Advertisement

Representing Instructional Improvement in Lesson Study through Principled Analysis of Research Lessons in Singapore: A Case of Equivalent Fractions

  • Yanping FangEmail author
  • Xiong Wang
  • Christine Lee Kim-Eng
Chapter
Part of the Advances in Mathematics Education book series (AME)

Abstract

This chapter reports our effort in developing a principled way of representing instructional improvement in lesson study in the form of a process analysis, based on a thorough analysis of classroom discourse of four research lessons on equivalent fractions, a third-grade topic in Singapore, which we conducted at the early stage of our lesson study work in 2006–2007. Our social-cultural view guided a systematic effort in making consistent and iterative improvements within an instructional system mediated dynamically at multilevels – the content, discourse, activity, tasks, and tools level. Each level of the analysis was conceptualized to build coding schemes. The coded patterns were quantitatively and qualitatively presented to indicate how a balance in mathematical representation was achieved and how construction of the meaning-making was escalated across the research lessons. This principled way of representation has not only enabled us to represent and articulate the instructional improvements systematically but also further informed and improved our own ongoing lesson study with teachers locally and the lesson study work globally.

Keywords

Lesson study Instructional improvements Discourse analysis 

References

  1. Ball, D. (1993). Halves, pieces and twoths: Constructing and using representational contexts in teaching fractions. In T. P. Carpenter, E. Fennema, & T. A. Romberg (Eds.), Rational numbers: An integration of research (pp. 49–84). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  2. Bruner, J. (1966). Toward a theory of instruction. London: Harvard University Press.Google Scholar
  3. Cai, J. (2007). What is effective mathematics teaching? A study of teachers from Australia, Mainland China, Hong Kong SAR, and the United States. ZDM, 39(4), 265–270.CrossRefGoogle Scholar
  4. Cai, J., Kaiser, G., Perry, G., & Wong, N. Y. (2009). Effective mathematics teaching from teachers’ perspectives. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  5. Campbell, P. F., & Rowan, T. E. (1997). Teacher questions + student language + diversity =mathematical power. In M. J. Kenney (Ed.), Multicultural and gender equity in the mathematics classroom: The gift of diversity (pp. 60–70). Reston: National Council of Teachers of Mathematics.Google Scholar
  6. Cazden, C. (2001). Classroom discourse: The language of teaching and learning. Portsmouth: Heinemann.Google Scholar
  7. Chen, X. (2017). Theorizing Chinese lesson study from a cultural perspective. International Journal for Lesson and Learning Studies, 6(4), 283–292.CrossRefGoogle Scholar
  8. C. Chen, & Z. Zhou (Eds.) (2005). Mathematics for 4th grade, textbooks for nine-year compulsory education. Shanghai: Shanghai Education Press.Google Scholar
  9. Clarke, D. J., Keitel, C., & Shimizu, Y. (2006). Mathematics classrooms in twelve countries: The insider’s perspective. Rotterdam: Sense Publishers.CrossRefGoogle Scholar
  10. Cobb, P. (1995). Cultural tools and mathematical learning: A case study. Journal for Research in Mathematics Education, 26(4), 362–385.CrossRefGoogle Scholar
  11. Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resource, instruction, and research. Education Policy Analysis Archives, 25(2), 119–142.CrossRefGoogle Scholar
  12. Cole, M., John-Steiner, V., Scribner, S., & Souberman, E. (Eds.). (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar
  13. Corte, E. D., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 491–549). New York: Macmillan.Google Scholar
  14. Dossey, J. A., Mullis, I. V. S., Lindquist, M. M., & Chambers, D. L. (1988). The mathematics report card: Are we measuring up? Trends and achievement based on the 1986 National Assessment. Princeton: Educational Testing Service.Google Scholar
  15. Dudley, P. (2011). Lesson study development in England: From school networks to national policy. International Journal for Lesson and Learning Studies, 1(1), 85–100.CrossRefGoogle Scholar
  16. Fang, Y., Lee, C. K. E., & Haron, S. T. S. (2008). Lesson study in mathematics: Three cases for Singapore. In K. Y. Wong, P. Y. Lee, B. Kaur, P. Y. Foong, & S. F. Ng (Eds.), Mathematics education: The Singapore journey (pp. 104–129). Singapore: World Scientific.Google Scholar
