Learning professional opportunities experienced by a teacher within a in-service teacher training procces regarding mathematical reasoning
DOI:
https://doi.org/10.5007/1981-1322.2026.e99328Keywords:
Teacher learning opportunities, Mathematical reasoning, Teacher professional knowledgeAbstract
Teacher training, both initial and continuing, presents a long history of difficulties aggravated, among other factors, by the lack of connection between teacher training and practice and a lack of understanding of how teachers learn. Studies indicate that efficient training processes consider the teacher's practical reality and must include what is understood as professional learning opportunities. Thus, in the field of training teachers who teach mathematics, this work presents an excerpt from a Master's thesis that focuses on analyzing the opportunities for professional teaching learning promoted throughout a training process anchored in practice that addresses mathematical reasoning. In this section, the objective is to understand the professional learning opportunities regarding the mathematical reasoning processes experienced by a teacher when having her class planned, developed, and reflected collectively in a training process. To achieve what was proposed, the research, of an interpretive qualitative nature, included semi-structured interviews and a script of answers, answered by the teacher in question. The result is an analysis of the different professional learning opportunities expressed by the teacher in relation to content and student knowledge and content and teaching knowledge that are related to mathematical reasoning at three distinct moments in the cycle of planning, developing and reflect
References
Araman, E. M. DE O. & Serrazina, M. DE L. (2020). Processos de raciocínio matemático na resolução de tarefas exploratórias no 3 o ano de escolaridade. Revista Paranaense de Educação Matemática. Recuperado de https://periodicos.unespar.edu.br/index.php/rpem/article/view/6189
Ball, D. L. & Even, R. (2009). The professional education and development of teachers of mathematics. Nova Iorque: Springer.
Ball, D. L. & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In: Darling-Hammond, L. & Sykes, G. (Eds.), Teaching as the Learning Profession: Handbook of Policy and Practice. San Francisco: Jossey-Bass.
Ball, D. L., Thames, M. H. & Phelps, G. (2008). Content Knowledge for Teaching. Journal of Teacher Education. Recuperado de http://journals.sagepub.com/doi/10.1177/0022487108324554
Bransford, John. D., Brown, Ann. L. & Cocking, Rodney. R. (2000). How People Learn: Brain, Mind, Experience, and School. In: Early Childhood Development and Learning: New Knowledge for Policy. Washington, D.C. National Academies Press, p. 57–86.
Brasil. Ministério da Educação. Base Nacional Comum Curricular: educação é a base. Brasília: MEC, (2018). Recuperado em http://basenacionalcomum.mec.gov.br/images/BNCC_EI_EF_110518_versaofinal_site.pdf
Carneiro, L. F. G. (2021). Processos de raciocínio matemático mobilizados por alunos do ensino fundamental. (Dissertação de Mestrado Profissional em Matemática em Rede Nacional - PROFMAT). Universidade Tecnológica Federal do Paraná, Londrina.
Darling-Hammond, L. et al. (2017). Effective teacher professional development. Palo Alto: Learning Policy Institute.
Depaepe, F., Verschaffel, L. & Kelchtermans, G. (2013). Pedagogical contente knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education. Recuperado de https://linkinghub.elsevier.com/retrieve/pii/S0742051X1300053X
Fiorentini, D. et al. (2016). O professor que ensina matemática como campo de estudo: concepção do projeto de pesquisa. In: Fiorentini, D., Brancaglion, C. L. P. & Lima, R. C. R. (Eds.), Mapeamento da pesquisa acadêmica brasileira sobre o professor que ensina matemática: período 2001 - 2012. Campinas: FE/UNICAMP.
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. Recuperado de http://link.springer.com/10.1007/s10857-013-9245-4
Jaworski, B. & Huang, R. (2014). Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching. ZDM. Recuperado de http://link.springer.com/10.1007/s11858-014-0574-2
Jeannotte, D. & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics. Recuperado de http://link.springer.com/10.1007/s10649-017-9761-8
Lampert, M. & Ball, D. L. (1998). Teaching, multimedia and mathematics. Nova Iorque: Teacher College Press.
Lampert, M. (2010). Learning Teaching in, from, and for Practice: What Do We Mean? Journal of Teacher Education. Recuperado de http://journals.sagepub.com/doi/10.1177/0022487109347321
Lannin, J. K., Ellis, A. B. & Elliot, R. (2011). Developing Essential Understanding of Mathematical Reasoning for Teaching Mathematics in Prekindergarten-grade 8. [s.l.] National Council of Teachers of Mathematics.
Mayor, C. (2007). El asesoramiento pedagógico para la formación docente del profesorado universitario. Sevilla: Editorial Universidad de Sevilla - Secretariado de Publicaciones.
Marcelo, C. (2009). La evaluacion del desarrollo profesional docente: de la cantidad a la calidad. Revista Brasileira de Formação de Professores, v. 1(1), 43–70.
Mata-Pereira, J. (2012). O raciocínio matemático em alunos do 9.º ano no estudo dos números reais e inequações. Dissertação (Mestrado em Educação) – Universidade de Lisboa, Lisboa.
