, T.: 1997, 'The cognitive and symbolic analysis of the generalization process: The comparison of algebraic signs with geometric figures', in E. Pehkonen (ed.), Proceedings of the 21st International Conference for Psychology of Mathematics Education. Lahti, Finland, pp. 105–112.
- Kaput, J. and Blanton, M.: 2001, 'Algebrafying the elementary mathematics experience', in H. Chick, K. Stacey, J. Vincent and J. Vincent (eds.), Proceedings of the 12th ICMI Study Conference on the Future of the Teaching and Learning of Algebra (Vol. 1), Melbourne, Australia, pp. 344–351.
- Orton, A. and Orton, J.: 1999, 'Pattern and the approach to algebra', in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics. Cassell, London, pp. 104–120.
- Threlfall, J.: 1999, 'Repeating patterns in the primary years', in A. Orton (ed.), Pattern in the Teaching and Learning of Mathematics, Cassell, London, pp. 18–30.
- Zazkis, R. and Liljedahl, P.: 2001, 'Exploring multiplicative and additive structure of arithmetic sequence', in M. van den Heuvel-Panhuizen (ed.), Proceedings of the 25th International Conference for Psychology of Mathematics Education, Utrecht, Netherlands, pp. 439–446.
Cited by
Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future
Gutiérrez, Á., & Boero, P. (2006) · BRILL eBooks · doi:10.1163/9789087901127 · Cited by 351
Miller, J. (2019) · ZDM · doi:10.1007/s11858-019-01096-y · Cited by 144
Knowledge building in mathematics: Supporting collaborative learning in pattern problems
Moss, J., & Beatty, R. (2006) · International Journal of Computer-Supported Collaborative Learning · doi:10.1007/s11412-006-9003-z · Cited by 117
Understanding Primes: The Role of Representation
Zazkis, R., & Liljedahl, P. (2004) · Journal for Research in Mathematics Education · doi:10.2307/30034911 · Cited by 98
Self-citationAmit, M., & Neria, D. (2008) · ZDM · doi:10.1007/s11858-007-0069-5 · Cited by 93
Metadata
- Authors
- Zazkis, R., & Liljedahl, P.
- Affiliations
- Simon Fraser University (CA)
- Corresponding author
- Zazkis, Rina
- Venue
- Educational Studies in Mathematics
- Published
- 2002-03
- Volume
- 49
- Issue
- 3
- Pages
- 379-402
- ISSN
- 0013-1954 (ISSN-L)
- 1573-0816
- OpenAlex
- W1494946542
- Cited by
- 183
- References
- 19
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 8 · 2023: 3 · 2022: 11 · 2021: 14 · 2020: 16 · 2019: 10 · 2018: 11 · 2017: 14 · 2016: 6 · 2015: 9 · 2014: 7 · 2013: 16 · 2012: 16
- FWCI
- 8.12
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springernature.com/gp/researchers/text-and-data-mining (tdm)
- www.springernature.com/gp/researchers/text-and-data-mining (vor)
- Locations
- Educational Studies in Mathematics (publishedVersion)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Mathematics Education and Pedagogy
- Social Sciences › Arts and Humanities › History and Philosophy of Science › History and Theory of Mathematics
- Keywords
- algebraic thinking, algebraic notation, generalization, number patterns, visual patterns, pre-service primary teachers, symbolization, mathematics teacher education
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Generalization of patterns: the tension between algebraic thinking and algebraic notation. https://app.cochat.ai/papers/10.1023/a:1020291317178
- The paper
- Zazkis, R., & Liljedahl, P. (2002). Generalization of patterns: the tension between algebraic thinking and algebraic notation. Educational Studies in Mathematics. https://doi.org/10.1023/a%3A1020291317178
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.
