Korean Preservice Elementary Teachers’ Abilities to Identify Equiprobability Bias and Teaching Strategies

  • Mimi Park
  • Eun-Jung LeeEmail author


Equiprobability bias (EB) is one of the frequently observed misconceptions in probability education in K-12 and can be affected by a problem context. As future teachers, preservice teachers need to have a stable understanding of probability and to have the knowledge to identify EB in their students regardless of the problem context. However, there are few studies to explore how preservice teachers identify students’ EB and how they respond to students’ EB. This study investigated Korean preservice elementary school teachers’ abilities to identify students’ EB in two problem contexts, marble and baseball problems, as well as their teaching strategies for correcting students’ EB within each problem. Ninety-six preservice elementary school teachers participated in this study. They were presented with two problems with students having EB and were asked to write lesson plays. From the analysis of their lesson plays, it was found that 87% of the preservice teachers identified students’ EB in both problems, and in the baseball problem, 13% of them did not. Three teaching strategies for correcting students’ EB in each problem were found. Based on the results, implications for preservice elementary teacher education were discussed.


Chance Equiprobability bias Lesson play Preservice elementary school teachers Problem context 


  1. Ang, L. H. & Shahrill, M. (2014). Identifying students’ specific misconceptions in learning probability. International Journal of Probability and Statistics, 3(2), 23–29. Scholar
  2. Anway, D. & Bennett, E. (2004, August). Common misperceptions in probability among students in an elementary statistics class. Paper presented at the ARTIST Roundtable Conference on Assessment in Statistics, Lawrence University.Google Scholar
  3. Australian Curriculum, Assessment and Reporting Authority (2015). Australian Curriculum: Mathematics. Retrieved from
  4. Batanero, C., Arteaga, P., Serrano, L. & Ruiz, B. (2014). Prospective primary school teachers’ perception of randomness. In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 345–366). New York, NY: Springer.CrossRefGoogle Scholar
  5. Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S. & Sánchez, E. (2016). Research on teaching and learning probability. Retrieved from
  6. Batanero, C., Godino, J. D. & Cañizares, M. J. (2005). Simulation as a tool to train pre-service school teachers. In J. Addler (Ed.), Proceedings of ICMI First African Regional Conference. Retrieved from
  7. Batanero, C., Henry, M. & Parzysz, B. (2005). The nature of chance and probability. In G. A. Jones (Ed.), Exploring probability in school (pp. 15–37). Boston, MA: Springer.CrossRefGoogle Scholar
  8. Batanero, C., Navarro-Pelayo, V. & Godino, J. D. (1997). Effect of the implicit combinatorial model on combinatorial reasoning in secondary school pupils. Educational Studies in Mathematics, 32(2), 181–199.CrossRefGoogle Scholar
  9. Batanero, C. & Sánchez, E. (2005). What is the nature of high school students’ conceptions and misconceptions about probability? In G. A. Jones (Ed.), Exploring probability in school (pp. 241–266). Boston, MA: Springer.CrossRefGoogle Scholar
  10. Biehler, R. (2016). Professional development for teaching probability and inference statistics with digital tools at upper secondary level. Paper presented at the 13th International Congress on Mathematical Education, Hamburg.Google Scholar
  11. Borovcnik, M., Bentz, H.-I. & Kapadia, R. (1991). A probabilistic perspective. In A. I. Bishop (Ed.), Chance encounters: Probability in education (pp. 73–105). Dordrecht, The Netherlands: Springer Science+Business Media.CrossRefGoogle Scholar
  12. Callaert, H. (2004). In search of the specificity and the identifiability of stochastic thinking and reasoning. In M. A. Mariotti (Ed.), Proceedings of the Third Conference of the European Society for Research in Mathematics Education. Retrieved from
  13. Fielding-Wells, J. (2014, July). Where’s your evidence? Challenging young students’ equiprobability bias through argumentation. Paper presented at the 9th International Conference on Teaching Statistics (ICOTS9), Flagstaff, Arizona, USA. Retrieved from's_your_evidence_Challenging_young_students'_equiprobability_bias_through_argumentation.
