Re: The state of education in the USA.

In article <96f5293a-fdfa-45c2-b75b-5531b7ea675c@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, tgdenning@xxxxxxxxxxxxx wrote:
On Apr 8, 10:23 am, Robert Grumbine <b...@xxxxxxxxxxxxxxxxxx> wrote:
In article <ddb839e3-e5c3-4e32-92d1-8c331c005...@xxxxxxxxxxxxxxxxxxxxxxxxxx>, tgdenn...@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.


My initial comments in this thread were prompted by what I consider
vague and poorly thought out assertions. I would be happy to listen to
some concrete examples, but even your specific anecdote doesn't tell
me very much at all.

Hmm. I've missed the posts where you presented your research on
the topic that supports your position. Or anybody else's research.
Or even a decent anecdote that the engineers you expect to be relying
solely on software actually _cannot_ do the elementary math the software
is doing for them when they do use the software.

If your vague and poorly thought out assertions are to be treated
with respect, as you seem to believe, you should accord others the
same.


I think what you are trying to describe (since that's the only way you
would have the information) are students who either 'show the work' or
those who don't. I really don't see how you draw any conclusion about
pushing buttons and calculators, since I have certainly seen students
who suffered from not writing down the work even when there were no
calculators involved.

Perhaps you could be more explicit about the problems you gave them if
you wish to support your contention.

Really quite simple. I had the students add, subtract, multiply, and
divide small integers, fractions, and decimals. The students who could
do so successfully (4, vs 20ish who turned in disasters) didn't reach
for calculators. Not a matter of what work they showed, there isn't
much that _could_ be showed for 6 * 9 = ? Most striking to me about
the innumeracy was the raft of students who gave the same answer (wrong
for both questions) to
1/2 + 1/4 = ?
1/2 - 1/4 = ?

Even without knowing much math at all, much less to be able to work
with fractions, it _should_ have struck them that in the second question
they were subtracting a number rather than adding one and should get a
smaller number for their answer; even if they couldn't figure correct
answers, they should at least have gotten different ones.

It was also striking to me the number of calculator users (attempted
at least) who did not know how to turn on their calculator. Or, once
on, to use it to add, subtract, multiply, or divide. It's _their_
calculator, not one that I gave them. (I turned it on for them and
showed them how to multiply or whatever their first usage question was.)

This was a college science class, and did have a college algebra
pre-requisite.

So, no, if people can't do the arithmetic by hand, they generally
can't by calculator either. If you have evidence to support otherwise,
do present it.


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