Math Mania: Why teach math? Why sing?

(cross posted from Daily Kos)

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 read on


   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

15 comments

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  1. My Algebra II teacher in high school, after several meetings after class, gave up on me, and my parents, unable to help with my homework, weren’t too concerned about my low math grades.  A shame, because I was fascinated with numbers before that eleventh grade math class.

    • Robyn on October 19, 2008 at 7:08 pm

    Well, one thing is negative numbers

    Fractions and long division are where most people get lost.  And long division is ultimately fairly useless until one proceeds into modular arithmetic (which can be taught much more easily using clocks) and abstract algebra.

    Fractions, though are vital…and we teach them badly because the subject elementary teachers are usually the worst at is math.

    • AAF on October 19, 2008 at 7:55 pm

    terrible at maths but I want to learn. Is there a course for dunces available on the net?

  2. We (my parents, brother/SIL/nephews & I) were just talking about teaching/learning math at shabbat dinner Friday night.

    I met with a woman last week to fill out some paperwork for an assortment of state services I have to (very reluctantly) apply for. I get two checks a month from Worker’s Comp — same amount, every two weeks, that’s my income (family is a wonderful thing, or else I’d be living in a cardboard box somewhere). I had two check stubs right there. At one point (I didn’t know where she was going with this) , she wrote down:

    ###

    x 2

    ____

    and proceeded to laboriously go through:0 x 0 = 0 (not speaking aloud, thank gods, but tracking the numbers with her pen). She apologized for not having her calculator.

    I told her what the final number was (she didn’t even have to carry a 10!) — and then it turned out that what she really wanted to know–

    The final number she was looking for–

    Was what half my monthly income is.

    I managed not to react at the time, but, damn.

    I strongly doubt that the woman is constitutionally incapable of memorizing some times tables, or of understanding that half of two identical things is one thing. But somehow, the concepts weren’t there.  

    • frosti on October 20, 2008 at 2:48 am

    I put a deposit on a couple  of pasta bowls, and bought a couple of mugs in addition when I went to pick up the bowls.  The clerks used a computer to add up the total, and I told them the total was wrong, because I added it in my head.  They argued with me because the “computer said so”.  This went on for  some time–they were sure the computer couldn’t be wrong, until I rounded each item up to the nearest dollar and it was still less than they charged.  Of course, the computer had added the deposit as a charge instead of subtracting it as a payment.  

    Point is, people can’t do mental math anymore, and they thought I was nuts when I told them I was adding in my head!

    • kj on October 20, 2008 at 4:22 am

    i will NOT learn math.

    i will NOT learn math.

    i will NOT learn math.

    math has invisible numbers, ergo, math is not real.

    SO THERE you damn mathites!  

    patterns are pretty.

    math is stoopid.

    i have all the fingers i need to know math.

    damn mathites.

  3. at least to me. I see it in my head. I eventually got a degree in Physics, but don’t consider myself to be much of a math geek. I just see it. I think that’s where many stumble, they don’t let it in. That from my days tutoring; so many have just decided they can’t “do math.”

    My best case was a blind (from birth) student who was failing Algebra. I worked with her for most of a semester, stressing “visualization” of the way the equations worked. Interesting thing to try to do with someone who had never seen, and interesting since she worked in Braille. She got a “B” at the end. Her mother called me to let me know she did better than anyone expected.

    What makes me crazy is when I get a total of, say, $5.80 and I hand the cashier $11. They usually hand me back the $1 bill – they don’t get it that I want $5.20 back instead of more $1 bills and change. Or the people who can’t make change without the cash register telling them what the change is…. Sheesh.

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