Exploring Beginning Teachers’ Ability to Design Mathematical Games

Authors

DOI:

https://doi.org/10.46328/ijemst.5218

Keywords:

Problem posing, Novice teachers, Design mathematics games

Abstract

This paper investigates how novice secondary-school mathematics teachers develop problem-posing skills through the design of game-based mathematical tasks. Conducted within a graduate-level teacher education course, the study engaged 14 early-career teachers working in pairs to explore mathematical games, analyze their underlying structures, and create original classroom-ready tasks. Using a qualitative case study approach, we focus on two representative pairs: one that undertook a reflective inquiry into the classical NIM game and another that designed two novel, parity-based strategy games. The findings address how teachers engage with mathematical games as tools for creative task design, how the design process supports pedagogical insight and the development of teacher identity, and what forms of mathematical and instructional reasoning emerge during task creation. Participants reported heightened creativity, deeper conceptual understanding, strategic reasoning, and an evolving sense of pedagogical agency. The study underscores the value of integrating structured opportunities for problem design into mathematics teacher education programs as a means of cultivating reflective, innovative, and student-centered educators.

References

Applebaum, M., & Freiman, V. (2014). Use of Recreational Mathematics in the classroom: example of Bachet's game. Mathematics Teaching Journal, 241, 22-26.

Applebaum, M. (2025). Fostering creative and critical thinking through math games: A case study of Bachet’s game. European Journal of Science and Mathematics Education, 13(1), 16-26. https://doi.org/10.30935/scimath/15825

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?

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

Botes, W. (2022). Pre-Service Teachers’ Experiences on the Development of Educational Science Board Games. European Journal of STEM Education, 7(1), 02. https://doi.org/10.20897/ejsteme/11784

Bragg, L. A., Russo, J., & Russo, T. (2021). How primary teachers use games to support their teaching of mathematics. International Electronic Journal of Elementary Education, 13(4), 407–419. https://doi.org/10.26822/iejee.2021.200

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative research in psychology, 3(2), 77-101.

Cai, J., Jiang, C., & Hwang, S. (2015). Analyzing the conceptual learning of prospective elementary teachers in problem posing. Educational Studies in Mathematics, 89(1), 157–173. https://doi.org/10.1007/s10649-015-9590-0

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.

Chapman, O. (2012). Prospective elementary school teachers ways of making sense of mathematical problem posing. PNA: Revista de Investigación en Didáctica de la Matemática, 6(4), 135-146.

Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11, 395-415.

Cresswell, J. (2013). Qualitative inquiry & research design: Choosing among five approaches.

Emre-Akdoğan, E. (2023). Examining mathematical creativity of prospective mathematics teachers through problem posing. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(2), 150-169. https://doi.org/10.1093/teamat/hrac006

Kar, T., Öztürk, F., & Özkaya, M. (2025). Pose, solve and pose cycle: an examination on the change of pre-service mathematics teachers’ problem-posing performances. Teaching Mathematics and its Applications: An International Journal of the IMA, 44(2), 107-131. https://doi.org/10.1093/teamat/hrae010

Kontorovich, I. (2020). How do mathematicians generate new questions? A framework for question-posing in mathematics. Educational Studies in Mathematics, 103(3), 295–312. https://doi.org/10.1007/s10649-020-09934-5

Leavy, A., & Hourigan, M. (2020). Posing mathematically worthwhile problems: developing the problem-posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23(4), 341-361. https://doi.org/10.1007/s10857-018-09425-w

Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349–371.

Mallart Solaz, A., Font Moll, V., & Díez Palomar, F. J. (2018). Case study on mathematics pre-service teachers' difficulties in problem posing. Eurasia Journal of Mathematics Science and Technology Education, 14, ( 4), 1465-1481. https://doi.org/10.29333/ejmste/83682

McColgan, M., Colesante, R., & Andrade, A. (2018). Pre-service teachers learn to teach with serious games. Journal of STEM Education, 19(2).

Merriam, S. B. (1998). Qualitative Research and Case Study Applications in Education. Revised and Expanded from" Case Study Research in Education.". Jossey-Bass Publishers, 350 Sansome St, San Francisco, CA 94104.

Movshovitz-Hadar, N. (2011). Bridging between mathematics and education courses: Strategy games as generators of problem solving and proving tasks. In M. Strutchens & J. Quander (Eds.), Constructing knowledge for teaching secondary mathematics: Tasks to enhance prospective and practicing teacher learning (pp. 117–140). NCTM.

Pan, Y., Ke, F., & Xu, X. (2022). A systematic review of the role of learning games in fostering mathematics education in K-12 settings. Educational Research Review, 36, 100448. https://doi.org/10.1016/j.edurev.2022.100448

Paolucci, C., & Stepp, Z. A. (2021). Examining preservice teachers' understanding of slope through posing problems and embedding learning in real-world contexts. Teaching and Teacher Education, 107, 103476. https://doi.org/10.1016/j.tate.2021.103476

Peres, M., de Freitas Viana, F. H., Fernandes, K. M., Gonzalez, P. H., de M.B. Soares, L., Bezerra, E., dos Santos, J. A. F., & Brandão, D. (2024). Enhancing player levels in the Nim game using genetic algorithms. In Proceedings of the XXIII Simpósio Brasileiro de Jogos e Entretenimento Digital (SBGames 2024).

Polya, G. (1945). How to solve it: A new aspect of mathematical method. Princeton University Press.

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

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.

Singer, F. M., & Voica, C. (2015). Is problem posing a tool for identifying and developing mathematical creativity? Mathematical problem posing: From research to effective practice, 141-174.

Singer, F. M., Ellerton, N. F., & Cai, J. (Eds.). (2011). Mathematical problem posing: From research to effective practice. Springer. https://doi.org/10.1007/978-1-4419-8591-3

Stake, R. (1995). Case study research. Cham: Springer.

Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. Technology in mathematics education, 4(7), 518-525.

Stylianides, G. J., & Stylianides, A. J. (2009). Facilitating the transition from empirical arguments to proof. Journal for Research in Mathematics Education, 40(3), 314-352.

Vankúš, P. (2021). Influence of Game-Based Learning in Mathematics Education on Students’ Affective Domain: A Systematic Review. Mathematics, 9(9), 986. https://doi.org/10.3390/math9090986

Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press, Cambridge.

Yuan, X., & Sriraman, B. (2011). An exploratory study of relationships between students’ creativity and mathematical problem-posing abilities. The elements of creativity and giftedness in mathematics, 5-28.

Downloads

Published

2026-01-01

Issue

Section

Articles

How to Cite

Exploring Beginning Teachers’ Ability to Design Mathematical Games . (2026). International Journal of Education in Mathematics, Science and Technology, 14(1), 178-199. https://doi.org/10.46328/ijemst.5218