Fostering Creative Problem-Posing Skills of Pre-Service Mathematics Teachers within the Framework of Realistic Mathematics Education
DOI:
https://doi.org/10.46328/ijonse.5727Keywords:
Creativity, Measurement, Pre-service teachers, Problem-posing, Realistic mathematicsAbstract
In this study, we propose integrating creativity into problem-posing studies to ensure both measurability and conceptual integration. We highlight that creative activities, particularly those rooted in Realistic Mathematics Education (RME) and which promote real-world engagement, contribute to the development of pre-service mathematics teachers' (PMTs) problem-posing skills. We systematically examined the problem-posing competencies of students in relation to their creative processes, focusing on fluency, flexibility, and originality, which are considered core components of creativity. The study adopted both qualitative and quantitative methods; while the problem-posing processes of participants were examined qualitatively, the fluency, flexibility, and originality scores of the posed problems were evaluated quantitatively. The study involved 40 undergraduate students enrolled in the Problem-Solving in Mathematics Teaching course. Participants who were selected using the criterion sampling method carried out their tasks over a 16-week period. The findings of the study indicate that students' creative problem-posing performance differs based on the nature of the problem situation. Our findings indicate that students demonstrated better performance, particularly in the creative problem-posing context. Additionally, we found that significant and consistent relationships were observed between fluency, flexibility, and originality in students' creative problem-posing performance. The study's findings support the role of creativity components in RME for developing problem-posing competence, highlighting the need for further research in this field.
References
Altman, D. G. (1991). Practical statistics for medical research. Chapman and Hall.
Baumanns, L. (2023). Four mathematical miniatures on problem posing. In D. Sarikaya, L. Baumanns, K. Heuer, & B. Rott (Eds.) Problem posing and solving for mathematically gifted and interested students: Best practices, research and enrichment (pp. 3-25). Springer.
Baumanns, L., & Rott, B. (2022). 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
Bonotto, C., & Santo, D. L. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. In F. M. Singer, N. F. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 104-121). Springer.
Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics, 105(3), 287-301. https://doi.org/10.1007/s10649-020-10008-x
Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem posing research in mathematics: 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. (2002). Generalized and generative thinking in U.S. and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401-421. https://doi.org/10.1016/S0732-3123(02)00142-6
Chapman, O. (2012). Prospective elementary school teachers’ ways of making sense of mathematical problem posing. PNA, 6(4), 135-146. https://doi.org/10.30827/pna.v6i4.6137
Chen, L., Van Dooren, W., & Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders’ problem-posing and problem-solving abilities, beliefs, and attitudes: A design experiment. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to effective practice (pp. 309–331). Springer.
Cifarelli, V. V., & Cai, J. (2005). The evolution of mathematical explorations in open-ended problem-solving situations. The Journal of Mathematical Behavior, 24(3-4), 302-324. https://doi.org/10.1016/j.jmathb.2005.09.007
Council of Higher Education [CoHE] (2022). New teacher training undergraduate programs: Primary school mathematics teaching undergraduate program. CoHE, Turkey.
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. https://doi.org/10.1007/s10857-008-9081-0
English, L. D. (1997). Promoting a problem-posing classroom. Teaching Children Mathematics, 4(3), 172-179.
Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic.
Goldin, G. A. (2014). Perspectives on emotion in mathematical engagement, learning, and problem solving. In R. Pekrun & L. Linnenbrink-Garcia (Eds.), International handbook of emotions in education (pp. 391-414). Routledge.
Gravemeijer, K. (1994). Developing realistic mathematics education. Cd-ß Press.
Guilford, J. P. (1950). Creativity. The American Psychologist, 5(9), 444-454. https://doi.org/10.1037/h0063487
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45(2), 167-181. https://doi.org/10.1007/s11858-012-0467-1
Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Lawrence Erlbaum Associates.
Klavir, R., & Gorodetsky, M. (2011). Features of creativity as expressed in the construction of new analogical problems by intellectually gifted students. Creative Education, 2(3), 164-173. https://doi.org/10.4236/ce.2011.23023
Koichu, B. (2020). Problem posing in the context of teaching for advanced problem solving. International Journal of Educational Research, 102, 1-13. https://doi.org/10.1016/j.ijer. 2019.05.001
Kontorovich, I., Koichu, B., Leikin, R., & Berman, A. (2011). Indicators of creativity in mathematical problem posing: How indicative are they? In M. Avotina, D. Bonka, H. Meissner, L. Sheffield, & E. Velikova (Eds.), Proceedings of the 6th International Conference Creativity in Mathematics Education and the Education of Gifted Students (pp. 120-125). University of Latvia.
Leikin, R. (2009). Exploring mathematical creativity using multiple solution tasks. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in mathematics and the education of gifted students (pp. 129-145). Sense.
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, 1-13. https://doi.org/10.1016/j.ijer.2019.04.002
Leikin, R., & Sriraman, B. (2022). Empirical research on creativity in mathematics (education): From the wastelands of psychology to the current state of the art. ZDM Mathematics Education, 54(4), 1-17. https://doi.org/10.1007/s11858-022-01340-y
Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM Mathematics Education, 45(2), 183-197. https://doi.org/10.1007/s11858-012-0460-8
Lu, X., & Kaiser, G. (2022). Creativity in students’ modelling competencies: Conceptualisation and measurement. Educational Studies in Mathematics, 109(2), 287-311. https://doi.org/10.1007/s10649-021-10055-y
Mann, E. L. (2006). Creativity: The Essence of Mathematics. Journal for the Education of the Gifted, 30(2), 236-260. https://doi.org/10.4219/jeg-2006-264
Ministry of Education [MOE] (2015). Bringing out the best in every child. MOE, Singapore.
National Council of Teachers of Mathematics [NCTM] (2014). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics, Inc.
Ozgen, K. (2023). The nature, purpose and importance of mathematical problem solving. In K. Özgen, T. Kar, S. Çenberci, & Y. Zengin (Eds.) Problem solving and problem posing in mathematics (pp. 3-29). Pegem Academy.
Pólya, G. (1957). How to solve it. A new aspect of mathematical method (2nd ed.). Princeton University Press.
Ran, H., Cai, J., Hwang, S., Han, J., Ma, Y., & Muirhead, F. (2025). Effects of engaging in problem-posing interventions on learners’ cognitive mathematics outcomes: A comprehensive meta-analysis. Journal for Research in Mathematics Education, 56(5), 259-282. https://doi.org/10.5951/jresematheduc-2024-0105
Schön, D. (1983). The reflective practitioner: How professionals think in action. Basic Books.
Shulman, L. S., & Shulman, J. H. (2004). How and what teachers learn: A shifting perspective. Journal of Curriculum Studies, 36(2), 257-271. https://doi.org/10.1177/002205740918900-202
Silver, E. (1997). Fostering creativity through instruction rich in mathematical problem posing and problem solving. Zentralblatt für Didaktik der Mathematik, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.
Silver, E. A., & Cai, J. (2005). Assessing students' mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135. https://doi.org/10.5951/TCM.12.3.0129
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. https://doi.org/10.2307/749846
Singer, F. M., Ellerton, N., & 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
Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM Mathematics Education, 41(1-2), 13-27. https://doi.org/10.1007/s11858-008-0114-z
Sternberg, R. J., & Lubart, T. I. (1999). The concept of creativity: Prospects and paradigms. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 3-15). Cambridge University Press.
Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. C. Clarkson (Ed.), Technology in mathematics education (pp. 518-525). Mathematics Education Research Group of Australasia.
Sulistyowati, E., Sugiman., & Sayuti, S. A. (2024). Meta-analysis study of the effectiveness of the ethnomathematical approach on students’ achievement. Pegem Journal of Education and Instruction, 14(1), 197-204. https://doi.org/10.47750/pegegog.14.01.21
Tabach, M., & Friedlander, A. (2015). Problem posing as a learnable activity. Didactica Mathematicae, 37, 93-110. https://doi.org/10.14708/dm.v37i0.844
Torrance, E. P. (1966). Torrance tests of creative thinking: Directions manual and scoring guide. Personnel Press.
Torrance, E. P. (1962/1974). Torrance tests of creative thinking. Scholastic Testing Service.
Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. In S. Lerman (Ed.) Encyclopedia of mathematics education. Springer.
Van Den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational studies in Mathematics, 54, 9-35. https://doi.org/10.1023/B:EDUC.0000005212.03219.dc
Vygotsky, L. S. (1934/1986). Thought and language. The MIT Press.
Waynberg, A. L., & Leikin, R. (2012). Using multiple solution tasks for the evaluation of students’ problem-solving performance in geometry. Canadian Journal of Science, Mathematics and Technology Education, 12(4), 311-333.
Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem-posing abilities: Comparing Chinese and US students. In The elements of creativity and giftedness in mathematics (pp. 5-28). Brill.
Downloads
Published
Issue
Section
License
Copyright (c) 2026 International Journal on Studies in Education
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Articles may be used for research, teaching, and private study purposes. Authors alone are responsible for the contents of their articles. The journal owns the copyright of the articles. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of the research material.
The author(s) of a manuscript agree that if the manuscript is accepted for publication in the International Journal on Studies in Education (IJonSE), the published article will be copyrighted using a Creative Commons “Attribution 4.0 International” license. This license allows others to freely copy, distribute, and display the copyrighted work, and derivative works based upon it, under certain specified conditions.
Authors are responsible for obtaining written permission to include any images or artwork for which they do not hold copyright in their articles, or to adapt any such images or artwork for inclusion in their articles. The copyright holder must be made explicitly aware that the image(s) or artwork will be made freely available online as part of the article under a Creative Commons “Attribution 4.0 International” license.
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
