In article <email@example.com>, Herman Rubin <firstname.lastname@example.org> wrote:
> Computers can do things which they have beeen programmed to do > and nothing more. I have found that it can be somewhat unwise > to trust computer programs too much.
Not just "somewhat unwise", but 100% unwise. I say this as a computer programmer. The software represents nothing more than an implementation of an algorithm. The *intent* of the system is most often a very different thing! From a scientific perspective, the only way we can verify the correctness of the system is have that intent at a higher level of abstraction. The computer can't do that sort of thinking for you.
> As for what should be learned, memorization is useually a poor > way to learn anything, and might leave out alternatives. I would > expect a child to learn how to construct addition from counting, > and multiplication from addition, and to produce the tables for > himself or herself. This would also provide a quick means of > filling in a forgotten value.
Exactly. If the child does nothing more than memorize a table of values, their understanding of mathematics is not advancing. We (should) have kids learn tables because knowing them by heart allows us to more rapidly do more complex problem solving in the future. Computers (should) come in to do the heavy lifting not because we *can't*, but because we want to advance to a higher level of abstraction.
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