Re: education
From: Will Twentyman (wtwentyman_at_read.my.sig)
Date: 09/22/04
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Date: Wed, 22 Sep 2004 16:13:38 -0400
What level are you talking about? Some of your comments may apply well
to a grad student, but very poorly to a high school student.
Tron99 wrote:
> (1) To become knowledgeable in mathematics areas one must spend a lot
> of time on one's own learning and thinking about math.
I would edit that to "learning and thinking *correctly* about math."
> (2) Sitting before a teacher being lectured at whether it is a math
> teacher or a history teacher is interferring with the alone time
> needed to learn the math.
By this same logic, to learn karate one should practice kicks at home
and not have anyone show you the proper way to stand, recover, etc. The
purpose of the teacher is, among other things, to model the right way to
think about and do math.
> (3) What the math teacher presents is a small part of the total
> necessary to attain a deep understanding of the subject. The
> different math classes one takes at the same time are not unifying in
> the sense that the student solves the fundamental problems from a
> whole. Only personal research across several areas of math attains
> the whole view from which one can progress.
I'm not sure what this means. I had come to the general conclusion that
it is possible to understand something about all branches of math, but
to understand *all* of math is quite impossible. That's why there are
so many specialists.
> (4) Different books and paper lectures as well as written guidance are
> sufficient for the beginning student to attain mathematical maturity.
Without any form of feedback, this is very unlikely. A book can tell
you, through the answer in the back of the book, that you are wrong, but
not where your mistake is. I know of no books that will tell you
whether a geometry proof is right.
> (5) Those books are not free in the sense that the public education
> provides for them. Access to libraries is limited for the majority of
> people. There are some online free material such as the online
> cornell that can provide some measure of guidance sufficient to attain
> mathematical maturity.
At what level have you attained mathematical maturity?
> (6) Math education is essential for understanding the quantitative
> nature of the world as opposed to a "special-case" intuitive
> understanding.
I'm not sure what the "'special-case' intuitive understanding" refers to.
> (7) There comes a point where the education of english, literature,
> history, and the social sciences simply interfere with a genuine
> quantitative understanding of things. These classes do not teach the
> fundamental understanding of things. They are discordant with
> mathematical thinking as they are presented.
Try to solve a word problem when you don't understand what the words
mean. "I am twice as old as my sister was 3 years ago" refers to our
ages three years ago in the minds of many algebra students.
> (8) The internet exists as a medium for the placement of mathematical
> texts and for mathematical discussion such as this board.
The internet exists for many more reasons than that. We are merely the
beneficiaries of the US Government's willingness to share their network
with us.
> (9) The internet is the obvious choice for future education. Students
> come at different abilities and no teacher can cater to a set of
> students. The internet is the obvious choice to allow students to
> gain access to mathematical understanding at his/her pace.
It is *a* resource, but not always *the best* resource.
> (10) The teacher is wasting his time by teaching students every day
> year after year. There are people who at their inspiration could
> provide video lectures or even one-to-one attention if the teacher is
> in the presence of someone. One can if required present the material
> that he/she knows at one time at their inspiration over video, where
> it can then be stored/rated/catalogued by the viewers. This solves
> the problem of poor teachers and it solves the problem of students who
> wish to learn and research math from books as opposed to daily
> coddling or tyrannical lecturing by teachers.
It doesn't address one problem: students sometimes have questions.
> (11) Applied subjects can be presented in the same manner. However,
> the applied subject is always the result of mathematical thought.
> Many times that applied subject is not complete, but a mathematical
> maturity is needed to progress in the applied subject.
This seems to be either a narrow definition of applied subjects, or a
broad definition of mathematical thought. Conflict management is an
applied subject that would appear to have far more to do with psychology
than mathematics.
> (12) The forces necessary to gain this in fruition are in my opinion
> going to happen naturally. The more efficient way generally always
> wins.
Ok.
> (13) This type of obsession with the fundamentals and sharing of
> knowledge will lead to corporations and technical data to be more
> freely shared amongst people.
Within the limits of copyright/trademarks.
> (14) Obsession with mathematics is in my opinion natural and superior
> to any other endeavor. This obsession is what can make people truly
> gifted and lead them to be able to solve problems in the world.
Have you been in the elementary schools lately? Have you talked with
teenagers? An appreciation for mathematics and enjoyment of them is a
good thing, but it is hardly universal, and certain does nothing to make
an athlete more gifted, an artist more gifted, and little to help me get
along with my wife.
> (15) Math research takes time like I said above, and the sooner this
> sort of thing is enacted the better for mankind.
How do you propose to get everyone to engage in mathematical research?
-- Will Twentyman email: wtwentyman at copper dot net
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