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International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Analyzing experimental and theoretical probabilities in Japanese 7th and 8th grade textbooks
Ippo Ishibashi 1 *
1 Okayama University, Okayama, JAPAN
* Corresponding Author
APA
In-text citation: (Ishibashi, 2022)
Reference: 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
AMA
In-text citation: (1), (2), (3), etc.
Reference: 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
In-text citation: (Ishibashi, 2022)
Reference: 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
In-text citation: (Ishibashi, 2022)
Reference: 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
In-text citation: (Ishibashi, 2022)
Reference: 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
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: 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

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 7th and 8th grades through a textbook analysis. We analyzed seven, government approved Japanese 7th and 8th 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 7th and 8th grade textbook analysis

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).

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