What’s in a Name? Should we be Calling it a Game? Rethinking Choice, Strategy, and Mathematical Integrity
Keywords:
mathematics teacher education research, mathematical games, instructional design, student agency, conceptual understandingAbstract
Mathematical games are widely used in primary school classrooms, yet the activities that are labelled as "games" vary considerably in their structure, cognitive demands, and potential to support student reasoning. This conceptual paper offers a typology that distinguishes between pseudo-games, superficial games, gamification, and instructionally rich games. Drawing on examples from classroom practice and research literature, we argue that the presence of choice alone does not define a pedagogically effective game. Instead, instructional value depends on the nature of the choices available and their alignment with key mathematical ideas. We propose three design principles that characterise instructionally rich games, with particular emphasis on the role of strategic reasoning, embedded representations, and opportunities for students to make meaningful mathematical connections. This framework is intended to support teachers, researchers, and designers in critically evaluating and developing mathematical games that move beyond surface-level engagement to promote deep, conceptually grounded learning.
References
Attard, C. (2012). Engagement with mathematics: What does it mean and what does it look iike? Australian Primary Mathematics Classroom, 17(1), 9–13.
Boaler, J. (2019). Developing mathematical mindsets: The need to interact with numbers flexibly and conceptually. American Educator, 42(4), 28–33. https://www.aft.org/ae/winter2018-2019/boaler
Bragg, L. A. (2012). The effect of mathematical games on on-task behaviours in the primary classroom. Mathematics Education Research Journal, 24(4), 385–401. doi:10.1007/s13394-012-0045-4
Buchheister, K., Jackson, C., & Taylor, C. (2017). Maths games: A universal design approach to mathematical reasoning. Australian Primary Mathematics Classroom, 22(4), 7–12.
Casey, B. M., Caola, L., Bronson, M. B., Escalante, D. L., Foley, A. E., & Dearing, E. (2020). Maternal use of math facts to support girls' math during card play. Journal of Applied Developmental Psychology, 68, Article 101136. https://doi.org/10.1016/j.appdev.2020.101136
Cezarotto, M. A., Martinez, P. N., Torres Castillo, R. C., Stanford, T., Engledowl, C., Degardin, G., & Chamberlin, B. (2024). Open-ended mathematics learning: Implications from the design of a sandbox game. International Journal of Game-Based Learning, 14(1), 1–19. https://doi.org/10.4018/IJGBL.337795
Clarke, D., & Roche, A. (2010). The power of a single game to address a range of important ideas in fraction learning. Australian Primary Mathematics Classroom, 15(3), 18–23.
Cusi, A., & Morselli, F. (2025). Discussing about games: Focus on the teacher’s orchestration. In A. Cusi, A, Maffia, S. Palha, & A. M. Vogler (Eds.), Proceedings of the GAME conference (pp. 29–32). ERME.
Debrenti, E., & Bella, H. A. (2025). Teaching mathematics with non-digital tools: A case study with elementary school students using Poly-Universe game. Acta Didactica Napocensia, 18(1), 46–58.
Gough, J. (1999). Playing mathematical games: When is a game not a game? Australian Primary Mathematics Classroom, 4(2), 12–15.
Gough, J. (2001). Dice and board games. Australian Primary Mathematics Classroom, 6(2), 14–17.
Heshmati, S., Kersting, N., & Sutton, T. (2018). Opportunities and challenges of implementing instructional games in mathematics classrooms: Examining the quality of teacher-student interactions during the cover-up and un-cover games. International Journal of Science and Mathematics Education, 16(4), 777–796. https://doi.org/10.1007/s10763-016-9789-8
Hubbard, J. (2024). Year 2 students' self-determination when learning mathematics through sequences of challenging tasks. [Doctoral dissertation, Monash University]. https://doi.org/10.26180/26087530.v1
Kacmaz, G., & Dubé, A. K. (2022). Examining pedagogical approaches and types of mathematics knowledge in educational games: A meta-analysis and critical review. Educational Research Review, 35, Article 100428. https://doi.org/10.1016/j.edurev.2021.100428
Karnes, J., Barwasser, A., & Grünke, M. (2021). The effects of a math racetracks intervention on the single-digit multiplication facts fluency of four struggling elementary school students. Insights into Learning Disabilities, 18(1), 53–77.
Mousoulides, N., & Sriraman, B. (2014). Mathematical games in learning and teaching. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 383–385). https://doi.org/10.1007/978-94-007-4978-8
Nisbet, S., & Williams, A. (2009). Improving students' attitudes to chance with games and activities. Australian Mathematics Teacher, 65(3), 25–38.
Russo, J., Bragg, L., & 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://www.iejee.com/index.php/IEJEE/article/view/1302
Russo, J., Kalogeropoulos, P., Bragg, L. A., & Heyeres, M. (2024). Non-digital games that promote mathematical learning in primary years students: A systematic review. Education Sciences, 14(2), 200. https://doi.org/10.3390/educsci14020200
Russo, J., Klooger, M., & Russo, T. (2022). Let's play: Roll and allocate games. Prime Number, 37(3), 16–18.
Russo, J., & Russo, T. (2020). Transforming mathematical games into investigations. Australian Primary Mathematics Classroom, 25(2), 14–19.
Ryan, R. M., & Deci, E. L. (2017). Self-determination theory: Basic psychological needs in motivation, development and wellness. The Guildford Press.
Sailer, M., & Homner, L. (2020). The gamification of learning: A meta-analysis. Educational Psychology Review, 32(1), 77–112. https://doi.org/10.1007/s10648-019-09498-w
Skillen, J., Berner, V. D., & Seitz-Stein, K. (2018). The rule counts! Acquisition of mathematical competencies with a number board game. The Journal of Educational Research, 111(5), 554–563. https://doi.org/10.1080/00220671.2017.1313187
Sullivan, P., Clarke, D., Cheeseman, J., Mornane, A., Roche, A., Sawatzki, C., & Walker, N. (2014). Students’ willingness to engage with mathematical challenges: Implications for classroom pedagogies. In J. Anderson, M. Cavanagh, & A. Prescott (Eds.), Curriculum in focus: Research guided practice. Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia, Sydney (pp. 597–604). MERGA.
Swan, P., & Marshall, L. (2009). Mathematics games: Time wasters or time well spent? In Proceedings:
CoSMEd 2009 3rd International Conference on Science and Mathematics Education (pp. 540–544).
White, K., & McCoy, L. P. (2019). Effects of game-based learning on attitude and achievement in elementary mathematics. Networks: An Online Journal for Teacher Research, 21(1), 1–17.
