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Topic: "Chi-Tien Hsu" dissertation
Replies: 1   Last Post: Jun 24, 1995 5:16 AM

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Eileen Schoaff

Posts: 39
Registered: 12/3/04
"Chi-Tien Hsu" dissertation
Posted: Jun 23, 1995 11:05 PM
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While it may be good to contact engineers, scientists, economists, etc.
about what mathematics students need to enter these professions, we
would then be preparing students to enter these professions in 1995,
not 2010. Engineers, scientists, etc. have no idea what mathematics
their professions may need in the future -- any more that we mathematicians
do. And the mathematics examples they give will be in the form of
the types of problems they solve.

Many of us do understand the algorithms involved in computer software.
Technology empowers students to explore and learn, it does not do the work
for them. A computer is like a vacuum cleaner. You can turn it on and
it sits there. It doesn't do anything unless you push it.

What makes you think that the old way of teaching mathematics worked?
How many people remember how to find the square root using the algorithm
where you put bars over two digits, then after taking the square root of
the first group, you did this weird division where you put a number in
the answer and at the end of the divisor. Of those of you who remember
the algorithm, how many can explain why it works? Just because you
can proficiently apply a memorized algorithm does not mean you know
what you are doing. Actually asking students to guess at a square root,
square their guess, then correct their guess and check again, is a much\
better algorithm because students can understand why it works and its
relationship to the meaning of square root.

When students construct their own algorithm, they have constructed their
own knowledge. They have not just learned X, they learned how to learn.
Hopefully, humans will continue to learn all their lives, including
learning new math.

If all math done had to be tied to some practical purpose, then all the
neat new stuff would never have been discovered. I'd miss fractals,
knot theory, and other interesting ideas. Why even think about primes?
Are they used in engineering or science? (Probably, but off the cuff
I can't think of where.) Math is beautiful, why make it redundant and
Eileen Schoaff
Buffalo State College
I love discrete mathematics! Especially solving recurrence relations.
Now how practical is that? I also love geometry software. My math
ed students have also discovered that geometry is exciting and beautiful.
Have even had students discover new theorems. Beat that will an
algorithm. (Should be "Beat that with an algorithm." I have a louse editor.)

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