First, here is a famous excerpt from Seymour Papert's seminal book Mindstorms. In the preface Papert introduces the idea of body knowledge in a story about his childhood fascination with a set of gears. He says:
“Piaget’s work gave me a new framework for looking at the gears of my childhood. The gear can be used to illustrate many powerful ‘advanced’ mathematical ideas, such as groups or relative motion. But it does more than this. As well as connecting with the formal knowledge of mathematics, it also connects with the ‘body knowledge,’ the sensormotor schemata of a child. You can be the gear, you can understand how it turns by projecting yourself into its place and turning with it. It is this double relationship—both abstract and sensory—that gives the gear the power to carry powerful mathematics into the mind.”
My question is around this idea of 'body knowledge.' It seems Papert uses that phrase to mean that body experience in the world can, at a later time, be brought to bear on understanding mathematical ideas. His Logo geometry (which used a programmable object called a turtle) is said to be something you can “walk” through. From my perspective, programming a moving object is not actual walking or actual movement; it is, like Papert mentioned in his gears story, a projected walking—projecting body knowledge into the object itself.
Here's my question:
When thinking about the body's role in math learning, I wonder if Papert ever considered the inverse to such a process, specifically, how a body might participate in actively creating body knowledge of mathematics. The double relationship he mentions ("both abstract and sensory") seems to relate only to the sensory memory, not to the using the senses in the moment.
Any thoughts will be incredibly helpful. If I'm barking up the wrong tree, tell me. If you want me to clarify anything, let me know.
Thanks in advance. (Edit 12/9/13 -- check out the comments!!)