Logo Revista Latinoamericana de Investigación en Matemática Educativa

Special Article

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

SEMIOSIS AS A MULTIMODAL PROCESS

Submitted
October 28, 2024
Published
December 30, 2006

Abstract

Classical semiotic approaches are too narrow to investigate the didactical phenomena in the mathematics classroom. In addition to the standard semiotic resources used by students and teachers (e.g. written symbols and speech), other important semiotic ressources include also gestures, glances, drawings and extra-linguistic modes of expressions. However, these semiotic ressurces fit with difficulties within the constraints of the classical definitions of semiotic systems. To overcome such difficulties I adopt a vygotskian approach and present an enlarged notion of semiotic system, the semiotic bundle, which reveals particularly useful for framing all the semiotic resources we find in the learning processes in mathematics. The paper stresses some critical points in the usual description of the semiotic systems; it discusses the multimodal and embodied paradigm, which is emerging in these last years from researches in psycholinguistics and neuroscience and analyses gestures from a semiotic point of view. Then it introduces the notion of semiotic bundle and exemplifies it through a case study.

References

  1. Arzarello, F. (in press). Mathematical landscapes and their inhabitants: perceptions, languages, theories, Proceedings ICME 10, Plenary Lecture.
  2. Arzarello F., L.Bazzini, Chiappini G.P. (1994), Intensional semantics as a tool to analyse algebraic thinking, Rendiconti del Seminario Matematico dell’Università di Torino, 52 (1), 105-125.
  3. Arzarello, F & Edwards, L. (2005). Gesture and the Construction of Mathematical Meaning (Research Forum 2), Proc. 29th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 1, pp. 122-145). Melbourne, AU: PME.
  4. Arzarello F. & Robutti, O. (2004). Approaching functions through motion experiments. In: R. Nemirovsky, M. Borba & C. DiMattia (eds.), Bodily Activity and Imagination in Mathematics Learning, PME Special Issue of Educational Studies in Mathematics, 57.3, CD-Rom, Chapter 1.
  5. Arzarello, F., Ferrara, F., Paola, D., Robutti, O., (2005). The genesis of signs by gestures. The case of Gustavo, Proc. 29th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 1, pp. 73-80). Melbourne, AU: PME.
  6. Arzarello, F., Bazzini, L., Ferrara, F., Robutti, O., Sabena, C., Villa, B. (2006). Will Penelope choose another bridegroom? Looking for an answer through signs, Proc. 30th Conf. of the Int. Group for the Psychology of Mathematics Education. Prague.
  7. Arzarello, F. & Robutti, O. (to appear). Framing the embodied mind approach within a multimodal paradigm, in: Lyn English, M. Bartolini Bussi, G. Jones, R. Lesh e D. Tirosh (ed.), Handbook of International Research in Mathematics Education (LEA, USA), 2nd revised edition.
  8. Bara, B.G. & Tirassa, M. (1999). A mentalist framework for linguistic and extralinguistic communication. In: S. Bagnara (ed.), Proceedings of the 3rd European Conference on Cognitive Science. Siena, Italy. Roma: Istituto di Psicologia, CNR.
  9. Barbero R, Bazzini L., Ferrara F., Villa B. (in press). The Penelope’s story: learning through action, speech and gestures, Proc. CIEAEM 57, Piazza Armerina, Italy, July 2005.
  10. Bartolini, M.G. & Mariotti, M.A. (to appear). Semiotic mediation in the mathematics classroom, in: Lyn English, M. Bartolini Bussi, G. Jones, R. Lesh e D. Tirosh (ed.), Handbook of International Research in Mathematics Education (LEA, USA), 2nd revised edition.
  11. Bosch, M. & Chevallard, Y. (1999). La sensibilité de l’activité mathématique aux ostensifs, Recherches en Didactique des Mathématiques, 19 (1), 77-124.
  12. Bucciarelli, M. (in press). How the construction of mental models improve learning, Mind and Society.
  13. Chevallard, Y. (1999), L’analyse des pratiques enseignantes en théorie anthropologique du didactique, Recherches en Didactique des Mathématiques, 19/2, 221-266.
  14. Cutica, I. & Bucciarelli, M. 2003. Gestures and the construction of models. The 2nd International Conference on Reasoning and Decision Making,Reasoning and understanding: Mental models, relevance and limited rationality approaches, Padova, March, the 17-18, 11.
  15. Detlefsen, M., 1986, Hilbert’s Program, Dordrecht: Reidel. Dörfler, W. (n.d.) How diagrammatic is mathematical reasoning? Retrieved May 4 2006, from http://www.math.uncc.edu/~sae/dg3/dorfler2.pdf
  16. Duval R. (1993). Registres de représentations sémiotique et fonctionnement cognitif de la pensée. Annales de Didactique et de Sciences Cognitives, 5, 37-65. ULP, IREM Strasbourg.
  17. Duval, R. (1999). Conversion et articulation des représentations analogiques. Lille, France: I.U.F.M. Nord pas de Calais.
  18. Duval, R. (2001). The cognitive analysis of problems of comprehension in the learning of mathematics. Paper presented at the Semiotics Discussion Group of the 25th PME International Conference, Freudenthal Institute, The Netherlands, July 2001.
  19. Duval, R. (2002). The cognitive analysis of problems of comprehension in the learning of mathematics. Mediterranean Journal for Research in Mathematics Education, 1(2), 1- 16.