  17. Fang, Y. P., Lee, K. E. C., & Haron, S. T. (2009). Lesson study in mathematics: Three cases from Singapore. In K. Y. Wong, P. Y. Lee, B. Kaur, P. Y. Foong, & S. F. Ng (Eds.), Mathematics education - the Singapore journey (pp. 104–129). Singapore: World Scientific.Google Scholar
  18. Fang, Y. P., Lee, K. E. C., & Yang, Y. (2011). Developing video cases from research lessons as curriculum and pedagogical support for teacher learning – A case of long division. International Journal of Lesson and Learning Studies, 1(1), 65–84.CrossRefGoogle Scholar
  19. Fernandez, C. (2002). Learning from Japanese approaches to professional development. Journal of Teacher Education, 53, 393–405.CrossRefGoogle Scholar
  20. Fernandez, C., Cannon, J., & Chokshi, S. (2003). A U.S.–Japan lesson study collaborative reveals critical lenses for examining practice. Teaching and Teacher Education, 19, 171–185.CrossRefGoogle Scholar
  21. Fong, H., Ramakrishnan, C., & Choo, M. (2003). My pals are here! Singapore: Federal Publications.Google Scholar
  22. Frobisher, L., Monaghan, J., Orton, A., Orton, J., Roper, T., & Threlfall, J. (1999). Learning to teach number. Cheltenham: Stanley Thornes.Google Scholar
  23. Goh, R., & Fang, Y. (2017). Improving English language teaching through lesson study: Case study of teacher learning in a Singapore primary school grade level team. International Journal for Lesson and Learning Studies, 6(2), 135–150.CrossRefGoogle Scholar
  24. Hairon, S., & Dimmock, C. (2012). Singapore schools and professional learning communities: Teacher professional development and school leadership in an Asian hierarchical system. Educational Review, 64(4), 405–424.CrossRefGoogle Scholar
  25. Hironaka, H., & Sugiyama, Y. (Eds.) (2006). Mathematics 4A for elementary school. Translated into English by Yoshida et al. Tokyo Shoseki, Co., Ltd.Google Scholar
  26. Hogan, D., & Gopinathan, S. (2008). Knowledge management, sustainable innovation, and pre-service teacher education in Singapore. Teachers and Teaching, 14(4), 369–384.CrossRefGoogle Scholar
  27. Hogan, D., Chan, M., Rahim, R., Towndrow, P., & Kwek, D. (2012). Understanding classroom talk in secondary 3 mathematics classes in Singapore. In B. Kaur (Ed.), Connections, reasoning and communication: New directions in mathematics education. Singapore: Springer.Google Scholar
  28. Huang, R., Fang, Y., & Chen, X. (2017). Chinese lesson study: A deliberate practice, a research methodology, and an improvement science. International Journal of Lesson and Learning Studies, 6(4), 270–282.CrossRefGoogle Scholar
  29. Hucker, J. (1994). Creating paths to mathematical literacy: A.S.B./A.P.P.A.travelling fellowship 1994 report. Auckland: Author.Google Scholar
  30. Hunting, R. (1984). Understanding equivalent fractions. Journal of Science and Mathematics Educations in S. E. Asia, 7(1), 26–33.Google Scholar
  31. Jigyel, K., & Afamasaga-Fuata’I, K. (2007). Students’ conceptions of models of fractions and equivalence. Australian Mathematics Teacher, 63(4), 17–25.Google Scholar
  32. Kamii, C., & Clark, F. B. (1995). Equivalent fractions: Their difficulty and educational implications. The Journal of Mathematical Behavior, 14, 365–378.CrossRefGoogle Scholar
  33. Kervin, K. (2007). Exploring the use of slow motion animation (Slowmation) as a teaching strategy to develop year 4 students’ understandings of equivalent. Fractions. Contemporary Issues in Technology and Teacher Education, 7(2), 100–106.Google Scholar
  34. Koh, K. H. (2011). Improving teachers’ assessment literacy through professional development. Teaching Education, 22(3), 255–276.CrossRefGoogle Scholar
  35. Kunter, M., Klusmann, U., Baumert, J., Richter, D., Voss, T., & Hachfeld, A. (2013). Professional competence of teachers: Effects on instructional quality and student development. Journal of Educational Psychology, 105(3), 805–820.CrossRefGoogle Scholar
  36. Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  37. Leon, J., Medina-Garrido, E., & Núñez, J. L. (2017). Teaching quality in math class: The development of a scale and the analysis of its relationship with engagement and achievement. Frontiers in Psychology, 8, 1–14.CrossRefGoogle Scholar
  38. Leong, Y., Ho, W., & Cheng, L. (2015). Concrete-pictorial-abstract: Surveying its origins and charting its future. The Mathematics Educator, 16(1), 1–19.Google Scholar
  39. Lewis, C. (2015). What is improvement sciences? Do we need it in education? Educational Researcher, 44(1), 54–61.CrossRefGoogle Scholar
  40. Lewis, C., & Tsuchida, I. (1998). A lesson is like a swiftly flowing river: Research lessons and the improvement of Japanese education. American Educator (Winter), 14–17, 50–52.Google Scholar
  41. Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study. Educational Researcher, 35(3), 3–14.CrossRefGoogle Scholar
