Dialectic on the Problem Solving Approach: Illustrating Hermeneutics as the Ground Theory for Lesson Study in Mathematics Education

Chapter

Abstract

Lesson study is the major issue in mathematics education for developing and sharing good practice and theorize a theory for teaching and curriculum development. Hermeneutic efforts are the necessary activities for sharing objectives of the lesson study and make them meaningful for further development. This paper illustrates hermeneutic efforts with two examples for understanding the mind set for lesson study. The first example, the internet communication between classrooms in Japan and Australia, demonstrates four types of interpretation activities for hermeneutic effort: Understanding, Getting others’ perspectives, Instruction from experience (self-understanding), and the hermeneutic circle. Using these concepts, we will illustrate the second example with dialectic discussion amongst students in the problem solving classroom engaged in a task involving fractions.

References

  1. Arcavi, A., & Isoda, M. (2007). Learning to listen: From historical sources to classroom practice. Educational Studies in Mathematics, 66(2), 111–129.CrossRefGoogle Scholar
  2. Brown, T. (1997). Mathematics education and language: Interpreting hermeneutics and post-structuralism. Dordrecht: Kluwer.Google Scholar
  3. Dilthey, W. (1900). Die Entstehung der Hermeneutik. Tübingen.Google Scholar
  4. Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1, 3–8.CrossRefGoogle Scholar
  5. Freudenthal, H. (1973). Mathematics as an educational task. Dordrecht: D. Reidel.Google Scholar
  6. Gadamer, G. (1960). Wahrheit und Methode: Grundzuge einer philosophischen Hermeneutik. Tübingen.Google Scholar
  7. Gadamer, G. (1993). Hermeneutik, Ästhetik, praktische Philosophie: Hans-Georg Gadamer im Gespräch. Hrsg. von Carsten Dutt.Heidelberg: C. Winter.Google Scholar
  8. Glassersfeld, E. (1995). Radical constructivism. London: Falmer Press.CrossRefGoogle Scholar
  9. Hibert, J. (1986). Conceptual and procedural knowledge: The case of mathematics. New Jersey: L. Erlbaum.Google Scholar
  10. Heath, T. (1912). The method of archimedes. Cambridge.Google Scholar
  11. Isoda, M., & Aoyama, K. (2000). The change of belief in mathematics via exploring historical text with technology in the case of undergraduates. In Proceeding of the Fifth Asian Technology Conference in Mathematics (pp. 132–141).Google Scholar
  12. Isoda, M., McCrae, B., & Stacey, K. (2006). Cultural awareness arising from internet communication between Japanese and Australian classroom. In G. K. S., Leung, K., Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural tradition (pp. 397–408). USA: Springer.Google Scholar
  13. Isoda, M., & Shigeo, K. (2012). Mathematical thinking: How to develop it in the classroom. Singapore: World Scientific.CrossRefGoogle Scholar
  14. Jahnke, H. N. (1994). The historical dimension of mathematics understanding; Objectifying the subjective. In P., Ponte et al. (Eds.), Proceedings of the International Conference for the Psychology of Mathematics Education (pp. 139–156).Google Scholar
  15. Kline, M. (1973). Why Johnny can’t add: the failure of the new math. New York: St. Martin’s Press.Google Scholar
  16. Ministry of Education. (1989). The course of study. Printing Bureau in Ministry of Finance (in Japanese).Google Scholar
  17. Nohda, N. (1981). A research study on children’s learning of fractional numbers based on a comparison between children’s concepts of common fraction before and after teaching. Research Journal of Mathematical Education, 37, 1–29.Google Scholar
  18. Rényi, A., & Vekerdi, L. (1972). Letters on probability. Detroit: Wayne State University Press.Google Scholar
  19. Schleiermacher, F. (1905). Hermeneutik: The handwritten manuscripts (from Japanese translation).Google Scholar
  20. Schubring, G. (2005). Conflicts between generalization, Rigor, and intuition. USA: Springer.Google Scholar
  21. Warnke, G. (1987). Gadamer: Hermeneutics, tradition and reason. Cambridge: Cambridge University Press.Google Scholar
  22. Wheeler, D. (1975). Humanizing mathematical education. Mathematics Teaching, 71, 4–9.Google Scholar

References in Japanese

  1. Isoda, M. (1992). Conceptual and procedural knowledge for Japanese problem solving approach. Hokkaido University of Education at Iwamizawa (78 p) (in Japanese).Google Scholar
  2. Isoda, M. (1993). Investigating the logic of understanding in the arithmetic class: The case study of social interaction from the cognitive model. In Editorial Committee of Research Book of Educational Practice in Hokkaido University of Education (Ed.), Subject, children, and language: Investigate the educational practice by language (pp. 126–139), Tokyo Shoseki (in Japanese).Google Scholar
  3. Isoda, M. (Ed.). (1996). Problem solving lesson to construct and discuss various ideas: Lesson plan about conflict and appreciation based on the inconsistency between the meaning and the procedure. Meiji Tosho (in Japanese).Google Scholar
  4. Isoda, M., & Tsuchida, T. (2001). Mathematics as a human enterprise through cultural awareness: For the perspective of mathematics activity. In The Proceeding of the 2001 Annual Meeting of Japan Society for Science Education (pp. 497–498) (in Japanese).Google Scholar
  5. Isoda, M. et al. (Eds.). (1999). Lesson study for problem solving approach at middle school mathematics: Using the conceptual and procedural knowledge. Meiji Tosho (in Japanese).Google Scholar
  6. Ishizuka, M., Lee, Y., Aoyama, K., & Isoda, M. (2002). A developmental study of mathematics communication environment for palmtop computer. Journal of Science Education in Japan, 26(1), 91–101. (in Japanese).Google Scholar
  7. Isoda, M. (2002). Hermeneutics for humanizing mathematics education. Tsukuba Journal of Educational Study in Mathematics, 23, 1–10. (in Japanese).Google Scholar
  8. Isoda, M. et al. (Eds.). (2005). Lesson study aimed for understanding at elementary school mathematics; Conceptual and procedural knowledge in matehmatics. Meiji Tosho (in Japanese).Google Scholar
  9. Isoda, M. et al. (Eds.). (2008). Lesson study aimed for argumentation at middle school mathematics. Meiji Tosho (in Japanese).Google Scholar
  10. Isoda, M. et al. (Eds.). (2010). Lesson study aimed for argumentation at; Elementary school mathematics. Meiji Tosho (in Japanese).Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of TsukubaTsukubaJapan

Personalised recommendations