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Abstract

Culturally responsive approaches in mathematics education have been widely advocated; however, empirical investigations that embed traditional artifacts into probability and statistics instruction remain limited. This study addresses this gap by employing Shagai—a traditional Mongolian four-sided ankle bone—as an ethnomathematical instrument to support the development of statistical reasoning. In total, 10,050 single-throw trials were conducted across three groups: community participants (n = 5,000), pre-service mathematics teachers (n = 5,000), and a researcher-led demonstration (n = 50). Empirical probabilities for the four Shagai outcomes—horse, camel, sheep, and goat—were estimated as 0.12, 0.13, 0.39, and 0.36, respectively, with convergence achieved after approximately 8,000 trials, indicating a statistically stable but non-uniform distribution. These results informed the design of a four-hour instructional workshop with nine doctoral students in education. Participants conducted Shagai-based experiments, calculated statistical measures, and analyzed data using SPSS. Qualitative reflections were subjected to thematic analysis, which revealed enhanced statistical understanding, interdisciplinary insight, and awareness of cultural integration. A paired-sample t-test confirmed a statistically significant improvement in conceptual understanding . The findings suggest that embedding traditional knowledge systems into statistics education can deepen conceptual comprehension and enrich culturally relevant pedagogy.

Keywords

Culturally Responsive Pedagogy Ethnomathematics Higher Education Probability Education Shagai (Mongolian Ankle Bones)

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How to Cite
Miyejav, I., & Otgonbaatar, K. (2025). Estimating probabilities through the Mongolian Shagai game: A culturally responsive approach to teaching statistics. Journal on Mathematics Education, 16(3), 1043–1062. https://doi.org/10.22342/jme.v16i3.pp1043-1062
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