April 18, 2012
“I have noted elsewhere (Papert, 1996b), that School’s math can be characterized by the fact that its typical act is making marks on paper. Explorations in the Space of Mathematics Education develops this idea by imagining an alternative mathematical education in which the typical activity begins with and consists of creating, modifying, or controlling dynamic computational objects. In this context the parabola may be first encountered by a child creating a videogame as the trajectory of an animal’s leap or a missile’s flight; here, the natural first formalism for the parabola is an expression in a child-appropriate computational language of something like “the path followed when horizontal speed and vertical acceleration are both constant.”
Many readers will say that is too abstract for children. This is because they have in mind children who grew up using the static medium of pencil and paper as the primary medium for representing mathematical ideas. Attempts to inject this treatment of the parabola as an isolated innovation into an otherwise unchanged School will confirm their negative view.
For children who have acquired true computational fluency by growing up with the dynamic medium as a primary representation for mathematical thinking, I argue that it would plausibly be more concrete, more intuitive, and far more motivating than quadratic equations. My experiments support this expectation by showing that the dynamic definition is indeed accessible even to elementary school children who are given the opportunity to acquire a degree of computational fluency that is still very limited though considerably more than a few students develop in what are misleadingly called computer labs in contemporary schools.”
Papert, S. (1995). Why School Reform is Impossible. The Journal of the Learning Sciences, 6(4), pp. 417-427.