Aller directement au menu principal Aller directement au contenu principal Aller au pied de page
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículo Especial

Vol. 9 No 4 (2006): Número Especial/ Diciembre

LEARNING MATHEMATICS: INCREASING THE VALUE OF INITIAL MATHEMATICAL WEALTH

Soumis
octobre 28, 2024
Publiée
2006-12-30

Résumé

En utilisant la perspective sémiotique peircienne, cet article introduit la notion de richesse mathématique. La première section soutient qu’il y a une relation intrinsèque entre les mathématiques, les apprenants des mathématiques et les signes. La deuxième section soutient que l’interprétation, l’objectivation et la généralisation sont des processus sémiotiques concomitants et qu’ils constituent une triade sémiotique. La troisième section soutient que la communication mathématique est un puissant moyen sémiotique d’objectivation. La quatrième section présente la notion de richesse mathématique, l’investissement de cette richesse par les apprenants et la croissance synchronique et diachronique de sa valeur à travers le discours de la salle de classe. La dernière section discute de la façon dont les enseignantes et enseignants, avec des perspectives théoriques différentes, agissent sur l’orientation de la discussion dans la salle de clase et sur l’enrichissement de la pensée mathématique initiale des apprenants.

Références

  1. Austin, J. L. & Howson A. G. (1979). Language and mathematical education.Educational Studies in Mathematics, 10, 161-197.
  2. Bauersfeld, H. (1998). About the notion of culture in mathematics education. In F. Seeger, J. Voigt, & U. Waschescio (Eds.), The culture of the mathematics classroom, (pp. 375- 389). Cambridge, UK: Cambridge University Press.
  3. Bishop, A. J. (1988). Mathematical enculturation: A cultural perspective on mathematics education. Dordrecht: Kluwer Academic Publishers. Bourdieu, P. (1991). Language and symbolic power. Cambridge, Massachusetts: Harvard University Press.
  4. Brousseau, G. (1997). Theory of didactical situations in mathematics. Edited by Nicolas Balacheff, Martin Cooper, Rosamund Sutherland, and Virginia Warfield. Dordrecht, The Netherlands: Kluwer Academic Press.
  5. Bruner, J. S. (1986). Actual minds, possible worlds. Cambridge, Massachusetts: Harvard University Press.
  6. Davis, P. J. & Hersh, R. (1981). The mathematical experience. Boston: Houghton Mifflin Company.
  7. Deacon, T. (1997). The symbolic species: The coevolution of language and the brain. New York: W. W. Norton & Company.
  8. Duval, R. (2006). The cognitive analysis of problems of comprehension in the learning of mathematics. In A. Sáenz-Ludlow, and N. Presmeg (Eds.), Semiotic perspectives on epistemology and teaching and learning of mathematics, Special Issue, Educational Studies in Mathematics, 61, 103-131.
  9. Ernest, P. (2006). A semiotic perspective of mathematical activity: The case of number. In A. Sáenz-Ludlow, & N. Presmeg (Eds.), Semiotic perspectives on epistemology and teaching and learning of mathematics, Special Issue, Educational Studies in Mathematics, 61, 67-101.
  10. Gay, W. (1980). Analogy and metaphor. Philosophy and Social Criticism, 7(3-4), 299- 317.
  11. Habermas, J. (1984). The theory of communicative action. 2. Boston: Beacon Press.
  12. Halliday, M. A. K. (1978). Language as social semiotics. London: Arnold. National Council of Teachers of Mathematics (2000). Principles and Standards of School Mathematics. Reston, Virginia: National Council of Teachers of Mathematics.
  13. Ongstad, S. (2006). Mathematics and mathematics education as triadic communication? In A. Sáenz-Ludlow, and N. Presmeg (Eds.), Semiotic perspectives on epistemology and teaching and learning of mathematics, Special Issue, Educational Studies in Mathematics, 61, 247-277.
  14. Parmentier, R. J. (1985). Signs’ place in medias res: Peirce’s concept of semiotic mediation. In E. Mertz & R.J. Parmentier (Eds.), Semiotic mediation (pp. 23-48). Orlando, Florida: Academic Press.
