The DOI matches its Crossref record; 47 of the 49 references it cites were found in a registry or an index, and 1 are not checked yet.
Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving
Overview
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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
“Given that researchers have used problem-posing tasks to gain insights into students’ and teachers’ mathematical understanding (e.g., Cai & Hwang, 2002; Yao et al., 2021), it seems reasonable to posit that teachers could also use problem posing to better understand their students’ mathematical thinking.”
From What Research Says About Teaching Mathematics Through Problem Posing (2022) · cites this paper as Yao et al., 2021
Citations
Cites
National Council of Teachers of Mathematics
(1979) · The Mathematics Teacher · doi:10.5951/mt.72.8.0637 · Cited by 8,499
Handbook of research on mathematics teaching and learning
(1992) · Choice Reviews Online · doi:10.5860/choice.30-2122 · Cited by 6,121
(1999) · Choice Reviews Online · doi:10.5860/choice.37-2294 · Cited by 1,829
Ma, L., & Ma, L. (1999) · Routledge eBooks · doi:10.4324/9781410602589 · Cited by 1,342
Relational Understanding and Instrumental Understanding
Skemp, R. R. (1978) · The Arithmetic Teacher · doi:10.5951/at.26.3.0009 · Cited by 1,290
Developing conceptual understanding and procedural skill in mathematics: An iterative process.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001) · Journal of Educational Psychology · doi:10.1037/0022-0663.93.2.346 · Cited by 1,075
Early Predictors of High School Mathematics Achievement
Siegler, R. S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M. I., & Chen, M. (2012) · Psychological Science · doi:10.1177/0956797612440101 · Cited by 790
Prospective Elementary and Secondary Teachers' Understanding of Division
Ball, D. L. (1990) · Journal for Research in Mathematics Education · doi:10.2307/749140 · Cited by 543
Conference Board of the Mathematical Sciences
Cohen, L. W. (1963) · Science · doi:10.1126/science.140.3565.416 · Cited by 417
Rational Number, Ratio, and Proportion
Behr, M. J., Harel, G., Post, T., & Lesh, R. (2006) · Handbook of Research on Mathematics Teaching and Learning · doi:10.1108/978-1-60752-874-620251018 · Cited by 403
Research works printed but not linked: 5
- Behr, M., Harel, O., Post, T., & Leah, R. (1987). Theoretical analysis: Structure and hierarchy, missing value proportion problems. In J. C. Bergeron et al., (Eds.), Proceedings of the international conference on the psychology of mathematics education (PME-11), Montreal, Canada, July 19–25, 1987 (p. 752).
- Harel, G., Koichu, B., & Manaster, A. (2006). Algebra teachers’ ways of thinking characterizing the mental act of problem posing: The mental act of problem posing. In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Eds.), Proceedings of the 30th conference of the international group for the psychology of mathematics education (Vol. 2, pp. 241–248). Charles University.
- Isik, C., & Kar, T. (2012). An error analysis in division problems in fractions posed by pre-service elementary mathematics teachers. Educational Sciences: Theory and Practice, 12(3), 2303–2309.
- Lamon, S. J. (2001). Presenting and representing from fractions to rational numbers. In A. A. Cuoco & F. R. Curcio (Eds.), The roles of representation in school mathematics (pp. 146–165). National Council of Teachers of Mathematics.
- National Research Council. (2001). Knowing and learning mathematics for teaching. National Academy Press.
Cited by
Rahmah, S., & Lubis, A. H. (2024) · Journal of Indonesian Primary School. · doi:10.62945/jips.v1i4.409 · Cited by 302
Empirical research on problem solving and problem posing: a look at the state of the art
Liljedahl, P., & Cai, J. (2021) · ZDM – Mathematics Education · doi:10.1007/s11858-021-01291-w · Cited by 171
Self-citationWhat Research Says About Teaching Mathematics Through Problem Posing
Cai, J. (2022) · Éducation et didactique · doi:10.4000/educationdidactique.10642 · Cited by 114
Self-citationMaking Mathematics Challenging Through Problem Posing in the Classroom
Cai, J., & Hwang, S. (2023) · Research in Mathematics Education · doi:10.1007/978-3-031-18868-8_7 · Cited by 39
Self-citationImpact of prompts on students’ mathematical problem posing
Cai, J., Ran, H., Hwang, S., Ma, Y., Han, J., & Muirhead, F. (2023) · The Journal of Mathematical Behavior · doi:10.1016/j.jmathb.2023.101087 · Cited by 36
Self-citation
Metadata
- Authors
- Yao, Y., Hwang, S., & Cai, J.
- Affiliations
- Hangzhou Normal University (CN)
- University of Delaware (US)
- Corresponding author
- Yao, Yiling
- Venue
- ZDM – Mathematics Education
- Published
- 2021-05-21
- Volume
- 53
- Issue
- 4
- Pages
- 937-949
- ISSN
- 1615-679X (ISSN-L)
- 1863-9690
- 1863-9704
- OpenAlex
- W3164419415
- Cited by
- 78
- References
- 49
- Citations by year
- 2026: 23 · 2025: 15 · 2024: 17 · 2023: 13 · 2022: 7 · 2021: 3
- FWCI
- 12.65
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- www.springer.com/tdm (vor)
- Locations
- ZDM (publishedVersion)
- Topics
- Social Sciences › Education › Mathematics Education and Teaching Techniques
- Social Sciences › Education › Mathematics Education and Pedagogy
- Social Sciences › Education › Mathematics Education and Programs
- Keywords
- pre-service teachers, mathematical understanding, conceptual understanding, fraction division, problem posing, problem solving, graphical representation, assessment of mathematical understanding, teacher professional development
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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: Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. https://app.cochat.ai/papers/10.1007/s11858-021-01277-8
- The paper
- Yao, Y., Hwang, S., & Cai, J. (2021). Preservice teachers’ mathematical understanding exhibited in problem posing and problem solving. ZDM – Mathematics Education. https://doi.org/10.1007/s11858-021-01277-8
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.
