NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/sci/math/17503

Internet Message Format | 1992-12-30 | 3.0 KB

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From: [e-mail] (Herman Rubin)
Subject: Re: Education crisis (was RE: how much math...)
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Date: Wed, 30 Dec 1992 13:52:48 GMT
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In article <[e-mail]> [e-mail] (Keith F. Lynch) writes:
>In article <[e-mail]> [e-mail] (Dan Prener) writes:
>> Little kids learn much faster. ...
>> But the fact that little kids' learning capacity is so much greater
>> than that of older people ...

>Is there any evidence for this?  It goes against my experience.

There is evidence on both sides of this.  It was claimed that children
can learn a language must faster than adults.  It does seem the case
that adults rarely learn to pronounce the way children learn, and there
is some evidence, including brain activity evidence, that children
acquire grammar at least differently than adults.  On the other hand,
an adult taking a strongly grammar-based foreign language course will
get a considerably larger vocabulary in one year than the vocabulary
of an eight-year-old.  But much of this may come from the type of
analysis which the adult can make due to experience, but the child
cannot.  It is also possible that the current teaching methods, which
concentrate on memorizing definitions, contributes to not thinking in
the new language.

For mathematical concepts, we do have the observation that the current
teachers cannot learn what the children can learn.  My own opinion, based
on observations of students from sophomores to PhD students, is that the
learning of methods, excessive formalism, and special cases interferes
with the learning of concepts.  Again, memorizing the definitions, and
even memorizing proofs, does not teach the concepts; they are learned
only when they can be used in new situations.  I believe that children
in the early grades, even first grade, can learn the use of variables
and the structure of the integers.  Success at teaching this seems to
deteriorate rapidly, although there may be adverse selection after the
high school algebra course.

Both in languages, including computer languages, and in mathematics,
understanding the structure can facilitate learning the details, and
acquiring proficiency in their use.  I am not convinced that going the
other way is even that common, although it is essential for good original
research.
--
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
Phone: [phone]
[e-mail] (Internet, bitnet)
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