Skip to main navigation menu Skip to main content Skip to site footer
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Special Article

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

LEARNING MATHEMATICS: INCREASING THE VALUE OF INITIAL MATHEMATICAL WEALTH

Submitted
October 28, 2024
Published
2006-12-30

Abstract

Using the Peircean semiotic perspective, the paper introduces the notion of mathematical wealth. The first section argues the intrinsic relationship between mathematics, learners of mathematics, and signs. The second argues that interpretation, objectification, and generalization are concomitant semiotic processes and that they constitute a semiotic triad. The third argues that communicating mathematically is a powerful means of semiotic objectification. The fourth section presents the notion of mathematical wealth, the learners’ investment of that wealth, and the synchronic-diachronic growth of its value through classroom discourse. The last section discusses how teachers, with different theoretical perspectives, influence the direction of classroom discourse and the growth of the learner’s initial mathematical wealth.

References

  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.

Downloads

Download data is not yet available.

Similar Articles

1 2 3 4 5 6 7 8 9 10 > >> 

You may also start an advanced similarity search for this article.