Saltar para menu de navegação principal Saltar para conteúdo principal Saltar para rodapé do site
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 26 N.º 3 (2023): Noviembre

EXPLORING LEARNING OPPORTUNITIES FOR PRIMARY TEACHERS: THE CASE OF KNOWLEDGE FOR TEACHING EARLY ALGEBRA

DOI
https://doi.org/10.12802/relime.23.2633
Enviado
outubro 7, 2024
Publicado
2023-11-30

Resumo

Compreender como constituir e desenvolver oportunidades para professores primários ensinarem álgebra precoce a crianças ainda é uma importante lacuna de pesquisa. Neste artigo, trazemos resultados de um programa de pesquisa desenvolvido no Brasil nos últimos cinco anos. Nosso objetivo é discutir como as oportunidades de aprendizagem profissional surgiram quando os professores planejaram, discutiram e analisaram coletivamente aulas envolvendo diferentes significados do símbolo da igualdade e o desenvolvimento do pensamento funcional. Desenvolvidos na perspectiva de uma pesquisa qualitativo-interpretativa, os dados analisados consistem em documentos curriculares, protocolos para a resolução de tarefas formativas, áudios e vídeos coletados durante os processos de formação de professores em serviço. Os resultados destacam que as tarefas de aprendizagem prof issional, combinadas com as ações dos formadores de professores durante as discussões coletivas, favoreceram os professores em serviço para diferenciar e compreender o raciocínio dos alunos. São discutidas algumas implicações para a formação de professores, bem como para o desenvolvimento profissional dos professores primários, especialmente no que diz respeito ao pensamento inicial da álgebra, pois os professores normalmente não têm a oportunidade de estudar esses conteúdos em suas próprias experiências na escola.

