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Re: Concepts vs. Algorithms
Posted:
Jul 9, 1995 7:47 PM


Norm:
I think we have very little difference here. We are almost circling here, so I will try to reply following Annie's rule.
I have no problem with the importance of real life situation, as you have no problem with the algorithm. In most cases, they can help each other grows. Agree? I think both are equally important. I just feel a little worried that the shift toward too much of "practical number sense" (which you seems to insist is the only number concept!) is a over correction. Two points follow:
(1) To get a complete understanding of the math ( pure and applied ) concepts and algorithms, both approach should be equally weighted. Has it occured to you that there are many "algorithms" in the applied side ( real life problems ) that many here identify them as concepts? like how to identify the key informations, how to translate the human language into math language.. etc. The same, the algorithms and concepts in applied side general grow together. (2) There are students who develop abtract number sense much earlier than their practical number sense, that does not mean they don't have math concepts.
In summary, to my opinion, there are pure math and applied math, and each of them have algorithms and concepts. In general, each of them can help the development of others, and they are equally important. For students who have unbalanced growth of these abilities, teacher should use their strength to help them develop other parts. But sometimes, it is very individualized especially for some very talented kids. One should not conclude that the kids is only an algorithm machine just because their practical number sense develop slower. Similarly for kids with strength in practical sense but slower in abstract number sense, we can help, but sometimes we just have to be patient, with constant encouragement and appreciation toward their talent.
ChiTien



