Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks

Ippo Ishibashi

doi:10.29333/iejme/12061

Full Text (PDF)

Ippo Ishibashi ¹ ^*

More Detail

¹ Okayama University, Okayama, JAPAN^* Corresponding Author

Abstract

Probability is a difficult concept, which is not always taught accurately. This study aims to clarify how experimental and theoretical probabilities are taught in Japanese 7^th and 8^th grades through a textbook analysis. We analyzed seven, government approved Japanese 7^th and 8^th grade textbooks each. Focusing on the definition and explanation of experimental and theoretical probabilities and the law of large numbers, we identified eight discrete perspectives. Findings revealed that, first, some textbooks aim to teach students to distinguish between experimental and theoretical probabilities, whereas others aim to teach students to be aware of the connection between the two. Second, after explaining theoretical probability, some textbooks asked questions to clarify the scope of theoretical probability, aiming to teach students to distinguish between the two probabilities. Third, in explaining the law of large numbers, textbooks do not adopt the perspective that experimental probability converges on true probability, but that it converges on theoretical probability.

Keywords

experimental and theoretical probability
true probability
law of large numbers
teaching probability in Japan
7^th and 8^th grade
textbook analysis

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 17, Issue 3, August 2022, Article No: em0690

https://doi.org/10.29333/iejme/12061

Publication date: 01 May 2022

Article Views: 1827

Article Downloads: 1204

Open Access Disclosures References How to cite this article

Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Aspinwall, L., & Tarr, J. E. (2001). Middle school students’ understanding of the role sample size plays in experimental probability. The Journal of Mathematical Behavior, 20(2), 229-245. https://doi.org/10.1016/S0732-3123(01)00066-9
Batanero, C., & Borovcnik, M. (2016). Statistics and probability in high school. Sense Publishers. https://doi.org/10.1007/978-94-6300-624-8
Batanero, C., & Chernoff, E. J. (2018). Preface. In C. Batanero, & E. J. Chernoff (Eds.), Teaching and learning stochastics (pp. v-ix). Springer. https://doi.org/10.1007/978-3-319-72871-1
Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on teaching and learning probability. Springer. https://doi.org/10.1007/978-3-319-31625-3
Borovcnik, M., & Kapadia, R. (2014). A historical and philosophical perspective on probability. In E. J. Chernoff, & B. Sriraman (Eds.), Probabilistic thinking (pp. 7-34). Springer. https://doi.org/10.1007/978-94-007-7155-0_2
Chernoff, E. J. (2008). The state of probability measurement in mathematics education: A first approximation. Philosophy of Mathematics Education Journal, 23. http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/pome23/Chernoff%20State%20of%20Probability.doc
Fujii, T., Majima, H., Akiyama, R., Asaga, J., Amano, H., Arai, K., Arai, H., Ikeda, Y., Ichikawa, S., Ichikawa, H., Oota, S., Ootani, M., Oono H., Okada, H., Odaka, Y., Kai, A., Kaneko, M., Kabasawa, K., Kawamura H., … Watanabe, K. (2021a). New mathematics 1. Tokyoshoseki (in Japanese).
Fujii, T., Majima, H., Akiyama, R., Asaga, J., Amano, H., Arai, K., Arai, H., Ikeda, Y., Ichikawa, S., Ichikawa, H., Oota, S., Ootani, M., Oono H., Okada, H., Odaka, Y., Kai, A., Kaneko, M., Kabasawa, K., Kawamura H., … Watanabe, K. (2021b). New mathematics 2. Tokyoshoseki (in Japanese).
Gillies, D. (2000). Philosophical theories of probability. Routledge.
