Ir al menú de navegación principal Ir al contenido principal Ir al pie de página del sitio
Logo Revista Latinoamericana de Investigación en Matemática Educativa

Artículos

Vol. 13 Núm. 2 (2010): Julio

A SEMIOTIC VIEW OF MATHEMATICAL ACTIVITY WITH A COMPUTER ALGEBRA SYSTEM

Enviado
abril 23, 2024
Publicado
2010-06-15

Resumen

En este artículo defendemos la tesis de que un marco semiótico permite entender mejor como el uso de un Sistema Computarizado para Algebra (CAS) puede ayudar, o limitar, la actividad matemática. Este trabajo se sitúa en un marco teórico en el que hacer y aprender matemática es considerado un comportamiento semiótico. Partiendo de la noción de signo triádico (representamen, objeto, interpretado) desarrollada por Peirce, afirmamos que el uso de los CAS para cambiar de representamen (representación) en el estudio de un objeto matemático puede ayudar al estudiante a producir varios interpretados (interpretaciones) para este objeto. Esos diferentes interpretados, basados en diferentes representaciones, permiten un acceso epistemológico al objeto. Utilizamos la distinción de Duval entre conversión y tratamiento para distinguir las diferentes formas de actividad semiótica con los CAS. Ilustramos este argumento mediante un extracto del diálogo entre dos estudiantes universitarios mientras resuelven un problema matemático usando las CAS.

Citas

  1. Artigue, M. (2002) Learning Mathematics in a CAS Environment: The Genesis of a Reflection about Instrumentation and the Dialectics between Technical and Conceptual Work. International Journal of Computers for Mathematical Learning, 7 (3), 245-274.
  2. Chandler, D. (2002). Semiotics: The Basics. Oxon: Routledge.
  3. Dörfler, W. (1993). Computer Use and Views of the Mind. In C. Keitel & K. Ruthven (eds.), Learning from Computers: Mathematics, Education and Technology (pp. 159-186). Berlin: Springer-Verlag
  4. Drijvers, P. (2000). Students Encountering Obstacles Using a CAS. International Journal of Computers for Mathematical Learning, 5 (3), 189-209. doi: 10.1023/A:1009825629417
  5. Drijvers, P. & Trouche, L. (2008). From Artifacts to Instruments: A Theoretical Framework Behind the Orchestra Metaphor. In M.K. Heid & G.W. Blume (eds.), Research on Technology and the Teaching and Learning of Mathematics. Volume 2.Cases and Perspectives (pp. 363-391). Charlotte, NC: Information Age.
  6. Drijvers, P. & Gravemeijer, K. (2005). Computer Algebra as an Instrument: Examples of Algebraic Schemes. In D. Guin, K. Ruthven, L. Trouche (eds.), The Didactical Challenge of Symbolic Calculators: Turning a Computational Device into a Mathematical Instrument. (pp. 163-196). New York: Springer.
  7. Duval, R. (2001). The Cognitive Analysis of Problems of Comprehension in the Learning of Mathematics. Paper Presented at Discussion Group on Semiotics and Mathematics Education
  8. at 25th Conf of the Int. Group for the Psychology of Mathematics Education, Utrecht htp/www.math.unce.edu/%7Esae/dg3/duval.pdf
  9. Duval. R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, 61 (1-2) 103-131. doc 10.1007/s10649 006-0400-z
  10. Heid, M. K. & Blume, G.W. (2008). Technology and the Development of Algebraic Understanding In M.K Heid & G.W. Blume (eds.). Research on Technology and the Teaching and Learning of Mathematics Volume 1. Research Syntheses (pp. 55-108). Charlotte, NC: Information Age
  11. Hitt, F. & Kieran, C. (2009) Constructing Knowledge Via a Peer Interaction in a CAS Environment with Tasks Designed from a Task-Technique-Theory Perspective International Journal of Computers for Mathematical Learning, 14 (2), 121-152. doi: 10.1007/s10758-009-9151-0
  12. Hoffmann, M.H.G. (2005), Signs As Means for Discoveries. In M. Hoffmann, J. Lenhard & F Seeger (Eds.), Activity and Sign - Grounding Mathematics Education (pp. 45-56). New York: Springer.
  13. Lagrange, J. (2005) Using symbolic calculators to study mathematics: The case of tasks and techniques. The Didactical Challenge of Symbolic Calculators: Turning a Computational Device into a Mathematical Instrument (pp. 113-135), New York: Springer,
  14. Otte, M. (2006). Proof and explanation from a semiotical point of view. Revista Latinoamericana de Investigación en Matemática Educativa, Número Especial, 23-43.
  15. Peirce, CS. (1998). In Peirce Edition Project (ed.), Volume 2. The Essential Peirce, Bloomington, Indiana University Press.
  16. Pierce, R. & Stacey, K. (2004). A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems. International Journal of Computers for Mathematical Learning, 9 (1), 59-93. doi: 10.1023/B:JCO.0000038246.98119.14
  17. Radford, L. (2000). Signs and Meanings in Students' Emergent Algebraic Thinking. A Semiotic Analysis. Educational Studies in Mathematics, 42 (3), 237-268. doi: 10.1023/A 1017530828058
  18. Radford, L. (2006) The Anthropology of meaning, Educational Studies in Mathematics, 61 (1-2) 39-65
  19. Rotman, B. (1993). Ad Infinitum: The Ghost in Turing's Machine. Stanford: Stanford University Press.
  20. Sfard, A. (2000), Symbolizing Mathematical Reality into Being - or How Mathematical Discourse and Mathematical Objects Create Each Other. In P. Cobb, E. Yackel, K. McClain (Eds) Symbolizing and Communicating in Mathematics Classrooms Perspectives on Discourse Tools, and Instructional Design (pp 37-98). Mahwah, NJ: Lawrence Erlbaum
  21. Stewart, J. (2003) Single Variable Calculus (fifth edition). Belmont: Brooks/Cole
  22. Tall, D., Smith, D. & Piez, C. (2008).Technology and Calculus. In MK Heid & GW. Blume (eds.) Research on Technology and the Teaching and Learning of Mathematics Volume 1. Rеsearch Syntheses (pp. 207-258), Charlotte, NC: Information Age
  23. Trouche, L. (2005). Instrumental Genesis, Individual and Social Aspects. In D. Guin, K. Ruthven, & L. Trouche (Eds), The Didactical Challenge of Symbolic Calculators: Turning a Computacional Device into a Mathematical Instrument (pp. 197-230) Dordrecht: Kluver Academic
  24. Vygotsky , L. S. (1978). Mind in Society, M. Cole, V. John-Steiner, S. Scribner, & E. Souberman (Eds.), Cambridge, Mass Harvard University Press.
  25. Vygotsky, L. S. (1981). The Genesis of Higher Mental Functions. In J.V. Weroch (Ed.), The Concept of Activity in Soviet Psychology (pp.144-188) Armonk, NY, M.E. Sharpe
  26. Wertsch, J.V. & Stone, C.A. (1985). The Concept of Internalisation in Vygotsky's Account of the Genesis of Higher Mental Functions. In Wertsch, J.V. (Ed.), Culture, Communication and Cognition (pp. 162-179). New York: Cambridge University Press.

Descargas

Los datos de descargas todavía no están disponibles.

Artículos similares

<< < 4 5 6 7 8 9 10 11 12 13 > >> 

También puede {advancedSearchLink} para este artículo.