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Topic: Perils of Modern Math Education
Replies: 19   Last Post: Jun 21, 2007 8:44 PM

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Dave L. Renfro

Posts: 4,792
Registered: 12/3/04
Re: Perils of Modern Math Education
Posted: Jun 20, 2007 11:53 AM
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Domenico Rosa wrote (in part):

> Richard, I was never taught the square root
> algorithm, and I have never taught interpolation.

Interesting. I think our teacher (algebra 1, 1973-74)
showed a square root algorithm to us in class, but
we didn't have to learn it. We just used the tables
at the back of the book. Of course, the better
students (top 5% of my graduating class) knew it,
as this was one of those things that all the school
nerds knew (along with the then 9 planets in order
from the sun, the nearest star, the fact that U-235
and not U-238 was used in atomic bombs, etc.).

On the other hand, interpolation was an instrumental
part of trigonometry when I was in high school,
and we covered logarithms before trigonometry so
that we would know how to use the logarithm tables.
As for *teaching* interpolation, I did this in
the first class I ever taught entirely on my own,
a trigonometry class at Indiana University in the
summer of 1983. Students had calculators, and we
often used them, but on the tests and quizzes
I required not only hand computations for a few
applied problems, but I also required that everything
done on those select problems by interpolating
the tables (i.e. do everything to one more decimal
place "accuracy" than were the values listed
in the tables). I told the students the they
would still need to (at that time) interpolate
tables of values that calculators didn't have.
(I think I mentioned statistical tables a lot.)
However, the next time I taught a trig. class,
Fall 1984, I didn't teach interpolation. In fact,
I've never required students to use interpolation
on tests since then, but I did sometimes explain
what interpolation was, as an interesting historical
detour in trig. classed or as an application of
linear approximation in calculus 1 classes.

Interestingly, I didn't get much, if any, protest
from the 1983 trig. students, as long as I gave them
plenty of time. I think many of them were simply
glad to be doing something that they knew they
could do, even if it was a bit tedious, than trying
to figure out how to prove nasty trig. identities
and stuff (which, of course, I also covered).

Dave L. Renfro

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