Student or educator? Sign up with your school email and get 6 months of Pro free.
Cited by 126

The DOI matches its Crossref record.

Problem-posing research in mathematics education: new questions and directions

Singer, Florence Mihaela, Ellerton, Nerida, Cai, Jinfa·2013·Educational Studies in Mathematics

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1007/s10649-013-9478-2

Cites

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

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?

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

No references could be resolved yet.

Research works printed but not linked: 43

  1. Brown, S., & Walter, M. (1983/2005). The art of problem posing (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates. · DOI · Paper page
  2. Cai, J. (2005). U.S. and Chinese teachers' knowing, evaluating, and constructing representations in mathematics instruction. Mathematical Thinking and Learning: An International Journal, 7(2), 135–169. · DOI
  3. Cai, J., & Cifarelli, V. (2005). Exploring mathematical exploration: how do two college students formulate and solve their own mathematical problems? Focus on Learning Problems in Mathematics, 27(3), 43–72.
  4. Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. Zentralblatt für Didaktik der Mathematik, 37(3), 149–158. · DOI · Paper page
  5. Cifarelli, V., & Cai, J. (2005). The evolution of mathematical explorations in open ended problem solving situations. The Journal of Mathematical Behavior, 24, 302–324. · DOI
  6. Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415. · DOI · Paper page
  7. Einstein, A., & Infeld, L. (1938). The evolution of physics. New York: Simon & Schuster.
  8. Ellerton, N. F. (1986). Children's made-up mathematics problems—a new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261–271. · DOI · Paper page
  9. Ellerton, N. F., & Clarkson, P. C. (1996). Language factors in mathematics teaching. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 987–1053). Netherlands: Kluwer.
  10. English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106. · DOI · Paper page
  11. English, L. D. (2003). Problem posing in the elementary curriculum. In F. K. Lester Jr. & R. I. Charles (Eds.), Teaching mathematics through problem solving: Prekindergarten—grade 6 (pp. 187–198). Reston: NCTM.
  12. Ervynck, G. (1991). Mathematical creativity. In D. Tall (Ed.), Advanced mathematical thinking (pp. 42–53). Dordrecht: Kluwer.
  13. Hadamard, J. W. (1945). Essay on the psychology of invention in the mathematical field. Princeton: Princeton University Press (page ref. are to Dover edition, New York 1954).
  14. Harel, G., Koichu, B., & Manaster, A. (2006). Algebra teachers' ways of thinking characterizing the mental act of problem posing. In I. J. Novotna, H. Moraova, M. Kratka, & N. Stehlikova (Eds.), Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 241–248). Prague: Charles University.
  15. Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123–147). Hillsdale: Lawrence Erlbaum Associates.
  16. Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2012). An exploratory framework for handling the complexity of mathematical problem posing in small groups. The Journal of Mathematical Behavior, 31(1), 149–161. · DOI · Paper page
  17. Leikin, R., & Lev, M. (2007). Multiple solution tasks as a magnifying glass for observation of mathematical creativity. In Proceedings of the International Group for the Psychology of Mathematics Education, Seoul, Korea, 8–13 July 2007 (pp. 161–168). Seoul, Korea: The Korea Society of Educational Studies in Mathematics.
  18. Leung, S. S. (1997). On the role of creative thinking in problem posing. Zentralblatt für Didaktik der Mathematik, 97(3), 81–85. · DOI
  19. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum Associates. · DOI · Paper page
  20. Mamona-Downs, J., & Downs, M. (2005). The identity of problem solving. The Journal of Mathematical Behavior, 24, 385–401. · DOI
  21. Nohda, N. (1995). Teaching and evaluating using “open-ended problems” in the classroom. Zentralblatt für Didaktik der Mathematik, 27(2), 57–61.
  22. Ponte, J. (2007). Investigations and explorations in the mathematics classroom. ZDM, 39, 419–430. · DOI
  23. Ponte, J., & Matos, J. F. (1992). Cognitive processes and social interactions in investigation activities. In J. Ponte et al. (Eds.), Mathematical problem solving and new information technologies: Research in contexts of practice (pp. 239–254). Berlin: Springer. · doi:10.1007/978-3-642-58142-7_17
  24. Popper, K. R., & Eccles, J. A. (1977). The self and its brain: An argument for interactionism. Berlin: Springer. · DOI · Paper page
