Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education

Micaela Martins; João Pedro da Ponte; Joana Mata-Pereira

doi:10.29333/ejmste/13127

Full Text (PDF)

Micaela Martins ¹ ^* , João Pedro da Ponte ¹ , Joana Mata-Pereira ¹

More Detail

¹ Instituto de Educação, Universidade de Lisboa, Lisboa, PORTUGAL^* Corresponding Author

Abstract

The aim of this study is to understand how prospective teachers can develop their knowledge about how to promote students’ mathematical reasoning in a set of sequential lesson studies. The research follows a qualitative approach and addresses the case of a prospective teacher without teaching experience. Data was analyzed according to a set of principles regarding the characteristics of tasks and the teacher’s actions that promote students’ mathematical reasoning. Reflecting on the students’ work in the lessons that the prospective teacher taught led her to understand the influence of the proposed tasks and her actions in promoting students’ reasoning, thus developing her knowledge. Furthermore, the sequential structure of the lesson studies allowed her to prepare the following lessons based on the in-depth analysis of the previous lessons and to put into practice what she planned, leading her to rethink her teaching strategies and improve her practice.

Keywords

mathematical reasoning
initial teacher education
lesson study
mathematics teaching

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 19, Issue 5, May 2023, Article No: em2255

https://doi.org/10.29333/ejmste/13127

Publication date: 01 May 2023

Online publication date: 29 Mar 2023

Article Views: 1372

Article Downloads: 944

Open Access References How to cite this article

References

AERA. (2011). Code of ethics. Educational Researcher, 40(3), 145-156. https://doi.org/10.3102/0013189X11410403
Almog, N., & Ilany, B. (2012). Absolute value inequalities: High school students’ solutions and misconceptions. Educational Studies in Mathematics, 81, 347-364. https://doi.org/10.1007/s10649-012-9404-z
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://doi.org/10.1177/0022487108324554
Bogdan, R. C., & Biklen, S. K. (2007). Quality research for education: An introduction to theory and methods. Pearson.
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer. https://doi.org/10.1007/978-0-387-09742-8
Brousseau, G., & Gibel, P. (2005). Didactical handling of students’ reasoning processes in problem solving situations. Educational Studies in Mathematics, 59, 13-58. https://doi.org/10.1007/s10649-005-2532-y
Buchbinder, O., & McCrone, S. (2020). Preservice teachers learning to teach proof through classroom implementation: Successes and challenges. Journal of Mathematical Behavior, 58, 100779. https://doi.org/10.1016/j.jmathb.2020.100779
Davidson, A., Herbert, S., & Bragg, L. A. (2019). Supporting elementary teachers’ planning and assessing of mathematical reasoning. International Journal of Science and Mathematics Education, 17, 1151-1171. https://doi.org/10.1007/s10763-018-9904-0
DGE. (2018). Aprendizagens essenciais de matemática A–10^o ano [Essential learning in mathematics A–10th grade]. Ministério da Educação e Ciência [Ministry of Education and Science]. http://www.dge.mec.pt/sites/default/files/Curriculo/Aprendizagens_Essenciais/10_matematica_a.pdf
Fujii, T. (2018). Lesson study and teaching mathematics through problem solving: The two wheels of a cart. In M. Quaresma, C. Winslow, S. Clivaz, J. P. Ponte, A. Ni Shuilleabháin, & A. Takahashi (Eds.), Mathematics lesson study around the world (pp. 1-21). Springer. https://doi.org/10.1007/978-3-319-75696-7_1
González, G., Villafañe-Cepeda, W., & Hernández-Rodríguez, O. (2023). Leveraging prospective teachers’ knowledge through their participation in lesson study. Journal of Mathematics Teacher Education, 26, 79-102. https://doi.org/10.1007/s10857-021-09521-4
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96, 1-16. https://doi.org/10.1007/s10649-017-9761-8
Lannin, J., Ellis, A., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in prekindergarten-grade 8. NCTM.
Leavy, A. M., & 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. https://doi.org/10.1016/j.tate.2016.04.002
Martins, M., Mata-Pereira, J., & Ponte, J. P. (2021). Os desafios da abordagem exploratória no ensino da matemática: Aprendizagens de duas futuras professoras através do estudo de aula [The challenges of the exploratory approach in mathematics teaching: Preservice teachers’ learning through lesson study]. Bolema: Boletim de Educação Matemática [Bolema: Mathematics Education Bulletin], 35(69), 343-364. https://doi.org/10.1590/1980-4415v35n69a16
Martins, M., Ponte, J. P., & Mata-Pereira, J. (2023). Preparing, leading, and reflecting on whole-class discussions: How prospective mathematics teachers develop their knowledge during lesson study. European Journal of Science and Mathematics Education, 11(1), 33-48. https://doi.org/10.30935/scimath/12432
