Abstract
Historically, the logico-rational mode of argumentation co-evolved with particular mathematical systems and particular geometrically informed manners of interpreting experience and perception. Davis examines some of the ways these geometries continue to shape the sensibilities, practices, and structures of much of educational discourse, in spite of the well-developed critiques of their associated logics. He then compares manufactured living environments with those of other cultures, drawing on fractal geometry to highlight a complementary mode of organizing cultural spaces. Davis develops the suggestions that (1) the available logics are associated with the available geometries of one’s living spaces and (2) fractal geometry is a mathematical analogue to such discourse fields as postmodernism, poststructuralism, and ecological theory.
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References
Aoki, D. S. (2000). The thing never speaks for itself: Lacan and the pedagogical politics of clarity. Harvard Educational Review, 70, 347–369.
Bastien, B. (2004). Blackfoot ways of knowing: The worldview of the Siksikaitsitapi. Calgary, AB: University of Calgary Press.
Borgmann, A. (1993). Crossing the postmodern divide. Chicago: University of Chicago Press.
Calvin, W. (1996). How brains think: Evolving intelligence, then and now. New York: Basic Books.
Capra, F. (1996). The web of life: A new scientific understanding of living systems. New York: Anchor Books.
Chapman, R. L. (Ed.). (1977). Roget’s international thesaurus (4th ed.). Toronto: Fitzhenry & Whiteside.
Chen, C., & Paul, R. J. (2001). Visualizing a knowledge domain’s intellectual structure. IEEE, 34, 65–71.
Cohen, J., & Stewart, I. (1994). The collapse of chaos: Discovering simplicity in a complex world. New York: Viking.
Davis, B., Sumara, D., & Luce-Kapler, R. (2015). Engaging minds: Cultures of education and practices of teaching (3rd ed.). New York: Routledge.
Derrida, J. (1980). Writing and difference (A. Bass, Trans.). Chicago: University of Chicago Press.
Dewdney, S. (1975). The sacred scrolls of the Southern Ojibway. Toronto: University of Toronto Press.
Eglash, R. (1999). African fractals: Modern computing and Indigenous design. New Brunswick, NJ: Rutgers University Press.
Eglash, R. (2003). Computation, complexity and coding in Native American knowledge systems. In J. Hankes & G. Fast (Eds.), Changing the faces of mathematics: Perspectives on indigenous people of North America (pp. 251–262). Reston, VA: National Council of Teachers of Mathematics.
Ehrlich, P. R. (2000). Human natures: Genes, cultures, and the human prospect. New York: Penguin.
Foucault, M. (1990). The history of sexuality: An introduction. New York: Vintage.
Gardner, M. (1976). In which ‘monster’ curves force redefinition of the word ‘curve’. Scientific American, 235(December), 124–129.
Gleick, J. (1987). Chaos: Making a new science. New York: Penguin.
Hoffman, D. D. (1998). Visual intelligence: How we create what we see. New York: W.W. Norton.
Irigaray, L. (1991). The Irigaray reader (M. Whitford, Ed.). Cambridge: Basil Blackwell.
Johnson, S. (2001). Emergence: The connected lives of ants, brains, cities, and software. New York: Scribner.
Kelly, K. (2010). What technology wants. New York: Penguin.
Kuhn, T. (1962). The structure of scientific revolutions. Chicago: University of Chicago Press.
Laplace, P. (1795/1951). A philosophical essay on probabilities. New York: Dover.
Lather, P. (1996). Troubling clarity: The politics of accessible language. Harvard Educational Review, 66, 525–545.
Latour, B. (1996). On interobjectivity. Mind, Culture, and Activity, 3(4), 228–245.
Lyotard, J.-F. (1984). The postmodern condition: A report on knowledge. Minneapolis: Minnesota Press.
Mandelbrot, B. (1977). Fractal geometry of nature. New York: W. H. Freeman.
Maturana, H. (1987). Everything said is said by an observer. In W. I. Thompson (Ed.), Gaia: A way of knowing (pp. 65–82). Hudson, NY: Lindisfarne Press.
Mitchell, M. (2009). Complexity: A guided tour. Oxford: Oxford University Press.
Popper, K. (1959). The logic of scientific discovery. London: Hutchinson.
Rorty, R. (1999). Philosophy and social hope. Toronto: Penguin.
Stewart, I. (1989). Does God play dice? Cambridge, MA: Blackwell.
Stewart, I. (1998). Life’s other secret: The new mathematics of the living world. New York: Wiley.
Stewart, I., & Cohen, J. (1997). Figments of reality: The evolution of the curious mind. Cambridge: Cambridge University Press.
Varela, F., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA: MIT Press.
Von Foerster, H. (1995). Metaphysics of an experimental epistemologist. In R. Moreno-Diaz & J. Mira-Mina (Eds.), Brain processes: Theories and models. Cambridge, MA: MIT Press.
Weaver, W. (1948). Science and complexity. American Scientist, 32, 536–544.
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Davis, B. (2018). Shaped by the Places We Reason? Contrasting the Rectilinearity of Western Educational Thought with Other Possibilities. In: Gerofsky, S. (eds) Contemporary Environmental and Mathematics Education Modelling Using New Geometric Approaches. Palgrave Pivot, Cham. https://doi.org/10.1007/978-3-319-72523-9_2
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