Referências

  1. Adler, J., & Ronda, E. (2014). An analytic framework for describing teachers’ mathematics discourse in instruction. In C. Nicol, P. Liljedahl, S. Oesterle, & D. Allan (Eds.), Proceedings of the Joint Meeting of PME 38 and PME-NA 36 (Vol 2, pp. 9-16). PME.
  2. Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: Equal sign and variable. Mathematical Thinking and Learning, 9(3), 249-272.
  3. Ball, D. L., Ben-Peretz, M., & Cohen, R. B. (2014). Records of practice and the development of collective professional knowledge. British Journal of Educational Studies, 62(3), 317-335.
  4. Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes, & L. Darling-Hammond
  5. (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). Jossey Bass.
  6. 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.
  7. Barboza, L. C. S. (2019). Conhecimento dos professores dos anos iniciais e o sinal de igualdade: Uma investigação com tarefas de aprendizagem profissional [Unpublished Master’s Thesis]. Universidade Federal do ABC.
  8. Blanton, M. (2008). Algebra in elementary classrooms: Transforming thinking, transforming practice. Heinemann.
  9. Blanton, M., & Kaput, J. (2005). Characterizing a classroom practice that promotes algebraic reasoning. Journal for Research in Mathematics Education, 36(5), 412-446.
  10. Blanton, M., & Kaput, J. (2008). Building disctrict capacity for teacher development in algebraic reasoning. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the Early Grades (pp. 133-160). Lawrence Erlbaum Associates.
  11. Borba, R. E. S. R., Lautert, S. L., & Silva, A. C. (2021). How Do Kindergarten Children Deal with Possibilities in Combinatorial Problems? In A. G. Spinillo, S. L. Lautert, & R. E. S. R. Borba (Eds.), Mathematical Reasoning of Children and Adults (pp. 141-167). Springer International Publishing.
  12. Borba, R. E. S. R., Pessoa, C. A. S., & Rocha, C. A. (2013). How Primary School students and teachers think about combinatorial problems. Educação Matemática Pesquisa, 15(4), 895-908.
  13. Bransford, J. D., Brown, A. L., & Cocking, R. R. (2000). How People Learn: Brain, Mind, experience, and school. National Academy Press.
  14. Brasil (2017). Base Nacional Comum Curricular: Matemática. MEC/SFE.
  15. Cañadas, M. C., Brizuela, B. M., & Blanton, M. (2016). Second graders articulating ideas about linear functional relationships. The Journal of Mathematical Behavior, 41, 87-103.
  16. Canavarro, P., Oliveira, H., & Menezes, L. (2012). Práticas de ensino exploratório da matemática: O caso de Célia. In P. Canavarro, L. Santos, A. Boavida, H. Oliveira, L. Menezes, & S. Carreira (Orgs.), Actas do Encontro de Investigação em Educação Matemática 2012: Práticas de Ensino da Matemática. Sociedade Portuguesa de Investigação em Educação Matemática.
  17. Carpenter, T. P., Levi, L., Franke, M. L., & Zeringue, J. K. (2005). Algebra in the elementary school: developing relational thinking. ZDM, 37(1), 53-59.
  18. Christiansen, B., & Walther, G. (1986). Task and activity. In B. Christiansen, A. G. Howson, & M. Otte (Eds.), Perspectives on Mathematics Education (pp. 243-307). Reidel.
  19. Craig, T., & Morgan, C. (2015). Language and communication in mathematics education. In S. J. Cho (Ed.), The Proceedings of the 12 th International Congress on Mathematical Education (pp. 529-533). Springer
  20. Crotty, M. (1998). The foundations of social research: Meaning and perspective in the research process. SAGE.
  21. Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3-14.
  22. Desimone, L. M. (2009). Improving impact studies of teachers’ professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181-199.
  23. Ferreira, M. C. N. (2017). Algebra in early grades: an analysis of the national curriculum documents. Rencima, 8(5), 16-34.
  24. Heyd-Metzuyanim, E., Tabach, M., & Nachlieli, T. (2016). Opportunities for learning given to prospective mathematics teachers: Between ritual and explorative instruction. Journal of Mathematics Teacher Education, 19(6), 547-574.
  25. Jacobs, V. R., Franke, M., Carpenter, T. P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258-288.
  26. Kieran, C. (1981). Concepts associated with the equality symbol. Educational Studies in Mathematics, 12, 317-326.
  27. Kieran, C., Pang, J., Schifter, D., & Ng, S. F. (2016). ICME-13. Early algebra: Research into its nature, its learning, its teaching. Springer.
  28. Llinares, A. Z. (2018). Cómo alumnos de educación primaria resuelven problemas de generalización de patrones. Una trayectoria de aprendizaje. Revista Latinoamericana de Investigación en Matemática Educativa, 21(1), 87-104.
  29. 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.
  30. McCrory, R., Floden, R., Ferrini-Mundy, J., Reckase, M. D., & Senk, S. L. (2012). Knowledge of Algebra for Teaching: A Framework of Knowledge and Practices. Journal for Research in Mathematics Education, 43(5), 584-615.