Mata-Pereira, J., & Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96, 169-186. https://doi.org/10.1007/s10649-017-9773-4
Mata-Pereira, J., & Ponte, J. P. (2018). Promover o raciocínio matemático dos alunos: Uma investigação baseada em design [Promoting students’ mathematical reasoning: A design-based research]. Bolema: Boletim de Educação Matemática [Bolema: Mathematics Education Bulletin], 32(62), 781-801. https://doi.org/10.1590/1980-4415v32n62a02
Mendes, F., Delgado, C., & Brocardo, J. (2022). Challenges faced by preservice teachers in planning and exploring tasks that promote mathematical reasoning. Acta Scientiae [Journal of Science], 24(4), 147-182. https://doi.org/10.17648/acta.scientiae.7123
NCTM. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
OECD. (2021). PISA 2021 mathematics framework. https://www.oecd.org/pisa/pisaproducts/pisa-2021-mathematics-framework-draft.pdf
Oliveira, H., & Henriques, A. (2021). Preservice mathematics teachers’ knowledge about the potential of tasks to promote students’ mathematical reasoning. International Journal of Research in Education and Science, 7(4), 1300-1319. https://doi.org/10.46328/ijres.2472
Ponte, J. P. (2012). Estudiando el conocimiento y el desarrollo profesional del profesorado de matemáticas [Studying the knowledge and professional development of mathematics teachers]. In N. Planas (Ed.), Teoría, crítica y prática de la educación matemática [Theory, criticism and practice of mathematics education] (pp. 83-98). Graó.
Ponte, J. P. (2017). Lesson studies in initial mathematics teacher education. International Journal for Lesson and Learning Studies, 6(2), 169-181. https://doi.org/10.1108/IJLLS-08-2016-0021
Ponte, J. P., & Chapman, O. (2016). Prospective mathematics teachers’ learning and knowledge for teaching. In L. English, & D. Kisrshner (Eds.), Handbook of international research in mathematics education (pp. 275-296). Routledge. https://doi.org/10.4324/9780203448946
Ponte, J. P., Quaresma, M., & Mata-Pereira, J. (2017a). The challenge of mathematical discussions in teachers’ professional practice. Didacticae [Didactic], 1, 45-59. https://doi.org/10.1344/did.2017.1.45-59
Ponte, J. P., Santos, L., Oliveira, H., & Henriques, A. (2017b). Research on teaching practice in a Portuguese initial secondary mathematics teacher education program. ZDM, 49, 291-303. https://doi.org/10.1007/s11858-017-0847-7
Potari, D., & Ponte, J. P. (2017). Current research on prospective secondary mathematics teachers’ knowledge. In M. E. Strutchens, R. Huang, L. Losano, D. Potari, M. C. C. T. Cyrino, & R. M. Zbiek (Eds.), The mathematics education of prospective secondary teachers around the world (pp. 3-15). Springer. https://doi.org/10.1007/978-3-319-38965-3_2
Ramos-Rodríguez, E., Flores Martínez, P., & Ponte, J. P. (2017). An approach to the notion of reflective teacher and its exemplification on mathematics education. Systemic Practice and Action Research, 30, 85-102.https://doi.org/10.1007/s11213-016-9383-6
Stein, M. K., Engle, R. A., Smith, M. S., & Hughes, E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10(4), 313-340. https://doi.org/10.1080/10986060802229675
Stylianides, G. J., Stylianides, A. J., & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11, 1463-1490. https://doi.org/10.1007/s10763-013-9409-9
Willems, I., & Bossche, P. Van den. (2019). Lesson Study effectiveness for teachers’ professional learning: A best evidence synthesis. International Journal for Lesson and Learning Studies, 8(4), 257-271. https://doi.org/10.1108/IJLLS-04-2019-0031

How to cite this article

APA

Martins, M., da Ponte, J. P., & Mata-Pereira, J. (2023). Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2255. https://doi.org/10.29333/ejmste/13127

Vancouver

Martins M, da Ponte JP, Mata-Pereira J. Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education. EURASIA J Math Sci Tech Ed. 2023;19(5):em2255. https://doi.org/10.29333/ejmste/13127

AMA

Martins M, da Ponte JP, Mata-Pereira J. Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education. EURASIA J Math Sci Tech Ed. 2023;19(5), em2255. https://doi.org/10.29333/ejmste/13127

Chicago

Martins, Micaela, João Pedro da Ponte, and Joana Mata-Pereira. "Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education". Eurasia Journal of Mathematics, Science and Technology Education 2023 19 no. 5 (2023): em2255. https://doi.org/10.29333/ejmste/13127

Harvard

Martins, M., da Ponte, J. P., and Mata-Pereira, J. (2023). Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education. Eurasia Journal of Mathematics, Science and Technology Education, 19(5), em2255. https://doi.org/10.29333/ejmste/13127

MLA

Martins, Micaela et al. "Learning to promote students’ mathematical reasoning: Lesson study contributions in initial teacher education". Eurasia Journal of Mathematics, Science and Technology Education, vol. 19, no. 5, 2023, em2255. https://doi.org/10.29333/ejmste/13127