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Topic: Saxon Calculus
Replies: 21   Last Post: Oct 16, 1998 2:45 PM

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Lee Wayand

Posts: 5
Registered: 12/8/04
Re: Saxon Calculus
Posted: Oct 14, 1998 11:41 AM
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>Victor Steinbok writes:

>>Why does it seem that the attitude of any working mathematician
>>OR school administrator is that cognitive research is a waste
>>of time?

>1) Some working mathematicians have had experience investigating
>claims made by advocates of cognitive research and feel, in
>retrospect, that the time spent in those investigations was
>indeed wasted. Perhaps if proponents of cognitive research
>could give us more focused citations (rather than telling us to
>go read some books on the theory) and make sure that the works
>cited actually bear on the issues in question, we would feel
>less like we'd been on a wild goose chase.
>2) Some mathematicians are, I believe, turned off by people who
>seem to overstate their case--using the word "know" when they
>probably mean "believe", or making absolute claims for which we
>are acquainted with counterexamples.
>3) Some mathematicians wish that advocates of cognitive research
>(and educational research in general) would do a better job of
>practicing what they preach. Think of us as your students; if
>we have had difficulty absorbing the principles of your theories
>might part of the problem be the way you have tried to teach
>them to us?
>Chris Grant

But, now you are saying "some" without "focused citations". Who? What
research did they look at? What did the research claim that turned out not
to be true? How did they feel it wasted their time? Who said "know" when
they really meant "believe"? What counterexamples? (Counter examples might
be when the instructor follows the stated situation exactly and it doesn't
work - not so easy in a field where human intuition and emotions are flying
around and where mathematicians might not be the best at reacting to such
actions. )

This game is too easy to play. It goes no where.

The whole idea of recommending books is that they have explanations of the
citations as well as the citations themselves. You can either believe the
explanations or not, but the citations are all there (bibliography) for you
to investigate for yourself, if you so choose.

It seems like a waste of time to me (I could be wrong) to suggest that
people, as a first reading, read articles on specific investigations. If I
wanted people to understand Galois Theory over Local Fields, I would not
ask them to first read Shiratani's "On p-adic Zeta Functions of the Lubin
Tate Groups".

People need an overall picture of what they are getting into and then get
down to the specifics that catch their attention.

It is simply not that big of a request for all mathematicians to read 5
books or 10 articles on what Cognitive Research has learned about how
people learn. "Working" mathematicians are in the classroom teaching our
future. They should spend sometime finding out what research is being done
and what results are being found on how people learn. It is simply
unacceptable to allow their research into learning to solely come from
their own teaching and thus conclude that it is the students' fault for not
trying hard enough. - Not my opinion, said out loud in many departmental
gatherings and e-mailings.

There is new information that says the way we traditionally teach is
ineffective. There are results that say the brain is more than a blank
slate for us to write on. There are results that say our traditional
evaluations are missing the mark.

There are.

I gave some specific suggestions for specific books that cite specific
research for people to specifically read. I picked the first ones off the
top of my head that would fall under the easy-to-read category. There are
perhaps better ones. (John Anderson's "The Architecture of Cognition" or
Howard Gardner's "Frames of Mind "). I can also suggest articles ("Abstract
Planning and Perceptual Chunks: Elements of Expertise in Geometry",
Cognitive Science 14: 511-550) to look up and read which are less than
easy-to-read, but plenty informative.

As for my students, I teach my students to be responsible for themselves,
to question, and to seek out knowledge. Responsibility involves meeting me

Lee Wayand

Lee Wayand
Calculus Remote at The Ohio State University (CROSU)
FAX: 614-688-5790

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