Skip to main content
SpringerLink
Log in

Developing Teachers’ Expertise in Mathematics Instruction as Deliberate Practice through Chinese Lesson Study

  • Chapter
  • First Online:
Theory and Practice of Lesson Study in Mathematics

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

This study explored how two lesson study groups developed the teachers’ expertise in mathematics instruction in China from the perspective of deliberate practice. The two lesson study groups, respectively, rehearsed and taught six research lessons on the same topic of division with fractions. They collaborated with knowledgeable others to develop research lessons based on a hypothetical learning trajectory. Guided by the learning trajectory, through exploring the deliberate practice of perfecting teaching of division of fraction, teachers developed their expertise with enacting two core practices of teaching mathematics, including revision of mathematical tasks and revision of mathematical representations.

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 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Ashlock, R. D. (1990). Error patterns in computation. New York: Macmillan.

    Google Scholar 

  • Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21, 132–144.

    Article  Google Scholar 

  • Ball, D. L. (2016). Uncovering the special mathematical work of teaching. In Plenary lecture at the 13th International Congress on Mathematical Education (ICME). Germany: Hamburg. Retrieved from https://deborahloewenbergball.com/presentations-intro/#presentations.

    Google Scholar 

  • Barash, A., & Klein, R. (1996). Seventh grades students’ algorithmic, intuitive and formal knowledge of multiplication and division of non negative rational numbers. In L. Puig & A. Gutierrez (Eds.), Proceedings of the 20th conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 35–42). Valencia: University of Valencia.

    Google Scholar 

  • Borko, H. (2004). Professional development and teacher learning: Mapping the terrain. Educational Researcher, 33(8), 3–15.

    Article  Google Scholar 

  • Borko, H., Eisenhart, M., Brown, C. A., Underhill, R., Jones, D., & Agard, P. (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.

    Article  Google Scholar 

  • Bronkhorst, L. H., Meijer, P. C., Koster, B., & Vermunt, J. D. (2011). Fostering meaning-oriented learning and deliberate practice in teacher education. Teaching and Teacher Education, 27, 1120–1130.

    Article  Google Scholar 

  • Bronkhorst, L. H., Meijer, P. C., Koster, B., & Vermunt, J. D. (2014). Deliberate practice in teacher education. European Journal of Teacher Education, 37(1), 18–34.

    Article  Google Scholar 

  • Carpenter, T. C., Lindquist, M. M., Brown, C. A., Kouba, V. L., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher, 36(4), 38–41.

    Article  Google Scholar 

  • Chen, X. (2017). Theorizing Chinese lesson study from a cultural perspective. International Journal for Lesson and Learning Studies, 6(4), 283–292.

    Article  Google Scholar 

  • Clements, D., & Sarama, J. (2004). Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81–89.

    Article  Google Scholar 

  • Clements, D., & Sarama, J. (2013). Rethinking early mathematics: What is research-based curriculum for young children? In L. English & J. Mulligan (Eds.), Reconceptualizing early mathematics learning: Advances in mathematics education. Dordrecht: Springer.

    Google Scholar 

  • Cochran-Smith, M., & Lytle, S. (1999). Relationships of knowledge and practice: Teacher learning community. Review of Research in Education, 24, 249–305.

    Google Scholar 

  • Cramer, K., Wyberg, T., & Leavitt, S. (2008). The role of representations in fraction addition and subtraction. Mathematics Teaching in the Middle School, 13(8), 490–496.

    Article  Google Scholar 

  • Cravens, X., & Wang, J. (2017). Learning from the masters: Shanghai’s teacher-expertise infusion system. International Journal for Lesson and Learning Studies, 6(4), 306–320.

    Article  Google Scholar 

  • Darling-Hammond, L., Wei, R. C., Andree, A., Richardson, N., & Orphanos, S. (2009). Professional learning in the learning profession: A status report on teacher development in the United States and abroad. Oxford: National Staff Development Council.

    Google Scholar 

  • Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in mathematics (Research Report No. 68). Madison: Consortium for Policy Research in Education.

    Google Scholar 

  • Deans for Impact. (2016), Practice with purpose: The Emerging science of teacher expertise, September, 5, 2017, Retrieved from https://deansforimpact.org/resources/practice-with-purpose/.

  • Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38, 181–200.

    Article  Google Scholar 

  • Desimone, L. M., & Garet, M. S. (2015). Best practices in teachers’ professional development in the United States. Psychology, Society, and Education, 7(3), 252–263.

    Article  Google Scholar 

  • Ericsson, K. A. (2003). Deliberate practice and the acquisition and maintenance of expert performance in medicine and related domains. Academic Medicine, 79(10), 70–81.

    Google Scholar 

  • Ericsson, K. A. (2005). Recent advances in expertise research: A commentary on the contributions to the special issue. Applied Cognitive Psychology, 19(2), 233–241.

    Article  Google Scholar 

  • Ericsson, K. A., & Pool, R. (2016). Peak. Boston: Houghton Mifflin Harcourt.