  20. Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics, Educational Studies in Mathematics, (61), 103-131.
  21. Ernest, P. (2006). A semiotic perspective of mathematical activity: the case of number, Educational Studies in Mathematics, (61), 67-101
  22. Frege, G. (1969). Funktion, Begriff, Bedeutung. Fünf logische Studien. Göttingen: Vandenhoeck & Company.
  23. Gallese, V. & Lakoff, G. (2005). The Brain’s Concepts: The Role of the Sensory-Motor System in Conceptual Knowledge. Cognitive Neuropsychology, 22(3/4), 455-479.
  24. Guala & Boero, 1999 Time complexity and Learning, Annals of the New York Academy of Sciences, June 30, 1999, 164-7.
  25. Goldin-Meadow, S. (2003). Hearing gestures: How our hands help us think. Chicago: Chicago University Press.
  26. Harper, E.. (1987). Ghosts of Diophantus, Educational Studies in Mathematics, Vol. 18, (75-90).
  27. Hilbert, D. (1962). Grundlagen der Geometrie, Stuttgart: Teubner (original edition in 1899).
  28. Lemaitre, A. (1905). Observations sur le langage interieur des enfants, Archives de psychologie, n.4,1-43
  29. Johnson-Laird P.N. 1983. Mental models: Towards a cognitive science of language, and consciousness. Cambridge University Press, Cambridge, UK.
  30. Johnson-Laird, P.N. 2001. Mental models and human reasoning. In Dupoux, E. (Ed.), Language, brain, and cognitive development: Essays in honor of Jacques Mehler, pp. 85-102. Cambridge, MA: The MIT Press.
  31. Kaput, J., Noss, R. & Hoyles, C.: 2002, Developing New Notations for a Learnable Mathematics in the Computational Era, in: English, L.D. (Ed.), Handbook of International Research in Mathematics Education: Lawrence Erlbaum Assoc., NJ, 51-75.
  32. Kita, S. (2000). How Representational Gestures Help Speaking. In McNeill, D. (ed.), Language and Gesture, pp. 162-185. Cambridge: Cambridge University Press.
  33. Malcom, N. & von Wright, G.H. (2001). Ludwig Wittgenstein : A Memoir. Oxford: Oxford University Press.
  34. McNeill, D. (1992) Hand and mind: What gestures reveal about thought. Chicago: Chicago University Press.
  35. Hartshorne, C. & Weiss, P. (Eds.) (1933), Collected Papers of Charles Sanders Peirce, vol. III, Cambridge (MA): Harvard University Press
  36. Kita, S. (2003). Interplay of gaze, hand, torso orientation, and language in pointing. In: S. Kita (ed.), Pointing. Where language, culture, and cognition meet. Mahwah: Erlbaum.
  37. Nemirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In N.A. Pateman, B.J. Dougherty & J.T. Zilliox (Eds.), Proc. 27th Conf. of the Int. Group for the Psychology of Mathematics Education (Vol. 1, pp. 103-135). Honolulu, Hawai‘I: PME.
  38. Ogden, C.K. & Richards, I.A. (1923). The Meaning of Meaning. London: Routledge & Kegan.
  39. Rabardel, P. (1995). Les hommes et les technologies, une approche cognitive des instruments contemporains. Paris: Armand Colin.
  40. 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.
  41. Radford, L. (2003a). Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students’ Types of Generalization. Mathematical Thinking and Learning, 5(1), 37–70.
  42. Radford, L., Demers, S., Guzmán, J. and Cerulli, M. (2003b). Calculators, graphs, gestures and the production of meaning, in: N. Pateman, B. Dougherty and J. Zilliox (eds.), Proceedings of the 27 Conference of the international group for the psychology of mathematics education (PME27 –PMENA25), University of Hawaii, Vol. 4, pp. 55-62.
  43. Radford, L. (2006). The Anthropology of Meaning, Educational Studies in Mathematics, (61), 39-65.
  44. Robutti, O. (2005). Hearing gestures in modelling activities with the use of technology, in F. Olivero & R. Sutherland (eds.), Proceedings of the 7th International Conference on Technology in Mathematics Teaching, University of Bristol, 252-261.
  45. Simpson, S.G: (1999). Subsystems of second order Arithmetic. New York: Springer.
  46. Sfard A. & McClain, 2002, Analyzing Tools: Perspectives on the Role of Designed Artifacts in Mathematics Learning, The Journal of the Learning Sciences, Volume 11, Numbers 2&3, Special Issue, 153-162.
  47. Steinbring, H. (2005). The Construction of New Mathematical Knowledge in Classroom Interaction. New York: Springer.
  48. Steinbring, H. (2006). What makes a sign a mathematical sign? An epistemological perspective on mathematical interaction, Educational Studies in Mathematics, (61), 133- 162.
  49. Vérillon, P., & Rabardel, P. (1995). Artefact and cognition: a contribution to the study of thought in relation to instrumented activity. European Journal of Psychology in Education, vol. IX, n°3.
  50. Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  51. Vygotsky, L. S. (1997). Collected works, Vol. 4 (R. Rieber, Ed.). New York: Plenum.
  52. Vygotsky, L.S. (1986), Thought and Language, Cambridge (MA): MIT Press.
  53. Wertsch, J. V., & Stone, C. A. (1985). The concept of internalization in Vygotsky’s account of the genesis of higher mental functions. In J.V. Wertsch (Ed.), Culture, communication and cognition: Vygotskian perspectives. Cambridge: Cambridge University Press.

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