Abstract
It is a paradoxical phenomenon that a seemingly unfavorable learning environment, such as the large-size classrooms dominated with traditional lecture-oriented instruction in China, produces high-achieving students in school mathematics (Fan & Zhu, 2004; Stevenson, Chen, & Lee, 1993). Some researchers have thus examined how Chinese students learn mathematics (Fan, Wong, Cai, & Li, 2004), and what Chinese mathematics classrooms look like (Huang, 2006; Huang & Leung, 2004; Huang & Li, 2009; Li & Huang, 2012; Lopez-Real, Mok, Leung, & Marton, 2004; Stevenson & Lee, 1995).
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References
Baroody, A. J., Feil, Y., & Johnson, A. R. (2007). An alternative reconceptualization of procedural and conceptual knowledge. Journal for Research in Mathematics Education, 38,115–131.
Biggs, J. B., & Watkins, D. A. (1996). The Chinese learner in retrospect. In D. A. Watkins & J. B. Biggs (Eds.), The Chinese learner: Cultural, psychological, and contextual influences (pp. 269–285). Hong Kong: Comparative Educational Research Center, The University of Hong Kong.
Brownell, W. A. (1938). Two kinds of learning in arithmetic. Journal of Educational Research, 31, 656–664.
Cai, J., & Wang, T. (2010). Conceptions of effective mathematics teaching within a cultural context: perspectives of teachers from China and the United States. Journal of Mathematics Teacher Education, 13, 265–287.
Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics classroom that promote understanding (pp. 19–32). Mahwah: Lawrence Erlbaum.
Clarke, D. (2006a). The LPS research design. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries (pp. 15–29). Rotterdam, The Netherlands: Sense.
Clarke, D. (2006b). Deconstructing dichotomies: Arguing for a more inclusive approach. In D. J. Clarke, J. Emanuelsson, E. Jablonka, & I. A. C. Mok (Eds.), Making connections: Comparing mathematics classrooms around the world. Rotterdam, The Netherlands: Sense.
Fan, L., & Zhu, Y. (2004). How have Chinese students performed in mathematics ? A perspective from large-scale international mathematics comparisons. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 348–381). Singapore: World Scientific.
Fan, L., Wong, N. Y., Cai, J., & Li, S. (2004). How Chinese learn mathematics: Perspectives from insiders. Singapore: World Scientific.
Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: An effective way of mathematics teaching in China. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 309–348). Singapore: World Scientific.
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 8, 524–549.
Hiebert, J., & Carpenter, P. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–97). New York, NY: Macmillan.
Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., Olivier, A., & Human, P. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth: Heinemann.
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester, Jr.(Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age.
Huang, R. (2006). Looking into mathematics classroom in Chinese communities. Journal of Mathematics Education, 2, 67–70.
Huang, R., & Cai, J. (2011). Pedagogical representations to teach linear relations in Chinese and U.S. classrooms: Parallel or hierarchical. The Journal of Mathematical Behavior, 30, 149–165.
Huang, R., & Cai, J. (2010). Implementing mathematics tasks in the U.S. and Chinese classroom. In Y. Shimizu, B. Kaur, R. Huang, & D., Clarke (Eds), Mathematical tasks in classrooms around the world (pp. 147–166).Rotterdam, The Netherlands: Sense.
Huang, R., & Leung, F. K. S (2004). Cracking the paradox of the Chinese learners: Looking into the mathematics classrooms in Hong Kong and Shanghai. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 348–381). Singapore: World Scientific.
Huang, R., & Li, Y. (2009). Pursuing excellence in mathematics classroom instruction through exemplary lesson development in China: A case study. ZDM—The International Journal on Mathematics Education, 41, 297–309.
Huang, R., Mok, I., & Leung, F. K. S. (2006). Repetition or variation: “Practice” in the mathematics classrooms in China. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 263–274). Rotterdam, the Netherlands: Sense.
Jacobs, J., Hiebert, J., Givvin, K., Hollingsworth, H., Garnier, H., & Weame, D. (2006). Does eighthgrade mathematics teaching in the United States align with the NCTM standards? Results from the TIMSS 1995 and 1999 video studies. Journal for Research in Mathematics Education, 36, 5–32.
Leung, F. K. S. (2005). The implications of TIMSS 1999 Video Study for Chinese mathematics curriculum reform. Journal of Mathematics Education, 14(1), 7–11.
Li, S. (2006). Practice makes perfect: A key belief in China. In F. K. S. Leung, K. D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions: A comparative study of East Asia and the West (pp. 129–138). New York, NY: Springer.
Li, Y., & Huang, R. (Eds.). (2012). How Chinese teach mathematics and improve teaching. New York, NY: Routledge.
Lopez-Real, F., Mok, A. C. I., Leung, F. K. S., & Marton, F. (2004). Identifying a pattern of teaching: An analysis of a Shanghai teacher’s lessons. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 382–412). Singapore: World Scientific.
Martin, T. S. (2007). Mathematics teaching today: Improving practice, improving student learning (2nd). Reston, VA: National Council of Teachers of Mathematics.
Marton, F., Dall’Alba, G., & Tse, L. K. (1996). Memorizing and understanding: The keys to the paradox? In D. A. Watkins & J. B. Biggs (Eds.), Cultural, psychological and contextual influences (pp. 69–83). Hong Kong: Comparative Education Research Centre, The University of Hong Kong.
Mok, I. A. C. (2006). Teacher-dominating lessons in Shanghai: The insiders’ story. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 87–98). Rotterdam, the Netherlands: Sense.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
National Research Council Institute of Medicine (NRCIM). (2004). Engaging schools: Fostering high school students’ motivation to learn. Washington, DC: National Academies Press.
Schoenfeld, A. H., & Pateman, N. (2008). A study of teaching multiple lenses, multiple views. Reston, VA: National Council of Teachers of Mathematics.
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching 77, 20–26.
Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36, 404–411.
Stevenson, H. W., & Lee, S. Y. (1995). The East Asian version of whole-class teaching. Education Policy, 9, 152–168.
Stevenson, H. W., Chen, C. C., & Lee, S. Y. (1993). Mathematics achievement of Chinese, Japanese, and American children: Ten years later. Science, 25, 53–59.
Wood, T., Shin, S. Y., & Doan, P. (2006). Mathematics education reform in three US classrooms. In D. J. Clarke, C. Keitel, & Y. Shimizu (Eds.), Mathematics classrooms in twelve countries: The insider’s perspective (pp. 75–86). Rotterdam, the Netherlands: Sense.
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Huang, R., Li, Y. (2014). Promoting Mathematical Understanding. In: Leung, F.K.S., Park, K., Holton, D., Clarke, D. (eds) Algebra Teaching around the World. Series Preface. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6209-707-0_12
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DOI: https://doi.org/10.1007/978-94-6209-707-0_12
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