Re: Not Just the US With Education Problems

On Jun 8, 11:43 pm, John McKendry <jlastn...@xxxxxxxxxxxxxxx> wrote:
On Sun, 08 Jun 2008 23:27:54 +0000, Paul J Gans wrote:
tgdenn...@xxxxxxxxxxxxx wrote:
On Jun 8, 2:58 am, "Mike Dworetsky" <platinum...@xxxxxxxxxxxxxxxxxxxx>
wrote:
"Paul J Gans" <g...@xxxxxxxxx> wrote in
messagenews:g2f2bi$87q$4@xxxxxxxxxxxxxxxxxxxx

Walter Bushell <pr...@xxxxxxx> wrote:
In article <6ask8qF38sc6...@xxxxxxxxxxxxxxxxxx>,
"alwaysaskingquestions" <alwaysaskingquesti...@xxxxxxxxx> wrote:

Some of it may have to do with personal inclination - I have
always been fascinated with both puzzles in general and with
knowing how things work; in
my first job - just before the introduction of desktop calculators
- I had
to learn how to use a slide rule and was thought it was a
fantastic invention.

Just how old are you. Frieden calculators from the styling my
predate WWII and maybe I.

The Friden calculator was in major use up through 1970.  I recall
doing the calculations for a paper on one in that year.

Fridens had 10 digit keyboards and the high end models could
automatically extract square roots of 20 digit numbers.

See <http://www.oldcalculatormuseum.com/fridenstw.html> for a view
of a late model.

I was at an advanced summer school for teens in 1961 and we had to do
orbit calculations with calculators (!).  During the course of the
programme we took delivery of the latest Friden calculator that could
extract square roots.  For amusement one day we tried taking
concatenated square roots of a number several times then squared it
back up again.  And that's when we learned a practical lesson about
the meaning of precision and significant digits in computations.

An excellent example. By removing the time, tediousness, and human error
associated with doing monkey-work  by hand, a far more expansive lesson
can be delivered. And that was with technology from almost 50 years ago.

Carl Friderich Gauss, undoubtedly one of the most brilliant
mathematicians who ever lived, wasted three years of his live manually
calculating the orbit of the moon.  Given his productivity, we lost out
on a bunch of "Gauss's Theorems" and tons of insights.

 First of all, I'm having a hard time finding corroboration of
this story at all, so it may not even be true. One of Gauss' earliest
accomplishments was the calculation of the orbit of the asteroid
Ceres on the basis of three observations, but if that's the story
you're thinking of, it really seems to be more a counterexample
to the claim you seem to be making, because it was the sort of
creative mathematics that absolutely could not have been accomplished
with a calculator alone; it required a deep familiarity with
the geometry of conic sections. And it took three months.http://www.maa.org/mathland/mathtrek_4_19_99.html

 But if he had taken three years to calculate the orbit of the moon,
I still doubt that it would have been lost time. You make it sound
like grunt-work arithmetic, like calculating seven hundred digits
of pi. Calculating the orbit of Ceres meant inventing a new method
of calculating.

 The broader argument here seems to be about what counts as monkey
work, and I have to vote with Tim Norfolk overall. I agree that
calculating the sine of 39 degrees is monkey work, but writing out
an expression for the sine of 67.5 degrees is not. Anyone who
wants to do any level of creative work involving math should
recognize the latter as a couple of applications of basic trig
identities to the sine of 45 degrees (or better, 135 degrees).
I don't care if he/she looks in a book for the trig identities;
the important thing is to know they exist. You will never learn
the trig identities from a calculator. If all you care about
is the numeric answer, it doesn't matter, but if all you care
about is the numeric answer, you'll never learn what it is
to do math, either.


There's a recurrent fallacy here---maybe several different ones
depending on the writer, although they speak to the same point.

The question that has to be answered is "what is the goal?", and it
has to be answered without emotive language but with clarity and
precision. *My* goal is to have a population that has a positive
attitude towards science, and uses reason and scientific reasoning to
arrive at decisions. I would suggest that once you set up an
educational system to do that, people will flow into the appropriate
professional disciplines, without mandates, based on their own
inclinations and perhaps economics.

I don't see that learning to perform algorithms that can be done by a
machine advances my goal. And I don't mean just computation, but
manipulation of symbolic forms. But what you and various others tend
to do is *define* the goal as learning to perform those algorithms.
And then some even set up the rather looney strawman that says
attempts to teach that de-emphasize those algorithms have 'failed'
because they don't produce people who *can* do the algorithms.

So yes, if you don't learn to rearrange symbols according to some
rules, you will not learn to rearrange symbols according to some
rules. But if you have a tool that will do that for you, the symbols
will still be rearranged. Tell me why that is a Bad Thing, *without
begging the question*.

-tg



John


.

Relevant Pages

  • Re: Not Just the US With Education Problems
    ... orbit calculations with calculators. ... calculating the orbit of the moon. ... The system that you describe wouldn't generate enough mathematicians, ... to do is *define* the goal as learning to perform those algorithms. ...
    (talk.origins)
  • Re: Not Just the US With Education Problems
    ... automatically extract square roots of 20 digit numbers. ... orbit calculations with calculators. ... calculating the orbit of the moon. ... I don't care if he/she looks in a book for the trig identities; ...
    (talk.origins)
  • Re: Not Just the US With Education Problems
    ... automatically extract square roots of 20 digit numbers. ... orbit calculations with calculators. ... calculating the orbit of the moon. ... I don't care if he/she looks in a book for the trig identities; ...
    (talk.origins)
  • Re: Not Just the US With Education Problems
    ... my first job - just before the introduction of desktop calculators ... automatically extract square roots of 20 digit numbers. ... orbit calculations with calculators. ... calculating the orbit of the moon. ...
    (talk.origins)
  • Re: Not Just the US With Education Problems
    ... like calculating seven hundred digits of pi. ... as a couple of applications of basic trig identities to the sine of 45 ... population that understands what mathematics is. ... So yes, if you don't learn to rearrange symbols according to some rules, ...
    (talk.origins)