Article Sidebar

Download
PDF Appendix A Appendix B
Statistic
Read Counter : 114 Download : 27

Downloads

Download data is not yet available.

Main Article Content

Abstract

The perspective on applying mathematics to solve practical problems is clearly expressed in Vietnam's Mathematics General Education Curriculum in 2018. Therefore, Realistic Mathematics Education (RME) is suitable for the goals of mathematics education in Vietnam and can become one of the fundamental theories for designing mathematics teaching models in high schools. This study presents an experimental result of teaching conditional probability based on RME and following a five-step process we develop, including problem setting, experience, rediscovering conditional probability, forming conditional probability, application. Worksheets containing problems were distributed to 42 students to solve, and their work was collected immediately afterwards. The works will be analyzed to identify emergent models constructed by students. The new result of the paper is from the study of De Lange, Jupri and Drijvers, we propose a mathematization process for teaching conditional probability in Vietnam. The data analysis method is a qualitative method, through observing the students' problem-solving process. Experimental results show that students actively participated in the process of reinventing conditional probability through solving learning tasks.

Keywords

Bayes’ Theorem Conditional Probability Model For Model Of Realistic Mathematics Education

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Nguyen, Q. A., Dao, N. H., Hoa, T. A., & Nguyen, N.-G. (2025). Teaching conditional probability in grade 12 using realistic mathematics education theory. Journal on Mathematics Education, 16(2), 603–632. https://doi.org/10.22342/jme.v16i2.pp603-632
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Batanero, C., & Álvarez-Arroyo, R. (2024). Teaching and learning of probability. ZDM – Mathematics Education, 56(1), 5–17. https://doi.org/10.1007/s11858-023-01511-5
  2. Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on Teaching and Learning Probability (pp. 1–33). https://doi.org/10.1007/978-3-319-31625-3_1
  3. Binder, K., Krauss, S., & Wiesner, P. (2020). A New Visualization for Probabilistic Situations Containing Two Binary Events: The Frequency Net. Frontiers in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.00750
  4. Borovcnik, M. (2011). Strengthening the Role of Probability Within Statistics Curricula (pp. 71–83). https://doi.org/10.1007/978-94-007-1131-0_11
  5. Borovcnik, M. (2012). Conditional Probability-a Review of Mathematical, Philosophical, and Educational Perspectives. http://www.icme12.org/sub/tsg/tsgload.asp?tsgNo=11
  6. Bui, A. K., & Tran, H. P. (2024). Using Social constructivist theory in the teaching of solving problems of conditional probability grade 12. CTU Journal of Science, 60(4), 187–196. https://doi.org/10.22144/ctujos.2024.390
  7. Carranza, P., & Kuzniak, A. (2008, December 30). Duality of probability and statistics teaching in French education. Joint ICMI/IASE Study: Teaching Statistics in School Mathematics IASE Roundtable Conference. https://doi.org/10.52041/SRAP.08206
  8. Da, N. T. (2022). Designing a teaching model based on the Realistic Mathematics Education (RME) approach and its application in teaching calculus. Journal of Mathematics and Science Teacher, 2(1), em006. https://doi.org/10.29333/mathsciteacher/11918
  9. De Lange, J. (2006). Mathematical literacy for living from OECD-PISA perspective. Tsukuba Journal of Educational Study in Mathematics. Special Issue on the APEC- TSUKUBA International Conference “Innovative Teaching Mathematics through Lesson Study,” 25, 13–35. http://www.criced.tsukuba.ac.jp/math/apec2006/
  10. Díaz, B., Batanero, C., & Contreras, M. (2010). Teaching Independence and Conditional Probability. BEIO Revista Oficial de La Sociedad de Estadística e Investigación Operativa, 26(2), 149–162. www.seio.es/BEIO.
  11. Díaz, C., & Batanero, C. (2009). University students’ knowledge and biases in conditional probability reasoning. International Electronic Journal of Mathematics Education, 4(3), 131–162. https://doi.org/10.29333/iejme/234
  12. Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1(1–2), 3–8. https://doi.org/10.1007/BF00426224
  13. Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics, 3(3–4), 413–435. https://doi.org/10.1007/BF00302305
  14. Freudenthal, H. (1983). Didactical Phenomenology of Mathematical Structures. Reidel Publishing Company.
  15. Freudenthal, H. (2002). Revisiting Mathematics Education: China lectures (Vol. 9). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47202-3
  16. Gigerenzer, G. (2002). Calculated risks: how to know when numbers deceive you. In Choice Reviews Online (illustrated, Issue 04). Simon & Schuster.
  17. Gravemeijer. (1994). Developing realistic mathematics education. CD β Press. https://www.fisme.science.uu.nl/publicaties/literatuur/1994_gravemeijer_dissertation_0_222.pdf
  18. Gravemeijer. (1999). How Emergent Models May Foster the Constitution of Formal Mathematics. Mathematical Thinking and Learning, 1(2), 155–177. https://doi.org/10.1207/s15327833mtl0102_4
  19. Gravemeijer, K., & Terwel, J. (2000). Hans Freudenthal: A mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777–796. https://doi.org/10.1080/00220270050167170
