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Topic: "more than half of the world's "
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Ted Alper

Posts: 51
Registered: 12/6/04
"more than half of the world's "
Posted: Jun 24, 1995 2:57 AM
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Bruce Braley wrote:
> ..... I've heard that over half the mathematical
> knowledge that exists was developed after WWII.


Of course, in some sense it's a meaningless statement (what does
"half" mean in this context? One part of thinking mathematically is to
be always alert to fuzzy uses of numeric concepts -- not that they are
always bad, but one must be wary of arguments in which they are used).
The usual justification for the statement is something like the number
of pages of math published in research journals, or the number of
theorems stated. It's a useful exercise to think of all the factors
that could distort such measures, from the increasing redundancy of
modern research to the smaller page size in modern journals.

Even more importantly, it isn't clear that the increase in
mathematical knowledge of the last 50 years itself justifies ANY
change in mathematics education. The new knowledge rests upon the
same foundations as the old knowledge. A student with the best 19th
century education (and perhaps a quick update on modern notation and
the advantages of computers) would be starting from a better position
to understand high-level modern math than a student with an average
1990s education.

Changes in mathematics education should be justified on specific
changes in educational needs or specific pedagogical advantages to
be gained through the use of technology, not on some vague idea
that older skills are no longer needed because they are old.

Ted Alper
alper@epgy.stanford.edu






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