Below is an excerpt from an interview with Dr Seymour Papert by the staff at Edutopia. I figured I wouldn’t forget it if I pasted it on my blog.
If you know the history, this is the way that mathematics happened: It started not as this beautiful, pure product of the abstract mind. It started as a way of thinking about controlling the waters of the Nile, building the Pyramids, sailing a ship. It started as mathematical thinking, just edging into real activities, what was really being used. And then, gradually, it got richer and richer and finally the jewel of the human mind — I’m a mathematician, I really think that it is the jewel of the human mind — gets broken off as pure mathematics.
In school, we reverse that process. We start off teaching pure math. Nothing is more pure in abstract mathematics than the stuff we teach in elementary schools. And it has to be if you’re going to have such a thing as the “mathematics classroom.” Because as soon as you have this other thing, it doesn’t fit into a “mathematics classroom” or “mathematics lesson.” I think we have to reverse this order of things — that the order in which we teach mathematics and science today starts with the most abstract, the most static, and you learn to do manipulation of numbers, then you learn to do algebra, then you learn to do calculus, and at last you can apply it to something real.
I want to turn that around. We’re going to start with applying it to something very real. So, I look for activities like — here again, I’ll use this example again — it’s just one of many, though: Building these robotic devices but putting mathematical principles into the way you build them. So that you’re doing physics and mathematics and engineering and project design all in one go, but your content is not what is usually considered to be age-appropriate in that way.