Mata-Pereira, J. & Ponte, J. P. (2012). Raciocínio matemático em conjuntos numéricos: Uma investigação no 3. o ciclo. Quadrante. Recuperado de https://quadrante.apm.pt/article/view/22879
Mata-Pereira, J. & Ponte, J. P. (2018). Promover o Raciocínio Matemático dos Alunos: uma investigação baseada em design. Bolema: Boletim de Educação Matemática. Recuperado de: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-636X2018000300781&lng=pt&tlng=pt
National Council of Teachers of Mathematics. (2009). Focus on high school mathematics: Reasoning and sense making. Reston: NCTM.
Organisation for Economic Co-operation and Development. (2007). Evidence in Education. Paris: OECD Publishing.
Opfer, V. D. & Pedder, D. (2011). Conceptualizing Teacher Professional Learning. Review of Educational Research. Recuperado de http://journals.sagepub.com/doi/10.3102/0034654311413609
Pedemonte, B. (2007). How can the relationship between argumentation and proof be analysed? Educational Studies in Mathematics. Recuperado de http://link.springer.com/10.1007/s10649-006-9057-x
Ponte, J. P. (1999). Teachers’ beliefs and conceptions as a fundamental topic in teacher education. In: Krainer, K. & Goffree, F. (Eds.), On research in teacher education. From study of teaching practices to issues in teacher education. Osnabrück: First Conference of the European Society for Research in Mathematics Education (CERME 1).
Ponte, J. P. (2012). Estudiando el conocimiento y el desarrollo profesional del profesorado de matemáticas. In: Planas, N. (Eds.), Teoría, crítica y prática de la educación matemática. Barcelona: Graó.
Ponte, J. P. & Quaresma, M. (2016). Teachers’ professional practice conducting mathematical discussions. Educational Studies in Mathematics. Recuperado de http://link.springer.com/10.1007/s10649-016-9681-z
Ponte, J. P. & Serrazina, L. (2004). Práticas profissionais dos professores de Matemática. Quadrante. Recuperado de https://revistas.rcaap.pt/index.php/quadrante/article/view/22780
Putnam, R. T. & Borko, H. (2000). What Do New Views of Knowledge and Thinking Have to Say About Research on Teacher Learning? Educational Researcher. Recuperado de http://journals.sagepub.com/doi/10.3102/0013189X029001004
Ribeiro, A. J. & Ponte, J. P. (2019). Professional learning opportunities in a practice-based teacher education programme about the concept of function. Acta Scientiae. Recuperado de http://www.periodicos.ulbra.br/index.php/acta/article/view/5002
Ribeiro, A. J. & Ponte, J. P. (2020). Modelo teórico para organizar e compreender as oportunidades de aprendizagem de professores para ensinar matemática. Zetetike. Recuperado de https://periodicos.sbu.unicamp.br/ojs/index.php/zetetike/article/view/8659072
Ribeiro, A. J., Aguiar, M. & Trevisan A. L. (2020). Oportunidades de aprendizagem vivenciadas por professores ao discutir coletivamente uma aula sobre padrões e regularidades. Quadrante. Recuperado de https://quadrante.apm.pt/article/view/23010
Serrazina, L. (2021). Aprender Matemática com compreensão: raciocínio matemático e ensino exploratório. Em Teia: Revista de Educação Matemática e Tecnológica Iberoamericana. Recuperado de https://periodicos.ufpe.br/revistas/emteia/article/view/250302
Serrazina, L., Rodrigues, M. & Araman, E. (2020). Envolver os alunos em processos de raciocínio matemático: As ações do professor. Revista Psicologia em Pesquisa. Recuperado de https://periodicos.ufjf.br/index.php/psicologiaempesquisa/article/view/27570
Silver, E. A., Clark, L. M., Ghousseini, H. & Charalambous, C. Y. (2007) Where is the mathematics? Examining teachers’ mathematical learning opportunities in practice-based professional learning tasks. Journal of Mathematics Teacher Education. Recuperado de http://link.springer.com/10.1007/s10857-007-9039-7
Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher. Recuperado de http://journals.sagepub.com/doi/10.3102/0013189X015002004
Stylianides, G. J. (2009). Reasoning-and-Proving in School Mathematics Textbooks. Mathematical Thinking and Learning. Recuperado de http://www.tandfonline.com/doi/abs/10.1080/10986060903253954
Trevisan, A. L., Ribeiro, A. J. & Ponte, J. P. (2019). Professional Learning Opportunities Regarding the Concept of Function in a Practice-based Teacher Education Program. International Electronic Journal of Mathematics Education. Recuperado de http://www.iejme.com/article/professional-learning-opportunities-regarding-the-concept-of-function-in-a-practice-based-teacher-6256
Smith, M. K. (2001). The learning organization. Recuperado de http://www.infed.org/biblio/learning-organization.htm
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. Recuperado de http://www.tandfonline.com/doi/abs/10.1080/10986060802229675
Veiga, I. P. A. (2009). A Aventura de Formar Professores. São Paulo: Papirus.
Webster-Wright, A. (2009). Reframing Professional Development Through Understanding Authentic Professional Learning. Review of Educational Research. Recuperado de http://journals.sagepub.com/doi/10.3102/0034654308330970
White, A. L, Jaworski, B., Agudelo-Valderrama, C & Gooya, Z. (2013). Teachers learning from teachers. In: Clements, M. A.; Bishop, A. J.; Keitel, C.; Kilpatrick, J.; Leung, F. K. S. (Eds.), Third international handbook of mathematics education. New York: Springer.
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