Re: Sarah Palin- creationist VP candidate?

On Sep 13, 10:53�am, tgdenn...@xxxxxxxxxxxxx wrote:
On Sep 12, 9:58�pm, Tim Norfolk <timsn...@xxxxxxx> wrote:

On Sep 12, 11:30 am, tgdenn...@xxxxxxxxxxxxx wrote:

On Sep 11, 1:11 pm, Tim Norfolk <timsn...@xxxxxxx> wrote:

tgdenn...@xxxxxxxxxxxxx wrote:
On Sep 10, 9:57 am, Tim Norfolk <timsn...@xxxxxxx> wrote:
tgdenn...@xxxxxxxxxxxxx wrote:
On Sep 9, 4:54 pm, Walter Bushell <pr...@xxxxxxxxx> wrote:
In article
<8f1fc5e8-6b1c-47e7-8cad-75a83a4c8...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Tim Norfolk <timsn...@xxxxxxx> wrote:

<snip>







For anyone with the stamina to wade through this thread for nuggets of
wisdom, I apologize for the length of this posting, but didn't want to
be accused of snipping relevant information to make select points.

I will leave it up to others to decide if I am being irrational, have
moved the goalposts or changed the subject, or am incapable of
constructing a verbal scientific argument.

However, perhaps you will agree with the following simplified synopsis
of the scientific process:

1. Make observations
2. Construct model
3. Make further observations
4. If evidence is found that completely refutes the model, go to 2.
If not, refine the model, and go to 3.

Throughout the threads in which we have contributed, your basic
hypothesis is that we can replace the learning of algorithms in
mathematics for all but (possibly) future researchers, using instead
software tools. The stated goals are to have a higher percentage of
the general population make reasoned decisions, as well as train
engineers better and more efficiently.

Your support for this thesis:

a) There are wonderful software tools that can be used to solve
mathematical models of various kinds. (Developed by mathematicians,
computer scientists and engineers)
b) So far in history, human society has survived and adapted to new
technology.

I've taken the liberty of snipping earlier posts since you've provided
(up to here) a nice synopsis. I will try to illustrate through an
experiment why I find your contention to be lacking in the elements of
a scientific theory (and why the elements of your laundry list below
are not for the most part helpful.)

I believe that those of us who do the grocery shopping will attest to
the outcome of the following, which can be performed by the local
supermarket chain in the interests of science.

Open up all the checkout aisles in all the stores so that we have a
large sample of cashiers. I assume all will agree that this is a
heterogeneous population with respect to education and ability, since
there will be many high school students (yes, almost all girls) as
well as older individuals. And we've all listened to them talking to
the baggers---some seem bright, some not.

Now, turn off the software that calculates the change returned to the
customer---the subjects will still type in the amount tendered, but
must do the math mentally or with pencil and paper if needed. We will
then accumulate data as to (a) speed and (b) accuracy of change
returned when the amount tendered is entered correctly.

I assume also that everyone will agree that there will be some
distribution for the data. Now I state the hypothesis: Turning on the
software will have no effect on the distribution.

And of course, the hypothesis will be falsified---once the software is
activated, both accuracy and speed will be at the high end
universally. Any fair minded person would have to agree that using the
software has increased the productivity *of the group*.

Now obviously, I extend this model to include things like 'solving'
quadratic equations (and even differential equations,) designing
bridges, predicting chemical reactions, plotting income distributions
(or even the phase space of a pendulum,) and so on. I really can't
conceive of how anyone could claim that *if we set up a similar
experiment*, the outcome will be different.

So my proposition is based on a clearly non-controversial idea, which
is that if students are more productive, they will have the
opportunity to do *more* not less work, and so will benefit. Paul J
Gans commented on his graduate chemistry class not being able to do
'real' problems because the software was too expensive. And it is
equally true for high school students for example---if you had bridge
design software, you could easily teach 'real' bridge design even to
freshmen I think, given a competent teacher and motivation. Your
students would be doing college-level work earlier rather than later.

Now that's *my* theory; If you wish to refute it, you must be able to
explain *why* whatever study or data you cite is relevant. And that
requires

1) That you be able to clearly state the nature and null hypothesis of
any experiment you are suggesting as a test, so we can see if it
actually applies to *my* proposition.

2) That you state your proposed causal mechanism(s), which must be *at
least* reasonable and not based on your personal faith. Note that I
provide such a mechanism for my theory, and that I and others have
offered such explanations for some of the outcomes you report.

If you really believe that your information supports your view, then
why not articulate just how it does that? �All you say below is that
tradition works better "for whatever reason"---that's just not
sufficient.

