Friday, February 17, 2006

On Math Education

Yet again, I long for a time machine, in which I could travel back to talk to my younger self. Not to save myself from embarassment or pain, but to deliver a simple message, just a few words long.

It's my Grade Eight self who needs to hear this message. He's about to completely slack off and send me (us?) into a spiral of lower and lower math grades, culminating in flunking Math 12, avoiding Chem 11 and 12 and Physics 11 and 12. And for no reason at all, besides laziness and apathy.

Well, there is one more reason. No one, not one person in high school, ever told me that math was fun. That's the message I'd take back, if I could.

My girlfriend (she who is both wise and beautiful) has recently started a math course, as one of the prerequisites she needs to get a teaching degree. When she signed up for it, she was worried, because she had always thought she was bad at math. I assured her that she was bright in every area, and of course, I was proved right. She has flown through the course so far, and is getting a mark in the mid ninetieth percentile.

The course is essentially every type of math you might teach in elementary school, from basic addition and subtraction to algebra, factoring and geometry. It includes not just what the students have to know, but the basic ideas and concepts behind the elementary school lesson plans. The entire course is crammed into one semester.

I've been following along in the textbook, so she'll have someone to study with. It's made me realize some things about the way I was taught math, and where I went wrong.

When I was a kid, I consistently did well in every elementary school subject, As and Bs predominating on every report card. When I was in Grade Six, I was plucked out of my regular class and with about 15 or 20 other kids, I was tossed into an advanced math class, the only class taught by our principal. He was a great math teacher, a man in love with the subject, and that love was infectious. I did pretty well, although I was far from the brightest kid in the group. Two years later, most of my advanced math classmates and I went to high school and jumped straight into Grade Nine math.

This is where I started to falter, and it was almost entirely my own fault. I'd done well in just about everything in elementary school, but I'd known since I learned to read that words were my first love. History, English and especially writing was where I could really shine. And everything else was boring. I started to slack off in math.

Again, I was lucky enough to have a teacher who loved his subject. He really encouraged everyone to take math all the way to Math 12, and Calculus, even though neither is required for graduation or even (back then) for entry into university in some arts programs. But I didn't care at the time, so my grades slipped and slipped, until I was failing a subject in which I'd once been considered gifted. My teachers deserve none of the blame, and the majority certainly rests on my shoulders.

My teachers, of course, tried the usual tactics to get me to do better and stay in the course. They told me about how many jobs need math, about how hard it is to get into some college courses without certain courses and grades. The thing is, I knew it didn't matter. I had decided by Grade Eight that I would be a reporter. It involved writing, and it would only require a two-year diploma, and then I could be out there working instead of sitting in another classroom. And my plan worked perfectly, in fact. I've been working full time since I was 19 years old. And no, I didn't need the higher math I missed out on.

I did, eventually, learn to miss the fact that I hadn't taken the math courses more seriously. I'm a science fiction nerd, and sometimes I knew I was missing things when I read SF or popular science books. I've picked up the odd mathematical fact here and there, but nothing systematic. Not until my girlfriend (who is both wise and beautiful) started her course.

Now I've discovered the joy that comes with getting it. The pleasure that comes from finding a solution to a seemingly unsolveable problem. I'm enjoying math in a way I haven't since I was in elementary school. (The fact that I can hash out the solution to problems with a loved one does not hurt at all, but I suspect it isn't strictly required.) Why am I discovering this now, and not then?

Because no one is forcing me to do it. Because I'm not being given purely utilitarian reasons for doing it. Because I can yell at the textbook when it deliberately obfuscates things, because I'm free to ask why a certain problem should be done a certain way.

While my teachers are not to blame for my failures, a part of the blame has to rest with the system they find themselves in. The entire high school educational system in Noth America is geared towards producing either basic high school graduates or college entrants. The requirements for both are basically arbitrary, at this point. The courses you take are either completely unneccessary for the unskilled, low wage jobs at the bottom of the barrel, or they are inadequate for the high-skilled jobs, which will require either technical or academic training at another institution. Everyone involved, from teachers to students, knows this. As students, we know there are a set number of hoops to jump through. You must have X, Y and Z courses from the humanities stream, and A, B and C from the sciences side, to graduate at all. Add in D, E and F courses to qualify for your postsecondary stream of choice, whether it's a trades apprenticeship or a university entrance. Our teachers, the better ones, try to get us interested in the course material for its own sake, and we take a course we like when we can, but mostly we're just trying to get to the next hoop. (I never took English Lit 12, either, because it conflicted with another course I needed more, but enjoyed less.)

