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(this is a repost of something I've put up in the past ... but long ago, and edited)

Math, to hear most people talk about it, particularly most students, is boring, irrelevant, difficult, pointless and just a great big waste of time.  Maybe they're right.  When's the last time you divided fractions? Or solved a quadratic equation?

No, they aren't right.  And if you want to know why I don't think they're right, just join me below.

   This series is for anyone.  There will be no advanced math used.  Nothing beyond high school, usually not beyond grade school.  But it'll go places you didn't go in elementary school or high school.

   If you "hate math" please read on.
   If you love math, please read on.

   I welcome thoughts, ideas, or what-have-you.  If anyone would like to write a diary in this series, that's cool too.  Just ask me.  Or if you want to co-write with me, that's fine.

   The rules:  Any math that is required beyond arithmetic and very elementary algebra will be explained.  Anything much beyond that will be VERY CAREFULLY EXPLAINED.

   Anyone can feel free to help me explain, but NO TALKING DOWN TO PEOPLE.  I'll hide rate anything insulting, but I promise to be generous with the mojo otherwise.

Why teach math?
OK, we need to know some basic arithmetic.  
Even in this day and age, we need to know how to make change, tell time, and so on.  But, let's face it, very few adults ever need algebra, or trigonometry, let alone calculus or number theory.

Why teach math?

Well, to hear some people, math is supposed to teach you how to think. I duuno.  I think I was thinking before high school....if anything, I did less thinking in high school than before or after.  And, while I like to think that I do a little bit of thinking nowadays, outside of work (and some of my diaries here), I don't use math much, probably no more than you.  (At work, I use math quite a bit, I am a statistician).

Why teach math?

Why teach music? Why teach painting?  After all, how often in adult life are most people called on to sing or paint?  

We ought to teach math for the same reason we ought to teach painting and music.  Because appreciating math, and doing math, is part of what makes us human; it's part of what makes life more than a mere struggle to postpone death.  We ought to teach math because math is beautiful, awe-inspiring, and, well, a whole lot of fun!

No, I'm not high on drugs.  I really mean it.  And if you ask any mathematician about why they do what they do, words like 'beauty' will come up.

The real question, then, is why we teach math so freakin' BADLY!  Why do the statements above strike many who do not do math as absurd?  After all, I can't paint or sing, but I think of them as beautiful and worthwhile.

We teach math not just badly in the way other things are taught badly (or well), but in ways that are almost guaranteed not to give the essence of the subject, and to turn people off the subject.  For example:

What's the most basic math?  Maybe 1 + 1 = 2.  This is a profound and amazing abstraction of the world.  What does it mean?  Two great mathematicians (Bertrand Russel and Alfred North Whitehead, in Principia Mathematica) spent an entire volume full of very dense math trying to figure out what this meant, and to prove it was true, and then Kurt Godel came along and said they got it wrong! In fact, he proved that they got it wrong.

We teach math as if 'not getting it' means you're stupid.  What's one of the first things that confuses a lot of kids?   Well, one thing is negative numbers.  But it took the greatest mathematicians thousands of years to really figure out what these were.  

And then, in adult conversation, we talk about math as if it is some sort of badge of honor to be bad at it.  

No wonder (almost) no one likes the subject!

We ought to teach math as a voyage of discovery on some of the most beautiful seas man has ever sailed; then arithmetic becomes the equivalent of learning how to sail a boat, while math becomes the trip.

Since writing the above, I have begun to explore the works of Alfred Posamentier a math educator who seems to think the way I do (it's nice to find one!  The above was all 'out of my head' as, although I have a degree in education, I've never taught in a school).  I've also run into the best math teachers I've ever seen, Bob and Ellen Kaplan, who run the Math Circle, in Boston.  I wrote about them here

Originally posted to plf515 on Sun Oct 19, 2008 at 04:29 AM PDT.

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Comment Preferences

    •  if everyone knew math and science... (12+ / 0-)

      there would be fewer republicans

    •  As a mathematician (5+ / 0-)

      I appreciate your post.  

      I would also add that much of our present understanding of the universe and how it works uses a lot of math, from calculus through differential geometry.  By writing that off, you are writing off huge advances in intellectual evolution.