  14. Gal, I. (2005). Towards “probability literacy” for all citizens: Building blocks and instructional dilemmas. In G. A. Jones (Ed.), Exploring probability in school (pp. 39–63). Boston, MA: Springer.CrossRefGoogle Scholar
  15. Glaser, B. & Strauss, A. (1967). The discovery of grounded theory. Hawthorne, NY: Aldine Transaction.Google Scholar
  16. Jones, G. A., Langrall, C. W. & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 909–955). Charlotte, NC: Information Age Publishing Inc..Google Scholar
  17. Lecoutre, M.-P. (1992). Cognitive models and problem spaces in “purely random” situations. Educational Studies in Mathematics, 23(6), 557–568. Scholar
  18. Li, J. (2000). Chinese students’ understanding of probability (Unpublished doctoral dissertation). Nanyang Technological University, Singapore.Google Scholar
  19. Li, J. & Pereira-Mendoza, L. (2002, July). Misconceptions in probability. In B. Phillips (Ed.), Proceedings of the 6th International Conference on Teaching Statistics (ICOTS6). Retrieved from
  20. Mamolo, A. & Zazkis, R. (2014). Contextual considerations in probabilistic situations: An aid or a hindrance? In E. J. Chernoff & B. Sriraman (Eds.), Probabilistic thinking: Presenting plural perspectives (pp. 641–656). New York, NY: Springer.CrossRefGoogle Scholar
  21. Ministry of Education (2014). The New Zealand Curriculum. Retrieved from
  22. Ministry of Education (2015a). Mathematics Curriculum (Notification No. 2015-74, Appendix 8). Seoul, Korea: Author.Google Scholar
  23. Ministry of Education (2015b). Mathematics teachers’ guidebook 6–1. Seoul, Korea: Chunjae Education.Google Scholar
  24. Ministry of Education (2015c). Mathematics textbook 6–1. Seoul, Korea: Chunjae Education.Google Scholar
  25. Ministry of Education, Science, and Technology (2011). Mathematics Curriculum (Notification No. 2011-361, Appendix 8). Seoul, Korea: Author.Google Scholar
  26. Moritz, J. B., Watson, J. M. & Collis, K. F. (1996). Odds: Chance measurement in three contexts. In P. C. Clarkson (Ed.), Technology in Mathematics Education: Proceedings of the 19th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 390–397). Melbourne, Australia: MERGA.Google Scholar
  27. Moyer, P. S. & Milewicz, E. (2002). Learning to question: Categories of questioning used by preservice teachers during diagnostic mathematics interviews. Journal of Mathematics Teacher Education, 5(4), 293–315. Scholar
  28. Oliveira, H. & Hannula, M. S. (2008). Individual prospective mathematics teachers: Studies on their professional growth. In K. Krainer & T. Wood (Eds.), Participants in mathematics teacher education (pp. 13–34). Rotterdam, The Netherlands: Sense Publishers.Google Scholar
  29. Polya, G. (1971). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press (Original work published 1957).Google Scholar
  30. Rubel, L. H. (2007). Middle school and high school students’ probabilistic reasoning on coin tasks. Journal for Research in Mathematics Education, 38(5), 531–556.Google Scholar
  31. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  32. ​Statistics Training Institute (2017). “Development of teaching-learning materials for high school practical statistics” to enhance statistical recognition. Seoul, Korea: Statistics Training Institute, Statistics Korea.Google Scholar
  33. Stohl, H. & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. The Journal of Mathematical Behavior, 21, 319–337.CrossRefGoogle Scholar
  34. Tarr, J. E. (2002). Confounding effects of the phrase “50-50 chance” in making conditional probability judgments. Focus on Learning Problems in Mathematics, 24(4), 35–53.Google Scholar
  35. Tarr, J. E. & Jones, G. A. (1997). A framework for assessing middle school students’ thinking in conditional probability and independence. Mathematics Education Research Journal, 9(1), 39–59. Scholar
  36. Zazkis, R., Sinclair, N. & Liljedahl, P. (2013). Lesson play in mathematics education: A tool for research and professional development. New York, NY: Springer.CrossRefGoogle Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2018

Authors and Affiliations

  1. 1.Korea National University of EducationCheongju-siRepublic of Korea
  2. 2.9/320. Department of Mathematics EducationSeoul National UniversitySeoulRepublic of Korea

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