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Re: Necessary and Sufficient Conditions For Genuine Scientific Research - Response To Greeno
Posted:
Nov 9, 2012 12:16 PM
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On Nov 8, 2012, at 11:43 PM, Clyde Greeno @ MALEI wrote:
> Re: Schremmer's: "It is interesting to see what happens when these
> same students are led
> on a different path, namely learning how to think by themselves the
> way mathematicians do rather than take the teacher's word---in
> other words on a reason based path."
>
> It also would be quite interesting to see a semi-detailed
> description of what happens ... with/to/for/within/etc. such
> students and their educational potentials.
At best, this would be anecdotic---certainly NOT "genuine scientific
research". By the way, I have always wondered why the research is
never LONGITUDINAL, that is why students are never followed as they
proceed through college. The only one I know is ...
<http://www.freemathtexts.org/IntegratedA2DC/LongitudinalStudy.pdf>
> It seems fair to presume that Alain is talking about students
> enjoying educational benefits that they could not acquire by
> following a traditional path ... and that such students emerge
> happier, mentally healthier, and potentially more productive and
> prosperous than they otherwise would.
Let's not get carried away. The experience I shied away from relating
above is that, every semester, out of 20 students starting
<http://www.freemathtexts.org/Standalones/RBA/Contents.php>
one or two can skip "Intermediate algebra" and get into Precalculus 1
<http://www.freemathtexts.org/Standalones/RAF/Contents.php>
But these students ALL keep on going to a standard Precalculus 2 and
then on to Calculus 1 and 2.
> To achieve that kind of results on a broad scale, through courses
> within normally structured TYC curricula, seemingly would be very
> difficult ... due to the parameters that presently constrain program
> operations, as well as how most TYC math teachers have been reared.
> The sorely needed initial models are far more likely to be produced
> *outside* the normal TYC structure.
I am afraid that you are correct. I am trying to have my basic algebra
section (where I use RBA) linked with a Developmental English course
in which the reading materials would be the materials used in RBA but
even though nobody is really happy with the status quo, nobody is
really interested in setting up the link.
>
> It almost seems that Schremmer is hinting toward some kind of a non-
> curricular "math internship" program for college-certain students to
> take BEFORE taking TYC courses of any kind ... focusing NOT on the
> "content preparation" of students, but on upgrading their
> "mathematical-thinking power-tools."
Absolutely NOT. The reason is that this would result in a sequence
that would be as long as the current sequence with exactly the same
deterring effect. On the contrary, I have quite a bit of evidence that
Arithmetic and Algebra integrated into a five-hour course followed by
Precalculus 1 and 2 and Calculus 1 integrated in two four-hours
courses would work.
The theme, by the way, is using decimal approximations throughout
Arithmetic and (Laurent) polynomial approximations (i.e. Lagrange's
approach) throughout the equivalent of Precalculus 1 - 2 and Calculus
1. See
> Might even be an arena for some educational research of a more
> scientific kind than what has been proposed by the NRC.
>
> Considering Obama's well publicized concerns about community
> colleges -- and less publicized groping for "science-based
> educational research" -- funding for such innovations are likely to
> become readily available.
You are dreaming. But at least, it isn't the nightmare that could have
been.
> But because those projects might be at odds with entrenched TYC
> programs and personnel, they might have to be conducted through
> universities
No way. As I think I might have mentioned, I once submitted a piece to
the Notices. They said they "liked" it very much but that it was too
long. I cut it down but, somehow, they never published it. It can be
found along with a presentation I gave at my school where it was also
liked but with no follow up whatsoever. The links are towards the
bottom of:
<http://www.freemathtexts.org/IntegratedA2DC/index.php>
> or other NPOs -- perhaps even through some school systems' Adult
> Education Programs.
>
> Any other such missionaries around?
>
> Cordially,
> Clyde
Regards
--schremmer
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