Most importantly, I don't remember anyone ever telling me that math is fun. It was suggested that it was needed to make me a well-rounded individual, that it would be useful for so many, many careers. But those strictly utilitarian arguements don't work on students who already have their own utilitarian plans for graduation and career lined up.

I'm not dismissing utility in education, of course. But we expect life to be more than the mere utility of eating, sleeping and passing on our genes. We have the best toybox in the history of life between our ears, and math is one of the toys inside. It's criminal not to tell students that, at least once. At least then, the system and the teachers would have tried.

Others have noticed that something is wrong with the way we teach and learn. A system that is supposed to teach us skills, doesn't. A system that desires to make us well rounded doesn't ask us what "well rounded" is. A system that should show us the pleasure of learning offers only dull utility as an explanation for all its courses.

Progressive Review has this story about the roots of the modern American education system. Kevin Carson has commentary on that article on his Mutualist Blog and on this article on a similar theme.

Meanwhile, over at Pharyngula, P.Z. Meyers is plenty pissed about a Washington Post column that suggests no one needs math for a fulfilling life, and that algebra might just be too hard for people. The comments section vigorously defends math, with mostly utilitarian arguments again. But some of the posters are questioning the way students are taught in the first place, which is a good start.


Anonymous said...


I found this entry a little surprising from you. Not because of the subject matter but because I felt that your message was quite mixed at the end of the passage.

You state the your math teacher was excellent and I heartily agree. I had him for three consecutive years (Math 11, Math 12, and Calculus AP) and he was always engaging and a very good educator, capable of explaining complex math topics with some ease. I can say that he was also always available after schools for help, and I availed myself of these times a few times during my Calculus course.

Anyway, you state, quite rightly, that your loss of interest in Math was almost entirely your own fault. So far so good. But then you nonsensically blame your Math teacher for offering you bland platitudes in an attempt to rekindle your interest in math. So even without saying it, you are passing the buck to some one else. You claim to hold anarchistic principles dearly, but the chief principle of anarchism is, and must be, personal responsibility. By passing the buck on this issue you are not really acccepting personal responsability for your choices. I know that you say you are responsible, but that does not come across in you essay, instead you focus on how some one else didn't do you justice in your school career.

Well, from what you have said, andd from my own personal experience with this teacher, I can say that he did the beest thing that a teacher can ever do to create interest in the subject he taught: he came to work each day and loved his subject and projected that love into his classroom. Really, this is the most that any teacher can do and this specific math teacher did it in spades.

So anyway, I just think that it's slightly hypocritical to talk about how it's your fault that you didn't go further in maths (and it is your fault) an then turn it around into a criticism of the education systeem when your criticism goes against the very principle of the political thought that you are try to put across.


Catherine Johnson said...

What a fabulous post!

For what it's worth, I don't think your loss of interest in math was your 'fault.'

I don't know what the answer is to capturing & then holding students' interest in math as they age. I'm struggling with that issue myself, as a parent.

Middle-schoolers are mostly interested in other middle-schoolers, as far as I can tell!

One thing I do know: kids like subjects in which they succeed.

I'm wondering whether your 8th grade course was structured so as to shift the 'burden' of academic persistence (best term I can come up with) too much to students at too early an age.

If you're interested, we have class descriptions from two superb 8th grade math teachers posted at Kitchen Table Math.

I don't know, of course, but my guess would be that classes like these - in which the teacher is the 'Maximum Leader' - may end up holding more kids in math long enough for them to reach the age at which utilitarian persuasion may work.

Here are the links, in case you're interested:

Smartest Tractor on teaching algebra

Smartest Tractor's description of her course

Gambill Method of teaching algebra

Like you, I have (very) belatedly discovered that math is fun.

Drew said...

Unlike you I started my school life hating math, there was a time in grade four learning how to multiply two digit numbers that I just wanted to quit. Since then I have moved on from there and now enjoy math very much. Particularly high school math, where class was just a 'good time'. You're right, that joy comes from figuring out a problem especially one which has been troubling for a long period.

The problem I believe, as do you (if I understand your position correctly) lies in the way math is delivered. In high school and elementary, after you've mastered the basic reading skills, so it is no longer a chore, reading becomes fun. Naturally this is because the material is interesting and lets the mind explore alternate relates, and thoughts. However you never truly master the 'basic' skills of math as they keep piling more on. Once you get the numbers, then there's addition/subtraction. After that multiplication/division, fractions, ratios, rational numbers, quantities, variables. It's just one rule, theory, or idea after another no time to actually enjoy the process or 'story' of the math.

I'm not really sure where I'm trying to go with this so I'll just stop there. But one needs to truly consider this, in a world which uses math almost as much (if not more) then written language, surly there must be a way to lend excitement to an otherwise mechanical, boring subject.