Skip to main content
SpringerLink
Log in

Teaching through Variation

An Asian Perspective – Is the Variation Theory of Learning Varying?

  • Chapter
Teaching and Learning Mathematics through Variation

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

  • 1395 Accesses

Abstract

In 1997, I invited Ference (Prof. Marton) for an academic visit to the Chinese University of Hong Kong, where I was serving. In a lecture, he said he would start with his personal encounter. He then talked about his cultural origin and how he immigrated to the West, and then got in touch later with the Eastern culture. Learning from him, I would also start with my personal encounter with the variation theory of learning as well as bianshi teaching.

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. (1960). The use of advance organizers in the learning and retention of meaningful verbal material. Journal of Educational Psychology, 51(5), 267–272.

    Article  Google Scholar 

  • Barlow, A. T., Prince, K., Lischka, A. E., & Duncan, M. D. (2017). Teaching algebraic reasoning through variation in the US. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Cheng, E. C., & Lo, M. L. (2013). Learning study: Its origins, operationalisation, and Implications (OECD Education Working Papers No. 94). Paris, France: OECD Publishing.

    Google Scholar 

  • Cooper, B., & Dunne, M. (1998). Anyone for tennis? Social class differences in children’s responses to National Curriculum Mathematics Testing. The Sociological Review, 46(1), 115–148.

    Article  Google Scholar 

  • Gao, L., & Watkins, D. A. (2001). Towards a model of teaching conceptions of Chinese secondary school teachers of physics. In D. A. Watkins & J. B. Biggs (Eds.), Teaching the Chinese learner: Psychological and pedagogical perspectives (pp. 27–45). Hong Kong: Comparative Education Research Centre, The University of Hong Kong.

    Google Scholar 

  • Gu, F., Huang, R., & Gu, L. (2017). Theory and development of teaching with variation in mathematics in China. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Gu, L. (1992). The Qingpu experience. Paper presented at the 7th International Congress of Mathematics Education, Quebec, Canada.

    Google Scholar 

  • Gu, L., Huang, R., & Marton, F. (2004). Teaching with variation: A Chinese way of promoting effective mathematics learning. 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 

  • Hino, K. (2017). Improving teaching through variation: A Japanese perspective. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Leung, A. (2017). Variation in tool-based mathematics pedagogy: The case of dynamic virtual tool. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Marton, F., & Booth, S. (1997). Learning and awareness. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • National Council of Supervisors of Mathematics, U.S.A. (1977). Position paper on basic mathematical skills. Washington, DC: National Institute of Education.

    Google Scholar 

  • National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

    Google Scholar 

  • Pang, M. F., Bao, J., & Ki, W. W. (2017). “Bianshi” and the variation theory of learning: Illustrating two frameworks variation and invariance in the teaching of mathematics. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Peled, I., & Leikin, R. (2017). Openness in the eye of the problem solver: Choice in solving problems in Israel. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Runesson, U. (1999). Variationens pedagogik: Skilda sätt att behandla ett matematiskt innehåll [The pedagogy of variation: Different ways of handling a mathematical topic] (In Swedish). Göteborg: Acta Universitatis Gothoburgensis. Retrieved from http://www.ped.gu.se/biorn/phgraph/civil/graphica/diss.su/runesson.html

  • Runesson, U., & Kullberg, A. (2017). Learning to teach with variation: Experiences from learning study in Sweden. In R. Huang & Y. Li. (Eds.), Teaching and learning mathematics through variations (this volume).

    Google Scholar 

  • Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.

    Google Scholar 

  • Watkins, D. A., & Biggs, J. B. (Eds.). (1996). The Chinese learner: Cultural, psychological and contextual influences. Hong Kong: Comparative Education Research Centre.

    Google Scholar 

  • Watkins, D. A., & Biggs, J. B. (Eds.). (2001). Teaching the Chinese learner: Psychological and contextual perspectives. Hong Kong: Comparative Education Research Centre.

    Google Scholar 

  • Wong, N. Y. (2002a). A review of research on conceptions of mathematics (數學觀研究綜述) [in Chinese]. Journal of Mathematics Education, 11(1), 1–8.

    Google Scholar 

  • Wong, N. Y. (2002b). Conceptions of doing and learning mathematics among Chinese. Journal of Intercultural Studies, 23(2), 211–229.

