Re: The state of education in the USA.

Robert Grumbine wrote:

In article
<ddb839e3-e5c3-4e32-92d1-8c331c0051c1@xxxxxxxxxxxxxxxxxxxxxxxxxx>,
tgdenning@xxxxxxxxxxxxx wrote:
On Apr 4, 10:59 pm, Tim Norfolk <timsn...@xxxxxxx> wrote:
On Apr 4, 3:54 pm, tgdenn...@xxxxxxxxxxxxx wrote:

On Apr 4, 1:21 pm, Tim Norfolk <timsn...@xxxxxxx> wrote:

On Apr 4, 11:21?am, tgdenn...@xxxxxxxxxxxxx wrote:

[trim]

See the above. Without a lot of rote knowledge of basic arithmetic,
algebra becomes hard to follow, no matter what technology is used. In
that case, the underlying ideas of variables and functions become
meaningless, and inapplicable. There is some good evidence that, if
the abstract process engendered by learning algebra (see Piaget) is
not accomplished by a certain age, it will never be acquired. This is
similar to the tragic cases of humans who have never been exposed to
speech by age 8 or so, and do not have the brain connections that make
speech possible - ever.

The mathematical education community awaits your great expertise and
wisdom, but consider the following

1. Mathematics is the only subject to have been consistently taught
for about 2,500 years
2. In mathemaqtics, that which doesn't work is tossed onto the trash
heap, or given only a passing reference as a failed idea, or one
supplanted
3. Euclid's answer to King Ptolemy, who was bored by his lessons
"There is no royal road to geometry (mathematics)".

In short, I have yet to see one single innovation in mathematics
education that left students better prepared for further study. If you
have, let's see your evidence. From my experience, it takes properly-
prepared students with a willingness to work harder than in the non-
science disciplines. If you honestly have the magic bullet, you could
get a bunch of money from Bill Gates, and pretty much every major
corporation, since  most post-graduate management programs include a
screening test of 8th-grade mathematics.

[trim]

Most people I've had this discussion with who take your position end
up using some version of the same logical fallacy as you do---although
you seem to have thrown in some strawmen along with the traditional
question-begging.

Everything you've said relies on *defining* success as doing the
little rote manipulations and performing the little rote algorithms
that you've been doing and teaching for 30 years. What you've ignored
is that people who *use* mathematics as a tool to develop all the
wonderful tech that you describe (scientists and engineers) use
software to solve their math problems. There's nothing in the courses
you define as 'advanced' and 'abstract' that can't be done with
Mathematica or something similar.

Unfortunately, the 'win by definition' approach is yours. Not least,
you've declared what the other people are doing without really listening.

You've been given the longer answer with illustration and reference
from much experience. Here's the shorter (necessarily overgeneral):

People who can't do arithmetic with pen and paper can't
do it with a calculator either.

I was shocked to see this happen, but it did as I gave my college
astronomy students (as Tim has mentioned) a grade 8 (what used to
be) math test. Students who could get the answer by pen and paper may
or may not have used the calculators. Students who were trying only
the calculators missed almost everything.

You might think, and I used to until I saw the reality, that people
don't need to know the arithmetic themselves -- they only need to know
which keys to press. But, you're simply wrong. As Tim mentioned
about the 2500 years of experience, there really is some background
to say that certain things are needed to learn mathematics.

My son, who is currently teaching high school math in Manhattan and is
somewhat frustrated at the lack of interest of his students, gave me the
book The Math Gene for Christmas. The book is unfortunately largely about
The Language Gene (we are of course here really talking about multiple
genes), but does make some interesting points. One of these is that people
who are good at math tend to think about numbers as friends. This seems to
be true for me - I can more easily remember unit conversion factors than
people's names. A corollary is that a calculator will only get you deeper
into trouble quicker if you don't have a feel for the numbers (this is like
my new Taylormade golf driver - I can now hit the ball 20 yards deeper into
the woods).

--
Yours, Bill Morse

.

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