      I teach math a lot more than I research math, and I try not to teach it badly.  But, I do feel on some levels my hands are tied -- with calculus, for instance, it is so important to several majors and there are concepts that took two millenia to develop, then another several hundred years to iron out, and we have to squeeze it in in three semesters; as well as teach them the algebra they need to be able to understand it.  Some students really fly, but I think most just barely slink by thinking taking the derivative means bringing the exponent down and subtracting one.

      I've created a course for freshmen in my school based around the evolution of the concept of zero (structured loosely around Stief's book, Zero, the Birth of a Dangerous Idea) to try and get an understanding of how a wholly abstract concept can become "concrete" in our minds by working with it and understanding it in different ways, in different structures.  I think most people think of "zero" as concrete, really.  I think this semester my students are rather enjoying it.  They think it is hard, though.  (I am getting into calculus concepts.)

      Well, anyway, I have to go back to work.  :P

      •  IMO, every educated person. . . (6+ / 0-)

        needs to read Plato and Shakespeare and have a basic understanding of what calculus is and how it works.  That doesn't mean everyone will be proficient at using calculus but people need to understand that the mathematics of change is the great intellectual breakthrough that paved the way to the modern world.  Without that understanding we live in complete alienation from the knowledge basis of the world we inhabit and technology becomes a kind of incomprehensible magic.

        •  Ergo ... (4+ / 0-)

          My lost journalism major.  Coming from a family of engineers and not being intuitively brilliant at math, I still was shocked and apalled at the idea of graduating college without taking calculus!  So I had to switch my major to Psych.  And I got a nice chunk of statistics into the bargain, which has served me well ever since.  But it wasn't until I hit the internet during slow days on academic job, that I got introduced to Plato.  And that's a real shame, because Plato helps you understand the beauty in math, and the reason why it would be important whether you had to calculate statistical significance or orbital trajectories or NOT.

          Magic isn't incomprehensible.  Magic is ABOUT comprehension of how and why everything works.  Which is why my first teacher sat me down with a set of Isaac Asimov general science books on physics, chemistry, geology, astronomy, and math history and ran me through a full semester of science review and fundamentals before I ever cracked a volume of Crowley.  And why I won't teach Potions until a kid has finished Organic.

          Really.  The majority of trained ceremonial magicians in this country work as highly-paid IT specialists. Haven't you ever wondered why they call themselves "wizards" and make such outrageous salaries?

  •  This is early on a slow morning so I'll risk a (8+ / 0-)

    slightly off topic question.

    Are mathematical truths objective statements about the world or are they merely statements about human apperception?  IOW, Kant or Hegel?

    (Sorry, I knows it's still early.)

    •  My view is that they are objective truths (10+ / 0-)

      about any conceivable universe.

      3 is prime because it is, not because of how we conceive of multiplication.

      The way we state these truths, and which truths we discover, may be due to our apperception ... certainly using 10 as a base, for example, is likely due to our have 10 fingers.  But that's not the mathematical truth, that's just the language those truths are stated in.

      Some other civilization (or species) might discover truths that we haven't discovered, but they would still be true for us

      And that's different from provable.  Godel showed that there will always be statements that can neither be proven nor disproven; but that's not the same as saying whether they are true

    •  they can't be (5+ / 0-)

      mathematical truths are true within the realm of mathematics which is apriori defined. That's it. The fact that real things can, to greater or lesser degree, be modeled with math, is an entirely different point.

      I mean really, MajorFlaw, I thought you were an attorney and hip to such things :)

    •  objective truth is a social construct (3+ / 0-)
      Recommended by:
      MajorFlaw, plf515, jessical

      sayeth the historian.

      surf putah, your friendly neighborhood central valley samizdat

      by wu ming on Sun Oct 19, 2008 at 05:18:44 AM PDT

      [ Parent ]

    •  Not off topic at all. (3+ / 0-)
      Recommended by:
      haileysnana, MajorFlaw, plf515

      The diary brought up logicism.  Russell's logicism, at least, was an attempt to provide an account of objective mathematical truth that avoided the platonism tacitly referred to by some others that have responded to you.  Platonism is just the idea that mathematical objects exist in a non-physical realm, that they are timeless and necessarily existing.  

      Many philosophers have found platonism to be a tough pill to swallow, for a number of reasons.  One reason is that having posited these abstract objects to make true our mathematical statement it becomes difficult to understand how we've come to know anything about them.  Plato believed that human souls existed in the "world of the forms" before birth and that we obtained mathematical knowledge through recollection (the Greek word is "anamnesis").  Others, including myself, have found that implausible and fanciful.

