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

Artículo Especial

Vol. 9 N.º 4 (2006): Número Especial/ Diciembre

SEMIOTIC OBJECTIFICATIONS OF THE COMPENSATION STRATEGY: EN ROUTE TO THE REIFICATION OF INTEGERS

Enviado
outubro 28, 2024
Publicado
2006-12-30

Resumo

Reportamos aqui o análise de uma experiencia que reproduce o trabalho de investigação “Object-Process Linking and Embedding” (OPLE) en o caso da ensino da aritmética dos inteiros, desenvolvida por Linchevski e Williams (1999) na tradição da Educação Matemática Realista (realistic mathematics education (RME)). Nossa análise aplica a teoria da objetivação de Radford, com o propósito de surgir novas pistas sobre a forma em que a reificação tem lugar. Em particular, o método de análise mostra como a generalização factual da estratégia chamada de compensação encapsula a noção de “agregar de um lado é o mesmo que quitar do outro lado”; uma base fundamental disso que será, mais tarde, as operações com inteiros. Discutimos, de igual modo, outros aspectos da objetivação suscetíveis de chegar a ser importante na cadeia semiótica que os alunos executam na seqüência OPLE, seqüência que pode levar a um fundamento intuitivo das operações com os inteiros. Sustentamos que é necessário elaborar teorías semióticas para compreender o papel vital dos modelos e da modelação na implementação das reificações no seio da Educação Matemática Realista (RME).

Referências

  1. Cobb, P. (1994). Where Is the Mind? Constructivist and Sociocultural Perspectives on Mathematical Development. Educational Researcher, 23(7), 13-20.
  2. Cobb, P., Gravemeijer, K., Yackel, E., McClain, K., & Whitenack, J. (1997). Mathematizing and Symbolizing: The Emergence of Chains of Signification in One First-Grade Classroom.
  3. In D. Kirshner & J. A. Whitson (Eds.), Situated Cognition. Social, Semiotic, and Psychological Perspectives (pp. 151-233). Mahwah, N.J.: Lawrence Erlbaum Associates.
  4. Dirks, M. K. (1984). The integer abacus. Arithmetic Teacher, 31(7), 50–54.
  5. Goodson-Espy, T. (1998). The roles of reification and reflective abstraction in the development of abstract thought: transitions from arithmetic to algebra. Educational Studies in Mathematics, 36(3), 219-245.
  6. Gravemeijer, K. (1997a). Instructional design for reform in mathematics education. In K. P. E. G. M. Beishuizen, and E.C.D.M. van Lieshout (Ed.), The Role of Contexts and Models in the Development of Mathematical Strategies and Procedures (pp. 13-34). Utrecht: CD-ß Press.
  7. Gravemeijer, K. (1997b). Mediating Between Concrete and Abstract. In T. Nunez & P. Bryant (Eds.), Learning and Teaching in Mathematics. An International Perspective (pp. 315-345). Sussex, UK: Psychology Press.
  8. Gravemeijer, K. (1997c). Solving word problems: A case of modelling? Learning and Instruction, 7(4), 389-397.
  9. Gravemeijer, K., Cobb, P., Bowers, J., & Whitenack, J. (2000). Symbolising, Modelling and Instructional Design. Perspectives on Discourse, Tools and Instructional Design. In P. Cobb, E. Yackel & K. McClain (Eds.), Symbolizing and Communicating in Mathematics Classrooms (pp. 225-273). Mahwah, NJ: Lawrence Erlbaum Associates.
  10. Koukkoufis, A., & Williams, J. (2005). Integer Operations in the Primary School: A Semiotic Analysis of a «Factual Generalization». Paper presented at the British Society for Research in to the Learning of Mathematics Day Conference November 2005, St. Martin’s College, Lancaster.
  11. Liebeck, P. (1990). Scores and forfeits – an intuitive model for integer arithmetic. Educational Studies in Mathematics, 21(3), 221–239.
  12. Linchevski, L., & Williams, J. (1999). Using intuition from everyday life in ‘filling’ the gap in children’s extension of their number concept to include the negative numbers. Educational Studies in Mathematics, 39(1-3), 131-147.
  13. Lytle, P. A. (1994). Investigation of a model based on neutralization of opposites to teach integers. Paper presented at the Nineteenth International Group for the Psychology of Mathematics Education, Universidade Federal de Pernambuco, Recife, Brazil.
  14. Radford, L. (2002). The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14-23.
  15. Radford, L. (2003). Gestures, speech, and the sprouting of signs. Mathematical Thinking and Learning, 5(1), 37-70.
  16. Radford, L. (2005). The semiotics of the schema. Kant, Piaget, and the Calculator. In M. H. G. Hoffmann, J. Lenhard & F. Seeger (Eds.), Activity and Sign. Grounding Mathematics Education (pp. 137-152). New York: Springer.
  17. Sfard, A. (1991). On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1-36.
  18. Sfard, A., & Linchevski, L. (1994). The gains and pitfalls of reification: the case of algebra. Educational Studies in Mathematics, 26, 87–124.
  19. Walkerdine, V. (1988). The mastery of reason. London: Routledge.
  20. Williams, J. & Wake, G. (in press). Metaphors and models in translation between College and workplace mathematics. Educational Studies in Mathematics.

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.