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What Knowledge Do Teachers Use in Lesson Study? A Focus on Mathematical Knowledge for Teaching and Levels of Teacher Activity

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Theory and Practice of Lesson Study in Mathematics

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

Abstract

This chapter combines the frameworks of Ball, Thames, and Phelps (J Teach Educ 59:389–407, 2008) and Margolinas, Coulange, and Bessot (Educ Stud Math 59:205–234, 2005) to demonstrate the elements of subject and pedagogical content knowledge utilized at varying levels of teacher activity in a cycle of lesson study. Qualitative data generated in a mathematics-based lesson study, conducted with eight primary school teachers in Switzerland, is analyzed and visualizations of the knowledge occurring at each phase of lesson study are provided. This fine-grained analysis of the mathematical knowledge incorporated by teachers in lesson study demonstrates that all forms of Mathematical Knowledge for Teaching, at each level of teacher activity, can occur across a cycle. In addition, the paper provides evidence that phases of lesson study do not necessarily occur in succession but can rather take place in a confluence of teachers’ work across a full cycle.

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Notes

  1. 1.

    Milieu is the usual translation for Brousseau’s French term “milieu.” However, in French it refers not only to the sociological milieu, but it is also used in biology or in reference to Piaget’s work. A more accurate translation would be “environment.”

References

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59, 389–407.

    Article  Google Scholar 

  • Batteau, V. (2017). Using lesson study in mathematics to develop primary school teachers’ practices: A case study. Quadrante, 26, 127–157.

    Google Scholar 

  • Bloch, I. (1999). L’articulation du travail mathématique du professeur et de l’élève dans l’enseignement de l’analyse en première scientifique. Détermination d’un milieu – connaissances et savoirs. Recherches en Didactique des Mathématiques, 19, 135–194.

    Google Scholar 

  • Bloch, I. (2005). Quelques apports de la théorie des situations à la didactique des mathématiques dans l’enseignement secondaire et supérieur: contribution à l’étude et à l’évolution de quelques concepts issus de la théorie des situations didactiques en didactique des mathématiques. HDR, Paris 7.

    Google Scholar 

  • Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer.

    Google Scholar 

  • Clivaz, S. (2014). Des mathématiques pour enseigner? Quelle influence les connaissances mathématiques des enseignants ont-elles sur leur enseignement à l’école primaire? La Pensée Sauvage: Grenoble.

    Google Scholar 

  • Clivaz, S. (2015a). Des mathématiques pour enseigner? Quelques réflexions à partir d’un cas de combinaison de cadres théoriques. In L. Bacon, D. Benoit, C. Lajoie, & I. Oliveira (Eds.), Croisements variés de concepts, d’approches et de théories: les enjeux de la création en recherche en didactique des mathématiques. Colloque du groupe de didactique des mathématiques du Québec 2014. Montréal: UQAM.

    Google Scholar 

  • Clivaz, S. (2015b). French Didactique des Mathématiques and Lesson Study: A profitable dialogue? International Journal for Lesson and Learning Studies, 4, 245–260.

    Article  Google Scholar 

  • Clivaz, S. (2016). Lesson study: From professional development to research in mathematics education. Quadrante, XXV, 97–112.

    Google Scholar 

  • Clivaz, S. (2017). Teaching multidigit multiplication: Combining multiple frameworks to analyse a class episode. Educational Studies in Mathematics, 96(3), 305–325.

    Article  Google Scholar 

  • Davis, B., & Renert, M. (2013). Profound understanding of emergent mathematics: Broadening the construct of teachers’ disciplinary knowledge. Educational Studies in Mathematics, 82, 245–265.

    Article  Google Scholar 

  • Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25.

    Article  Google Scholar 

  • Dorier, J.-L. (2012). La démarche d’investigation en classe de mathématiques: quel renouveau pour le questionnement didactique ? In B. Calmettes (Ed.), Démarches d’investigation. Références, représentations, pratiques et formation. Paris: L’Harmattan.

    Google Scholar 

  • Dudley, P. (2013). Teacher learning in lesson study: What interaction-level discourse analysis revealed about how teachers utilised imagination, tacit knowledge of teaching and fresh evidence of pupils learning, to develop practice knowledge and so enhance their pupils’ learning. Teaching and Teacher Education, 34, 107–121.

    Article  Google Scholar 

  • Fernandez, C., Cannon, J., & Chokshi, S. (2003). A US–Japan lesson study collaboration reveals critical lenses for examining practice. Teaching and Teacher Education, 19, 171–185.

    Article  Google Scholar 

  • Fujii, T. (2014). Implementing Japanese lesson study in foreign countries: Misconceptions revealed. Mathematics Teacher Education and Development, 16, 65–83.

    Google Scholar 

  • Fujii, T. (2018). Lesson study and teaching mathematics trough problem solving: The two wheels of a cart. In M. Quaresma, C. Winsløw, S. Clivaz, J. P. Da Ponte, A. Ni Shuilleabhain, A. Takahashi, & T. Fujii (Eds.), Mathematics lesson study around the world: Theoretical and methodological issues. Cham: Springer.