Ikeda, T., Hitotsumatsu, S., Uemura, T., Okada, Y., Machida, S., Arakawa, A., Araki, N., Ishii, T., Ishiguro, Y., Ishihara H., Ibaraki, T., Iwachido, H., Ueda, A., Oosawa, H., Ootsuka, M., Oowada, T., Kagami, K., Kazama, K., Kawasaki, M., …, & Wada, S. (2021a). Lower secondary school mathematics 1. Gakkotosho (in Japanese).
Ikeda, T., Hitotsumatsu, S., Uemura, T., Okada, Y., Machida, S., Arakawa, A., Araki, N., Ishii, T., Ishiguro, Y., Ishihara H., Ibaraki, T., Iwachido, H., Ueda, A., Oosawa, H., Ootsuka, M., Oowada, T., Kagami, K., Kazama, K., Kawasaki, M., … Wada, S. (2021b). Lower secondary school mathematics 2. Gakkotosho (in Japanese).
Ireland, S., & Watson, J. (2009). Building a connection between experimental and theoretical aspects of probability. International Electronic Journal of Mathematics Education, 4(3), 339-370. https://doi.org/10.29333/iejme/244
Konold, C., Madden, S., Pollatsek, A., Pfannkuch, M., Wild, C., Ziedins, I., Finzer, K., Horton, N. J., & Kazak, S. (2011). Conceptual challenges in coordinating theoretical and data-centered estimates of probability. Mathematical Thinking and Learning, 13(1-2), 68-86. https://doi.org/10.1080/10986065.2011.538299
Krippendorff, K. (2004). Content analysis: An introduction to its methodology. SAGE.
MEXT. (2018a). The lower secondary school education curriculum guidelines (Date of notice: 2017). Higashiyamashobo (in Japanese).
MEXT. (2018b). Commentary to the course of study for lower secondary school (Date of notice: 2017). Mathematics version. Kyoikushuppan (in Japanese).
MEXT. (n.d.a). Improvement of academic abilities (courses of study). https://www.mext.go.jp/en/policy/education/elsec/title02/detail02/1373859.htm
MEXT. (n.d.b). Japan’s school textbook. https://www.mext.go.jp/en/policy/education/elsec/title02/detail02/sdetail02/1383719.html
Okabe, K., Akita, M., Adachi, H., Ishida, Y., Ito, K., Imaoka, M., Iwata, T., Uegatani, Y., Ootake, H., Oonishi, T., Okita, S., Ozawa, M., Kitajima, S., Kawabuchi, H., Sakamoto, M., Shinagawa, M., Sugawara, M., Taira, K., Tsukahara, K., … Watanabe, K. (2021a). Mathematics for future 1. Sukenshuppan (in Japanese).
Okabe, K., Akita, M., Adachi, H., Ishida, Y., Ito, K., Imaoka, M., Iwata, T., Uegatani, Y., Ootake, H., Oonishi, T., Okita, S., Ozawa, M., Kitajima, S., Kawabuchi, H., Sakamoto, M., Shinagawa, M., Sugawara, M., Taira, K., Tsukahara, K., … Watanabe, K. (2021b). Mathematics for future 2. Sukenshuppan (in Japanese).
Okamoto, K., Morisugi, K., Nemoto, H., Nagata, J., Aoki, Y., Aoyama, K., Abe, Y. Araki, S., Iijima, Y., Igarashi, K., Ikeda, T., Imai, T., Iwasaki, H., Ueda, K., Oota, N., Ogasawara, T., Oka, S., Okabe, Y., Ogihara, F., … Watanabe, M. (2021a). Gateway to the future mathematics 1. Keirinkan (in Japanese).
Okamoto, K., Morisugi, K., Nemoto, H., Nagata, J., Aoki, Y., Aoyama, K., Abe, Y. Araki, S., Iijima, Y., Igarashi, K., Ikeda, T., Imai, T., Iwasaki, H., Ueda, K., Oota, N., Ogasawara, T., Oka, S., Okabe, Y., Ogihara, F., … Watanabe, M. (2021b). Gateway to the future mathematics 2. Keirinkan (in Japanese).
Pfannkuch, M., & Ziedins, I. (2014). A modelling perspective on probability. In E. J. Chernoff, & B. Sriraman (Eds.), Probabilistic thinking: Advances in mathematics education (pp. 101-116). Springer. https://doi.org/10.1007/978-94-007-7155-0_5
Prodromou, T. (2012). Connecting experimental probability and theoretical probability. ZDM–Mathematics Education, 44(7), 855-868. https://doi.org/10.1007/s11858-012-0469-z
Rezat, S., & Sträßer, R. (2015). Methodological issues and challenges in research on mathematics textbooks. Nordic Studies in Mathematics Education, 20(3-4), 247-266. http://ncm.gu.se/wp-content/uploads/2020/06/20_34_247266_rezat.pdf
