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Re: meeting other mathematics people
Posted:
Jan 24, 2004 6:00 PM
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On 03 Oct 1999, Kirby Urner wrote:
>
>On 02 Oct 99, Newton Liebniz wrote re.
>
>>Should people who dislike a profession be allowed to write a
>>curriculum for it?:
>>
>> I think it is best to ignore Kirby's current dribble on
>> this subject as it does not pertain to k-12 mathematics
>> or the NCTM letter. It appears to be the fulfillment of
>>a vendetta he has for the mathematics profession.
>>
>
>Excuse me? You would allow yourself to cheapen an interesting
>discussion to this degree? Of course it has everything to do
>with K-12 mathematics. And I don't know what you mean by
>"a vendetta". I am in good communication with a number of
>professional mathematicians.
>
>> Kirby you are confusing some of the great computer scientist with
>> professional mathematicians. They are important for the science of
>
>Like Pythagoras? My point was that this concept of "professional
>mathematician" can only be pushed back so far, before it loses
>sense. That doesn't mean math books shouldn't talk about
>Pythagoras, obviously. But it does mean that an historical
>approach shouldn't sacrifice accuracy in pursuit of some
>agenda to "adorn" text books with a lot of inappropriate
>departmental propoganda.
>
>In the early grades, we're keeping options open for kids,
>exposing them to numeracy, giving them literacy with a lot
>of math-related grist for the mill. We're not training them
>to be clones of "purists" of any stripe, or pronouncing them
>failures if they don't fit some mold of "professional" by
>the end of 12th grade. Such specialization comes later.
>
>In the early grades, it's wholly appropriate to keep computer
>science, engineering, mathematics and science more "blended"
>and less compartmented. We don't have "computer science"
>or "engineering" in 4th grade after all (not usually). But
>we do have computers and eager learners wanting to gain
>mastery. And we don't want all those computers to just be
>used as glorified word processors or adding machines either.
>So in many necks of the woods, math class is getting the
>job of transmitting computer languages as a part of the
>mix. Is this so surprising to you?
>
>I live in the Silicon Forest were much of this is already
>taken for granted. In a local community college I know,
>the chairman of the math department (yes, math department)
>teaches in a classroom where every student has a laptop,
>wired to the network by radio frequency ethernet. Is this
>really such a horrible development?
>
>Look at 'Godel, Escher, Bach' -- lots of "computer science"
>in that book. Lots of genetics too. A problem? Escher
>wasn't a pure mathematician after all, let alone Bach.
>
>Consider Dr. Stuart Kaufmann, doing groundbreaking work
>in dynamical systems theory. He also happens to be a
>medical doctor. Problem with that? Is the Santa Fe
>Institute doing "mathematics". Is it "pure"?
>
>Should we let our students in on the fact that most large
>real world projects which involve mathematics also involve
>teamwork across a number of professions, none of which
>has a monopoly on thinking mathematically?
>
>Are we using K-12 to clone "professional mathematicians"
>or to inspire people in many walks of life to think
>competently and coherently using their vast heritage
>of mathematical tools and concepts? I say the latter.
>
>And you're really fooling yourself if you think it's
>"just Kirby" you're ignoring, if you decide to wall out
>all the computer stuff we're planning to phase in to
>early math education.
>
>My <a
href="http://www.inetarena.com/~pdx4d/ocn/trends2000.html">http://www.inetarena.com/~pdx4d/ocn/trends2000.html
>
>is about real trends, not just my bright ideas for
>bringing our kids into the 21st century in a way they'll
>enjoy and profit from.
>
>> computers and are well respected for their accomplishments
>> in that field. They are already included in the list of
>> heroes that dedicated their lives to computer science.
>> We honor them by talking about them in computer classes,
>> not mathematics classes.
>>
>
>This is a kind of dichotomy we don't need to reinforce in
>early math education -- and I should be allowed to promulgate
>this view (which many share) without your silly accusations
>of pursuing a "vendetta" against mathematicians.
>
>You hurt your own cause by debasing the very real differences
>between us in that way.
>
>Make your case on its merits, as I do.
>
>> It is really amazing that you are writing a mathematics
>> curriculum and at the same time you appear through your
>> writings not to understand:
>>
>
>Amazing to you maybe.
>
>> 1. the mathematics profession and what it means to be
>> a mathematician,
>
>Early math ed is simply not about indoctrinating students
>into sharing your brand of academic provincialism. That
>comes later, when kids have had more time to scope out
>the many disciplines and get a sense of their options.
>
>When someone like me comes along and suggests that the
>historical record might be used towards some other end,
>you encourage everyone to ignore me, as I'm clearly a
>heretic who shouldn't be allowed to write curriculum,
>and who has a "vendetta" against your sacred teachings.
>
>You want to "adorn" theorems with their discoverers so
>that students become properly respectful of "professional
>mathematicians" and their discipline. I have no problem
>with healthy respect, and I admire many mathematicians,
>both living and dead. But I think point 5 of the letter
>you propose is needed for balance. Your agenda is too
>narrow.
>
>> 2. the definition of pure mathematics as it relates to applied
>> mathematics (its not what you say),
>
>I haven't proferred any definitions that I can recall.
>Perhaps you would like to cite a specific paragraph.
>
>> 3. why pure mathematics is treasured for its usefulness,
>> abstraction, and beauty,
>
>For lots of reasons. Most the "math is beautiful" books
>and TV I've seen fade in and out between pictures of
>natural structures, architectural wonders and so forth.