    Google Scholar 

  • Ericsson, K. A., Ralf, K., & Clemens, T. (1993). The role of deliberate practice in the acquisition of expert performance. Psychological Review, 100(3), 363–406.

    Article  Google Scholar 

  • Fang, Y. (2017). School-based teaching research and Lesson-case study in mediating the second-cycle curriculum reform in Shanghai. International Journal for Lesson and Learning Studies, 6(4), 293–305.

    Article  Google Scholar 

  • Fendel, D. M. (1987). Understanding the structure of elementary school mathematics. Newton: Allyn and Bacon.

    Google Scholar 

  • Franke, M., Kazemi, E., Shih, J., Biagetti, S., & Battey, D. (2005). Changing teachers’ professional work in mathematics: One school’s journey. In T. A. Romberg, T. P. Carpenter, & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 209–229). Mahwah: Erlbaum.

    Google Scholar 

  • Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945.

    Article  Google Scholar 

  • Grossman, P. L., Wineburg, S. S., & Woolworth, S. (2001). Toward a theory of teacher community. Teachers College Record, 103(6), 942–1012.

    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 through variations (pp. 13–42). Rotterdam: Sense.

    Chapter  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. 309–348). Singapore: World Scientific.

    Chapter  Google Scholar 

  • Han, X., & Paine, L. (2010). Teaching mathematics as deliberate practice through public lessons. The Elementary School Journal, 110(4), 519–541.

    Article  Google Scholar 

  • Han, X., Gong, Z., & Huang, R. (2017). Teaching mathematical concepts through variation and learning progression: A case study of division of fractions. In R. Huang & Y. Li (Eds.), Teaching and learning through variations (pp. 267–293). Rotterdam: Sense.

    Chapter  Google Scholar 

  • Hart, L. C., Alston, A. S., & Murata, A. (2011). Lesson study research and practice in mathematics education: Learning together. New York: Springer.

    Book  Google Scholar 

  • Hu, G. (2005). Professional development of secondary EFL teachers: Lesson from China. Teachers College Record, 107(4), 654–705.

    Article  Google Scholar 

  • Huang, R., & Bao, J. (2006). Towards a model for teacher’s professional development in China: Introducing keli. Journal of Mathematics Teacher Education, 9, 279–298.

    Article  Google Scholar 

  • Huang, R., & Han, X. (2015). Developing mathematics teachers’ competence through parallel lesson study. International Journal for Lesson and Learning Studies, 4(2), 100–117.

    Article  Google Scholar 

  • Huang, R., & Shimizu, Y. (2016). Improving teaching, developing teachers and teacher developers, and linking theory and practice through lesson study in mathematics: An international perspective. ZDM Mathematics Education, 48, 393–409.

    Article  Google Scholar 

  • Huang, R., Gong, Z., & Han, X. (2016a). Implementing mathematics teaching that promotes students’ understanding through theory-driven lesson study. ZDM Mathematics Education, 48, 425–439.

    Article  Google Scholar 

  • Huang, R., Ye, L., & Prince, K. (2016b). Professional development system and practices of mathematics teachers in Mainland China. In B. Kaur & K. O. Nam (Eds.), Professional Development of Mathematics Teachers: An Asian Perspective (pp. 17–32). New York: Springer.

    Google Scholar 

  • Huang, R., Fang, Y., & Chen, X. (2017a). Chinese lesson study: An improvement science, a deliberate practice, and a research methodology. International Journal for Lesson and Learning Studies, 6(4), 270–282.

    Article  Google Scholar 

  • Huang, R., Haupt, M., & Barlow, A. (2017b). Developing high-leverage practices as deliberate practice through lesson study. International Journal for Lesson and Learning Studies, 6(4), 365–379.

    Article  Google Scholar 

  • Lampert, M., & Graziani, F. (2009). Instructional activities as a tool for teachers’ and teacher educators’ learning in and for practice. Elementary School Journal, 109(5), 491–509.

    Article  Google Scholar 

  • Lampert, M., Franke, M., Kazemi, E., Ghousseini, H., Turrou, A., Beasley, H., Cunard, A., & Crowe, K. (2013). Keeping it complex: Using rehearsals to support novice teacher learning of ambitious teaching. Journal of Teacher Education, 64(3), 226–243.

    Article  Google Scholar 

  • Lewis, C., & Hurd, J. (2011). Lesson study step by step: How teacher learning communities improve instruction. Portsmouth: Heinemann.

    Google Scholar 

  • Lewis, C., & Perry, R. (2017). Lesson study to scale up research-based knowledge: A randomized, controlled trial fractions learning. Journal for Research in Mathematics Education, 48(3), 261–299.

    Article  Google Scholar 

  • Lewis, C., Perry, R., Friedkin, S., & Roth, J. (2012). Improving teaching does improve teachers: Evidence from lesson study. Journal of Teacher Education, 63, 368–375.

    Article  Google Scholar 

  • Little, J. W. (2002). Locating learning in teachers’ communities of practice: Opening up problems of analysis in records of everyday work. Teaching and Teacher Education, 18(8), 917–946.