    Article  Google Scholar 

  • Wong, N. Y. (2004). The CHC learner’s phenomenon: Its implications on mathematics education. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese learn mathematics: Perspectives from insiders (pp. 503–534). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Wong, N. Y. (2006). From “entering the way” to “exiting the way”: In search of a bridge to span “basic skills” and “process abilities”. In F. K. S. Leung, G.-D. Graf, & F. J. Lopez-Real (Eds.), Mathematics education in different cultural traditions: The 13th ICMI Study (pp. 111–128). New York, NY: Springer.

    Google Scholar 

  • Wong, N. Y. (2009). Exemplary mathematics lessons: What lessons we can learn from them? ZDM Mathematics Education, 41, 379–384.

    Article  Google Scholar 

  • Wong, N. Y. (2013). The Chinese learner, the Japanese learner, the Asian learner – inspiration for the (mathematics) learner. Scientiae Mathematicae Japonicae, 76(2), 376–384.

    Google Scholar 

  • Wong, N. Y., Marton, F., Wong, K. M., & Lam, C. C. (2002). The lived space of mathematics learning. Journal of Mathematical Behavior, 21, 25–47.

    Article  Google Scholar 

  • Wong, N. Y., Han, J. W., & Wong, Q. T. (2005). Conceptions of mathematics and mathematics education (數學觀與數學教育) [in Chinese]. In N. Y. Wong (Ed.), Revisiting mathematics education in Hong Kong for the new millennium – Festschrift for Prof. M. K. Siu’s retirement (pp. 77–99). Hong Kong: Hong Kong Association for Mathematics Education.

    Google Scholar 

  • Wong, N. Y., Chiu, M. M., Wong, K. M., & Lam, C. C. (2005). The lived space of mathematics learning: An attempt for change. Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education, 9(1), 25–45.

    Google Scholar 

  • Wong, N. Y., Lam, C. C., Chan, A. M. Y., & Wang, Y. (2008). The design of spiral bianshi curriculum: Using three primary mathematics topics as examples (數學變式課程設計——以小學三個課題爲例) [in Chinese]. Education Journal, 35(2), 1–28.

    Google Scholar 

  • Wong, N. Y., Lam, C. C., Sun, X., & Chan, A. M. Y. (2009). From “exploring the middle zone” to “constructing a bridge”: Experimenting the spiral bianshi mathematics curriculum. International Journal of Science and Mathematics Education, 7(2), 363–382.

    Article  Google Scholar 

  • Wong, N. Y., Kong, C. K., Lam, C. C., & Wong, K. M. P. (2010). Changing students’ conceptions of mathematics through the introduction of variation. Korea Society of Mathematical Education Series D: Research in Mathematical Education, 14(4), 361–380.

    Google Scholar 

  • Wong, N. Y., Lam, C. C., & Chan, A. M. Y. (2012). Teaching with variation: Bianshi mathematics teaching. In Y. Li & R. Huang (Eds.), How Chinese teach Mathematics and improve teaching (pp. 105–119). New York, NY: Routledge.

    Google Scholar 

  • Wong, N. Y., Wong, W. Y., & Wong, E. W. Y. (2012). What do Chinese value in (mathematics) education? ZDM Mathematics Education, 44(1), 9–19.

    Article  Google Scholar 

  • Wong, N. Y., Zhang, Q., & Li, X. Q. (2013). (Mathematics) curriculum, teaching and learning. In Y. Li, & G. Lappan (Eds.), Mathematics curriculum in school education (pp. 607–620). Dordrecht, The Netherlands: Springer.

    Google Scholar 

  • Wong, N. Y., Ding, R., & Zhang, Q. P. (2016). From classroom environment to conception of mathematics. In R. B. King & A. B. I. Bernardo (Eds.), The psychology of Asian learners (pp. 541–557). Singapore: Springer.

    Chapter  Google Scholar 

  • Zhang, Q. P., & Wong, N. Y. (2015). Beliefs, knowledge and teaching: A series of studies among Chinese mathematics teachers. In L. Fan, N. Y. Wong, J. Cai, & S. Li (Eds.), How Chinese teach mathematics: Perspectives from insiders (pp. 457–492). Singapore: World Scientific.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Education University of Hong Kong, Hong Kong SAR, China

    Ngai-Ying Wong

Authors
  1. Ngai-Ying Wong
    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

Wong, NY. (2017). Teaching 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_21

Download citation

  • DOI: https://doi.org/10.1007/978-94-6300-782-5_21

  • Publisher Name: SensePublishers, Rotterdam

  • Online ISBN: 978-94-6300-782-5

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation