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Mark VandeWettering
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 Posted: Mon Jun 09, 2008 10:45 am Post subject: Re: Not Just the US With Education Problems |
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On 2008-06-09, Vernon Balbert <vbalbert@gmail.nospam.com> wrote:
| Quote: |
On 6/8/2008 2:51 PM, alwaysaskingquestions went clickity clack on the
My first programmable calculator was a Texas which I got in 1976 - can't
remember the model but it had 99 programmable steps including conditional
branching and 10 memories . Boy did I have fun with that - it's what first
got me into the whole concept of computer programming which I'm still
involved in today.
That sounds like the TI-58, the little brother to my TI-59. The TI-59
had more memory as well as a magnetic card reader which made it nice to
save programs. I miss that calculator. Heh.
|
I had one of these:
http://www.rskey.org/detail.asp?manufacturer=Texas+Instruments&model=SR-52
My favorite calculator today is my hp48g.
Mark |
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Norton
Guest
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| Posted: Tue Jun 10, 2008 12:49 am Post subject: Re: Not Just the US With Education Problems |
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John McKendry <jlastname@comcast.dot.net> wrote:
| Quote: |
On Sun, 08 Jun 2008 23:27:54 +0000, Paul J Gans wrote:
tgdenning@earthlink.net wrote:
On Jun 8, 2:58 am, "Mike Dworetsky" <platinum...@pants.btinternet.com
wrote:
"Paul J Gans" <g...@panix.com> wrote in
messagenews:g2f2bi$87q$4@reader2.panix.com...
Walter Bushell <pr...@xxx.com> wrote:
In article <6ask8qF38sc6...@mid.individual.net>,
"alwaysaskingquestions" <alwaysaskingquesti...@gmail.com> 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
|
I've doubtless misrecalled. It was probably yet another
famous mathematician.
| Quote: |
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.
|
Oh, I agree with this. Which is why in a previous post I've
made a clear (I hope) separation between the concept and the
computational method.
--
Norton. |
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Norton
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| Posted: Tue Jun 10, 2008 12:57 am Post subject: Re: Not Just the US With Education Problems |
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Walter Bushell <proto@xxx.com> wrote:
| Quote: |
In article <g2hqdq$in7$4@reader2.panix.com>,
Paul J Gans <gans@panix.com> wrote:
What happens is that many kids, not understanding how
to compute a square root decide that they will never
master math.
The algorithm for the computation isn't important. The
concept of the square root is.
A caculator allows students to play with square roots
without having to know the algorithm -- which is complex
and very difficult to prove to grade or high school
students.
x[n+1]=(x[n]+c/x[n])/2 where c is the number we are taking the square
root of.
is hard to prove, given a sloppy guess it converges fast as a little
experience will show. Not only that errors do not accumulate.
|
Yup. That's Newton's method. Easy enough to prove once
one has a year of calculus under one's belt.
The method I was taught in school was a manual method rather
like long division. One bunched the number whose root you
wanted into pairs of digits, and went on from there. It
actually is a longhand method of completing the square.
I don't know why they never taught Newton's method. It
is fairly quick even longhanded. And it converges as you
know, quadratically, so that the number of correct digits
doubles each time through. So one can get the first digit
almost in one's head. One more pass gets two, which involves
only a two digit division. The next pass gets four, which
is about what precision we worked to by hand.
And it converges no matter what guess you start with. That's
not always true for Newton's method, but it is for taking
square roots.
--
Norton. |
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Bob Casanova
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| Posted: Tue Jun 10, 2008 6:06 am Post subject: Re: Not Just the US With Education Problems |
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|
On Mon, 9 Jun 2008 03:08:39 -0700 (PDT), the following
appeared in talk.origins, posted by tgdenning@earthlink.net:
<snip>
| Quote: |
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*.
|
It's not a Bad Thing (TM), but IMHO it comes down to whether
you're running a trade school or a university. If the
former, nothing is required but a thorough education in the
current techniques, whatever they may be and whatever their
basis. But if the latter, and you want to produce students
who can start from the current techniques and go on to make
original contributions, a thorough grounding in the theory
and history of the field, ISTM, would be far better
preparation than a simple "this is how we do it today". So I
guess it depends on your ultimate goals and what you think
the purpose of a higher education is. And I don't think that
rote learning of current techniques, whatever the field, is
likely to produce "a population that has a positive attitude
towards science, and uses reason and scientific reasoning to
arrive at decisions"; that's what I'd expect from actually
learning what all that "mumbo-jumbo" actually *means*, and
how we know. Just my 20 mills, and YMMV (and apparently
does).
--
Bob C.
"Evidence confirming an observation is
evidence that the observation is wrong."
- McNameless |
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Vernon Balbert
Guest
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| Posted: Tue Jun 10, 2008 6:21 am Post subject: Re: Not Just the US With Education Problems |
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|
On 6/9/2008 5:21 PM, Bob Casanova went clickity clack on the keyboard
and produced this interesting bit of text:
| Quote: |
On Sun, 8 Jun 2008 23:25:14 +0000 (UTC), the following
appeared in talk.origins, posted by Paul J Gans
gans@panix.com>:
Walter Bushell <proto@xxx.com> wrote:
In article <g2f8pa$4en$1@reader2.panix.com>,
Paul J Gans <gans@panix.com> wrote:
Walter Bushell <proto@xxx.com> wrote:
In article <g2f2bi$87q$4@reader2.panix.com>,
Paul J Gans <gans@panix.com> wrote:
Walter Bushell <proto@xxx.com> wrote:
In article <6ask8qF38sc6eU1@mid.individual.net>,
"alwaysaskingquestions" <alwaysaskingquestions@gmail.com> 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.
I did a least squares fit in 1967 on one. I think it took a week or two.
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.
The mechanical calculator is arguably the finest example of the
mechanical engineer's art. They were enormously complex
instruments powered by an electric motor. The insides were
a three dimensional mass of gears, levers, cams, and whatnots.
The reference above shows some "inside" shots.
The pocket calculator killed them off fairly quickly.
Cheaper, faster and smaller will win every time. Not to mention quieter.
Also, they quickly became more capable.
Yup. They killed off base 10 logs too.
Since base ten logs were mostly for ease in calculations. But they
survive as decibels and order of magnitude calculations.
Sure, which is why calculators still allow you to compute them.
Long ago, in the early days of the republic, I memorized the
logs to the base 10 of both 2 and 3 to five decimal place.
It was amazing how much off the cuff calculation I could
do. Logs of all the single digit integers except 7 were
rapidly available.
I still know them. They sit there taking up space in my
limited memory capacity and won't go away.
Was Gauss one of your ancestors? ;-)
|
Does he have a magnetic personality?
--
You will know unexpected happiness. You will know the sorrow of seeing
what is dearest to you cut down before your eyes. Accept that. That is
the nature of human existence, and you have no time to buffer this fact
with fairy tales and illogical explanations. -- Deng Ming-Dao |
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John McKendry
Guest
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| Posted: Tue Jun 10, 2008 6:54 am Post subject: Re: Not Just the US With Education Problems |
|
|
On Mon, 09 Jun 2008 03:08:39 -0700, tgdenning wrote:
| Quote: |
On Jun 8, 11:43Â pm, John McKendry <jlastn...@comcast.dot.net> wrote:
On Sun, 08 Jun 2008 23:27:54 +0000, Paul J Gans wrote:
tgdenn...@earthlink.net wrote:
On Jun 8, 2:58Â am, "Mike Dworetsky"
platinum...@pants.btinternet.com> wrote:
"Paul J Gans" <g...@panix.com> wrote in
messagenews:g2f2bi$87q$4@reader2.panix.com...
Walter Bushell <pr...@xxx.com> wrote:
In article <6ask8qF38sc6...@mid.individual.net>,
"alwaysaskingquestions" <alwaysaskingquesti...@gmail.com> 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. Â 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 (!). Â During the course of
the programme we took delivery of the latest Friden calculator that
could extract square roots. Â For amusement one day we tried taking
concatenated square roots of a number several times then squared it
back up again. Â 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. Â 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 think we've identified the difference, then. My goal is to have a
population that understands what mathematics is. I think such a population
will also have a positive attitude towards science and so forth, just
like your imaginary population, but my imaginary population will have
the additional advantage of being able to do creative things with math.
| Quote: |
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
|
Math is not rearranging symbols according to rules. That's a logician's
canard; no practicing mathematician believes it. If you think that,
I have to wonder whether you have ever had the experience of understanding
a theorem. Mathematics happens when you finally see why it is that the
antiderivative is the integral, or why the area under the hyperbola 1/x
between x=1 and x=2 is the same as the area between x=2 and x=4, or
how to get the trig identities by multiplying rotation matrices.
Getting the symbols rearranged correctly is the booby prize if it
doesn't help you get the big general concepts. It seems like you
agree with the first part of that statement, but I don't see any
evidence that you understand the second part. It looks as if you
think that getting the symbols rearranged correctly is all there is
to mathematics.
Maybe I'm reading you wrong; I confess I haven't read everything
you've written about this. But everything I *have* read from you says
that all you want is the number or the expression at the end of the
calculation.
John |
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Tim Norfolk
Guest
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| Posted: Wed Jun 11, 2008 2:45 am Post subject: Re: Not Just the US With Education Problems |
|
|
On Jun 10, 9:54�am, tgdenn...@earthlink.net wrote:
| Quote: |
On Jun 9, 9:54�pm, John McKendry <jlastn...@comcast.dot.net> wrote:
On Mon, 09 Jun 2008 03:08:39 -0700, tgdenning wrote:
On Jun 8, 11:43�pm, John McKendry <jlastn...@comcast.dot.net> wrote:
...
�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 think we've identified the difference, then. My goal is to have a
population that understands what mathematics is. I think such a population
will also have a positive attitude towards science and so forth, just
like your imaginary population, but my imaginary population will have
the additional advantage of being able to do creative things with math.
Ok, but first let's be clear about what population we are talking
about. I'm talking about the entire population of the US, not the
population of math grad students. I would be pretty confident in
saying that at no time in the past, despite the teaching of four or
five or six ways of 'solving' quadratic equations (metaphor alert),
has any but a tiny percentage of that population been able to do
'creative' things with math. (Probably a very consistent percentage.)
What we have mostly are people who can't do *non*-creative things that
rely on very basic principles, and so they are misinformed about and
alienated from math and science, and subject to manipulation by
businesses and politicians. But you seem to be wiling to discuss some
specifics below, so let's see if that will clarify further.
I agree with your statements about people's performance. However, how |
do we find the ones that need, and can succeed at the higher levels?
You have already argued on a different thread that selecting at each
level is elitist, at least if it is done by people like me. The
Catch-22 is this: there is an increasing need in industry and
government for those with talent in mathematics and related areas, and
a limited pool who appear to have those talents. If we don't select
them at a fairly early age, say 12-13, and train them to carry our
knowledge further, then we have the current system, which tries to
take everyone as far as they can. It is terribly cruel, as we push too
may past their abilities.
As for your main wish, I would love for the average person to make
their decisions more rationally, but don't see any evidence that they
can. How many believe in homeopathy and other alternative 'therapies'
for which the lack of scientific evidence is clear?
| Quote: |
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*.