    Google Scholar 

  • Goldsmith, L. T., Doerr, H. M., & Lewis, C. C. (2014). Mathematics teachers’ learning: A conceptual framework and synthesis of research. Journal of Mathematics Teacher Education, 17, 5–36.

    Article  Google Scholar 

  • Hill, H. C. (2010). The nature and predictors of elementary teachers’ mathematical knowledge for teaching. Journal for Research in Mathematics Education, 41, 513–545.

    Article  Google Scholar 

  • Hodgen, J. (2011). Knowledge and identity: A situated theory of mathematics knowlege in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching. London: Springer.

    Google Scholar 

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

    Article  Google Scholar 

  • Jacobs, V. R., Lamb, L. L. C., & Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41, 169–202.

    Article  Google Scholar 

  • Krauss, S., Baumert, J., & Blum, W. (2008). Secondary mathematics teachers’ pedagogical content knowledge and content knowledge: Validation of the COACTIV constructs. ZDM Mathematics Education, 40, 873–892.

    Article  Google Scholar 

  • Leavy, A., & Hourigan, M. (2016). Using lesson study to support knowledge development in initial teacher education: Insights from early number classrooms. Teaching and Teacher Education, 57, 161–175.

    Article  Google Scholar 

  • Lesson Study Alliance. (2012). LessonNote. Chicago.

    Google Scholar 

  • Lewis, J. M. (2016). Learning to lead, leading to learn: How facilitators learn to lead lesson study. ZDM Mathematics Education, 48, 1–14.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Lewis, C., Perry, R., & Murata, A. (2006). How should research contribute to instructional improvement? The case of lesson study. Educational Researcher, 35, 3–14.

    Article  Google Scholar 

  • Lewis, C., Perry, R., & Hurd, J. (2009). Improving mathematics instruction through lesson study: A theoretical model and North American case. Journal of Mathematics Teacher Education, 12, 285–304.

    Article  Google Scholar 

  • Margolinas, C. (2002). Situations, milieux, connaissances: Analyse de l’activité du professeur. In J.-L. Dorier, M. Artaud, M. Artigue, R. Berthelot, & R. Floris (Eds.), Actes de la 11e école d’été de didactique des mathématiques. Grenoble: La Pensée Sauvage.

    Google Scholar 

  • Margolinas, C. (2004). Modeling the teacher’s situation in the classroom. In H. Fujita, Y. Hashimoto, B. Hodgson, P. Lee, S. Lerman, & T. Sawada (Eds.), Proceedings of the ninth international congress on mathematical education. Dordrecht: Springer Netherlands.

    Google Scholar 

  • Margolinas, C., Coulange, L., & Bessot, A. (2005). What can the teacher learn in the classroom? Educational Studies in Mathematics, 59, 205–234.

    Article  Google Scholar 

  • Miyakawa, T., & Winsløw, C. (2009). Didactical designs for students’ proportional reasoning: An “open approach” lesson and a “fundamental situation”. Educational Studies in Mathematics, 72, 199–218.

    Article  Google Scholar 

  • Murata, A., Bofferding, L., Pothen, B. E., Taylor, M. W., & Wischnia, S. (2012). Making connections among student learning, content, and teaching: Teacher talk paths in elementary mathematics lesson study. Journal for Research in Mathematics Education, 43, 616–650.

    Article  Google Scholar 

  • Ni Shuilleabhain, A. (2015). Developing mathematics teachers’ pedagogical content knowledge through lesson study: A multiple case study at a time of curriculum change. Doctor of Philosophy Ph.D, Trinity College Dublin.

    Google Scholar 

  • Ni Shuilleabhain, A. (2016). Developing mathematics teachers’ pedagogical content knowledge in lesson study: Case study findings. International Journal for Lesson and Learning Studies, 5, 212–226.

    Article  Google Scholar 

  • Ni Shuilleabhain, A., & Clivaz, S. (2017). Analyzing teacher learning in lesson study: Mathematical knowledge for teaching and levels of teacher activity. Quadrante, 26, 99–125.

    Google Scholar 

  • Ni Shuilleabhain, A., & Seery, A. (2017). Enacting curriculum reform through lesson study: A case study of mathematics teacher learning. Professional Development in Education, 44, 1–15.

    Google Scholar 

  • Prediger, S., Bikner-Ahsbahs, A., & Arzarello, F. (2008). Networking strategies and methods for connecting theoretical approaches: First steps towards a conceptual framework. ZDM Mathematics Education, 40, 165–178.

    Article  Google Scholar 

  • Putnam, R. T., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29, 4–15.

    Article  Google Scholar 

  • Roditi, E. (2011). Recherches sur les pratiques enseignantes en mathématiques: apports d’une intégration de diverses approches et perspectives. Paris V: Université René Descartes.

    Google Scholar 

  • Rowland, T., Huckstep, P., & Thwaites, A. (2005). Developing mathematics teaching: The genesis of the knowledge quartet. Gent: Rijksuniversiteit Gent.