      The logicist project began with Frege.  Frege's system was not without abstract objects.  His Basic Law V posited the existence of "concept correlates".  It would take us pretty deep into the weeds to adequately discuss that law, but it might be understood as giving both an account of what abstract objects are AND how we come to grasp them.  Sadly, Basic Law V falls to the Russell Paradox and Frege's system, indeed his life's work, was shown to be inconsistent.  

      Russell replaces Basic Law V with an axiom of infinity in the system of Principia Mathematica.  As I noted in a post below, he succeeds in deriving the Peano Axioms for arithmetic (and much more) in this system.  However, it now seems that the system is no longer purely logical because it is not clear how an axiom stating the existence of infinitely many objects is a logical axiom.  Also, Goedel showed that the system of PM cannot prove every arithmetical truth.

      •  I have a hard problem with most metaphysics (2+ / 0-)
        Recommended by:
        play jurist, cynndara

        My reaction is usually "Does anyone really think that?"  :-)

        •  Some "traditional" questions have become (1+ / 0-)
          Recommended by:
          plf515

          irrelevant as scientific discovery replaces philosophical inquiry.  Over time, the Empiricists win.

          •  I don't know if I agree with that. (4+ / 0-)
            Recommended by:
            haileysnana, MajorFlaw, plf515, cynndara

            Philosophers remain divided, of course, as ever.  It's said that mathematicians are platonists throughout the work week and formalists on Sundays.  Similarly, I'd bet that most scientists are realists throughout the week and empiricists on Sundays.

            •  Not sure I follow. (2+ / 0-)
              Recommended by:
              haileysnana, plf515

              Scientists are by definition empiricists.  It's the difference between scientific method and philosophical speculation.  Why speculate when there is evidence.  When Plato, Aristotle etc. tried to understand  the cosmos they could only turn inward.  Now we have Astronomy.  

              •  IF (3+ / 0-)
                Recommended by:
                MajorFlaw, play jurist, plf515

                you can get far enough away from the city to actually see the stars at night. Which is not a bad metaphor for clearing out the musty smog of social illusions/delusions before getting down to clear perception and thought.

                There are a HELL of a lot of social illusions centered around Science, too.

              •  We have different ideas of "empiricism". (4+ / 0-)
                Recommended by:
                haileysnana, MajorFlaw, plf515, cynndara

                Of course, science by definition involves subjecting theories to observational scrutiny.  If that's what you mean by "empiricist" then you are correct.  That seems to be the common meaning of the term for a lot of people.  In philosophy specialized meanings have arisen.  The distinction between a realist and empiricist (very, very roughly) is that a realist thinks observation provides evidence that things like atoms, electrons, quarks, etc. actually exist while the empiricist holds that we never have reason to believe anyhting more than that our theory is empirically adequate.  The empiricist thinks of things we cannot directly observe (things like electrons) as theoretical constructs not real entities.

                Theoretical phycists, btw, still do plenty of inward turning.  You are correct that they also turn outward and aim to check their theories by observation (hopefully, eventually, etc--see string theory).  But I think that the contrast between Plato/Aristotle, etc. is not as strong as you might think.  In Physics Aristotle opposede Parmenides on motion and change because the fact of change was evident to the senses, for example.  Plato and the Pythagoreans founded a research program of using mathematics to study the world.  It's true that they were less advanced than we are, but it is not clear that our advances are due to fundamental methodological differences so much as time and technology.

        •  LOL (1+ / 0-)
          Recommended by:
          plf515

          With six billion humans on the planet right now, I think you could find SOMEBODY who believes ANYTHING.

          Even flying spaghetti monsters, may Its Noodly Appendage touch us all.

          •  Really? (0+ / 0-)

            Anyone who believes that 1 + 1 = 17,322,306?

            Or how about someone who believes that we are actually living on one of the moons of Neptune, and that the idea that we are living on Earth is an illusion, fostered by the evil overlords, who have occupied the Earth since their home planet, Zarkon, is no longer big enough?

            :-)

            •  Welll ... (1+ / 0-)
              Recommended by:
              plf515

              The first is easy, given self-replicating biological systems; it just takes a while.  But with bacteria, probably no more than twelve hours.

              The second, you'd have to give me time to write the story, and plant and feed it for a while, then distribute it on the internet through viral propaganda channels working off the old UFO/Men In Black networks.  That could take a couple of years; I lost my main contact for that group when I left the university.  But then, there ARE the Victorian Goth sf fans my apprentice wanted to hook me up with over the holidays ...

              Remember that magicians practice believing six impossible things before breakfast every morning.  It keeps the mind flexible.

            •  It can be.... (1+ / 0-)
              Recommended by:
              plf515

              ... if 1+1=0.

              (Shame I missed this diary yesterday, missed out on really fun conversation :( )

              Insofar as I may be heard by anything, which may or may not care what I say... (from "Creatures of Light and Darkness", R. Zelazny)

              by SadEagle on Mon Oct 20, 2008 at 04:36:17 PM PDT

              [ Parent ]

  •  math is life (6+ / 0-)

    it is what I tell my students...

  •  I"got"math in cooking class,1/3 C meant something (7+ / 0-)

    fractions introduced in math class were a mystery,in cooking class fractions made perfect sense.

  •  Have to admit I had math block (9+ / 0-)

    most of my life.  Finally got over it as an adult after being forced to take statistics.  Funny thing is I never had a problem with design classes when I was an art major, which used lots of geometry.  

    Perhaps the problem was the way math was taught when I was a kid - perhaps it has changed; I'm not familiar with  grade school math teaching methods.

    Anthropologists for human diversity; opposing McCain perversity

    by Denise Oliver Velez on Sun Oct 19, 2008 at 04:44:36 AM PDT

    •  Stat is different... (6+ / 0-)

      I passed statistics and I suck at math. my wife took every math class in college she could find, got an A in all of them, but stumbled in statistics. i think stat might be different enough that non-math minds can get it a little better; I'm in the social sciences so could make some sense of stat. But not Algebra!

      •  I was scared to death to take stat. (3+ / 0-)
        Recommended by:
        tnichlsn, plf515, Pandoras Box

        Plus had the most boring prof on the planet.  Fell asleep during his lectures but did manage to pull off a B.  

        Thanks to working with folks like our diarist ;)
        I was thrown into the real world of quantitative data analysis - and dragged out my old stat texts to attempt to understand what colleagues were discussing.

        Now algebra - is another story.  I won't ever get it, and that's okay.  Only subject I failed and had to repeat in HS.  

        Anthropologists for human diversity; opposing McCain perversity

        by Denise Oliver Velez on Sun Oct 19, 2008 at 05:14:19 AM PDT

        [ Parent ]

        •  heh - I am the only sibling in my family (2+ / 0-)
          Recommended by:
          plf515, Deoliver47

          who really got algebra in high school.  I am the youngest of six and my brothers and sister before me did just horribly at it.  I ended up with the SAME algebra teacher they had and aced all my tests and homework...yet - when grades came out I got a "C" from my teacher.  When I asked him why - he said I got the grade I deserved (I guess he assumed I cheated since my siblings did so badly before me)

          That teacher retired halfway through the school year and it was straight A's for the rest of my high school math classes...

          "We struck down evil with the mighty sword of teamwork and the hammer of not bickering!" - The Shoveler

          by Pandoras Box on Sun Oct 19, 2008 at 05:36:08 AM PDT

          [ Parent ]

          •  he prejudged you (2+ / 0-)
            Recommended by:
            plf515, Pandoras Box

            and that's a shame. i've seen it work the other way too...had a family of 7 kids, all but one great writers, but the one son was merely ok but skated due to his sisters' reputation.

          •  Rosenthal's famous Pygmalion studies (0+ / 0-)

            found the same phenomenon. While everybody remembers that the kids who were labelled "bloomers" did better than expected, relatively few people remember that the kids who weren't labelled "bloomers" but nonetheless did better than expected (for perfectly ordinary reasons; kids experience intellectual growth spurts just like they experience physical growth spurts) were viewed negatively by their teachers and frequently labelled "disruptive." It seems a lot of people get ticked off when they're proven wrong, even when it's in a "positive" way.

            I do like conducting hearings in an actual hearing room -- John Conyers

            by ebohlman on Sat Oct 25, 2008 at 11:00:27 AM PDT

            [ Parent ]

    •  Grade school math teaching methods (6+ / 0-)

      seem to change with the seasons....

      The real problem isn't just the method, but that many of the people applying the methods aren't that interested.

      •  heh... (3+ / 0-)
        Recommended by:
        haileysnana, plf515, Deoliver47

        ...had to get this far down in the comments before disagreeing with anything.  What a lovely diary!!!

        But...eh.  Math is still taught as a series of rote techniques, repeated more or less annually, with a predisposition to favor competitive, "I'm smart you're stupid" formulae.  By high school it's "math team" for those who excel in that framework.  

        If we want interested teachers, maybe we should be looking at how we teach them.  Unfortunately, by the time your average or even very above average elementary teacher has reached their student teaching period, they've been told that they are stupid about math so many times it's a wonder they don't burst into tears when the subject comes up.

        Maybe we should look, not at the enthusiasm of the teachers, but how the subject is framed in the cirriculum -- the whole "tree ring" approach currently used.

      •  I guess (1+ / 0-)
        Recommended by:
        plf515

        I had many good teachers.  I can remember them going through the steps of deriving proofs and techniques; some of them seemed quite excited although looking back I'm amazed at how they could generate enthusiasm for a show they must have staged so many times.

        Still, after we got through the boring part of memorizing sums and multiplication tables, I always enjoyed the new concepts and logic patterns.  It was the endless drills afterwards that were so boring.  If you GOT it, why did you then have to repeat it, faster than you could write, fifteen hundred times?  I often got lower grades because I wanted to write out the whole progression, step by step, instead of just answers.  Of course I never had a problem with story or word problems applying the concepts.  It was just that everything was always rush, rush, RUSH in class, and then endless mounds of homework when one or two problems was enough to prove the point.

        Thinking about teaching it ... why would the teacher want to grade so MANY damned homework problems?

    •  You might be better at math than you think (5+ / 0-)

      Am artist is someone with an intuitive grasp of concepts with deep mathematical significance.  You were simply never taught to recognize this. That is the great tragedy of mathematical "education".

      •  Thank you - I never looked at it that way (3+ / 0-)
        Recommended by:
        dharmafarmer, plf515, xgy2

        as "intuitive".  Makes me feel better :)

        Anthropologists for human diversity; opposing McCain perversity

        by Denise Oliver Velez on Sun Oct 19, 2008 at 05:48:55 AM PDT

        [ Parent ]

        •  Absolutely. (1+ / 0-)
          Recommended by:
          plf515

          Aesthetics seems to be built on intuitive recognition of two mathematical basics: symmetry and the irregular but incremental repetition characteristic of chaotic functions (that's why graphs of chaos functions are so beautiful people frame them as art).  "Intuitive" simply  means that your mind handles the calculations by Fuzzy Logic on an unconscious level and doesn't bore you with the details.  There are advantages from doing these things consciously, mostly in correcting the occasional errors of fuzzy logic and in teaching, where it helps to know WHAT and WHY you're doing what you're doing in order to show people.  But for actually DOING it -- subconscious cognition is about ten times faster and usually much more satisfying.

  •  Three words ... (6+ / 0-)

    Yes, Joe Biden, I can count:

    "Margin of Error".

    How are you ever going to understand polling if you don't know what mathematics of statistics underly the method of calling 1,000 ("randomly chosen") people and decide how the country as a whole is going to vote ?

    Do you know what "randomly chosen" means ?

    Do you know how to skew the results by getting this "wrong" (i.e., bend the rules to your advantage) ?

    I could go on ... and on ... and on ....

  •  I remember reading years ago about (11+ / 0-)

    the Fibonacci sequence and how it expressed itself in nature so beautifully.  

    My husband decided one year that, for vacation reading, he would take up reading about chaos theory and fractals...wow...all i can say is that if god is ANYWHERE...it's right there...expressed in beauty and power and infinity

    math is amazing indeed

    I like a nice Mandelbrot set to go with my morning coffee!  :p

    "We struck down evil with the mighty sword of teamwork and the hammer of not bickering!" - The Shoveler

    by Pandoras Box on Sun Oct 19, 2008 at 04:47:12 AM PDT

  •  I am not proud of being bad at math (5+ / 0-)

    I've always been rather ashamed and pained with feelings of inadequacy. Seriously. When friends of mine who are in the sciences ask why I didn't go to medical school or get a PhD in psychology, i tell them the math requirements in college scared me off. Plus physics and organic chem might as well be math classes. i got through statistics in a county college with a B+, a major accomplishment for me. I have no idea why I can't do math; I have a decent IQ and can write and read well. But numbers leave me utterly speechless. yet my son, who can't pass a reading test to save his life, takes to math without an issue. Gets it from his mom, not me. he doesn't even bother to ask me to go over his math HW, because I don't get it.

    •  The weird thing is that although I'm a physicist, (4+ / 0-)
      Recommended by:
      jerseydan, plf515, jessical, Neon Vincent

      I'm not all that great at math.  I can do all the math I need to do physics, but at it's core, physics isn't math.  

      And organic chemistry is just smelly and nasty, and I refuse to have anything to do with it.

      •  Organic chemistry (2+ / 0-)
        Recommended by:
        plf515, Neon Vincent

        is COOKING.  I sucked at labs until I figured that out; I honestly thought it was "Science".  Actually,  it's about mixing ingredients, adding a little heat and physical manipulation, maybe a freeze-thaw, and of course, knowing when to spit on the stirring rod and when to keep your paws off ... oh, and all those wonderful tinker-toy models of molecules hung from the lab ceiling ...

        I do so wish I had known that all before I was three-quarters of the way through college and couldn't change my majors any more.  I'll admit, though, that it helps to keep your windows greased and the fan over the stove in working order.  Especially if you get phone calls in the middle of projects ...

      •  Ya know (1+ / 0-)
        Recommended by:
        plf515

        I had a friend in college who was not so hot in math, but passed the placement exam. So did I, incredibly. He told the advisor he didn't like math, but believe it or not he was an accounting major...the advisor, in all seriousness, said he was not surprised by that at all. I guess my notions about math oriented professions are wrong. And even in grad school in social work, I kept running into people who had MS degrees in microbiology and computer science, and I was like, what the hell are you doing here in social work? Then again a lot of people come into it from other professions, so who knows. And we do have our share of numbers crunchers in this field, believe it or not ( all tied into funding ).

  •  Here's a joke for you from Cambridge MA plf! (4+ / 0-)
    Recommended by:
    plf515, Pandoras Box, jessical, Jimdotz

    Q-  How can you tell the difference between the MIT students waiting in the '10 or less items' check-out line and the Harvard students waiting in the '10 or less items' check-out line in the grocery store, with 15 items in their carts?

    A-  You can't! The MIT students can read and the Harvard students can count!

    Yuck, yuck! A friend from MIT who worked a cashier's job one summer about a hundred year's ago told me that one! I, personally hate calculus. I had a really dreadful teacher my first semester undergrad and never recovered. It is the main reason why I've never took to the calculations heavy side of chemistry. This country needs to invest heavily in skilled math and science teachers in january if we are ever going to get back on track after the huge wastes of time and resources fending off the creationist idiots these past 8 years.

    Support democracy at home and abroad, join the ACLU & Amnesty International http://www.aclu.org and http://takeaction.amnestyusa.org Your voice is needed!

    by tnichlsn on Sun Oct 19, 2008 at 05:07:34 AM PDT

  •  agreed (7+ / 0-)

    and to this i would add that people don't always know what they're good at, or enjoy doing, until they get several tries at it, often with different teachers or methods, and at different points in their lives.

    thus, we should teach math because some people might discover that they really like it. it might open doors to other stuff that they hadn't expected. or they might suck at it, but still find their understanding of the world expanded and enriched because of studying it.

    same goes for everything.

    surf putah, your friendly neighborhood central valley samizdat

    by wu ming on Sun Oct 19, 2008 at 05:18:16 AM PDT

  •  math is everything! (5+ / 0-)

    my kids got sick of hearing it, but they know their math (and science) ;)

    Electronic media creates reality - Meatball Fulton The less you know, the more you believe - Bono

    by zeke7237 on Sun Oct 19, 2008 at 05:32:06 AM PDT

  •  Math and God (5+ / 0-)
    Recommended by:
    plf515, jessical, cynndara, TL Eclipse, xgy2

    Here's my personal reason for studying math.
    The Bible (or the Torah, or the Koran) is supposed to be the word of God.  But, there are so many different versions of it, and so many blatant contradictions in it that it's "infallibility" is impossible.  
    So, if we want to understand God, where should we look?  

    The Universe.  His creation.  

    Every science has, at its roots, mathematics.  If you want to make a model of a star, you need four simple equations.  If you want to see where a planet will be, you need one equation.  If man was meant to fly, he'd know about Bernoullis's equations, and would figure out aerodynamics.  

    The Universe is an open book.  It is written in mathematics.  If you want to READ that book, you need to study math.  

  •  The Problem (3+ / 0-)
    Recommended by:
    haileysnana, plf515, cynndara

    Peter,

    I think you're missing an important point. Here's the question I raise: Given the limited time available to educate the young, and given the near-infinite variability of their interests, talents, abilities, capacities, and so on, does it make good sense to lock in ANY discipline, subject, or course?

    Life, liberty, and the pursuit of happiness require maximum exploitation of the full range of human potential. Math? Yes. Music? Yes. Painting? Yes. Manual dexterity? Yes. Mental model building? Yes. Etc., etc., etc.

    A curriculum that attempts to standardized the un-standardizable is, IMHO, irrational. Great mathematicians, scientists, singers, painters, surgeons, etc. aren't products of an educational system that runs every kid through the same regimen, and schooling that does that wastes human potential at a near-criminal rate.

    Math? Yes. But don't put "the "math naturals" in a class with 29 singers, painters, actors, writers, or others intent on rebuilding transmissions, feeding the hungry, healing the sick...

    •  Hi Marion (2+ / 0-)
      Recommended by:
      haileysnana, cynndara

      In this diary, I don't think I said anything about standardizing anything.  I'm certainly not in favor of a standardized education .... one size does not fit all.

      I agree that math naturals should not be in a class with singers; but math naturals need to be exposed to music, and music naturals to math.  And, just as someone who can't paint at all (e.g. me) can still look at a Rembrandt and say "wow", so someone who can't do math at all can learn to look at, say, Euclid's proof of the infinitude of the primes and say "wow".

  •  Re: Russell and Goedel (3+ / 0-)
    Recommended by:
    scrutinizer, sngmama, plf515

    First, Principia Mathematica (PM) developed much more logicist mathematics than basic arithmetic.  Second, PM provides a consistent system that proves the axioms of Peano arithmetic.  Third, Goedel didn't show that Russell and Whitehead got anything wrong.  What he showed was that they couldn't "get" everything right.  That is, the system of PM is incomplete because it cannot prove every truth of arithmetic.  In fact, EVERY (first-order) axiom system strong enough to prove the Peano axioms is incomplete.  This MIGHT be taken as dooming the logicist program in philosophy of mathematics (to reduce mathematical truth to logical truth), but it is far from showing that any of the formal results of PM (including that 1+1=2) are incorrectly derived.

  •  btw... (2+ / 0-)
    Recommended by:
    haileysnana, plf515

    ...plf, I don't keep up with but a fraction of your work here and elsewhere, but have read a fair number of your essays.  And I have to say, to this reader...this is perhaps the best.  It combines passion and openheartedness and interesting peices of the world at that intersection where the 300 to 800 words we get per essay becomes art.

    Thank you!

  •  I love statistics (1+ / 0-)
    Recommended by:
    plf515

    I always got A's and B's in all of my math subjects. Unfortunately, I didn't know I could make a career out of it. In my next life, I hope I can make a good living out of my love for math.

  •  When my 9yo daughter says she hates math (1+ / 0-)
    Recommended by:
    plf515

    I tell her that she is confusing "math" with "arithmetic."

    "Perhaps it is music that will save the world." —Pablo Casals

    by Fredegonde on Sun Oct 19, 2008 at 06:30:21 AM PDT

  •  Whenever I sub in math (2+ / 0-)
    Recommended by:
    plf515, Neon Vincent

    I tell the kids to work hard and learn it, no matter what.  I tell them that getting to my tender age and being math phobic is very nearly a disability.  I also tell them that the surest way to get cheated out of hard-earned $$ is to not know math.  I don't know if any of that makes an impression.  They have learned to save real math questions for when their teacher comes back.  Every once in awhile, they put a hand up and, as I start toward their desk, they say,  "Oops!  Never mind.  I'll wait."  God bless 'em :-)

    -7.62, -7.28 "We told the truth. We obeyed the law. We kept the peace." - Walter Mondale

    by luckylizard on Sun Oct 19, 2008 at 07:34:46 AM PDT

  •  math is good or bad in large part depending on (1+ / 0-)
    Recommended by:
    plf515

    what you do.

    It's impossible to avoid it completely but there are certainly some professions that either use it less or use it by instinct.

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