  25. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  26. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75–80. · DOI · Paper page
  27. Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521–539. · DOI · Paper page
  28. Silver, E. A., & Cai, J. (2005). Assessing students' mathematical problem posing. Teaching Children Mathematics, 12(3), 129–135. · DOI · Paper page
  29. Silver, E. A., Kilpatrick, J., & Schlesinger, B. (1990). Thinking through mathematics: Fostering inquiry and communication in mathematics classrooms. New York: The College Board.
  30. Silver, E. A., Mamona-Downs, J., Leung, S., & Kenney, P. A. (1996). Posing mathematical problems: an exploratory study. Journal for Research in Mathematics Education, 27(3), 293–309. · doi:10.2307/749366
  31. Singer, F. M. (2007). Beyond conceptual change: Using representations to integrate domain-specific structural models in learning mathematics. Mind, Brain, and Education, 1(2), 84–97. · DOI
  32. Singer, F. M. (2008). Enhancing transfer as a way to develop creativity within the dynamic structural learning. In R. Leikin (Ed.), Proceedings of the 5th International Conference on Creativity in Mathematics and the Education of Gifted Students (pp. 223–230). Tel Aviv: CET.
  33. Singer, F. M. (2009). The dynamic infrastructure of mind—a hypothesis and some of its applications. New Ideas in Psychology, 27, 48–74. · DOI
  34. Singer, F. M. (2010). Children's cognitive constructions: From random trials to structures. In J. A. Jaworski (Ed.), Advances in sociology research (Vol. 6, pp. 1–35). Hauppauge: Nova.
  35. Singer, F. M. (2012). Boosting the young learners' creativity: Representational change as a tool to promote individual talents (plenary lecture). In The 7th International Group for Mathematical Creativity and Giftedness (MCG) International Conference Proceedings (pp. 3–26). Busan, South Korea: MCG.
  36. Singer, F. M., Ellerton, N., Cai, J., Leung, E. (2011). Problem posing in mathematics learning and teaching: A research agenda. In B. Ubuz (Ed.), Developing mathematical thinking. Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 137–166). Ankara, Turkey: PME.
  37. Singer, F. M., & Moscovici, H. (2008). Teaching and learning cycles in a constructivist approach to instruction. Teaching and Teacher Education, 24(6), 1613–1634. · DOI
  38. Singer, F. M., Pelczer, I., & Voica, C. (2011). Problem posing and modification as a criterion of mathematical creativity. In T. Rowland & E. Swoboda (Eds.) Proceedings of the 7th Conference of the European Society for Research in Mathematics Education (CERME 7) University of Rzeszów, Poland, 9–13 February, 2011.
  39. Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students' problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (pp. 518–525). Melbourne: Mathematics Education Research Group of Australasia.
  40. Torrance, E. P. (1974). Torrance tests of creative thinking: Norms and technical manual. Bensenville: Scholastic Testing Services.
  41. Verschaffel, L., & De Corte, E. (1997). Teaching realistic mathematical modeling in the elementary school. A teaching experiment with fifth graders. Journal for Research in Mathematics Education, 28, 577–601. · DOI
  42. Voica, C., & Singer, M. (2012). Creative contexts as ways to strengthen mathematics learning. In M. Aniţei, M. Chraif & C. Vasile (guest Eds.), Procedia—Social and Behavioral Sciences, PSIWORLD 2011 (vol. 33, 538–542). Available at http://www.sciencedirect.com/science/article/pii/S1877042812001875 . Accessed 3 Oct 2013.
  43. Yuan, X., & Sriraman, B. (2010). An exploratory study of relationships between students' creativity and mathematical problem posing abilities. In B. Sriraman & K. Lee (Eds.), The elements of creativity and giftedness in mathematics (pp. 5–28). Rotterdam: Sense Publishers.

Cited by

See all 126

Metadata

Authors
Singer, F. M., Ellerton, N., & Cai, J.
Venue
Educational Studies in Mathematics
Published
2013-03-21
Volume
83
Issue
1
Pages
1-7
ISSN
  • 0013-1954
  • 1573-0816
Cited by
126
References
0
Language
en
Licence
www.springer.com/tdm (tdm)

About these checks

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.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Problem-posing research in mathematics education: new questions and directions. https://app.cochat.ai/papers/10.1007/s10649-013-9478-2
The paper
Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: new questions and directions. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-013-9478-2

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.