Curriculum forms: on the assumed shapes of knowing and knowledge
Historically, the logico-rational mode of argumentation co-evolved with particular mathematical systems and particular geometrically-informed manners of interpreting experience and perception. We examine some of the ways these geometries continue to shape the sensibilities, practices and structures of much of curriculum discourse, in spite of the well-developed critiques of their associated logics. We draw on fractal geometry, a new field of mathematical study, to illustrate the pervasiveness and the constraining tendencies of classical geometries. We develop the suggestion that fractal geometry is a mathematical analogue to such discourse fields as post-modernism, post-structuralism and ecological theory. We attempt to show how, through the visual metaphor of a fractal image, conventional theories of knowing and knowledge might be seen as not only compatible, but as nested in and suggestive of one another. We briefly examine how fractal geometry can complement and inform other emergent sensibilities in curriculum, in particular, those discussions critical of the linear structures associated with classical logic.