Teachers’ leading whole-class discussions in a mathematics lesson study: From initial understanding to orchestration in practice

Filipa Alexandra Baptista Faria 1 * , João Pedro da Ponte 1 2, Margarida Rodrigues 2 3 4
More Detail
1 Instituto de Educação da Universidade de Lisboa, Lisboa, PORTUGAL
2 UIDEF, Lisboa, PORTUGAL
3 CIEd, Lisboa, PORTUGAL
4 Escola Superior de Educação do Instituto Politécnico de Lisboa, Lisboa, PORTUGAL
* Corresponding Author
EUR J SCI MATH ED, Volume 12, Issue 1, pp. 156-174. https://doi.org/10.30935/scimath/14149
Published: 25 January 2024
OPEN ACCESS   970 Views   707 Downloads
Download Full Text (PDF)

ABSTRACT

This study aims to identify how mathematics teachers understand whole-class discussions and to know the influence of lesson study on the way they orchestrate these discussions. This is a qualitative study, conducted with two groups of middle school teachers. We analyze data concerning three teachers, Patrícia, Marta, and Diana, collected through initial individual interviews and observation of three research lessons. Data are analyzed by discourse analysis, establishing a relationship between the discourse about the teachers’ understanding of whole-class discussions in the initial interview and their subsequent orchestration of this lesson moment. From this relation, we consider the influence of the lesson studies on the teachers’ orchestration practice. The teachers’ discourse in the interviews suggest the existence of a tension between their understanding of the goals of a whole-class discussion and their practice in orchestrating the discussion, causing several challenges. The lesson study contributed to lower these tensions and challenges through the definition of a fluid lesson structure and the appreciation, selection and recording of the students’ activity, enriching the discussion. However, carrying out effective questioning and managing time proved to be complex challenges that deserve attention from further research.
Keywords: whole-class discussion, mathematical communication, lesson study, teacher education

CITATION

Faria, F. A. B., da Ponte, J. P., & Rodrigues, M. (2024). Teachers’ leading whole-class discussions in a mathematics lesson study: From initial understanding to orchestration in practice. European Journal of Science and Mathematics Education, 12(1), 156-174. https://doi.org/10.30935/scimath/14149

