Mathematical Memories


There’s this post, you see, up at a new blog called Hyperbolic Guitars, that’s dredged up some old memories:

We should have, as a goal, to never hear the question “why are we learning this?” again.  No one asks why we learn to read.  The same should be true for basic mathematics.  Once students go beyond the basics, they should learn what their natural interests require of them.  The job of a mathematics teacher, once a student achieves basic mathematical fluency, should be to shine light on where mathematics lives in the world, and to point the curious student in the direction that they wish to go.  And then to stand aside.

The teachers, the engineers, the musicians, the artists, the scientists – all of us need to demonstrate – not EXPLAIN – how the quantitative complements the qualitative; the reasons that knowing why is as important as knowing how.  Or what.  Or when.  Or who.

I remember math.  I remember spending a good part of elementary school living in dread of it, because after I’d proudly learned my numbers and some basic addition and subtraction, it started getting nonsensical.  No one told me multiplication and division could be cool, just that they had to be done.  We had timed tests.  Those timed tests comprised a goodly portion of my academic dread (and I was a nervous child, mind).  I’d freeze.  I’d fail.  And freezing and failure led to more freezing and failure, until I became convinced that mathematics was an Evil Subject that Was Not For Me.


Something clicked early in middle school – don’t know what – but we got to the more complex stuff at the end of the basic math courses and all of a sudden, I was flying.  Math was fun.  I could own this shit.  It made sense.  Numbers spoke to me.  Oh, and the tests weren’t timed, so that pressure was off.  Just a nice, happy communing with numbers – until the school said, “Congratulations!  You’re doing so well we’ll just let you skip the rest of this and get right into pre-algebra.”


It was rather like someone deciding a hole in the ground was as good as a finished foundation and trying to slap a house up on top of it.  I collapsed.  Numbers, once more, made no damned sense.  And the book – oh, that book, with its horrible word problems.  My dad, incensed that his daughter, the daughter of a civil engineer, couldn’t do pre-algebra, sat down one night to explain to me just how easy it was.  He looked at the book.  He fell silent mid-rant.  He flipped a few pages.  And then he told me he didn’t understand it, either.  What, he asked, did any of this have to do with real life?  This wasn’t how math behaved in the real world.


He worked thirteen hour days, so he didn’t have time to teach me when the teachers couldn’t.  He tried, but by then, I needed too much time and attention, and his books were decades out of date, and what he did the teachers tried to undo the next day, because it wasn’t the way it would be on the test, and so he gave up.  We both did.  Math became one of those subjects that I scraped by in.  The numbers never talked to me, and I could see no possible way it would ever be relevant to my interests.  I didn’t need algebra to balance a checkbook.  I had calculators to deal with the calculations.  And all I ever wanted or needed to be was a writer, and what writer needs calculus?


SF authors, actually, but nobody ever told me that.


There was only one more time when math made sense.  It was in high school chemistry, and our chemistry teacher didn’t take for granted we’d have learned any of the algebra we’d need.  So he taught it to us.  It had context, it was directly applicable to what we were doing, it helped us do interesting stuff with chemicals, and I loved it.  I could do it.  I could solve the problems.  But he was the only one who ever did that.  It was back to story problems and divorced-from-my-reality-bullshit-complete-with-blond-jokes-in-geometry for the rest of my academic career.  


And no one ever told me, ever, in all that time, that music and math were related.  Never told me where algebra came from, or how powerful it was.  No one ever said that calculus had been only a comparatively recent invention, and what a universe it had unlocked.  Math was never put in context.  The closest my math teachers got was some vague hand-waving about algebra being useful if you forgot to record a check in your checkbook (like we couldn’t just call the bank) and some extraordinarily lame “What if you were trapped on a desert island without a calculator?” bullshit when they tried to get us to go without calculators.


I felt that, in that case, solving for x wouldn’t be high on my list of priorities.


So I missed out.  There’s a whole enormous universe of numbers out there, and I don’t speak the lingo.  I can’t understand what they’re trying to say.  I never knew about “happy primes” until I watched Doctor Who and thought no such thing existed.  But they do.  There’s whole realms of happy and sad numbers.  Why don’t they teach recreational mathematics? 

I can’t tell you how to fix education.  But I can tell you what I needed: I needed teachers who loved the subject.  I needed less teaching to the test and a lot more exploration.  I needed strong foundations built.  I needed the who and the what and the when and the where and the why.  I needed teachers who demonstrated what math was good for, and the astonishing things it could reveal, and how art and music and myth and fiction and science and engineering and politics and just about everything else used math, could be inspired by it, could be given power and potential by it.  I needed to be shown how math tied in to other subjects.  I didn’t need it walled off from everything else, as if it was a noble gas that refused to react with anything else.  I needed to see it as something every bit as dramatic and exciting as a great story (which it can tell), and as uplifting and inspiring as a song (which it can be).  I needed to make friends with numbers.  I needed to understand you don’t have to be born good at math in order to become good at it.  And I needed to know it was beautiful.

If my teachers had done even a fraction of that, I’d very possibly have gotten right up through calculus.  Equations would still hold mystery, but they wouldn’t be mysterious.  I’d be able to suss out their secrets.  We’d be able to converse, these numbers and I.  Instead, we’re doomed to stuttering, stilted conversations held only when translators are available, and I don’t understand a tenth of what they’re saying.  That hurts, sometimes physically hurts, and it’s held me back in life.  It’s kept me from delving as far into science as I’d like to go.

So yes, education in this country is failing miserably, and I’m damned glad there’s a good place to have a conversation about it.  Maybe someday, if enough of us get talking, we can change the academic world.

Comments

  1. Lyle says

    It is interesting that Feynman in his lectures in physics shows a love of the subject as well and it shows in how he is able to explain things. So your comments apply at all levels, if a teacher really loves and gets his subject she does a better job.

  2. Karen says

    I struggled mightily with first year calculus in college; failed the first exam in the fall quarter, and had to spend time in the Student Services Center listening to "math-anxiety" tapes to get myself un-freaked. Squeaked by that quarter. Then, in the winter quarter, I took physics. Suddenly calculus started to make sense! It was a way of expressing relationships between concepts like mass, energy, motion… Solving the problems was still hard, but they had meaningful answers, and you could tell if the answers were making sense. That was when I really started to learn calculus.

  3. says

    Same here, Karen. I didn't have a clue what most of the mathematics I learned could be useful for until I started taking physics. I don't know why that is – many of the teachers I had were at least interested in the subject. I think it just takes having to actually work with something to see its utility.Heck, Isaac Newton was supposed to have developed integral calculus on his own to help him work out principles of physics.