>The aesthetic is one of natural order in the universe,
>and our ability to appreciate it. But perhaps this isn't
>pure enough for you? Perhaps math shows should never
>show a nautilus shell or sunflower or rippling wave in
>a pond -- that would be marine biology or fluid dynamics
>or something, which is inappropriate material, the
>province of other departments.
>
>> 4. basic history of mathematics (Pythagoras and Newton
>> studied math for math's sake, but they also had other interest)
>
>Newton had a lot of theological ideas wired up to his study
>of mathematics -- it wasn't all so neatly compartmentalized
>as you seem to think. Pythagoras did not have the mental
>categories you retroactively employ, neatly carving out
>"mathematics" as this "pure discipline" in the academic way
>you're imagining it. That's where your lack of sophistication
>about intellectual history shows very clearly.
>
>Another fallacy you seem to have bought is that mathematicians
>all recognize their contemporaries as worthy, as professionals
>even. In actual fact, Hermann Grassmann, today recognized as
>one of the creators of linear algebra, was coldly dismissed
>in his own time, seen as nothing more than a school teacher
>with some half-baked ideas. He wasn't one of the inner circle
>"professionals". Cantor was treated shabbily by some with more
>established reputations.
>
>The lesson to be learned from this is that "professional
>mathematicians" shouldn't be counted on in their own day
>to always serve as the best guides as to who, in retrospect,
>will achieve Hall of Fame status (same goes for other
>disciplines as well -- although in math it's more up for
>grabs in many ways, because "breakthroughs" don't have
>the same consequences as, say, the invention of a new
>technique for rapidly decoding DNA).
>
>This being the case, we can't say to our students that we
>really know for sure how math in the future will look, just
>going by what the "professional mathematicians" of today
>are teaching. Ian Stuart (a mathematician, and prolific
>popularizer of the discipline) says he can well imagine
>going into a room sometime in the future where "mathematics"
>is going on, but he can't fathom any of it -- yet he's open
>to calling it mathematics. Math is a dynamic, living
>discipline -- and for this very reason is not something
>we should expect students to "prepare for" in the sense
>of simply mastering material already known to others.
>The math of tomorrow is still up for grabs -- and this
>is exciting.
>
>So who are the leading lights we should be studying today,
>to get to the frontiers of tomorrow? Not always that easy
>to say. Not an easy question to answer. So lets leave this
>matter open and teach early math in such a way as to not
>limit our scope to the already recognized "professional
>mathematicians" as the only candidates in the "leading
>light" category. Some of those shaping tomorrow's math
>will not be considered "insiders" today. The discipline
>will continue to be shaped by outsiders -- part of the
>historical pattern.
>
>> 5. that "outsiders" are really "insiders" (Both Newton and Einstein
>> are considered GREAT mathematicians for reasons NOT related to
>> physics).
>
>Einstein is not considered all that great a mathematician
>by some mathematicians. Depends who you talk to. He himself
>was not boastful about his math abilities -- but did cite
>imagination and intuition as critical to his success as a
>thinker.
>
>> 6. the reasons for partitioning a school curriculum into different
>> subject areas,
>
>You presume to know all these things of course. You plan to
>sit on some high horse and lecture me about these points no
>doubt. Or do you just plan to enumerate my deficiencies?
>
>> 7. why specialization occurs in academic fields of study
>>and why it is important to specialize,
>
>Is it ever important NOT to specialize? Do you know about
>inbreeding in biology (a cause of species extinction).
>Do you admit that "overspecialization" might actually be
>a negative in ANY context? Is there such a thing as
>"specializing too early?".
>
>> 8. why it is important to teach pure math (as well as
>> applied math),
>
>I'm sure this is important and I didn't say it isn't. But
>I do question your wanting to use the NCTM as a bully pulpit
>for trying to push your "pure math" propaganda. I consider
>this inappropriate. I expect the NCTM will agree with me
>(new posters around Portland these days, advertising the
>advantages of knowing some math -- NCTM logo in the lower
>right).
>
>> 9. how the interplay between different fields of study
>> comes about and why it works.
>
>Quite a list. I should all sit at your feet now, presuming
>that you're here to fill this tremendous void in my appreciation
>of western culture.
>
>> For the most part I have been ignoring your agenda of converting
>> mathematics classes into computer science classes (I suspect most
>> people have and that's why nobody caught your little error). But
>
>More interesting discussion re these threads on k12.ed.math
>right now, I'm the first to admit (including stemming from my
>little error -- ever hear of Chief SOHCAHTOA?).
>
>> after your post on history, I have to wonder what qualifies you to
>> develop a curriculum in mathematics at all? Your apparent
>> disrespect for the profession you are creating a curriculum
>> for can only be destructive for your students. I truly pity the
>> students who going to be forced through your curriculum.
>
>I hear this a fair amount from people who don't have any
>cogent objections left at the bottom of their buckets, and
>decide it's time to gush pity for my "poor students" who
>a helpless victims of my "dangerous" curriculum.
>
>My students are free to read these debates I have on line
>with such as yourself (I link a lot of them from my websites).
>I make no secret of the fact that a lot of people whine
>about my school of thought.
>
>My students are free to make up their own minds about where
>they think the most useful curriculum writing is coming
>from. I get plenty of positive feedback.
>
>Kirby
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