    Article  Google Scholar 

  • Lo, M. L., & Marton, F. (2012). Towards a science of the art of teaching: Using variation theory as a guiding principle of pedagogical design. International Journal for Lesson and Learning Studies, 1, 7–22.

    Article  Google Scholar 

  • Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Lawrence Erlbaum.

    Book  Google Scholar 

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

    Article  Google Scholar 

  • McLaughlin, M. W., & Talbert, J. E. (2001). Professional communities and the work of high school teaching. Chicago: University of Chicago Press.

    Google Scholar 

  • Ott, J. M., Snook, D. L., & Gibson, D. L. (1991). Understanding partitive division of fractions. In The Arithmetic Teacher (Vol. 39, pp. 7–11).

    Google Scholar 

  • Payne, J. N. (1976). Review of research on fractions. In R. Lesh (Ed.), Number and measurement (pp. 145–188). Athens: University of Georgia.

    Google Scholar 

  • Perry, R. R., & Lewis, C. C. (2011). Improving the mathematical content base of lesson study summary of results. Oakland: Mills College Lesson Study Group. Retrieved from http://www.lessonresearch.net/IESAbstract10.pdf.

  • Petit, M., Laird, R. E., & Marsden, E. L. (2010). A focus on fractions: Bringing research to the classroom. New York: Taylor & Francis.

    Book  Google Scholar 

  • Porter, A. C., Garet, M. S., Desimone, L. M., & Birman, B. F. (2003). Providing effective professional development: Lessons from the Eisenhower program. Science Educator, 12(1), 23–40.

    Google Scholar 

  • Selling, S. K., Garcia, N., & Ball, D. L. (2016). What does it take to develop assessments of mathematical knowledge for teaching?: Unpacking the mathematical work of teaching. The Mathematics Enthusiast, 13, 35–51.

    Article  Google Scholar 

  • Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing effective fractions instruction for kindergarten through 8th grade: A practice guide (NCEE#2010–4039). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://ies.ed.gov/ncee/wwc/pdf/practice_guides/fractions_pg_093010.pdf.

    Google Scholar 

  • Simon, M. A. (1995). Prospective elementary teachers’ knowledge of division. Journal for Research in Mathematics Education, 24, 233–254.

    Article  Google Scholar 

  • Son, J. W., & Crespo, S. (2009). Prospective teachers’ reasoning and response to a student’s nontraditional strategy when dividing fractions. Journal of Mathematics Teacher Education, 12, 235–261.

    Article  Google Scholar 

  • Sowder, J., Sowder, L., & Nickerson, S. (2010). Reconceptualizing mathematics for elementary school teachers. New York: W. H. Freeman & Company.

    Google Scholar 

  • Tirosh, D., Fishbein, E., Graeber, A., & Wilson, J.W. (1998). Prospective Elementary Teachers’ Conceptions of Rational Numbers. Retrieved from http://jwilson.coe.uga.edu/texts.folder/tirosh/pros.el.tchrs.html

    Google Scholar 

  • Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31, 5–25.

    Article  Google Scholar 

  • Van den Heuvel-Panhuizen, M. (2000). Mathematics education in the Netherlands: A guided tour. Freudenthal Institute Cd-rom for ICME9. Utrecht: Utrecht University.

    Google Scholar 

  • van Gog, T., Ericsson, K. A., Rikers, R. M. J. P., & Paas, F. (2005). Instructional design for advanced learners: Establishing connections between the theoretical frameworks of cognitive load and deliberate practice. Educational Technology Research and Development, 53(3), 73–81.

    Article  Google Scholar 

  • Wang, J. (2013). Mathematics education in China: Tradition and reality. Singapore: Galeasia Cengage Learning.

    Google Scholar 

  • Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense making. Mathematical Thinking and Learning, 8(2), 91–111.

    Article  Google Scholar 

  • Wilson, S. M., & Berne, J. (1999). Teacher learning and the acquisition of professional knowledge: An examination of research on contemporary professional development. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of research in education (Vol. 24, pp. 173–209). Washington, DC: AERA.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Louis University, Chicago, IL, USA

    Xue Han

  2. Middle Tennessee State University, Murfreesboro, TN, USA

    Rongjin Huang

Authors
  1. Xue Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rongjin Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xue Han .

Editor information

Editors and Affiliations

  1. Middle Tennessee State University, Murfreesboro, TN, USA

    Rongjin Huang

  2. College of Education, DePaul University, Chicago, IL, USA

    Akihiko Takahashi

  3. College of Education, University of Lisbon, Lisbon, Portugal

    João Pedro da Ponte

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Han, X., Huang, R. (2019). Developing Teachers’ Expertise in Mathematics Instruction as Deliberate Practice through Chinese Lesson Study. In: Huang, R., Takahashi, A., da Ponte, J.P. (eds) Theory and Practice of Lesson Study in Mathematics. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-04031-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04031-4_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04030-7

  • Online ISBN: 978-3-030-04031-4

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation