Mathematical Problem-Posing Research: Revisiting Some Answered and Unanswered Questions

Authors

DOI:

https://doi.org/10.35763/aiem28.8124

Keywords:

Problem posing, Mathematics, Cognitive processes, Student learning, Curriculum

Abstract

In 2015, Cai et al. reviewed the state of knowledge in problem-posing research. The purpose of the current review is to explore what we have learned as a field over the last 10 years by focusing on three questions from Cai et al.’s (2015) review: Can students and teachers be effectively trained to pose high-quality problems? What do we know about the cognitive processes of problem posing? How are problem-posing activities included in mathematics curricula? Specifically, we review what we know currently with respect to the three questions, including the progress made so far and additional findings on mathematical problem-posing research. We conclude this review by offering additional questions and suggestions for future research.

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References

Baumanns, L., & Rott, B. (2022a). Developing a framework for characterising problem-posing activities: A review. Research in Mathematics Education, 24(1), 28−50. https://doi.org/10.1080/14794802.2021.1897036

Baumanns, L., & Rott, B. (2022b). The process of problem posing: Development of a descriptive phase model of problem posing. Educational Studies in Mathematics, 110(2), 251−269. https://doi.org/10.1007/s10649-021-10136-y

Baumanns, L., & Rott, B. (2023). Identifying metacognitive behavior in problem-posing processes: Development of a framework and a proof of concept. International Journal of Science and Mathematics Education, 21(5), 1381−1406. https://doi.org/10.1007/s10763-022-10297-z

Baumanns, L., & Rott, B. (2025). Problem posing in curriculum standards and primary school textbooks in Germany. Asian Journal for Mathematics Education, 4(2), 167−185. https://doi.org/10.1177/27527263251346205

Bokhove, C. (2025). The language of mathematical problem posing: A comparison between England, U.S., and Singapore curricula. Asian Journal for Mathematics Education, 4(2), 186–200. https://doi.org/10.1177/27527263251346212

Cai, J. (2022). What research says about teaching mathematics through problem posing. Éducation & Didactique, 16, 31–50. https://doi.org/10.4000/educationdidactique.10642

Cai, J. (2025a). Integrating problem posing into school mathematics. Asian Journal for Mathematics Education, 4(2), 159–166. https://doi.org/10.1177/27527263251346990

Cai, J. (2025b). Special issue: Mathematical problem posing in curricula: Premises and challenges. Asian Journal for Mathematics Education, 4(2).

Cai, J., Chen, T., Li, X., Xu, R., Zhang, S., Hu, Y., Zhang, L., & Song, N. (2020). Exploring the impact of a problem-posing workshop on elementary school mathematics teachers’ conceptions on problem posing and lesson design. International Journal of Educational Research, 102, 101404. https://doi.org/10.1016/j.ijer.2019.02.004

Cai, J., & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: Conceptualization and initial findings of a problem-posing project. ZDM–Mathematics Education, 53(6), 1403–1416.

Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 3–34). Springer.

Cai, J., Hwang, S., & Melville, M. (2023). Mathematical problem-posing research: Thirty years of advances building on the publication of “On Mathematical Problem Posing.” In J. Cai, G. J. Stylianides, & P. A. Kenney (Eds.), Research studies on learning and teaching of mathematics: Dedicated to Edward A. Silver (pp. 1–25). Springer International.

Cai, J., & Jiang, C. (2017). An analysis of problem-posing tasks in Chinese and US elementary mathematics textbooks. International Journal of Science and Mathematics Education, 15(8), 1521–1540.

Cai, J., Koichu, B., Rott, B., & Jiang, C. (2024). Advances in research on mathematical problem posing: Focus on task variables. Journal of Mathematical Behavior, 76, 101186. https://doi.org/10.1016/j.jmathb.2024.101186

Cai, J., & Rott, B. (2024). On understanding mathematical problem-posing processes. ZDM Mathematics Education, 56, 61−71.

https://doi.org/10.1007/s11858-023-01536-w

Chinese Ministry of Education. (2001). Curriculum standards for school mathematics of nine-year compulsory education (Trial version). Beijing Normal University Press.

Chinese Ministry of Education. (2022). Quanrizhi yiwu jiaoyu shuxue kecheng biaozhun [Mathematics Curriculum Standard of compulsory education (2022 version)]. People’s Education Press.

Cifarelli, V. V., & Cai, J. (2005). The evolution of mathematical explorations in open-ended problem-solving situations. The Journal of Mathematical Behavior, 24, 302–324.

Einstein, A., & Infeld, L. (1938). The evolution of physics. Simon & Schuster.

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, 87–101. https://doi.org/10.1007/s10649-012-9449-z

Han, J., Hwang, S., Muirhead, F., & Cai, J. (2024). Exploring middle school teachers’ views about problem-posing tasks. The Journal of Mathematical Behavior, 73, 101140.

Hwang, S., Han, J., Muirhead, F., Brown, A., Melville, M., & Cai, J. (2025). Textbooks as a resource for teaching mathematics through problem posing: Catalyzing instructional change. ZDM–Mathematics Education, 57, 987-1001. https://doi.org/10.1007/s11858-025-01694-z

Jia, S., & Yao, Y. (2021). 70 years of problem posing in Chinese primary mathematics textbooks. ZDM–Mathematics Education, 53, 951−960. https://doi.org/10.1007/s11858-021-01284-9

Koichu, B. (2020). Problem posing in the context of teaching for advanced problem solving. International Journal of Educational Research, 102, 101428. https://doi.org/10.1016/j.ijer.2019.05.001

Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83, 71–86. https://doi.org/10.1007/s10649-012-9431-9

Kul, Ü., & Çelik, S. (2020). A meta-analysis of the impact of problem posing strategies on students’ learning of mathematics. Romanian Journal for Multidimensional Education/Revista Romaneasca pentru Educatie Multidimensionala, 12(3), 341–368. https://doi.org/10.18662/rrem/12.3/325

Liljedahl, P., & Cai, J. (2021). Empirical research on problem solving and problem posing: A look at the state of the art. ZDM – Mathematics Education, 53(4), 723–735. https://doi.org/10.1007/s11858-021-01291-w

Muirhead, F., Cai, J., Hwang, S., Han, J., Ӧlmez, İ. B., Ma, Y., & Brown, A. (2025). Implementing problem posing in U.S. classrooms based on a middle school mathematics curriculum. Asian Journal for Mathematics Education, 4(2), 217−234. https://doi.org/10.1177/27527263251340427

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Author.

National Council of Teachers of Mathematics. (2020). Catalyzing change in middle school mathematics: Initiating critical conversations. Author.

Ӧlmez, İ. B., Hwang, S., Han, J., & Cai, J. (in press). Reviewing the current state of knowledge in mathematical problem-posing research. In J. Cai & R. Leikin (Eds.), Research in mathematical problem posing: New advances and directions. Springer.

Pittalis, M., Christou, C., Mousoulides, N., & Pitta-Pantazi, D. (2004). A structural model for problem posing. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 49–56). Bergen University College.

Ran, H., Cai, J., Hwang, S., Han, J., Ma, Y., & Muirhead, F. (in press). Effects of engaging in problem-posing interventions on learners’ cognitive mathematics outcomes: A comprehensive meta-analysis. Journal for Research in Mathematics Education.

Ran, H., Cai, J., Muirhead, F., & Hwang, S. (2025). An analysis of unexpected responses in middle school students’ mathematical problem posing from the perspective of problem-posing processes. Educational Studies in Mathematics, 119, 467-486. https://doi.org/10.1007/s10649-025-10399-9

Rosli, R., Capraro, M. M., & Capraro, R. M. (2014). The effects of problem posing on student mathematical learning: A meta-analysis. International Education Studies, 7(13), 227–241. https://doi.org/10.5539/ies.v7n13p227

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

Silver, E. A. (2013). Problem-posing-research in mathematics education: Looking back, looking around, and looking ahead. Educational Studies in Mathematics, 83(1), 157–162. https://doi.org/10.1007/s10649-013-9477-3

Singer, F. M., Ellerton, N. F., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1–7. https://doi.org/10.1007/s10649-013-9478-2

Singer, F. M., Ellerton, N., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. Springer.

Smith, M. S., & Stein, M. K. (2011). 5 practices for orchestrating productive mathematics discussions. National Council of Teachers of Mathematics.

Toh, T. L., & Chua, P. H. (2025). Problem posing in the Singapore mathematics classroom: A review of the Singapore mathematics curriculum. Asian Journal for Mathematics Education, 4(2), 256−279. https://doi.org/10.1177/27527263251339205

Wang, M., & Walkington, C. (2023). Investigating problem-posing during math walks in informal learning spaces. Frontiers in Psychology, 14. https://doi.org/10.3389/fpsyg.2023.1106676

Wang, M., Walkington, C., & Rouse, A. (2022). A meta-analysis on the effects of problem-posing in mathematics education on performance and dispositions. Investigations in Mathematics Learning, 14(4), 265–287. https://doi.org/10.1080/19477503.2022.2105104

Zhang, C., Zhou, Y., Wijaya, T. T., Chen, J., & Ning, Y. (2024). Effects of a problem posing instructional interventions on student learning outcomes: A three-level meta-analysis. Thinking Skills and Creativity, 53, 101587. https://doi.org/10.1016/j.tsc.2024.101587

Zhang, H., & Cai, J. (2021). Teaching mathematics through problem posing: Insights from an analysis of teaching cases. ZDM-Mathematics Education, 53, 961–973.

Zhang, L., Cai, J., Song, N., Zhang, H., Chen, T., Zhang, Z., & Guo, F. (2022). Mathematical problem posing of elementary school students: The impact of task format and its relationship to problem solving. ZDM–Mathematics Education, 54, 497−512. https://doi.org/10.1007/s11858-021-01324-4

Zhang, L., Stylianides, G. J., & Stylianides, A. J. (2024). Enhancing mathematical problem posing competence: A meta-analysis of intervention studies. International Journal of STEM Education, 11, Article 48. https://doi.org/10.1186/s40594-024-00507-1

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Published

2025-10-30

How to Cite

Ӧlmez İbrahim B., Han, J., Hwang, S., & Cai, J. (2025). Mathematical Problem-Posing Research: Revisiting Some Answered and Unanswered Questions. Advances of Research in Mathematics Education, (28), 11–30. https://doi.org/10.35763/aiem28.8124

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