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Artículos

Vol. 15 No. 2 (2012): Julio

THE NORMATIVE AND META-NORMATIVE DIMENSIONS IN A CONTEXT OF EXPLORATORY-INVESTIGATIVE CLASSES

Submitted
July 14, 2023
Published
2012-07-01

Abstract

This paper explores the normative and meta-normative dimensions that regulate the interactions in mathematics classroom and shape the participation of teachers and students in a context of an exploratory-investigative task about patterns. This task was implemented in a 7th grade of a basic public school (approximately 12-years-old pupils). Norms andmeta-norms were identified using as theoretical tools two models of analysis designed to describe and to interpret the processes of interaction in the classroom. We conclude by highlighting the importance of the teacher becomes aware of the complex network of norms and meta-norms involved in mathematical and didactic practices, as an important resource for managing (negotiating or changing) them, at each moment of the activity, to ensure optimization of student learning.

References

  1. Arcavi, A. (2007). El desarrollo y el uso del sentido de los simbolos. UNO Revista de Didáctica de las Matemáticas 44, 59-75.
  2. Banchi, H. & Bell, R. (2008), The many levels of inquiry. Science and Children 46(2), 26-29,
  3. Bruner J. (2002). Atos de significação, Porto Alegre, Brasil: Artmed editora.
  4. Brousseau, G. (1988). Le contrat didactique: le milieu. Recherches en Didactique des Mathématiques 9(3), 309-336.
  5. Carraher, D. W. & Schliemann, A. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 669-705). Reston, VA: National Council of Teacher of Mathematics.
  6. D' Amore, B., Font, V. y Godino, J. D. (2007). La dimensión metadidáctica en los procesos de enseñanza y aprendizaje de las matemáticas. Paradigma 28(2), 49-77.
  7. Ernest, P. (1996) Varieties of constructivism: a framework for comparison. In L. Steffe, P. Nesher, P. Cobb, G. Goldin & B.Greer (Eds.), Theories of Mathematical Learning. New Jersey, England: Lawrence Erlbaum Associates.
  8. Frade, C. e Meira, L.(no prelo). Interdisciplinaridade na escola: subsídios para uma zona de desenvolvimento proximal como espaço simbólico. Educação em Revista.
  9. Fernandes, F. L. P. (2010). Letramento algébrico em um contexto de aulas exploratório-investigativas. Encontro Brasileiro de Estudantes de Pós-Graduação em Educação Matemática (EBRAPEM), Recuperado em 24 de julho de 2010, em <http://ebrapem.mat.br/inscricoes/trabalhos/GT08_Fernandes_TA.pdf>.
  10. Font, V., Planas, N. y Godino, J. D. (2010). Modelo para el análisis didáctico en educación matemática. Infancia y Aprendizaje 33(1), 89-105.
  11. Franke, M. L., Kazemi, E. & Battey, D. (2007). Mathematics teaching and classroom practice. InJ. F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 226256). Reston, VA: National Council of Teacher of Mathematics.
  12. Godino, J. D. (2002). Un enfoque ontológico y semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques 22 (2/3), 237-284.
  13. Godino, J. D. y Batanero, C. (1994), Significado institucional y personal de los objetos matemáticos. Recherches en Didactique des Mathématiques 14(3), 325-355.
  14. Godino, J. D., Bencomo, D., Font, V. y Wilhelmi, M. R. (2006). Análisis y valoración de la idoneidad didáctica de procesos de estudio de las matemáticas. Paradigma 27(2), 221-252.
  15. Godino, J. D., Contreras A. y Font, V. (2006), Análisis de procesos de instrucción basado en el enfoque ontológico-semiótico de la cognición matemática. Recherches en Didactiques des Mathematiques 26(1), 39-88.
  16. Godino, J. D., Font, V., Wilhelmi, M. R. y Castro, C. (2009). Aproximación a la dimensión normativa en didáctica de las matemáticas desde un enfoque ontosemiótico. Enseñanza de las Ciencias 27(1), 59-76.
  17. Greeno, J. G. (1997). On claims that answer the wrong questions. Educational Researcher 26(1), 5-17.
  18. Guzmán, M. (1992). Tendencias innovadoras en educación matemática. Buenos Aires, Argentina: Olimpiada Matemática Argentina.
  19. Hiebert, J. S. & Grouws, D. A. (2007) The effects of classroom mathematics teaching on students' learning. In J. F. K. Lester (Ed), Second Handbook of Research on Mathematics Teaching and Learning (pp. 371-404). Reston, VA: National Council of Teacher of Mathematics.
  20. Hmelo-Silver, C. E., Duncan, R. G. & Chinn, C. A. (2007). Scaffolding and achievement in Problem-Based and inquiry learning: a response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42(2), 99-107.
  21. Martin, L., Towers, J. & Pirie, S. (2006). Collective mathematical understanding as improvisation. Mathematical Thinking and Learning 8(2), 149-183.
  22. NCTM (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teacher of Mathematics.
  23. Planas, N. y Iranzo, N. (2009). Consideraciones metodológicas para el análisis de procesos de interacción en el aula de matemáticas. Revista Latinoamericana de Investigación en Matemática 12(2), 179-213.
  24. Ponte, J. P. (2003). Investigar, ensinar e aprender. Actas do ProfMat 2003 (CD-ROM, pp. 25-39). Lisboa, Portugal: APM.
  25. Ponte, J. P. (2005). Álgebra no currículo escolar. Educação e Matemática 85, 36-42. Ponte, J. P. (2006). Números e Álgebra no curriculo escolar. Em I. Vale, T. Pimental, A.Barbosa,
  26. L. Fonseca, L. Santos e P. Canavarro (Eds.), Números e Algebra na aprendizagem da Matemática e na formação de professores (CD-ROM, pp. 5-27). Lisboa, Portugal: Secção de Educação Matemática da Sociedade Portuguesa de Ciências da Educação.
  27. Ponte, J.P., Brocardo, J. e Oliveira, H. (2006). Investigações matemáticas na sala de aula. Belo Horizonte, Brasil: Autêntica.
  28. Ponte, J. P., Fonseca, H. e Brunheira, L. (1999). As atividades de investigação, o professor e a aula de Matemática. Actas do ProfMat 1999 (CD-ROM, pp. 91-101). Lisboa, Portugal: APM.
  29. Souza, E. R. e Diniz, M. I. S. (1996). Álgebra: das variáveis às equações e funções. 2ed. São Paulo: IME-USP.
  30. Voigt, J. (1995). Thematic patterns of interaction and sociomathematical norms. In P. Cobb, H. Bauersfeld (Eds.), The emergence of mathematical meaning: Interaction in classroom cultures (pp. 163-199), New Jersey, England: Lawrence Erlbaum Associates.
  31. Welzel, M. & Roth, W. (1998). Do interviews really assess students' knowledge? International Journal Science Education 20(1), 25-44.
  32. Yackel, E. & Cobb, P. (1996). Socialmathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education 27(4), 458-477.
  33. Zazkis, R. & Liljedahl, P. (2002). Generalization of patterns: The tension between algebraic thinking and algebraic notation. Educational studies in mathematics 49, 379-402.

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