  20. Huerta, M. P. (2009). On Conditional Probability Problem Solving Research – Structures and Contexts. International Electronic Journal of Mathematics Education, 4(3), 163–194. https://doi.org/10.29333/iejme/235
  21. Inci, A. M., Peker, B., & Kucukgencay, N. (2023). Realistic mathematics education. In book: Current Studies in Educational Disciplines 2023 (pp.66-83) Edition 1, Chapter 5. Publisher: ISRES Publishing. ISRES Publishing. https://www.researchgate.net/publication/377209600_Realistic_Mathematics_Education
  22. Larsen, S. (2018). Didactical phenomenology: the engine that drives realistic mathematics education. For the Learning of Mathematics, 38(3), 25–29. https://www.jstor.org/stable/26548508
  23. Le, T. T., Pham, A. G., & Nguyen, T. T. (2021). Applying realistic mathematics education theory in teaching: Some challenges, principles and recommendations. Vietnam Journal of Education, 494(2), 37–43. https://tcgd.tapchigiaoduc.edu.vn/index.php/tapchi/article/view/22
  24. Loc, N. P., Tran, N., & Tien, T. (2020). Approach to realistic mathematics education in teaching mathematics: A case of cosine theorem-geometry 10. International Journal of Scientific & Technology Research, 8, 1173–1178.
  25. Nguyen, A. Q. (2022). Teaching conditional probability in grade 12 according to the general education curriculum in mathematics in 2018. Vietnam Journal of Educational Sciences, 11(3), 40–46. https://doi.org/10.15625/2615-8957/12211107
  26. Nguyen, D. N. (2020). Some problems in realistic mathematics education. Vietnam Journal of Education, 487(1), 15–21. https://mysite.tnu.edu.vn/files/users/nguyendanhnam/487_Nguyn_Danh_Nam.pdf
  27. Nguyen, T. T. T., & Quach, T. Sen. (2023). Some methods of teaching statistic and probability topics for 6th grade students with the support of information technology. Vietnam Journal of Educational Sciences, 19( 7), 27–34. https://doi.org/10.15625/2615-8957/12310705
  28. Nguyen, T. T., Trinh, T. P. T., Ngo, H. T. V., Hoang, N. A., Tran, T., Pham, H. H., & Bui, V. N. (2020). Realistic mathematics education in Vietnam: Recent policies and practices. International Journal of Education and Practice, 8(1), 57–71. https://doi.org/10.18488/journal.61.2020.81.57.71
  29. Shao, X. (2015). An analysis of difficulties in learning Probability in high school. 7th ICMI-East Asia Regional Conference on Mathematics Education, 561–568. https://mathted.weebly.com/uploads/7/8/5/0/7850000/pp_561_shao_xiayan__final_paper_edited.pdf
  30. Streefland, L. (1985). Wiskunde als activiteit en de realiteit als bron (Mathematics as an activity and reality as a source). Nieuwe Wiskrant, 5(1), 60–67. http://www.fisme.science.uu.nl/wiskrant/artikelen/artikelen00-10/051/0501september_streefland.pdf
  31. Tomlinson, S., & Quinn, R. (1997). Understanding conditional probability. Teaching Statistics, 19(1), 2–7. https://doi.org/10.1111/j.1467-9639.1997.tb00309.x
  32. Tran, T. T. H., & Tran, C. (2021). Potential of applying realistic mathematics education to the teaching of probability - statistics at the universities of medicine and pharmacy. Journal of Science Educational Science, 66(5), 209–216. https://doi.org/10.18173/2354-1075.2021-0249
  33. Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics instruction: The Wiskobas Project. Springer Dordrecht.
  34. Treffers, A. (1991). Didactical background of a mathematics program for primary education. In: L. Streefland (ed.). Realistic mathematics education in primary school. In Realistic mathematics education in primary school (pp. 21–56). CDß press/Freudenthal Institute, Utrecht University, Utrecht, The Netherlands. https://www.fisme.science.uu.nl/publicaties/literatuur/1991_streefland_0-209.pdf
  35. Van Den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour 1. Freudenthal Institute CD-rom for International Commission on Mathematics Education (ICME) 9. https://p4mriunismuh.wordpress.com/wp-content/uploads/2010/08/mathematics-education-in-the-netherlands.pdf
  36. Van Den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic mathematics education: An example from a longitudinal trajectory on percentage. Educational Studies in Mathematics, 54(1), 9–35. https://doi.org/10.1023/B:EDUC.0000005212.03219.dc
  37. Van Den Heuvel-Panhuizen, M. (2005). The role of contexts in assessment problems in mathematics. For the Learning of Mathematics, 25(2), 2–23.
  38. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. In Encyclopedia of Mathematics Education (pp. 521–525). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_170
  39. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic Mathematics Education. In Encyclopedia of Mathematics Education (pp. 713–717). Springer International Publishing. https://doi.org/10.1007/978-3-030-15789-0_170
  40. Vicent, M. L., Palau, M. P. H., & Fariña, M. C. (2012). Conditional probability problems in textbooks an example from Spain. Revista latinoamericana de investigación en matemática educativa, 15(3), 319-337. https://www.scielo.org.mx/pdf/relime/v15n3/v15n3a4.pdf
  41. Vietnam Ministry of Education and Training. (2018). Mathematics General Education Curriculum of Vietnam (32/2018/TT-BGDĐT).
  42. Yackel, E., Stephan, M., Rasmussen, C., & Underwood, D. (2003). Didactising: Continuing the work of Leen Streefland. Educational Studies in Mathematics, 54(1), 101–126. https://doi.org/10.1023/B:EDUC.0000005213.85018.34
  43. Zulkardi. (2010). How to Design Mathematics Lessons based on the Realistic Approach? http://repository.unsri.ac.id/id/eprint/6362