�Math is not rearranging symbols according to rules. That's a logician's
canard; no practicing mathematician believes it. If you think that,
I have to wonder whether you have ever had the experience of understanding
a theorem. Mathematics happens when you finally see why it is that the
antiderivative is the integral, or why the area under the hyperbola 1/x
between x=1 and x=2 is the same as the area between x=2 and x=4, or
how to get the trig identities by multiplying rotation matrices.
My concept of the term "understanding" is as follows:
The first step is the ability to describe something in words. But
since such a description may be memorized, we test for understanding
by requiring the ability to articulate the concept in different ways.
Further, we test for the ability to articulate how the concept might
apply in different situations.
I would also observe that one improves these abilities over time, by
'practicing one's craft'; I do not suggest at all that it isn't
necessary to 'do problems' in order to achieve understanding.
The question at hand has to do with *what* concepts we would like the
general population (excluding math grad students but including large
parts of the science and engineering community as well as 'voters') to
understand, and *what problems they should be doing* to achieve that
understanding.
|
And I will repeat my experiences, which are that removing the hard
work from this learning results in less learning, not more.
As some anecdotal evidence, a few years ago, I was teaching
prospective future teachers. For the final exam, I gave them unlimited
time, use of any calculator that they wished, and a formula sheet of
their choosing. The topic was geometry. In one question, I asked them
to estimate how much ice cream was in a cone. Several gave close to
the correct answer. The next question was to estimate how many scoops/
cones were in one liter of ice cream. One student who had answered the
first part correctly gave 65,000 as the result, with no comment as to
how unlikely this was. A later question was to estimate the volume of
water in the Earth's oceans, given certain figures (surface area,
average depth, percentage of the surface covered in water). One
student gave the answer of 1.5 liters, again, without any surprise.
| Quote: |
�I see it as a rather stark choice, between (again metaphor alert)
sitting in a classroom doing 5 different ways to solve quadratic
equations, and sitting in a classroom working on examples (using
mathematical tools on computers of course) that demonstrate that
correlation does not imply causality. But maybe that's another
logician's canard, even though I don't consider myself a logician ;-).
Anyway, this always gets too long, so my question is: Why *is* it that
the antiderivative is the integral? How should we understand it,
outside the context of rearranging symbols?
|
Which is exactly why we give proofs and other motivations. Pehaps it
has been a while since you were in a math classroom.
| Quote: |
�Getting the symbols rearranged correctly is the booby prize if it
doesn't help you get the big general concepts. It seems like you
agree with the first part of that statement, but I don't see any
evidence that you understand the second part.
No, that's exactly my point. I'm saying that we waste enormous amounts
of time having students *not* get any concept at all, because the very
large majority of their time is spent rearranging symbols, and so
that's what they understand math to be.
-tg
It looks as if you
think that getting the symbols rearranged correctly is all there is
to mathematics.
�Maybe I'm reading you wrong; I confess I haven't read everything
you've written about this. But everything I *have* read from you says
that all you want is the number or the expression at the end of the
calculation.
John- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text -- Hide quoted text -
- Show quoted text - |
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Guest
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| Posted: Thu Jun 12, 2008 11:24 pm Post subject: Re: Not Just the US With Education Problems |
|
|
On Jun 12, 4:57 pm, Bob Casanova <nos...@buzz.off> wrote:
| Quote: |
On Mon, 09 Jun 2008 18:06:36 -0700, the following appeared
in talk.origins, posted by Bob Casanova <nos...@buzz.off>:
Don't you want to address this response, or can I take your
lack of response as agreement with my points? After all,
*you* wanted someone to answer your question.
|
Sorry, I was too busy observing the lack of response to my own request
for discussions of specific topics. ;-)
The problem is that we need to be talking about the same thing and on
this subject it seems to be impossible. I'm talking about K-12 as the
primary issue, although I quite understand that a good part of what
(we?) experienced as, say, 10-12, is now a matter of higher
education.
