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I like this bit: "In the LOGO environment new ideas are often acquired as a means of satisfying a personal need to do something one could not do before. In a traditional school setting, the beginning student encounters the notion of variable in little problems such as: 5 + X = 8. What is X? Few children see this as a personally relevant problem, and even fewer experience the method of solution as a source of power. They are right. In the context of, their lives, they can't do much with it. In the LOGO encounter, the situation is very much different. Here the child has a personal need: To make a spiral. In this context the idea of a variable is a source of personal power, power to do something desired but inaccessible without this idea. Of course, many children who encounter the not~ion of variable in a traditional setting do learn to use it effectively. But it seldom conveys a sense of "mathpower," not even to the mathematically best and brightest. And this is the point of greatest contrast between an encounter with the idea of variables in the traditional school and in the LOGO environment. In LOGO, the concept empowers the child, and the child experiences what it is like for mathematics to enable whole cultures to do what no one could do before."

This book is way up there on my list to read! And I really should, because I probably don't agree with everything, but I probably also know nothing.

Rant follows:

I went home from school every day seeing an application in my own projects for everything I learnt, from mathematics to history, because I could include it in my software projects, or table top related games, so the text reminded me of teenager's typical complaints regarding learning mathematics.

Kids say that they don't need mathematics because it has no application in the real world, but if kids were qualified to make that comment, then they should be out working from a very young age, to gain real world experience.

"5 + X = 8" represents abstract thought, which kids find challenging, and teenagers don't like to be challenged, whereas, when kids start to read and write, they love being challenged, and yet, they comfortably learn a tool which also represents abstract thought.

I think teenagers are just learning to be sufficiently lazy and pragmatic, but that they aren't qualified to know how to stretch their brains in the long term.

Teaching math in the absence of its applications is the problem. Algebra and calculus seem pointless when you don’t know why you’d really use it beyond simple word problems on exams. Given an interesting reason and purpose to use math would probably improve learning a lot. Having a class called math is maybe not the best place to learn math, maybe they should learn it in physics instead.

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