  15. Peirce, C. S. (1903). The three normative sciences. In The Essential Peirce, 2, (pp. 1893-1913) edited by The Peirce Edition Project, (pp. 196-207). Bloomington, Indiana: Indiana University Press.
  16. Peirce, C. S. (1956). The essence of mathematics. In James R. Newman (Ed.), The World of Mathematics, 3, (pp. 1773-1783), New York: Simon and Schuster.
  17. Peirce, C. S. (1974). Collected Paper (CP). C. Hartshorne, and P. Weiss (Eds.), 1-4. Cambridge, Massachusetts: Harvard University Press. (Reference is made to volumes and paragraphs).
  18. Peirce, C. S. (1976). The New Elements of Mathematics (NEP). Carolyn Eisele (Ed), 1- 4. The Hague: Mouton Publishers.
  19. Presmeg, N. C. (1997). Generalization using imagery in mathematics. In L. D. English (Ed.), Mathematical reasoning: Analogies, metaphors, and images (pp. 299-312). Mahwah, New Jersey: Lawrence Erlbaum Associates.
  20. Radford, L. (2003). Gestures, speech, and the sprouting of signs: A semiotic-cultural approach to learners’ types of generalization. Mathematical Thinking and Learning, 5(1), 37-70.
  21. Radford, L. (2006a). The anthropology of meaning. In A. Sáenz-Ludlow, & N. Presmeg (Eds.), Semiotic perspectives on epistemology and teaching and learning of mathematics, Special Issue, Educational Studies in Mathematics, 61, 39-65.
  22. Radford, L. (2006b). Glossary of internal document of the symposium of the Symbolic Cognition Group. Vermont, January 3-9, 2006.
  23. Radford, L. (in press). Semiótica cultural y cognición. In R. Cantoral & O. Covián (Eds.), Investigación en Matemática Educativa en Latinoamérica. México.
  24. Rossi-Landi, F. (1980). On linguistic money. Philosophy and Social Criticism, 7(3-4), 346-372.
  25. Rotman, B. (2000). Mathematics as sign. Stanford, California: Stanford University Press. Sáenz-Ludlow, A. (2003). A collective chain of signification in conceptualizing fractions. Journal of Mathematical Behavior, 22, 181-211.
  26. Sáenz-Ludlow, A. (2004). Metaphor and numerical diagrams in the arithmetical activity of a fourth-grade class. Journal for Research in Mathematics Education, 1(35), 34-56.
  27. Sáenz-Ludlow, A. (2006). Classroom interpreting games with an illustration. In A. Sáenz- Ludlow, & N. Presmeg (Eds.), Semiotic perspectives on epistemology and teaching and learning of mathematics, Special Issue, Educational Studies in Mathematics, 61, 183- 218.
  28. Seeger, F. (1998). Discourse and beyond: On the ethnography of classroom discourse. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp.85-101). Reston, Virginia: National
  29. Sierpinska, A. (1998). Three epistemologies, three views of classroom communication: Constructivism, sociocultural approaches, interactionism. In H. Steinbring, M. G. Bartolini Bussi, & A. Sierpinska (Eds.), Language and communication in the mathematics classroom (pp. 30-62). Reston, Virginia: National Council of Teachers of Mathematics.
  30. Skemp, R. (1987). The psychology of learning mathematics. Lawrence Erlbaum Associates.
  31. Steinbring, H., Bartolini Bussi, M. G., & Sierpinska, A. (Eds.) (1998). Language and communication in the mathematics classroom. Reston, Virginia: National Council of Teachers of Mathematics.
  32. Van Dormolen, J. (1986). Textual analysis. In B. Chirstiansen, A. G. howson, & M. Otte (Eds.), Perspectives on mathematics education, (pp. 141-171). Boston: B. Reidel Publishing Company.
  33. Vygotsky, L. S. (1987). Thinking and speech. New York: Plenum Press.
  34. White, L. A. (1956). The locus of mathematical reality: An anthropological footnote. In James R. Newman (Ed.), The World of Mathematics, 4, (pp. 2348-2364). New York: Simon and Schuster.
  35. Wilder, R. (1973/1968). Evolution of mathematical concepts. Milton Keyness, England:
  36. The Open University Press.

Téléchargements

Les données relatives au téléchargement ne sont pas encore disponibles.

Articles similaires

1 2 3 4 5 6 7 8 9 10 > >> 

Vous pouvez également Lancer une recherche avancée de similarité pour cet article.