    Google Scholar 

  • Rowland, T., Ruthven, K., & Hodgen, J. (2011). Knowing and identity: A situated theory of mathematics knowledge in teaching. In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching. Dordrecht: Springer Netherlands.

    Chapter  Google Scholar 

  • Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its educational applications. New York: Routledge.

    Book  Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15, 4–14.

    Article  Google Scholar 

  • Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Revue, 57, 1–22.

    Article  Google Scholar 

  • Speer, N. M., King, K. D., & Howell, H. (2015). Definitions of mathematical knowledge for teaching: Using these constructs in research on secondary and college mathematics teachers. Journal of Mathematics Teacher Education, 18, 105–122.

    Article  Google Scholar 

  • Steinbring, H. (1998). Elements of epistemological knowledge for mathematics teachers. Journal of Mathematics Teacher Education, 1, 157–189.

    Article  Google Scholar 

  • Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the worlds teachers for improving education in the classroom. New York: The Free Press.

    Google Scholar 

  • Stigler, J. W., & Hiebert, J. (2016). Lesson study, improvement, and the importing of cultural routines. ZDM Mathematics Education, 48, 1–7.

    Article  Google Scholar 

  • Suh, J., & Seshaiyer, P. (2015). Examining teachers’ understanding of the mathematical learning progression through vertical articulation during lesson study. Journal of Mathematics Teacher Education, 18, 207–229.

    Article  Google Scholar 

  • Takahashi, A. (2014). The role of the knowledgeable other in lesson study: Examination of comments of experienced lesson study practitioners. Mathematics Teacher Education and Development, 16, 4–21.

    Google Scholar 

  • Takahashi, A., & Mcdougal, T. (2016). Collaborative lesson research: Maximizing the impact of lesson study. ZDM Mathematics Education, 48, 1–14.

    Article  Google Scholar 

  • Takahashi, A., & Mcdougal, T. (2018). Collaborative lesson research (CLR). In M. Quaresma, C. Winsløw, S. Clivaz, J. P. Da Ponte, A. Ni Shuilleabhain, A. Takahashi, & T. Fujii (Eds.), Mathematics lesson study around the world: Theoretical and methodological issues. Cham: Springer.

    Google Scholar 

  • Tepylo, D. H., & Moss, J. (2011). Examining change in teacher mathematical knowledge through lesson study. In L. C. Hart, A. S. Alston, & A. Murata (Eds.), Lesson study research and practice in mathematics education. Dordrecht: Springer Netherlands.

    Google Scholar 

  • Warfield, V. (2014). Invitation to didactique. New York: Springer.

    Book  Google Scholar 

  • Warwick, P., Vrikki, M., Vermunt, J. D., Mercer, N., & Van Halem, N. (2016). Connecting observations of student and teacher learning: An examination of dialogic processes in lesson study discussions in mathematics. ZDM Mathematics Education, 44, 1–15.

    Google Scholar 

  • Widjaja, W., Vale, C., Groves, S., & Doig, B. (2017). Teachers’ professional growth through engagement with lesson study. Journal of Mathematics Teacher Education, 20, 357–383.

    Article  Google Scholar 

  • Winsløw, C., Bahn, J., & Rasmussen, K. (2018). Theorizing lesson study: Two related frameworks and two Danish case-studies. In M. Quaresma, C. Winsløw, S. Clivaz, J. P. Da Ponte, A. Ni Shuilleabhain, A. Takahashi, & T. Fujii (Eds.), Mathematics lesson study around the world: Theoretical and methodological issues. Cham: Springer.

    Google Scholar 

  • Xu, H., & Pedder, D. (2015). Lesson study: An international review of the research. In P. Dudley (Ed.), Lesson study: Professional learning for our time. London/New York: Routledge.

    Google Scholar 

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Acknowledgments

This research was supported, in part, by a Charlemont Award from the Royal Irish Academy and by the Movetia Swiss National Agency.

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Authors and Affiliations

  1. UER MS and Lausanne Laboratory Lesson Study, Lausanne University of Teacher Education, Lausanne, Switzerland

    Stéphane Clivaz

  2. School of Mathematics & Statistics, University College Dublin, Dublin, Ireland

    Aoibhinn Ni Shuilleabhain

Authors
  1. Stéphane Clivaz
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  2. Aoibhinn Ni Shuilleabhain
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Corresponding author

Correspondence to Stéphane Clivaz .

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

Appendix

Appendix

The indicators are in italics. The codes are in color, corresponding to Figs. 2, 3, 5, and 7

A text document represents C C K, H C K, S C K, K C T, K C S, K C C.
A text document represents the L S phase, which includes studying the curriculum and formulating content-specific goals, 2 plans, doing research lessons, reflect.
A text document represents the level of teacher activity, which includes 3 values and conceptions about learning and teaching, the global didactic project, the local didactic project, and so on.

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Clivaz, S., Ni Shuilleabhain, A. (2019). What Knowledge Do Teachers Use in Lesson Study? A Focus on Mathematical Knowledge for Teaching and Levels of Teacher Activity. 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_20

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  • DOI: https://doi.org/10.1007/978-3-030-04031-4_20

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