Re: Is there really that big of a change in high school geometry teaching in the past 15 years?

In article <48782$4915faa8$626186e6$29476@xxxxxxxxxxxxxxxxxx>,
rabbits77 <rabbits77@xxxxxxxxxxx> wrote:
Dave L. Renfro wrote:

.................

In recent years, with the rise of discussion groups (and later,
the rise of the internet), we can even find the same phenomenon
being played out there, as the following post from roughly your
HS era shows.

[snipped]

Wow! Very interesting and enlightening!
Thanks for replying.
I wonder if there is some single way to settle all these
"methods" arguments. That is, if it were possible to demonstrate(or not)
that students are still, in the end, learning the material.
But this may lead to a standardized testing discussion which again gets
people all worked up.

The current emphasis in the geometry course, as in other
courses, is in memorizing the facts, and learning how to
do calculations. This is readily lost, and also, unless
the student is really bright and lucky, does not lead to
any insight. In mathematics, proof is what is required.

For those who will not need to prove theorems in the future,
what is needed is understanding of the concepts, including
that to know something in mathematics is to have a proof.
Facts and methods of calculation can be looked up; concepts
need to be internalized.

The change did not take place in the last 15 years, but in
the 40 years before, and quickly. Understanding concepts
and being able to produce unseen proofs cannot be tested
by "objective" tests, to which, as you see, I object.

A large proportion of the high school teachers of mathematics
do not understand, but have just learned facts and methods.
Even those who have learned more just present the above.

Teaching what and how, without the why first, makes it
difficulty to learn the why. Most of the current teachers
seem unable to understand what should be required of all
who even consider going to college.

If one does not understand induction, one does not understand
the positive or non-negative integers. Try it on the teachers.
--
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@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.

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