In article <ds69e5-3sn.ln1@[EMAIL PROTECTED]
>, Penny Gaines <penny@[EMAIL PROTECTED]
>
wrote:
>Banty wrote:
>[snip]
>> I haven't read the article, but I suspect it's not invoking real world
examples
>> that have hobbled math education. Rather, it's the reliance on
expressing math
>> oin *verbal* terms in the kind of examples that elementary schools have
favored
>> lately (see many threads in misc.kids about that).
>There seems to be a fuller press release here:
>http://www.eurekalert.org/pub_releases/2008-04/osu-ced042108.php
>It says that teaching *college* students with abstract examples enabled
>them to grasp the underlying maths more easily then when they learnt a
>system using concrete examples.
>The NYT article also discussed some experiments with 11yo children
>(which aren't in the press release).
>I don't think that you can necessatily extrapolate further to children
>of the age to be using ths Everyday maths, which seems to be
>Kindergarten to Grade 6.
>--
>Penny Gaines
>UK mum to three
From my experience with my children, and also from seeing
what happens to college students, including PhD students
in mathematics and statistics, the biggest problem with
starting with concrete examples and special cases is that
the excess baggage from the special cases is hard to
discard. This also holds for people with my abilities.
Children can understand abstract ideas, up to a reasonable
level of complexity. Much of mathematics has ideas which
are not that complex, and are much simpler than what is
now taught. The axioms for the development of the integers,
especially the ordinal ones which are complete, are much
simpler than the use of decimal notation. The complete
rules for formal logic can be done on a couple of pages.
The use of symbols for entities, the key part of algebra,
can be taught with beginning reading; the entities can
be anything, including words and phrases.
As the children grow older, and get taught mainly by
memorization and routine, this ability gets smothered,
and it is difficult to reawaken later.
Children understand abstract ideas; it is worse than
pulling teeth to try to get this though the heads of
most adults. Getting it by just being shown examples
requires research ability.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@[EMAIL PROTECTED]
Phone: (765)494-6054 FAX: (765)494-0558
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