To answer your specific point: Perhaps you could read my last reply to
John McKendry. I've yet to hear anyone offer specifics about what
would be lacking if we dropped mechanical stuff that computers can do
in favor of encouraging the kind of creative or critical thinking that
I (and perhaps you) seem to favor. The point is that we seem to be
preparing people for tech school much more than for university, using
the traditional paradigm.
-tg
| Quote: |
On Mon, 9 Jun 2008 03:08:39 -0700 (PDT), the following
appeared in talk.origins, posted by tgdenn...@earthlink.net:
snip
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*.
It's not a Bad Thing (TM), but IMHO it comes down to whether
you're running a trade school or a university. If the
former, nothing is required but a thorough education in the
current techniques, whatever they may be and whatever their
basis. But if the latter, and you want to produce students
who can start from the current techniques and go on to make
original contributions, a thorough grounding in the theory
and history of the field, ISTM, would be far better
preparation than a simple "this is how we do it today". So I
guess it depends on your ultimate goals and what you think
the purpose of a higher education is. And I don't think that
rote learning of current techniques, whatever the field, is
likely to produce "a population that has a positive attitude
towards science, and uses reason and scientific reasoning to
arrive at decisions"; that's what I'd expect from actually
learning what all that "mumbo-jumbo" actually *means*, and
how we know. Just my 20 mills, and YMMV (and apparently
does).
--
Bob C.
"Evidence confirming an observation is
evidence that the observation is wrong."
- McNameless |
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Tim Norfolk
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| Posted: Fri Jun 13, 2008 1:58 am Post subject: Re: Not Just the US With Education Problems |
|
|
On Jun 12, 7:24�pm, tgdenn...@earthlink.net wrote:
| Quote: |
On Jun 12, 4:57�pm, Bob Casanova <nos...@buzz.off> wrote:
On Mon, 09 Jun 2008 18:06:36 -0700, the following appeared
in talk.origins, posted by Bob Casanova <nos...@buzz.off>:
Don't you want to address this response, or can I take your
lack of response as agreement with my points? After all,
*you* wanted someone to answer your question.
Sorry, I was too busy observing the lack of response to my own request
for discussions of specific topics. ;-)
The problem is that we need to be talking about the same thing and on
this subject it seems to be impossible. I'm talking about K-12 as the
primary issue, although I quite understand that a good part of what
(we?) experienced as, say, 10-12, is now a matter of higher
education.
To answer your specific point: Perhaps you could read my last reply to
John McKendry. I've yet to hear anyone offer specifics about what
would be lacking if we dropped mechanical stuff that computers can do
in favor of encouraging the kind of creative or critical thinking that
I (and perhaps you) seem to favor. The point is that we seem to be
preparing people for tech school much more than for university, using
the traditional paradigm.
-tg
On Mon, 9 Jun 2008 03:08:39 -0700 (PDT), the following
appeared in talk.origins, posted by tgdenn...@earthlink.net:
snip
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*.
It's not a Bad Thing (TM), but IMHO it comes down to whether
you're running a trade school or a university. If the
former, nothing is required but a thorough education in the
current techniques, whatever they may be and whatever their
basis. But if the latter, and you want to produce students
who can start from the current techniques and go on to make
original contributions, a thorough grounding in the theory
and history of the field, ISTM, would be far better
preparation than a simple "this is how we do it today". So I
guess it depends on your ultimate goals and what you think
the purpose of a higher education is. And I don't think that
rote learning of current techniques, whatever the field, is
likely to produce "a population that has a positive attitude
towards science, and uses reason and scientific reasoning to
arrive at decisions"; that's what I'd expect from actually
learning what all that "mumbo-jumbo" actually *means*, and
how we know. Just my 20 mills, and YMMV (and apparently
does).
--
Bob C.
"Evidence confirming an observation is
evidence that the observation is wrong."
� � � � � � � � � � � � � - McNameless- Hide quoted text -
- Show quoted text -
|
I believe that my last reply, including the discussion of our current
selection process in education, might partially answer your question. |
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