Re: The state of education in the USA.

On Apr 14, 12:55 pm, Robert Grumbine <b...@xxxxxxxxxxxxxxxxxx> wrote:
In article <d51970f7-97a1-452a-a15b-e71fde61b...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, tgdenn...@xxxxxxxxxxxxx wrote:> On Apr 11, 11:35 am, Robert Grumbine <b...@xxxxxxxxxxxxxxxxxx> wrote:
In article <96f5293a-fdfa-45c2-b75b-5531b7ea6...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, tgdenn...@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]



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.

Sorry, this is the kind of thing that sets me off, as did Tim's
complaints that students at an open enrollment institution aren't well
prepared. Duh. *Your* students somehow passed the college algebra
class with one of *your* colleagues, apparently without the ability to
add subtract multiply and divide, or turn on their calculators.
What's up with that?  Why don't you march down to the registrar and
throw the class list in his/her face? Or call out your math
department? What do calculators or whatever the latest excuse is have
to do with the behavior at your institution?

  I wondered how you were going to avoid the point.

  Anyhow, just what should I have complained about, in your view?  
The students, I have no doubt, knew enough 'math' to pass their
courses for each of the previous 14 years.  The ones from that area
also had passed a state test for basic competency in math, among
other things.  All this is perfectly consistent with what you have
been arguing for.  _My_ sort of concern about competence has been
totally absent from your posts.  Indeed you've been explicit that
my concern is part of what's 'holding back' math education.

  As I mentioned, and you didn't respond, in a different post,
your view appears to be that math is just a matter of typing.
Once they learn to turn on the calculator and hit the right symbols,
they're done with arithemtic.  Should be done by 4th grade.  

  So what should I have complained about?  That their math teachers
hadn't taught them well enough how to turn on calculators?  Bah.
Students forget things after classes are over.  Not everything, but
some.  So what if some forgot the turning on of calculators.

  The students had been taught math in the way that you want --
that addition and subtraction are what happens when you hit the
+ or - key on the calculator.  Whatever number comes out is The
Answer.  (of course with division it gets quite absurd and
they divide about 1 by about 7 and give me an answer of
exactly .14287581)

  Yet these students who had been taught as you want did
poorly in doing anything with the subject.  Rather than
reconsider how good an idea you had, you sidetrack to
blaming Tim and me, who had no hand at all in how these
students had been taught.


But you did have a hand in it. You are not somehow *entitled* to have
students who meet your standard of preparation. You have ill-prepared
students because you accept them into your class, or acquiesce in
their enrollment. So you are not that different from the elementary
school teacher who yields to the pressure of social promotion or
parental complaints, and it is unreasonable for you to blame them for
the nature of your students. If you refused to accept weak students,
you would put pressure on the system to do better all the way down the
line. Since you claim that there was a college algebra requirement,
and these are sophomore or junior science majors (you said 14 years,
right?), you could start by walking over to the math and/or physics
building to express your concerns.

As for the subject. In the square root post, I gave an indication of
what I am really talking about, which is nothing like what you claim
except that I think you can accomplish much more in a shorter time
than we do now. I think that there should be a strict high school
graduation requirement for problem-solving skills that employ
mathematics, and some of that will include 'topics' that are now only
taught in 300-level courses. The problem is that you then need
teachers who are competent to teach problems at that level. Using
software to do the monkey-work algorithms doesn't change that, just as
using calculators doesn't take away the need for teachers to know and
communicate the underlying principles. Now, that's a pragmatic
argument against my proposition, but I don't think it is
insurmountable once the goal is adopted.

-tg





--
Robert Grumbinehttp://www.radix.net/~bobg/Science faqs and amateur activities notes and links.
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences


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