-tg



When pressed for more evidence, you gave a Maple work*** in which
the problem had been solved before coding, and asked a physics problem
which you worded in such a way that the question was meaningless.

You appear to be stuck on step 2. above, and insisting that we change
our complete curriculum according to your opinion.

In contention, my hypothesis is that traditional training in
mathematics is, for whatever reason, necessary for higher learning. In
addition, my observation is that attempting to do what you propose not
only will not generate a significant increase in 'critical thinking'
skills in the general population, but will hamper the learning of
those students who have that intrinsic skill.

I will also note that I do not suggest that the use of technology is
not justified, only that it should come after the basic skills and
algorithms have been mastered. I also do not claim that there is no
better way to train people in the analytical subjects, only that we do
not appear to have found one. Not that the mathematical community
haven't tried. Witness Euclid's comment to King Ptolemy, "Sire, there
is no royal road to geometry".

Observations in support of my thesis:

a) Successful experiments in replacing classrooms with computer labs
as places like VPI have so far failed to translate to the general
student population, and the effects in select groups have mostly been
transitory.
b) Even though the ACT and SAT supposedly are not dependent on
specific coursework, high math scores on these tests correlate
positively with college-level math success and graduation rates,
regardless of major.
c) Attempts at large universities with computer- and calculator-based
algebra-free statistics courses have given very poor results, in terms
of students being able to phrase questions properly after the courses
are completed.
d) It is in the interest of higher education ...

read more �- Hide quoted text -

- Show quoted text -- Hide quoted text -

- Show quoted text -


1. The cashiers are a selected group within a store. It is common
practice that being off by $1 more than once will get you fired.
2. Many cashiers appear to have been 'Peter Principled' into their
jobs. I have been given wrong change more times than I can count, and
am delayed almost every shopping trick by a cashier presented with a
non-standard problem, such as a credit card.
3. Making change is a very concrete task, as repetitive as factory
work. More abstract reasoning stops everything. Witness the confusion
when I saw a sign for sports drinks advertised at a price of .88
cents, and I tried to explain the problem.

Now, as to why I still believe that your approach will not work, I
have some thoughts:

1. Human learning is by association, from the concrete to the
abstract.
2. Mathematics is probably the most abstract of all human endeavours,
and is only required at all because it has given science and business
some fabulously useful tools, despite that fact that the constructs in
mathematics have no existence outside of our thought processes.
3. In the standard curriculum, we start with

a) Positive integers and operations - almost anyone can master these
operations.
b) Negative integers - some get lost at this point, and don't see what
they 'mean'.
c) Fractions - many more get lost here, even though such processes can
be made concrete.
d) Decimal expansions - more misunderstanding, and more who don't
grasp the concept.
e) Basic algebra - taking the operations, properties (like the
distributive law) and relations, and applying them to collections of
objects : 2x represents, in the real, the process of doubling an
arbitrary number. Many more cannot understand the point, or master the
algorithms.

Another anecdote, but germane to our discussion: my sister-in-law (who
is quite bright) was unable to pass high school algebra, because she
just couldn't grasp that'x' could be 5 in one problem, and 6 in
another. It appears, from others that I have talked to, that this is
not uncommon. Each person appears to have their own natural level of
abstract understanding. Given the right training, they can get to that
level, but no further. It is sad, but undergraduate mathematics
programs are full of people who have squeaked their way through the
algorithmic courses in the calculus and linear algebra, but just
cannot understand the higher-level reasoning in advanced calculus and
abstract algebra, which require a thorough mastery of most of the
algorithms and results in those more concrete courses.

f) Functions - abstracting all operations to new ones, leading to the
analysis tools of the calculus, including multivariate calculus and
linear algebra. Only perhaps 10% of the population can master the
basics.
g) Calculus, where we manipulate the functions themselves, and deduce
their properties, hence deriving differential equations, the language
of physics and engineering.
h) Other abstractions include of course group theory (used in quantum
physics), graph theory (network analysis and other problems), spectral
theory of moperators (abstracting the eigenvalue problem in linear
algebra), leading to the major results in the existence of solutions
in differential and integral equations.

At each step, we still deal in quantities like '2x' or '2f(x)', and
move back to the concrete models of a) above. Your hypothetical
cashiers actually deal out the change, and have some idea what they
should do. Absent the traditional grounding described, what is the
meaning to be given to the eigenvalues of the control operator,
regardless of how it is derived? More training in the algorithms
(supplemented as we do with sophisticated tools) gives those students
who have the innate skill a better foundation to understand the
results that they generate.

.