Sakai, Y., Kotani, M., Ookubo, K., Ootaki, K., Ooneda, Y., Oshino, N., Onoda, T., Kanemoto, Y., Kyogoku, K., Koishizawa, K., Sanada, K., Shimoda, T., Suzuki, N., Suzuki, M., Suda, M., Seo, T., Takahashi, J., Takayama, T., Tanaka, S., … Yoshino, S. (2021a). Lower secondary school mathematics 1. Kyoikushuppan (in Japanese).
Sakai, Y., Kotani, M., Ookubo, K., Ootaki, K., Ooneda, Y., Oshino, N., Onoda, T., Kanemoto, Y., Kyogoku, K., Koishizawa, K., Sanada, K., Shimoda, T., Suzuki, N., Suzuki, M., Suda, M., Seo, T., Takahashi, J., Takayama, T., Tanaka, S., … Yoshino, S. (2021b). Lower secondary school mathematics 2. Kyoikushuppan (in Japanese).
Shigematsu, K., Koyama, M., Iida, S., Ishikawa, K., Inui, H., Iwagou, K., Iwasaki, H., Iwata, K., Okazaki, M., Katou, H., Kawauchi, M., Kunitsugi, T., Kobayashi, Y., Sasaki, T., Shimizu, N., Shimomura, O., Shoda, M., Shirota, N., Sutou, A., … Yamada, A. (2021a). Lower secondary school mathematics 1. Nihonbunkyoshuppan (in Japanese).
Shigematsu, K., Koyama, M., Iida, S., Ishikawa, K., Inui, H., Iwagou, K., Iwasaki, H., Iwata, K., Okazaki, M., Katou, H., Kawauchi, M., Kunitsugi, T., Kobayashi, Y., Sasaki, T., Shimizu, N., Shimomura, O., Shoda, M., Shirota, N., Sutou, A., … Yamada, A. (2021b). Lower secondary school mathematics 2. Nihonbunkyoshuppan (in Japanese).
Stacey, K., & Vincent, J. (2009). Modes of reasoning in explanations in Australian eighth-grade mathematics textbooks. Educational Studies in Mathematics, 72(3), 271-288. https://doi.org/10.1007/s10649-009-9193-1
Stohl, H. (2005). Probability in teacher education and development. In G. A. Jones (Ed.), Exploring probability in school: Challenges for teaching and learning (pp. 345-366). Springer. https://doi.org/10.1007/0-387-24530-8_15
Stohl, H., & Tarr, J. E. (2002). Developing notions of inference using probability simulation tools. The Journal of Mathematical Behavior, 21(3), 319-337. https://doi.org/10.1016/S0732-3123(02)00132-3
Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Kluwer. https://doi.org/10.1007/978-94-007-0844-0
Yoshida, M., Souma, K., Ishiwata, K., Ibaraki, S., Emori, H., Kazama, K., Kubo, Y., Kumakura, H., Koundo Y., Satou, E., Sawada, M., Shiozawa, Y., Suzuki, Y., Sutou, Y., Tashiro, M., Hashimoto, Y., Hisanaga, Y., Hishikawa, Y., Hori, K., … Wada, Y. (2021a). The world of mathematics 1. Dainippontosho (in Japanese).
Yoshida, M., Souma, K., Ishiwata, K., Ibaraki, S., Emori, H., Kazama, K., Kubo, Y., Kumakura, H., Koundo Y., Satou, E., Sawada, M., Shiozawa, Y., Suzuki, Y., Sutou, Y., Tashiro, M., Hashimoto, Y., Hisanaga, Y., Hishikawa, Y., Hori, K., … Wada, Y. (2021b). The world of mathematics 2. Dainippontosho (in Japanese).

How to cite this article

APA

Ishibashi, I. (2022). Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks. International Electronic Journal of Mathematics Education, 17(3), em0690. https://doi.org/10.29333/iejme/12061

Vancouver

Ishibashi I. Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks. INT ELECT J MATH ED. 2022;17(3):em0690. https://doi.org/10.29333/iejme/12061

AMA

Ishibashi I. Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks. INT ELECT J MATH ED. 2022;17(3), em0690. https://doi.org/10.29333/iejme/12061

Chicago

Ishibashi, Ippo. "Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks". International Electronic Journal of Mathematics Education 2022 17 no. 3 (2022): em0690. https://doi.org/10.29333/iejme/12061

Harvard

Ishibashi, I. (2022). Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks. International Electronic Journal of Mathematics Education, 17(3), em0690. https://doi.org/10.29333/iejme/12061

MLA

Ishibashi, Ippo "Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks". International Electronic Journal of Mathematics Education, vol. 17, no. 3, 2022, em0690. https://doi.org/10.29333/iejme/12061