Skip to main content
SpringerLink
Log in

Teaching Geometrical Concepts through Variation

A Case Study of a Shanghai Lesson

  • Chapter
Teaching and Learning Mathematics through Variation

Part of the book series: Mathematics Teaching and Learning ((MTAL))

Abstract

Chinese students’ superior performance in mathematics in various international comparative studies (Fan & Zhu, 2004; OECD, 2010, 2014) has led to an increasing interest in exploring the characteristics of mathematics instruction in China (Fan, Wong, Cai, & Li, 2015; Li & Huang, 2013).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Ausubel, D. P. (1968). Educational psychology: A cognitive view. New York, NY: Holt, Rinehart & Winston.

    Google Scholar 

  • Chen, X., & Li, Y. (2010). Instructional coherence in Chinese mathematics classroom – A case study of lessons on fraction division. International Journal of Science and Mathematics Education, 8, 711–735.

    Article  Google Scholar 

  • Duval, R. (1999, October 23–26). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. Proceedings of the Annual Meeting of the North American Chapter of the International group for the Psychology of Mathematics education, Morelos, Mexico.

    Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131.

    Article  Google Scholar 

  • Fan, L., & Zhu, Y. (2004). How have Chinese students performed in mathematics? A perspective from large-scale international comparisons. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 3–26). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Fan, L., Wong, N. Y., Cai, J., & Li, S. (2015). How Chinese teach mathematics: Perspectives of insiders. Singapore: World Scientific.

    Book  Google Scholar 

  • Fischbein, E. (1993). The theory of figural concepts. Educational Studies in Mathematics, 24(2), 139–162.

    Article  Google Scholar 

  • Gu, F., Huang, R., & Gu, L. (2017). Theory and development of teaching through variation in mathematics in China. In R. Huang & Y. Li (Eds.), Teaching and learning mathematics through variation (this volume). Rotterdam, The Netherlands: Sense Publishers.

    Google Scholar 

  • Gu, L. (1994). Theory of teaching experiment: The methodology and teaching principles of Qingpu [In Chinese]. Beijing: Educational Science Press.

    Google Scholar 

  • 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. 309–347). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and cognition: A research synthesis by the International group for the psychology of mathematics education (pp. 70–95). Cambridge: Cambridge University Press.

    Chapter  Google Scholar 

  • Hershkowitz, R., Bruckheimer, M., & Vinner, S. (1987). Activities with teachers based on cognitive research. In M. M. Lindquist (Ed.), Learning and teaching geometry, K-12: 1987 Year book (pp. 222–235). Reston, VA: National Council of Teachers of Mathematics.

    Google Scholar 

  • Huang, R. (2002). Mathematics teaching in Hong Kong and Shanghai: A classroom analysis from the perspective of variation (Unpublished doctoral dissertation). The University of Hong Kong, Hong Kong.

    Book  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Huang, R., & Leung, F. K. S. (2005). Deconstructing teacher-centeredness and student-centeredness dichotomy: A case study of a Shanghai mathematics lesson. The Mathematics Educators, 15(2), 35–41.

    Google Scholar 

  • Huang, R., Miller, D., & Tzur, R. (2015). Mathematics teaching in Chinese classroom: A hybrid-model analysis of opportunities for students’ learning. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese teach mathematics: Perspectives from insiders (pp. 73–110). Singapore: World Scientific.

    Chapter  Google Scholar 

  • 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 Publishers.

    Google Scholar 

  • Leung, F. K. S. (2005). Some characteristics of East Asian mathematics classrooms based on data from the TIMSS 1999 video study. Educational Studies in Mathematics, 60, 199–215.

    Article  Google Scholar 

  • Li, Y., & Huang, R. (2013). How Chinese teach mathematics and improve teaching. New York, NY: Routledge.

    Google Scholar 

  • Marton, F., & Pang, M. F. (2006). On some necessary conditions of learning. The Journal of the Learning Sciences, 15, 193–220.

    Article  Google Scholar 

  • Marton, F., & Tsui, A. B. M. (2004). Classroom discourse and the space of learning. Mahwah, NJ: Erlbaum.

    Google Scholar 

  • OECD. (2010). PISA 2009 results: What students know and can do: Student performance in reading, mathematics and science (Vol. I). Paris: OECD Publishing.

    Book  Google Scholar 

  • OECD. (2014). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know. Paris: OECD Publishing.

    Google Scholar 

  • Paine, L. W. (1990). The teacher as virtuoso: A Chinese model for teaching. Teachers College Record, 92(1), 49–81.

    Google Scholar 

  • Qingpu Experiment Group. (1991). Learn to teaching [In Chinese]. Beijing: Peoples’ Education Press.

    Google Scholar 

  • Stevenson, H. W., & Lee, S. (1995). The East Asian version of whole class teaching. Educational Policy, 9, 152–168.

    Article  Google Scholar 

  • Vinner, S. (1981). The nature of geometrical objects as conceived by teachers and prospective teachers. In Equipe De Recherche, PĂ©dagogique (Eds.), Proceedings of the 5 th PME international Conferences, 1, 375–380.

    Google Scholar 

  • Vinner, S. (1991). The role of definitions in the teaching and learning of mathematics. In D. Tall (Ed.), Advanced mathematical thinking (pp. 65–81). Dordrecht, Netherlands: Kluwer.

    Google Scholar 

  • Vinner, S., & Hershkowitz, R. (1983). On concept formation in geometry. ZDM-The International Journal on Mathematics Education, 83(1), 20–25.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Middle Tennessee State University, USA

    Rongjin Huang

  2. The University of Hong Kong, China

    Frederick K. S. Leung

Authors
  1. Rongjin Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frederick K. S. Leung
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Middle Tennessee State University, USA

    Rongjin Huang

  2. Texas A&M University, USA

    Yeping Li

  3. Shanghai Normal University, China

    Yeping Li

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Sense Publishers

About this chapter

Cite this chapter

Huang, R., Leung, F.K.S. (2017). Teaching Geometrical Concepts through Variation. In: Huang, R., Li, Y. (eds) Teaching and Learning Mathematics through Variation. Mathematics Teaching and Learning. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-782-5_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-6300-782-5_9

  • Publisher Name: SensePublishers, Rotterdam

  • Online ISBN: 978-94-6300-782-5

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation