Topology and Abstraction

Wednesday, October 19th, 2005

One of the most difficult elements of learning (and teaching) is abstraction. The real down and dirty knowledge stuff is typically abstract material, whether it be related to numbers or relations. I’ve noticed this in children. Ask five year olds to think back to the year 1976 and typically they wont know what you’re after because they haven’t yet objectified the notion of time, not to mention the idea of relating time to someone else in symbolic terms where time T is related to an already abstracted set of notions such as pi times the square root of string length L divided by gravity as represented by G.

Abstraction then. A map is an abstracted view of a complex set of relations. I’ve noticed that S (my son Sam) is much taken by the old Cole and Degan magic school bus books, where a bus takes children into a hurricane and other assorted tough messes for the sake of hands on learning. These are not easy books to read to children because of the numerous topological elements in the texts. There’s typically a brief narrative element that forms the core adventure story as well as a collection of lists, dialogue bubbles, illustrative graphics, and other sundries.

But what has helped my son to read magic school-bus like books–books with complex layouts and cognitive demands–is his experience fiddling with digital games whose topological elements demand some amount of abstract thinking and spatial analysis. For example, Kya, Dark Lineage provides the player with multiple way of figuring the space of the game: a 3-D environment, a one-dimensional map, and a two-dimensional representation of Kya’s world. In other words, to figure out where you are in the game, you can access the map. Reading the digital space serves to reinforce all kinds of neat skills in children.

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