Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 122

The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.

Affect in mathematical problem posing: conceptualization, advances, and future directions for research

Cai, Jinfa, Leikin, Roza·2020·Educational Studies in Mathematics
DOI 10.1007/s10649-020-10008-x
Open this paper in CoChat — free account

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/s10649-020-10008-x

Cites

3 of 3 references verified0 citation errors · 0 not checkable

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

Show all 3 references

Research works printed but not linked: 59

  1. Attard, C. (2014). I don’t like it, I don’t love it, but I do it and I don’t mind: Introducing a framework for engagement with mathematics. Curriculum Perspectives, 34(3), 1–14.
  2. Bicer, A., Lee, Y., Perihan, C., Capraro, M., & Capraro, R. (2020). Considering mathematical creative self-efficacy with problem posing as a measure of mathematical creativity. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-09995-8 · DOI · Paper page
  3. Brown, S. I., & Walter, M. I. (1983). The art of problem posing. Hillsdale, NJ: Lawrence Erlbaum Associates.
  4. Cai, J., & Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research, 102, 101420. · DOI
  5. Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem posing research in mathematics: Some answered and unanswered questions. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3–34). New York, NY: Springer. · DOI
  6. Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2017). Clarifying the impact of educational research on students’ learning. Journal for Research in Mathematics Education, 48(2), 118–123. · doi:10.5951/jresematheduc.48.2.0118
  7. Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students’ learning. Educational Studies in Mathematics, 83(1), 57–69. · DOI
  8. Çakır, A., & Akkoc, H. (2020). Examining socio-mathematical norms related to problem posing: A case of gifted and talented mathematics classrooms. Educational Studies in Mathematics, 105(1), 19–34. · DOI
  9. Chen, T., & Cai, J. (2020). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research, 102, 101420. · DOI
  10. Cifarelli, V. V., & Sevim, V. (2015). Problem posing as reformulation and sense-making within problem solving. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 177–194). New York, NY: Springer. · DOI
  11. Di Martino, P., & Zan, R. (2015). The construct of attitude in mathematics education. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs to dynamic affect systems in mathematics education (pp. 51–72). Cham: Springer. · DOI
  12. Dreyfus, T., & Eisenberg, T. (1986). On the aesthetics of mathematical thought. For the Learning of Mathematics, 6(1), 2–10.
  13. Dweck, C. S., Chiu, C., & Hong, Y. (1995). Implicit theories and their role in judgments and reactions. A world from two perspectives. Psychological Inquiry, 6, 267–285. · DOI · Paper page
  14. Ellerton, N. F. (1986). Children’s made-up mathematics problems—A new perspective on talented mathematicians. Educational Studies in Mathematics, 17, 261–271. · DOI · Paper page
  15. Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101. · DOI · Paper page
  16. Farrington, C. A., Roderick, M., Allensworth, E., Nagaoka, J., Keyes, T. S., Johnson, D., & Beechum, N. O. (2012). Teaching adolescents to become learners: The role of noncognitive factors in shaping school performance. Chicago: University of Chicago Consortium on Chicago School Research.
  17. Felmer, P., Kilpatrick, J., & Pehkonen, E. (Eds.). (2016). Posing and solving mathematical problems: Advances and new perspectives. New York: Springer.
  18. Fullmer, L., Wiezel, A., Tarr, G., Zhang, X., Cullicott, C., Middleton, J. A., & Jansen, A. (2020). Engagement and affect patterns in high school mathematics classrooms that exhibit spontaneous problem posing: An exploratory framework and study. In Educational Studies in Mathematics.
  19. Goldin, G. A. (2002). Affect, meta-affect, and mathematical belief structures. In G. Leder, E. Pehkonen, & G. Tôrner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 59–72). Dordrecht: Kluwer. · DOI
  20. Goldin, G. A. (2009). The affective domain and students’ mathematical inventiveness. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 181–194). Leiden: Brill Sense. · doi:10.1163/9789087909352_013
  21. Goldin, G. A., Hannula, M. S., et al. (2016). Attitudes, beliefs, motivation and identity in mathematics education: An overview of the field and future directions. Berlin: Springer.
  22. Gómez-Chacón, I. M. (2000). Affective influences in the knowledge of mathematics. Educational Studies in Mathematics, 43, 149–168. · doi:10.1023/a:1017518812079
  23. Grootenboer, P., & Marshman, M. (2016). Mathematics, affect and learning: Middle school students’ beliefs and attitudes about mathematics education. Singapore: Springer. · DOI
  24. Guo, M., Leung, F. K. S., & Hu, X. (2020). Affective determinants of mathematical problem posing: The case of Chinese Miao students. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-09972-1 · DOI
  25. Hadamard, J. (1945). An essay on the psychology of invention in the mathematical field. Princeton: Princeton University Press.
  26. Hannula, M. S. (2015). Emotions in problem solving. In S. J. Cho (Ed.), Selected regular lectures from the 12th international congress on mathematical education (pp. 269–288). Cham: Springer. · DOI
  27. Hannula, M. S., Leder, G. C., Morselli, F., Vollstedt, M., & Zhang, Q. (Eds.). (2019). Affect and mathematics education: Fresh perspectives on motivation, engagement, and identity. Berlin: Springer. · doi:10.1007/978-3-030-13761-8
  28. Hannula, M. S., Pantziara, M., & Di Martino, P. (2018). Affect and mathematical thinking: Exploring developments, trends, and future directions. In T. Dreyfus, M. Artigue, D. Potari, S. Prediger, & K. Ruthven (Eds.), Developing research in mathematics education: Twenty years of communication, cooperation and collaboration in Europe (pp. 128–141). London: Routledge. · DOI
  29. 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, NJ: Lawrence Erlbaum Associates.
