Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course

Leonor Santos; Joana Mata-Pereira; João Pedro da Ponte; Hélia Oliveira

doi:10.29333/ejmste/11488

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Leonor Santos ¹ ^* , Joana Mata-Pereira ¹ , João Pedro da Ponte ¹ , Hélia Oliveira ¹

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

Abstract

A teaching practice consistent with the development of students’ mathematical reasoning requires teachers to hold a profound understanding of mathematical reasoning. The aim of this research is to study the development of middle and secondary mathematics teachers’ understanding about the processes of generalizing and justifying in a professional development course. Data collection included observation of the course sessions, with video recordings, and document collection of teachers’ and their students’ productions. A qualitative in-depth analysis was carried out focusing on the ways and complexity of generalizing identified by the teachers. The results indicate that teachers progressively focus their attention on these reasoning processes, identifying and characterizing them. The way the course was designed and enacted appears to have contributed to enable the teachers to deepen their understanding of two central mathematical reasoning processes, generalizing and justifying, in addition to their ability to foster and identify such processes in the work with their students.

Keywords

generalizing
justifying
mathematical reasoning
teacher education
teachers’ understanding of reasoning processes

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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, 2022, Volume 18, Issue 1, Article No: em2067

https://doi.org/10.29333/ejmste/11488

Publication date: 03 Jan 2022

Article Views: 1709

Article Downloads: 931

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Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Bardin, L. (2003). L’Analyse de contenu [Content analysis] (10th ed.). Presses Universitaires de France.
Borko, H., Jacobs, J., & Koellner, K. (2010). Contemporary approaches to teacher professional development. International Encyclopedia of Education, 7, 548-556. https://doi.org/10.1016/B978-0-08-044894-7.00654-0
Brodie, K. (2010). Teaching mathematical reasoning in secondary school classrooms. Springer US. https://doi.org/10.1007/978-0-387-09742-8
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
Davis, P., & Hersh, R. (1986). A experiência matemática [The math experience] (3rd ed.). Francisco Alves.
El Mouhayar, R. (2020). Investigating quality of class talk in grade 7: The case of pattern generalization. International Journal of Science and Mathematics Education, 19, 1015-1036. https://doi.org/10.1007/s10763-020-10092-8
Ellis, A. (2007). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38, 194-229. https://doi.org/10.2307/30034866
Ellis, A., Ozgur, Z., & Reiten, L. (2019). Teacher moves for supporting student reasoning. Journal of Mathematics Education Research, 31, 107-132. https://doi.org/10.1007/s13394-018-0246-6
Herbert, S. & Bragg, L. A. (2020). Factors in a professional learning program to support a teacher’s growth in mathematical reasoning and its pedagogy. Mathematics Education Research Journal, 33, 409-433. https://doi.org/10.1007/s13394-020-00310-5
Hoyles, C., & Küchemann, D. (2002). Student´s understanding of logical implication. Educational Studies in Mathematics, 51(3), 193-223. https://doi.org/10.1023/A:1023629608614
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
Keazer, L. (2014). Teachers’ learning journeys toward reasoning and sense making. In J. Lo, K. Leatham, & L. Zoest (Eds.), Research trends in mathematics teacher education (pp. 155-180). Springer International. https://doi.org/10.1007/978-3-319-02562-9_9
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Research Council.
Lannin, J., Ellis, A., & Elliot, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in Prekindergarden – grade 8. NCTM.
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67, 255-276. https://doi.org/10.1007/s10649-007-9104-2
Mata-Pereira, J., & Ponte, J. P. (2012). Raciocínio matemático em conjuntos numéricos: Uma investigação no 3.º ciclo [Mathematical reasoning in numerical sets: An investigation in the 3rd cycle]. Quadrante, 21(2), 81-110. https://doi.org/10.48489/quadrante.22879
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(2), 169-186. https://doi.org/10.1007/s10649-017-9773-4
Mata-Pereira, J., & Ponte, J. P. (2018). Teacher’s actions to promote students’ justification. Acta Scientiae, 20(3), 487-505. https://doi.org/10.17648/acta.scientiae.v20iss3id3910
National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics.
OECD. (2018). PISA 2021 mathematics framework (Draft). https://pisa2021-maths.oecd.org/files/PISA%202021%20Mathematics%20Framework%20Draft.pdf
Pólya, G. (1945). How to solve it: A new aspect of the mathematical method. Princeton University Press. https://doi.org/10.1515/9781400828678
Pólya, G. (1990). Mathematics and plausible reasoning. Princeton University Press.
Schwandt, T. (1994). Constructivist, interpretivist approaches to human inquiry. In N. Denzin, & Y. Lincoln (Eds.), Handbook of qualitative research (pp. 118-137). SAGE.
Silva, A. P. (2009). A problemática da descoberta e da prova [The problematic of discovery and proof]. Educação & Matemática, 101, 37-41.
Smith, M. (2001). Practice-based professional development for teachers of mathematics. NCTM.
Sowder, L., & Harel, G. (1998). Types of students’ justifications. The Mathematics Teacher, 91(8), 670–675. https://doi.org/10.1007/s10649-005-2532-y
Stylianides, G. J. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9-16. https://doi.org/10.1007/s10763-013-9409-9
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(6), 1463-1515.
Watson, F. R. (1980). The role of proof and conjecture in mathematics and mathematics teaching. International Journal of Mathematics Education and Technology, 11(2), 163-167. https://doi.org/10.1080/0020739800110202
Weiss, I., & Pasley, J. (2006). Scaling up instructional improvement through teacher professional development: Insights from the local systemic change initiative. CPRE Policy Briefs, 44, 1–16. https://doi.org/10.12698/cpre.2006.rb44
Widjaja, W., Vale, C., Herbert, S., Loong, E., & Bragg, L. A. (2020). Linking comparing and contrasting, generalising and justifying: a case study of primary students’ levels of justifying. Mathematics Education Research Journal, 33(1), 1-23. https://doi.org/10.1007/s13394-019-00306-w

How to cite this article

APA

Santos, L., Mata-Pereira, J., da Ponte, J. P., & Oliveira, H. (2022). Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2067. https://doi.org/10.29333/ejmste/11488

Vancouver

Santos L, Mata-Pereira J, da Ponte JP, Oliveira H. Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course. EURASIA J Math Sci Tech Ed. 2022;18(1):em2067. https://doi.org/10.29333/ejmste/11488

AMA

Santos L, Mata-Pereira J, da Ponte JP, Oliveira H. Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course. EURASIA J Math Sci Tech Ed. 2022;18(1), em2067. https://doi.org/10.29333/ejmste/11488

Chicago

Santos, Leonor, Joana Mata-Pereira, João Pedro da Ponte, and Hélia Oliveira. "Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 1 (2022): em2067. https://doi.org/10.29333/ejmste/11488

Harvard

Santos, L., Mata-Pereira, J., da Ponte, J. P., and Oliveira, H. (2022). Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2067. https://doi.org/10.29333/ejmste/11488

MLA

Santos, Leonor et al. "Teachers’ Understanding of Generalizing and Justifying in a Professional Development Course". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 1, 2022, em2067. https://doi.org/10.29333/ejmste/11488