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On the Development of Human Representational Competence from an Evolutionary Point of View

From Episodic To Virtual Culture
Chapter
Part of the Mathematics Education Library book series (MELI, volume 30)

Abstract

Recent work by the evolutionary psychologist Merlin Donald (1991) argues that human cognition has developed across evolutionary time through a series of four distinct stages, each growing out of its predecessor and yielding its own cultural form. They began with episodic (ape-like) memory and passed through mimetic (physical-action-based), mythic (spoken), and theoretical (written) transformations. In the chapter it is argued that we are entering, via computational media, a fifth stage of cognitive development leading to a virtual culture, which will replace the writing-based theoretic culture and which will support and be supported by a new hybrid mind, just as each of the predecessor stages subsumed its prior stage (Shaffer & Kaput, in press). Additional support for this claim is provided by the recent work of Terrence Deacon (1997), who argues that the development of human linguistic competence needs to be viewed in a new way, through the co-evolution of brain and language, and where the major defining features of real human language are its embodiment of a relatively small number of recombinable (syntactical) elements and symbolic reference, features not shared by communication devices used by other species. It is suggested that the evolutionary perspective needs to complement mathematics educators’ other ways of understanding the learning and use of mathematics, especially the semiotic side of the subject. It turns out that mathematics has played a critical role in the development of both writing and computational media, each the means by which a new stage of cognition was reached. Further, our understanding of language, especially its referential nature and its relationship to brain function, has implications for how we understand the symbolic aspects of mathematics and how they may be learned. in the first part of the chapter the Merlin Donald analyses is recounted. Afterwards the co-evolution of writing and the earliest mathematics is examined, and this is followed by a description of the new stage into which we are emerging.

Keywords

Mathematics Education External Representation Computational Medium Alphabetic Writing Prior Stage 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bochner, S. (1966). The role of mathematics in the rise of science. Princeton, NJ: Princeton University Press.Google Scholar
  2. Bruner, J. (1973). Beyond the information given: Studies in the psychology of knowing. New York: W. W. Norton.Google Scholar
  3. Bruner, J. (1986). Actual minds, possible worlds. Cambridge, MA: Harvard University PressGoogle Scholar
  4. Bruner, J. (1990). Acts of meaning. Cambridge, MA: Harvard University Press.Google Scholar
  5. Bruner, J. (1996). The culture of education. Cambridge, MA: Harvard University Press.Google Scholar
  6. Cajori, F. (1929). A history of mathematical notations, Vol. 1: Notations in elementary mathematics. La Salle, IL: The Open Court Publishing Co.Google Scholar
  7. Casti, J. (1996). Would-be worlds: How simulation is changing the frontiers of science. New York: John Wiley and Sons.Google Scholar
  8. Cohen, J. and Stewart, I. (1994). The collapse of chaos: Discovering simplicity in a complex world. New York: Viking Books.Google Scholar
  9. Deacon, T. (1997). The symbolic species: The co-evolution of language and the brain. New York: W. W. Norton.Google Scholar
  10. Donald, M. (1991). Origins of the modern mind: Three stages in the evolution of culture and cognition. Cambridge, MA: Harvard University Press.Google Scholar
  11. Hall, N. (1994). Exploring chaos: A guide to the new science of disorder. New York: W. W. Norton. Harris, R. (1986). The origin of writing. London: Duckworth.Google Scholar
  12. Heim, M. (1993). The metaphysics of virtual reality. New York: Oxford University Press.Google Scholar
  13. Holland, J. H. (1995). Hidden order: How adaptation builds complexity. New York: Addison-Wesley.Google Scholar
  14. Kaput, J. (1989). Linking representations in the symbol system of algebra. In C. Kieran and S. Wagner (Eds.), A research agenda for the teaching and learning of algebra. Hillsdale, NJ: Erlbaum, pp. 167–194.Google Scholar
  15. Kaput, J. (1996). Overcoming physicality and the eternal present: Cybernetic manipulatives. In R.S.J. Mason (Ed.), Technology and visualization in mathematics education. London: Springer Verlag, pp. 161–177.Google Scholar
  16. Kauffman, S. (1995). At home in the universe: The search for the laws of self-organization and complexity. New York: Oxford.Google Scholar
  17. Klein, J. (1968). Greek mathematical thought and the origins of algebra. Cambridge, MA: MIT Press. Kline, M. (1972). Mathematical thought from ancient to modern times. New York: Oxford University Press.Google Scholar
  18. McLuhan, M. (1962). The Gutenberg Galaxy: The making of typographic man. Toronto: University of Toronto Press.Google Scholar
  19. Nelson, K. (1996). Language in cognitive development: Emergence of the mediated mind. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  20. Nemirovsky, R. (1998). How one experience becomes another. Paper presented at the InternationalGoogle Scholar
  21. Conference on Symbolizing and Modeling in Mathematics Education, Utrecht, June, 1998.Google Scholar
  22. Noss, R. and Boyles, C. (1996). Windows on mathematical meanings: Learning cultures and computers Google Scholar
  23. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
  24. Papert, S. (1980). Mindstorms: Children, computers, and powerful ideas. New York: Basic Books.Google Scholar
  25. Resnick, M. (1994). Turtles, termites, and traffic jams: Explorations in massively parallel microworlds. Cambridge, MA: MIT Press.Google Scholar
  26. Schmandt-Besserat, D. (1978). The earliest precursor of writing. Scientific American, 238.Google Scholar
  27. Schmandt-Besserat, D. (1992). Before writing: From counting to Cuneiform (Vol 1 ). Austin, TX: University of Texas Press.Google Scholar
  28. Schmandt-Besserat, D. (1994). Before numerals. Visible Language, 18.Google Scholar
  29. Shaffer, D.W., and Kaput, J. (1999). Mathematics and virtual culture: An evolutionary perspective on technology and mathematics education. Educational Studies in Mathematics, 37, pp. 97–119.CrossRefGoogle Scholar
  30. Swetz, F. (1987). Capitalism and arithmetic: The new math of the I5’ 5 Century. La Salle: Open Court.Google Scholar
  31. Turing, A.M. (1992). Mechanical intelligence. Amsterdam: Elsevier Science Pub.Google Scholar
  32. Von Neumann, J. (1966). Theory of self-reproducing automata. Urbana, IL: University of Illinois Press.Google Scholar
  33. Wilensky, U. (1991). Abstract meditations on the concrete and concrete implications for mathematics education. In I. Hard and S. Papert (Eds.), Constructionism: Research reports and essays. Norwood, NJ: Ablex, pp. 193–203.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Massachusetts-DartmouthDarthmouthUSA
  2. 2.Department of Digital MedicineHarvard Medical SchoolCambridgeUSA

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