  42. Little, J. W. (1999). Organizing schools for teacher learning. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 233–262). San Francisco: Jossey-Bass.Google Scholar
  43. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum.Google Scholar
  44. Ministry of Education. (2007). Primary mathematics syllabus. Singapore: Author.Google Scholar
  45. Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30(2), 122–147.CrossRefGoogle Scholar
  46. Munter, C. (2014). Developing visions of high-quality mathematics instruction. Journal for Research in Mathematics Education, 45(5), 584–635.CrossRefGoogle Scholar
  47. Nassaji, H., & Wells, G. (2000). What’s the use of ‘triadic dialogue’?: An investigation of teacher-student interaction. Applied Linguistics, 21, 376–406.CrossRefGoogle Scholar
  48. NEA Foundation for the Improvement of Education. (2003). Using data about classroom practice and student work to improve professional development for educators. Washington, DC: Author.Google Scholar
  49. Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26, 400–417.CrossRefGoogle Scholar
  50. Noss, R., & Hoyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers. Dordrecht: Kluwer.CrossRefGoogle Scholar
  51. Paine, L. W. (1990). The teacher as virtuoso: A Chinese model for teaching. Teachers College Record, 92(1), 49–81.Google Scholar
  52. Paine, L. W., & Fang, Y. P. (2006). Reform as hybrid model of teaching and teacher development in China. International Journal for Education Research, 45(4–5), 279–289.CrossRefGoogle Scholar
  53. Perry, R. R., & Lewis, C. C. (2009). What is successful adaptation of lesson study in the U.S.? Journal of Educational Change, 10(4), 365–391.CrossRefGoogle Scholar
  54. Schleppenbach, M., Flevares, L. M., Sims, L. M., & Perry, M. (2007). Teachers’ responses to student mistakes in Chinese and U.S. mathematics classrooms. Elementary School Journal, 108, 131–147.CrossRefGoogle Scholar
  55. Schoenfeld, A. H. (2002). A highly interactive discourse structure. Social Constructivist Teaching, 9, 131–169.CrossRefGoogle Scholar
  56. Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1(2), 157–189.CrossRefGoogle Scholar
  57. Steinbring, H. (2005). The construction of new mathematical knowledge in classroom interaction: An epistemological perspective. New York: Springer.Google Scholar
  58. Steinbring, H. (2006). What makes a sign a mathematical sign?–An epistemological perspective on mathematical interaction. Educational Studies in Mathematics, 61(1–2), 133–162.CrossRefGoogle Scholar
  59. Stigler, J. W., & Hiebert, J. (1999). The teaching gap; best ideas from the world’s teachers for improving education in the classroom. New York: The Free Press.Google Scholar
  60. Streefland, L. (1991). Fractions in realistic mathematics education: A paradigm of developmental research. Dordrecht: Kluwer.CrossRefGoogle Scholar
  61. Truxaw, M. P. (2005). Orchestrating whole group discourse to mediate mathematical meaning. DigitalCommons@UConn.Google Scholar
  62. Wells, G. (1999). Dialogic inquiry: Toward a sociocultural practice and theory of education. New York: Cambridge University Press.CrossRefGoogle Scholar
  63. Wells, G. (2002). The role of dialogue in activity theory. Mind, Culture, and Activity, 9(1), 43–66.CrossRefGoogle Scholar
  64. Westenskow, A., & Moyer-Packenham, P. (2016). Using an iceberg intervention model to understand equivalent fraction learning when students with mathematical learning difficulties using different manipulatives. International Journal for Technology in Mathematics Education, 23(2), 45–62.Google Scholar
  65. White, A. L., & Lim, C. S. (2008). Lesson study in Asia Pacific classrooms: Local responses to a global movement. ZDM – The International Journal on Mathematics Education, 40(6), 915–925.CrossRefGoogle Scholar
  66. Wong, M., & Evans, D. (2007). Students’ conceptual understanding of equivalent fractions. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice (Proceedings of the 30th annual conference of the Mathematics Education Group of Australasia) (pp. 824–833). Adelaide: MERGA.Google Scholar
  67. Yang, Y., & Ricks, T. E. (2011). How crucial incidents analysis support Chinese lesson study. International Journal for Lesson and Learning Studies, 1(1), 41–48.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yanping Fang
    • 1
    Email author
  • Xiong Wang
    • 2
  • Christine Lee Kim-Eng
    • 1
  1. 1.National Institute of EducationNanyang Technological UniversitySingaporeSingapore
  2. 2.Secondary EducationUniversity of AlbertaEdmontonCanada

Personalised recommendations