
Re: Algebraic Manipulation
Posted:
Jan 19, 1999 11:12 AM


Thought experiment: If a typical subscriber to calcreform completely forgot long division algorithm, how long would it take him/her to learn it very well?
Since the answer is 'not long', we are talking not so much about teaching long division algorithm itself (or any other algorithm or "piece" of mathematics) but more about teaching what can be called "general mathematical development". And I can see that practicing that algorithm contributes to arithmetical development of students through, for example, "how many 14's is there in 88?"
But I wouldn't go as far as to say that we have to teach long division. Although basic efficiency in mental arithmetic is needed, it can be achieved in many ways (for example by playing games), not necessarily through practicing long division. More, some weak students may resent being forced to struggle so hard with something what they can do so easily on calculator and the educational effect would be lost.
The long division algorithm is only one example here. In general, algorithms can be performed by computers and they should be taught to people only to the extent that they help develop conceptual understanding, help develop "sense for something" (like "number sense"). And we should not forget that even if such algorithms do help, they may still be not the best help available. And I would guess that one of the jobs of reformers is to look for better ways.
Kazimierz Wiesak

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