REFERENCES

  • AERA. (2011). Code of ethics. Educational Researcher, 40(3), 145-156. https://doi.org/10.3102/0013189X11410403
  • Ball, D. (2001). Teaching, with respect to mathematics and students. In T. Woods, B. Nelson, & J. Warfield (Eds.), Beyond classical pedagogy: Teaching elementary school mathematics. Routledge.
  • Bishop, A. J., & Goffree, F. (1986). Dinâmica e organização da sala de aula [Classroom dynamics and organization]. In B. Christiansen, A. G. Howson, & M. Otte (Eds.), Perspectives on mathematics education (pp. 309-365). Kluwer. https://doi.org/10.1007/978-94-009-4504-3_8
  • Canavarro, A. P. (2011). Ensino exploratório da matemática: Práticas e desafios [Exploratory teaching of mathematics: Practices and challenges]. Educação e Matemática [Education and Mathematics], 115, 11-17.
  • Canavarro, A. P., Mestre, C., Gomes, D., Santos, E., Santos, L., Brunheira, L., Vicente, M., Gouveia, M. J., Correia, P., Marques, P., & Espadeiro, G. (2021). Aprendizagens essenciais de matemática no ensino básico [Essential mathematics learning in basic education]. ME-DGE. https://www.dge.mec.pt/noticias/aprendizagens-essenciais-de-matematica
  • Clivaz, S., & Takahashi, A. (2020). Lesson study, enseignement par la résolution de problèmes et neriage: Réflexions autour de l’observation d’une leçon de mathématiques [Lesson study, teaching through problem solving and learning: Reflections on observing a mathematics lesson]. Revue de Mathématiques pour L’école [Review of Mathematics for School], 233, 6-15. https://doi.org/10.26034/vd.rm.2020.1732
  • DGIDC (2009). Perímetros e áreas. Proposta de conjunto de tarefas para o 5.º ano – 2.º ciclo [Perimeters and areas. Proposed set of tasks for the 5th year – 2nd cycle].
  • Fairclough, N. (1992). Discurso e mudança social [Speech and social change]. Editora Universidade de Brasília.
  • Franke, M. L., Kazemi, E., & Battey, D. (2007). Understanding teaching and classroom practice in mathematics. In F. Lester (Ed.), Second handbook of mathematics teaching and learning (pp. 225-256). Information Age.
  • Fujii, T. (2018). Lesson study and teaching mathematics through problem solving: The two wheels of a cart. In M. Quaresma, C. Winsløw, S. Clivaz, J. P. da Ponte, A. N. Shúilleabháin, & A. Takahashi (Eds.), Mathematics lesson study around the world (pp. 1-21). https://doi.org/10.1007/978-3-319-75696-7_1
  • Gomes, P., Ponte, J. P., & Quaresma, M. (2022). Leading whole-class discussion: From participating in a lesson study to teaching practice. International Journal for Lesson and Learning Studies, 12(2), 139-151. https://doi.org/10.1108/IJLLS-02-2022-0022
  • Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116. https://doi.org/10.2307/30034933
  • Jorgensen, M., & Phillips, L. J. (2002). Discourse analysis as theory and method. SAGE. https://doi.org/10.4135/9781849208871
  • Kooloos, C. C. (2022). Eye on variety: The teacher’s work in developing mathematical whole-class discussions [PhD thesis, Radboud Universiteit Nijmegen].
  • Leuverink, K. R., & Aarts, A. M. L. (2021). Changes in teachers’ professional behavior through conducting teacher research. Journal of Educational Change, 23, 61-84. https://doi.org/10.1007/s10833-020-09409-9
  • Mason, J. (2000) Asking mathematical questions mathematically. International Journal of Mathematical Education in Science and Technology, 31(1), 97111. https://doi.org/10.1080/002073900287426
  • Menezes, L., & Nacarato, A. M. (2020). Comunicação no ensino e na aprendizagem da matemática [Communication in teaching and learning mathematics]. Quadrante, 29(2), 1-5. https://doi.org/10.48489/quadrante.22568
  • NCTM. (2014). Principles to actions: Ensuring mathematical success for all. National Council of Teachers of Mathematics.
  • Ponte, J. P. (2005). Gestão curricular em matemática [Curriculum management in mathematics]. In GTI (Ed.), O professor e o desenvolvimento curricular [The teacher and curriculum development] (pp. 11-34). APM.
  • Ponte, J. P., Silvestre, A. I., Garcia, C., & Costa, S. (2010). O desenvolvimento do conceito de proporcionalidade direta pela exploração de regularidades. Tarefas para o 1.º e o 2.º ciclos do Ensino Básico [The development of the concept of direct proportionality through the exploration of regularities. Tasks for the 1st and 2nd cycles of Basic Education].
  • Quaresma, M., & Ponte, J. P. (2015). Comunicação, tarefas e raciocínio: Aprendizagens profissionais proporcionadas por um estudo de aula [Communication, tasks and reasoning: Professional learning provided by a class study]. ZETETIKÉ: Revista de Educação Matemática [Mathematics Education Magazine], 23(2), 297-310. https://doi.org/10.20396/zet.v23i44.8646540310
  • Sherin, M. G. (2002). A balancing act: Developing a discourse community in the mathematics classroom. Journal of Mathematics Teacher Education, 5, 205-232. https://doi.org/10.1023/A:1020134209073
  • Stein, M. K., & Smith, M. S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3(4), 268-275. https://doi.org/10.5951/MTMS.3.4.0268
  • Stein, M. K., Engle, R. A., Smith, M., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10, 313-340. https://doi.org/10.1080/10986060802229675
  • Swan, M. (2018). Conceber tarefas e aulas que desenvolvam a compreensão concetual, a competência estratégica e a consciência crítica [Design tasks and lessons that develop conceptual understanding, strategic competence and critical awareness]. Educação e Matemática [Education and Mathematics], 144-146, 67-72.
  • Takahashi, A. (2021). Teaching mathematics through problem-solving: A pedagogical approach from Japan. Routledge. https://doi.org/10.4324/9781003015475
  • Wood, T. (1999). Creating a context for argument in mathematics class. Journal for Research in Mathematics Education, 30(2), 171-191. https://doi.org/10.2307/749609