Estimating probabilities through the Mongolian Shagai game: A culturally responsive approach to teaching statistics

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.