  30. Klein, S., & Leikin, R. (2020). Opening mathematical problems for posing open mathematical tasks: What do teachers do and feel? Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-09983-y · DOI
  31. Koichu, B. (2020). Problem posing in the context of teaching for advanced problem solving. International Journal of Educational Research, 102, 101428. · DOI
  32. Koichu, B., & Andžāns, A. (2009). Mathematical creativity and giftedness in out-of-school activities. In R. Leikin, A. Berman, & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 285–307). Leiden: Brill Sense. · doi:10.1163/9789087909352_019
  33. Kontorovich, I. (2020). Problem-posing triggers or where do mathematics competitions problems come from? Educational Studies in Mathematics. · DOI · Paper page
  34. Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 273–292). New York: Springer. · DOI
  35. Leikin, R. (2015). Problem posing for and through Investigations in a Dynamic Geometry Environment. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Problem posing: From research to effective practice (pp. 373–391). Dordrecht: Springer. · DOI
  36. Leikin, R. (2018). Openness and constraints associated with creativity-directed activities in mathematics for all students. In N. Amado, S. Carreira, & K. Jones (Eds.), Broadening the Scope of Research on Mathematical Problem Solving: A Focus on Technology, Creativity and Affect (pp. 387–397). Switzerland: Springer. · DOI
  37. Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424. · DOI
  38. Leont’ev, A.N. (1978). Activity, consciousness, and personality. Englewood Cliffs, N.J.: Prentice-Hall.
  39. Li, X., Song, N., Hwang, S., & Cai, J. (2020). Learning to teach mathematics through problem posing: Teachers’ beliefs and performance on problem posing. Educational Studies in Mathematics. · DOI
  40. Liu, Q., Liu, J., Cai, J., & Zhang, Z. (2020). The relationship between domain and task specific self-efficacy and mathematical problem-posing: A large-scale study of eighth-grade students in China. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-09977-w · DOI
  41. Matsko, V. J., & Thomas, J. (2015). Beyond routine: Fostering creativity in mathematics classrooms. In Mathematical Problem Posing (pp. 125–139). New York: Springer. · DOI
  42. McLeod, D. (1992). Research on affect in mathematics education: A reconceptualisation. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 575–596). New York: Macmillan.
  43. McLeod, D. B., & Adams, V. M. (1989). Affect and mathematical problem solving: A new perspective. Hillsdale: Lawrence Erlbaum Associates. · DOI · Paper page
  44. Moyer, J. C., Robison, V., & Cai, J. (2018). Attitudes of high-school students taught using traditional and reform mathematics curricula in middle school: A retrospective analysis. Educational Studies in Mathematics, 98, 115–134. · DOI
  45. Pellegrino, J. W., & Hilton, M. L. (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. Washington, D.C.: The National Academies Press.
  46. Pepin, B., & Roesken-Winter, B. (Eds.). (2015). From beliefs to dynamic affect systems in mathematics education. Cham: Springer.
  47. Radford, L. (2015). Of love, frustration, and mathematics: A cultural-historical approach to emotions in mathematics teaching and learning. In B. Pepin & B. Roesken-Winter (Eds.), From beliefs and affect to dynamic systems: Exploring a mosaic of relationships and interactions (pp. 25–49). Cham: Springer. · DOI
  48. Reznick, B. (1994). Some thoughts on writing for the Putnam. In A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 19–29). New York: Routledge.
  49. Roth, W. M. (2007). Emotion at work: A contribution to third-generation cultural-historical activity theory. Mind, Culture, and Activity, 14(1–2), 40–63. · DOI · Paper page
  50. Rothstein, R. (2004). Class and schools: Using social, economic, and educational reform to close the achievement gap. Washington: Economic Policy Institute.
  51. Schindler, M., & Bakker, A. (2020). Affective field during collaborative problem posing and problem solving: A case study. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-09973-0 · DOI · Paper page
  52. Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
  53. Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM-The International Journal on Mathematics Education, 97(3), 75–80. · DOI · Paper page
  54. 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
  55. Singer, F. M., Ellerton, N., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. New York, NY: Springer.
  56. Singer, F. M., & Voica, C. (2015). Is problem posing a tool for identifying and developing mathematical creativity? In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing (pp. 141–174). New York, NY: Springer. · DOI
  57. Voica, C., & Singer, F. M. (2020). How are motivation and self-efficacy interacting in problem posing and problem solving. In Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-10005-0 · DOI
  58. Weber, K., & Leikin, R. (2016). Recent advances in research on problem solving and problem posing. In A. Gutiérrez, P. Boero, & G. Leder (Eds.), The second handbook of research on the psychology of mathematics education (pp. 353–382). Rotterdam: Sense. · DOI
  59. Xu, B., Cai, J., Liu, Q., & Hwang, S. (2020). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 102, 101427. https://doi.org/10.1016/j.ijer.2019.04.005 · DOI

Cited by

See all 122

Metadata

Authors
Cai, J., & Leikin, R.
Venue
Educational Studies in Mathematics
Publisher
Springer Science and Business Media LLC
Published
2020-11
Volume
105
Issue
3
Pages
287-301
ISSN
  • 0013-1954
  • 1573-0816
DOI
10.1007/s10649-020-10008-x
Cited by
122
References
3
Language
en
Licence

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: Affect in mathematical problem posing: conceptualization, advances, and future directions for research. https://app.cochat.ai/papers/10.1007/s10649-020-10008-x
The paper
Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: conceptualization, advances, and future directions for research. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-020-10008-x

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.