Implementing mathematics teaching that promotes students’ understanding through theory-driven lesson study
Lesson study (LS) has been practiced in China as an effective way to advance teachers’ professional development for decades. This study explores how LS improves teaching that promotes students’ understanding. A LS group including didacticians (practice-based teaching research specialist and University-based mathematics educators) and mathematics teachers in China explored and documented how teacher participants shifted their attention to students’ learning by incorporating two notions of teaching: learning trajectory (LT) and variation pedagogy (VP). The former describes conjectured routes of children’s thinking and learning with pertinent tasks to move towards the learning goals along the route, while the latter suggests strategies for using systematic tasks progressively. The concepts of LT and VP are used to guide planning, teaching, and debriefing throughout the LS process. Data consist of lesson plans, videotaped lessons, post-lesson discussions, post-lesson quizzes, and teachers’ reflection reports. This study reveals that by building on the learning trajectory and by strategically using variation tasks, the lesson has been improved in terms of students’ understanding, proficiency, and mathematical reasoning. In addition, the LT was refined through the LS. This study displays how theory-driven LS could help teachers improve their teaching and develop the linkage between theory and practice.
KeywordsLesson study Learning trajectory Variation pedagogy Theory-driven lesson study
We thank anonymous reviewers for their invaluable feedback on the revisions of the paper. We appreciate Dr. Dovie Kimmins and Mr. James Willingham from Middle Tennessee State University for their contribution to the improvement of the article. Our thanks go to participating teachers and didacticians for their commitment to the Lesson Study and support of data collection.
- 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.Google Scholar
- Clements, D., Sarama, J., Spitler, M., Lange, A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: a large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42, 127–166.Google Scholar
- Common Core State Standards Initiative (CCSSI) (2010). Common Core State Standards for Mathematics. http://www.corestandards.org/Math/Practice.
- Huang, R., Su, H., & Xu, S. (2014). Developing teachers’ and teaching researchers’ professional competence in mathematics through Chinese Lesson Study. ZDM—The International Journal on Mathematics Education, 46, 239–251.Google Scholar
- Kieran, C., Krainer, K., & Shaughnessy, J. M. (2013). Linking research to practice: teachers as key stakeholders in mathematics education research. In M. A. Clements, A. J. Bishop, C. Keitel, J. Kilpatrick, & F. K. S. Leung (Eds.), Third international handbook of mathematics education (pp. 361–392). New York: Springer.Google Scholar
- Langley, G. J., Moen, R. D., Nolan, K. M., Nolan, T. W., Norman, C. L., & Provost, L. P. (2009). The improvement guide. San Francisco: Jossey-Bass.Google Scholar
- Li, Y. (2008). What do students need to learn about division of fractions? Mathematics Teaching in the Middle School, 13, 546–552.Google Scholar
- Lo, M. L., & Marton, F. (2012). Toward 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.Google Scholar
- Maloney, A. P., Confrey, J., & Nguyen, K. H. (2014). Learning over time: learning trajectories in mathematics. Charlotte: Informational age publishing.Google Scholar
- Marton, F., & Tsui, A. B. M. (with Chik, P. P. M., Ko, P. Y., Lo, M. L., Mok, I. A. C., Ng, F. P., Pang, M.F., et al.) (Eds.). (2004). Classroom discourse and the space of learning. Mahwah: Lawrence Erlbaum.Google Scholar
- Ministry of Education, P. R. China. (2011). Mathematics curriculum standards for compulsory education (grades 1–9). Beijing: Beijing Normal University Press.Google Scholar
- Murata, A. (2011). Introduction: conceptual overview of lesson study. In C. L., Hart, A. S., Alston, & A. Murata (Eds.), Lesson study research and practice in mathematics education: learning together (pp. 1–12). New York: Springer.Google Scholar
- National Council of Teachers of Mathematics. (2014). Principles to action: ensuring mathematical success for all. Reston: NCTM.Google Scholar
- Ott, J. M., Snook, D. L., & Gibson, D. L. (1991). Understanding partitive division of fractions. The Arithmetic Teacher, 39, 7–11.Google Scholar
- Patton, M. Q. (2002). Qualitative research & evaluation methods (3rd ed.). Thousand Oaks: Sage Publications.Google Scholar
- Silvia, E. M. (1983). A look at division with fractions. The Arithmetic Teacher, 30, 38–41.Google Scholar
- Sowder, J., Sowder, L., & Nickerson, S. (2010). Reconceptualizing mathematics for elementary school teachers. New York: W.H. Freeman & Company.Google Scholar
- Yang, Y., & Ricks, T. E. (2013). Chinese lesson study: developing classroom instruction through collaborations in school-based teaching research group activities. In Y. Li & R. Huang (Eds.), How Chinese teach mathematics and improve teaching (pp. 51–65). New York: Routledge.Google Scholar