Mathematics in the Sandbox: Investigating Spontaneous Mathematical Talk During Free Play

Diana Putri Prahasti; Muhammad Furqon; Vivi Anggraini; Fachri Aldin; Qisthi Efridita

doi:10.61987/gazette.v3i1.2054

Authors

Diana Putri Prahasti Universitas Nurul Jadid
Muhammad Furqon Universitas Islam negeri Maulana Malik Ibrahim Malang
Vivi Anggraini Universitas Nahdlatul Ulama Blitar
Fachri Aldin National Formosa University
Qisthi Efridita Kütahya Dumplupınar Üniversitesi

DOI:

https://doi.org/10.61987/gazette.v3i1.2054

Keywords:

Early Mathematics, Spontaneous Mathematical Talk, Free Play

Abstract

Children often explore mathematical ideas naturally while playing, yet these moments are rarely captured in early childhood classrooms. The purpose of this research is to investigate how spontaneous mathematical talk emerges during free play in a sandbox environment and to understand the types of mathematical ideas children express. A qualitative observational approach was used to document children’s conversations and interactions during unstructured sandbox play. Data were collected through field observations and audio recordings of children’s dialogue while they built, measured, compared, and organized materials in the sand. The recorded interactions were then coded and analyzed to identify patterns of mathematical language and concepts. The findings show that children frequently used informal mathematical talk such as counting, comparing sizes, estimating quantities, and describing shapes while collaborating with peers. These conversations appeared naturally without direct instruction and often emerged when children negotiated roles, shared materials, or solved small problems during play. The study suggests that free play spaces can become rich contexts for early mathematical thinking. Recognizing and supporting these moments may help educators encourage mathematical language in more natural and meaningful ways during everyday classroom activities.

References

Arslan, Z., Demirel, D., Çelik, D., & Güler, M. (2025). A study on how novice mathematics teachers respond to high-potential instances of student mathematical thinking. Thinking Skills and Creativity, 57, 101859. https://doi.org/10.1016/j.tsc.2025.101859

Chen, H., Disney, L., & Li, L. (2025). Children's mathematics concept learning of informal length measurement: Conceptual PlayWorld as an innovative approach in the beginning of primary school period. The Journal of Mathematical Behavior, 79, 101257. https://doi.org/10.1016/j.jmathb.2025.101257

Chen, W. (2025). Problem-solving skills, memory power, and early childhood mathematics: Understanding the significance of the early childhood mathematics in an individual's life. Journal of the Knowledge Economy, 16(1), 1–25.

https://doi.org/10.1007/s13132-023-01557-6

Cohrssen, C., Fielding, J., & Bird, J. (2025). Informal assessment of preschool children's concepts of zero. Early Childhood Education Journal, 53(3), 891–902.

https://doi.org/10.1007/s10643-024-01634-8

Donner, P., Lundström, S., & Heikkilä, M. (2024). A case study of young children's play negotiations in free play. Early Years, 44(3–4), 889–902. https://doi.org/10.1080/09575146.2023.2266590

Durmaz, B. (2025). Learning Mathematics in School Spaces Outside the Classroom. In Mathematics Beyond the Classroom: A Guide for Expansive Learning in Out-of-School Environments (pp. 17–41). Springer. https://doi.org/10.1007/978-3-032-05318-3_2

Ersan, C., & Biçer, F. R. (2025). Examining language development as a predictor of geometry and spatial perception skills in preschool children. Eğitimde Yeni Yaklaşımlar Dergisi, 8(2), 217–230. https://doi.org/10.70325/eyyad.1834253

Fadzil, N. M., & Osman, S. (2025). Scoping the landscape: Comparative review of collaborative learning methods in mathematical problem-solving pedagogy. International Electronic Journal of Mathematics Education, 20(2), em0820.

https://doi.org/10.29333/iejme/15935

Fragkandreas, T. (2025). Case study research on innovation systems: Paradox, dialectical analysis and resolution. Research Policy, 54(1), 105136. https://doi.org/10.1016/j.respol.2024.105136

Granone, F., & Pollarolo, E. (2025). Facilitating children's communication in problem-solving activities with a coding toy: teachers' semiotic mediation in early childhood education and care. Frontiers in Psychology, 15, 1426165.

https://doi.org/10.3389/fpsyg.2024.1426165

Graven, M., & Jorgensen, R. (2024). Early numeracy opportunities through number stories with marginalised families. ZDM–Mathematics Education, 56(3), 319–333.

https://doi.org/10.1007/s11858-023-01537-9

Haq, M., & Yasin, N. (2025). Qualitative, quantitative, and mixed methodology paradigms. Journal of Practical Studies in Education, 6(6), 15–29. https://doi.org/10.46809/jpse.v6i6.144

Henline-Hall, J. (2024). Introduction to Quantitative and Qualitative Research Methods. Radiologic Technology, 96(1).

Lewis Presser, A. E., Braham, E., & Vidiksis, R. (2025). Enhancing Preschool Spatial Skills: A Comprehensive Intervention Using Digital Games and Hands-On Activities. Education Sciences, 15(6), 727. https://doi.org/10.3390/educsci15060727

Li, R., Cevikbas, M., & Kaiser, G. (2024). Mathematics teachers' beliefs about their roles in teaching mathematics: orchestrating scaffolding in cooperative learning. Educational Studies in Mathematics, 117(3), 357–377. https://doi.org/10.1007/s10649-024-10359-9

Lüken, M. M. (2025). Young children's self-initiated pattern-making during free play. Mathematical Thinking and Learning, 27(2), 221–241. https://doi.org/10.1080/10986065.2023.2276798

Lundvin, M., & Palmér, H. (2025). A play-responsive approach to teaching mathematics in preschool, with a focus on representations. Education Sciences, 15(8), 999. https://doi.org/10.3390/educsci15080999

Mendez, J. A., & van Es, E. A. (2024). Examining teachers' relational noticing: promoting equity through positive interactions in mathematics education. Journal of Mathematics Teacher Education, 1–26. https://doi.org/10.1007/s10857-024-09635-5

Metcalfe, J., Xu, J., Vuorre, M., Siegler, R., Wiliam, D., & Bjork, R. A. (2025). Learning from errors versus explicit instruction in preparation for a test that counts. British Journal of Educational Psychology, 95(1), 11–25. https://doi.org/10.1111/bjep.12651

Nawaz, M., Nizamani, M., & Hameed, R. (2024). Analyze how children acquire language and the cognitive processes involved, including the role of environmental and social factors. Bulletin of Business and Economics (BBE), 13(3), 239–247.

https://doi.org/10.61506/01.00483

Osuna, J. M., & Munson, J. (2024). Exploring what teachers notice about students' interactional dynamics during collaborative mathematics problem-solving and their connections to instructional practice. Teaching and Teacher Education, 137, 104380. https://doi.org/10.1016/j.tate.2023.104380

Payne, T. (2024). The math talk learning environment: Testing an early childhood math intervention. Early Childhood Research Quarterly, 66, 224–233. https://doi.org/10.1016/j.ecresq.2023.10.012

Pyle, A., Wickstrom, H., Gross, O., & Kraszewski, E. (2024). Supporting literacy development in kindergarten through teacher-facilitated play. Journal of Early Childhood Research, 22(3), 428–441. https://doi.org/10.1177/1476718X231221363

Santos-Trigo, M. (2024). Trends and developments of mathematical problem-solving research to update and support the use of digital technologies in post-confinement learning spaces. In Problem Posing and Problem Solving in Mathematics Education: International Research and Practice Trends (pp. 7–32). Springer.

https://doi.org/10.1007/978-981-99-7205-0_2

Siregar, T. (2025). Strategy to Enhance Early Mathematics Learning in Early Childhood Education (PAUD). Available at SSRN 5752743. https://doi.org/10.2139/ssrn.5752743

Tisdell, E. J., Merriam, S. B., & Stuckey-Peyrot, H. L. (2025). Qualitative research: A guide to design and implementation. John Wiley & Sons.

Viera, C. A. (2023). Case study as a qualitative research methodology. Performance Improvement Journal, 62(4), 125–129. https://doi.org/10.56811/PFI-23-0005

Wang, S., Li, L., & Disney, L. (2025). Exploring challenges and strategies in teaching early mathematics: insights from rural Chinese kindergartens. Journal of Early Childhood Teacher Education, 1–26. https://doi.org/10.1080/10901027.2025.2599218

Wang, X., Ye, P., & Qiao, T. (2024). Free play and pedagogical play: a multiple-case study of teachers' views of play in Chinese early learning centers. Frontiers in Education, 9, 1359867. https://doi.org/10.3389/feduc.2024.1359867

Wickstrom, H., & Pyle, A. (2025). Supporting early math learning along a continuum of guided play. Early Childhood Education Journal, 53(4), 1053–1063.

https://doi.org/10.1007/s10643-024-01650-8

Winarti, D. W., Widjaja, W., Razi, F., Huzaimah, S., Prianggi, A., & Setyawan, I. A. (2025). Empowering early childhood educators to foster spatial and numeracy reasoning through play-based learning.

https://doi.org/10.22342/jme.v16i3.pp871-888

Zeng, S. A. (2025). Dialogues in Play: Conversational AI and Early Mathematical Thinking. Education Sciences, 15(11), 1516.

https://doi.org/10.3390/educsci15111516