  31. Mulligan, J., Oslington, G., & English, L. (2020). Supporting early mathematical development through a ‘pattern and structure’ intervention program. ZDM, 52(4), 663-676.
  32. Pang, J., & Sunwoo, J. (2022). An analysis of teacher knowledge for teaching functional thinking to elementary school students. Asian Journal for Mathematics Education, 1(3), 306-322.
  33. Pincheira, N., & Alsina, Á. (2021). Teachers’ Mathematics Knowledge for Teaching Early Algebra: A Systematic Review from the MKT Perspective. Mathematics, 9, 2590.
  34. Ponte, J. P. (2005). Gestão curricular em Matemática. In GTI (Ed.), O professor e o desenvolvimento curricular (pp. 11-34). APM.
  35. Ponte, J. P., & Branco, N. (2013). Algebraic thinking in initial teacher education. Educar em Revista, 1(40), 39-53.
  36. Putnam, R., & Borko, H. (2000). What do new views of knowledge and thinking have to say about research on teacher learning? Educational Researcher, 29(1), 4-15.
  37. Ribeiro, A. J., Aguiar, M., Trevisan, A. L., & Elias, H. R. (2021). How Teachers Deal with Students’ Mathematical Reasoning When Promoting Whole-Class Discussion During the Teaching of Algebra. In A. G. Spinillo, S. L. Lautert, & R. E. de S. R. Borba. (Org.), Mathematical Reasoning of Children and Adults (pp. 239-264). Springer International Publishing.
  38. Ribeiro, A. J., & Ponte, J. P. (2019). Professional learning opportunities in a practice-based teacher education program about the concept of function. Acta Scientiae, 21(2), 49-74.
  39. Ribeiro, A. J., & Ponte, J. P. (2020). A theoretical model for organizing and understanding teacher learning opportunities to teach mathematics. Zetetike, 28, e020027.
  40. Serrazina, M. L. (2017). Planificação do ensino-aprendizagem da Matemática. In GTI (Ed.), A prática dos professores: planificação e discussão coletiva na sala de aula (pp. 9-32). APM.
  41. Sevinc, S., & Galindo, E. (2022). Noticing Student Mathematical Thinking: Self-Contemplation of a Pre-Service Teacher. European Journal of Science and Mathematics Education, 10(2), 154-169. https://doi.org/10.30935/scimath/11489
  42. Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
  43. Silver, E. A., Clark, L. M., Ghousseini, H. N., Charalambous, Y. C., & Sealy, J. T. (2007). Where is the mathematics? Examining teachers’ mathematical learning opportunities in practice-based professional learning tasks. Journal of Mathematics Teacher Education, 10(4-6), 261-277.
  44. Smith, M. S. (2001). Practice-based professional development for teachers of mathematics. NCTM.
  45. 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.
  46. Tatto, M. T., & Senk, S. (2011). The mathematics education of future primary and secondary teachers: Methods and findings from the teacher education and development study in mathematics. Journal of Teacher Education, 62(2), 121-137.
  47. Trevisan, A. L., Ribeiro, A. J., & Ponte, J. P. D. (2020). Professional learning opportunities regarding the concept of function in a practice-based teacher education program. International Electronic Journal of Mathematics Education, 15(2), em0563.
  48. Trivilin, L. R., & Ribeiro, A. J. (2015). Mathematical Knowledge for Teaching Different Meanings of the Equal Sign: a study carried out with Elementary School Teachers. Bolema, 29(51), 38-59.
  49. Vermeulen, C., & Meyer, B. (2017). The equal sign: teachers’ knowledge and students’ misconceptions. African Journal of Research in Mathematics, Science and Technology Education, 21(2), 136-147.
  50. Warren, E., Trigueros, M., & Ursini, S. (2016). Research on the learning and teaching of algebra. In A. Gutiérrez, G. C. Leder, & P. Boero (Eds.), The second handbook of research on the psychology of mathematics education (pp. 73-108). Sense Publishers.
  51. Webster-Wright, A. (2009). Reframing professional development through understanding authentic professional learning. Review of Educational Research, 79(2), 702-739.
  52. Wilkie, K. J. (2014). Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra. Journal of Mathematics Teacher Education, 17, 397-428.
  53. Wilkie, K. J. (2016). Learning to teach upper primary school algebra: changes to teachers’ mathematical knowledge for teaching functional thinking. Mathematics Education Research Journal, 28, 245-275.
  54. Zaslavsky, O. (2008). Meeting the challenges of mathematics teacher education through design and use of tasks that facilitate teacher learning. In B. Jaworski, & T. Wood (Eds.), International handbook of mathematics teacher education: The mathematics teacher educator as a developing professional (Vol. 4, pp. 93-114). Sense Publishers.

Downloads

Não há dados estatísticos.

Artigos Similares

1 2 3 4 5 6 7 8 9 10 > >> 

Também poderá iniciar uma pesquisa avançada de similaridade para este artigo.

Artigos mais lidos do(s) mesmo(s) autor(es)