"Programming is a tool for learning other things, and is justified as such, put not as a subject in its own right. "
Amen! and the same goes for calculus. There's no justification for learning calculus other than it enhances your ability to understand the world. So does programming. To learn programming as a detached art form, without any motivating *real* questions is futile, and - yes - the same goes for calculus. I suspect that this might be the divide between those who loved calculus in high school and those who detested it: the former saw its beauty, in its capacity to describe and explain the world, the later saw it as a chore.
Programming can provide an alternative means of explaining / describing the world, which can be more accessible to some learners. See examples: diSessa, A.A., Hoyles, C. & Noss, R. (1995) Computers and Exploratory Learning (Heidelberg, Springer-Verlag). Hoyles, C. & Noss, R. (1996) Windows on Mathematical meaning:Learning Cultures and Computers (Dordrecht, Kluwer). diSessa: Turtle Geometry (sorry, don't have the reference on me)
And, from a very different perspective, Wolfram, S. (2002) A new kind of science (Champaign, Ill, Wolfram Media).
We (at the WebLabs project) use programming in ToonTalk and Lego RCX's as means for discussing number sequences, convergence, randomness, kinematics and more. We see children manipulating mathematical concepts way beyond their curriculum. I've just given a talk at the CSCL SIG Symposium in Lausanne on one reason why I think programming is a valuable alternative to other representations of mathematics (say, algebra). I'll send a link as soon as I put it on the web.
Oh, and there's one more advantage programming has over calculus: its easier.
I think there's an underlying deep question here, about what should be taught at school and why. My belief is that there is no difference between programming, maths, art and history. All should be taught iff they provide an instrument for understand the world, and enable learners to be fuller and happier beings. If you teach the most fundamental subject "for itself" it leaves the learners' brain a millisecond after the last exam, without leaving a trace. I have a university degree in maths, do you think I can tell you the derivative of sin(x^2)?
best,
- Yishay
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