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Can Math Be Taught?
Posted:
Oct 14, 2002 3:09 PM
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I have two days vacation, so
Can math be taught?
The short answer is 'not really'. A long answer depends on what one means
by "math" and "taught", or even by "can".
How can you teach what natural number is? Sure, you can show fingers, or
sticks, and hope for the best. But could you teach what number is? Learning
is an interaction between the brain and the environment. One can show a lot
of "units" lying around but if the brain does not come up with the concept
of number, what can one do? Fortunately, all humans discover the concept of
natural number. But my point should be clear. The most essential concepts
and, what we call 'mathematical sense', are close to impossible to
teach. What we can teach are secondary rules and procedures that result
from those basic ideas.
I would compare mathematics to dancing. One can teach the steps of dance X
or dance Y. But knowing the steps and dancing well are two different
things. There is much more to dancing than knowing the steps. And there is
much more to mathematics than knowing definitions or algorithms. I'll give
an example. A new guy came and made an exam that required some
"mathematical virtuoso". The result: 25% of students got As and 25% got
complete Fs. If the questions had been "repeat steps of dance X" then many
could have done it, but dancing (i.e. showing mathematical sense)? That's
too much.
Kaz
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