
Re: meeting other mathematics people
Posted:
Jan 24, 2004 6:00 PM


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 k12 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 K12 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 mathrelated 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 K12 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 halfbaked 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

