Abstract
In this study, we examined the instructional coherence in a Chinese mathematics classroom by analyzing a sequence of four videotaped lessons on the topic of fraction division. Our analysis focused on the characteristics of instructional coherence both within and across individual lessons. A framework was developed to focus on lesson instruction in terms of its content and process and the teacher's use of classroom discourse. The analyses of lesson instruction were further supplemented with the analyses of teaching materials and interviews with the teacher. The findings go beyond previous studies that mainly focused on a single lesson to provide further evidence about Chinese teachers' instructional practices and their possible impact on students' learning. In particular, the teacher tried to help students build knowledge connections and coherence through lesson instruction. Results also suggest that coherent curriculum and the teacher's perception of the knowledge coherence facilitated the teacher's construction of coherent classroom instruction.
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Armstrong, B. E., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 85–120). New York: SUNY.
Baranes, R. (1990). Factors influencing children's comprehension of a mathematics lesson. Unpublished doctoral dissertation, University of Chicago.
Borko, H., Eisenhart, M., Brown, C., Underhill, R. G., Jones, D., & Agard, P. C. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194–222.
Fernandez, C., Yoshida, M., & Stigle, J. (1992). Learning mathematics from classroom instruction: On relating lessons to pupils' interpretations. The Journal of the Learning Sciences, 2, 333–365.
Finley, S. (2000). Instructional coherence: The changing role of the teacher. Retrieved March 23, 2008, from http://www.sedl.org/pubs/catalog/items/teaching99.html.
Hiebert, J., Gallimore, R., Garnier, H., Giwin, K. B., Hollingsworth, H., Jacobs, J., et al. (2003). Teaching mathematics in seven countries: Results from the TIMSS 1999 video study. Washington: U. S. Department of Education, National Center for Education Statistics.
Jiangsu Province Research Group for Elementary and Middle School Mathematics Teaching. (2001a). Shuxue, dishiyice [Mathematics Vol. 11]. Jiangsu: Jiangsu Educational Publisher.
Jiangsu Province Research Group for Elementary and Middle School Mathematics Teaching. (2001b). Jiaoshi Zhidao Yongshu, dishiyice [Mathematics teacher's guidebook 11]. Jiangsu: Jiangsu Educational Publisher.
Leung, F. K. S. (2005). Some characteristics of East Asian mathematics classrooms based on data from TIMSS 1999 video study. Educational Studies in Mathematics, 60, 199–215.
Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13, 546–552.
Li, Y., & Chen, X. (2009). Lesson instruction to develop students' conceptual understanding with mandatory curriculum as a context. Paper presented at the Research Pre-session of National Council of Teachers of Mathematics Annual Meeting, Washington, DC, April 20–22.
Li, Y., & Li, J. (2009). Mathematics classroom instruction excellence through the platform of teaching contests. ZDM—The International Journal on Mathematics Education, 41, 263–277.
Li, Y., Chen, X., & Kulm, G. (2009). Mathematics teachers' practices and thinking in lesson plan development: A case of teaching fraction division. ZDM—The International Journal on Mathematics Education, doi:10.1007/s11858-009-0174-8.
Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah: Lawrence Erlbaum.
Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., & Chrostowski, S. J. (2004). Findings from IEA's trends in international mathematics and science study at the fourth and eighth grades. Chestnut Hill: TIMSS & PIRLS International Study Center, Boston College.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston: NCTM.
Robitaille, D. F., & Garden, R. A. (1989). The IEA study of mathematics II: Contexts and outcomes of school mathematics. New York: Pergamon.
Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum: The case of mathematics. American Educator, 26(2), 10–26. Retrieved July 19, 2007, from http://www.aft.org/pubs-reports/american_educator/summer2002/curriculum.pdf.
Segiguchi, Y. (2006). Coherence of mathematics lessons in Japanese eighth-grade classrooms. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, Prague, Czech Republic, 5, pp. 81–88.
Shimizu, Y. (2004). How do you conclude today's lesson? The form and functions of “matome” in mathematics lesson. Paper presented at the annual meeting of the American Educational Research Association, San Diego. Retrieved March 11, 2008, from http://extranet.edfac.unimelb.edu.au/DSME/lps/assets/YS_SummingUp.pdf.
Shimizu, Y. (2007). Explicit linking in the sequence of consecutive lessons in mathematics classroom in Japan. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, South Korea, 4, pp. 177–184.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1–22.
Sinincrop, R., Mick, H. W., & Kolb, J. R. (2002). Interpretations of fraction division. In B. Litwiller & G. Bright (Eds.), Making sense of fractions, ratios, and proportions (pp. 153–161). Reston: NCTM.
Sowder, J. T. (1995). Continuing the mathematical preparation of middle-grade teachers: An introduction. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 1–11). New York: SUNY.
Stein, N. L., & Glenn, C. G. (1982). Children's concept of time: The development of story schema. In W. J. Friedman (Ed.), The developmental psychology of time (pp. 255–282). New York: Academic.
Stevenson, H. W., & Stigler, J. W. (1992). The learning gap. New York: The Free Press.
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.
Stigler, J. W., & Perry, M. (1988). Mathematics learning in Japanese, Chinese, and American classrooms. New Directions for Child Development, 41, 27–54.
Thagard, P., & Verbeurgt, K. (1998). Coherence as constraint satisfaction. Cognitive Science, 22, 1–24.
Tomlin, R. S., Forrest, L., Pu, M. M., & Kim, M. H. (1997). Discourse semantics. In T. A. van Dijk (Ed.), Discourse as structure and process (pp. 63–111). London: Sage.
Trabasso, T., Secco, T., & van den Broek, P. (1984). Causal cohesion and story coherence. In H. Mandl, N. L. Stein & T. Trabasso (Eds.), Learning and comprehension of text (pp. 83–111). Hillsdale: Erlbaum.
Wang, T., & Murphy, J. (2004). An examination of coherence in a Chinese mathematic classroom. In L. Fan, N. Wong, J. Cai & S. Li (Eds.), How Chinese learn mathematics (pp. 107–123). Danvers: World Scientific Publication.
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Chen, X., Li, Y. INSTRUCTIONAL COHERENCE IN CHINESE MATHEMATICS CLASSROOM—A CASE STUDY OF LESSONS ON FRACTION DIVISION. Int J of Sci and Math Educ 8, 711–735 (2010). https://doi.org/10.1007/s10763-009-9182-y
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DOI: https://doi.org/10.1007/s10763-009-9182-y