In Ireland and the UK they use ‘maths’ as short for ‘mathematics’ and not ‘math’ as we do here in the States. I like ‘maths’ as it more properly conveys the richness and dimensions of mathematics. It should be a plural word as it’s an enterprise of many facets.
I was thinking about maths yesterday when my friend told me of her ambition to be a high school math teacher. The first thing I told her was the people most responsible for everyone hating math are high school math teachers. I’m very encouraging, don’t you think? But it’s not really their fault. There’s only so much time and so many school days and you have to have calculus-ready youngsters for college so you teach to that cohort of kids and let the rest fall by the wayside. There are two consequences to this weed-out process. One, you find out which kids are good at math. Two, you convince a bunch of other kids they can’t do math.
The problem with high school algebra is that it is only good for one thing: learning more algebra. You have to get to a certain facility with algebra before any kind of larger understanding or appreciation emerges. It’s just grammar before then, the rules of the road for mathematical relationships. Imagine English class as being nothing but grammar. No poetry, no speeches, no drama, no creative writing, no literature. Just grammar. That’s basic algebra. It gets dull quick. If you are good at it, it can be fun, like a puzzle. Even if you aren’t, it is pretty clear-cut if you are the analytical sort, and you can get through it without much trouble.
But if you are put off by the abstraction, or have some skill weaknesses in things like fractions, it can be rough going. I remember discovering at a very young age that I was never going to be a baseball player. I did not possess the necessary natural grace, hand-eye-coordination, and fast reaction times to succeed at the sport. Like athletic talent, math talent varies from person to person. Some people have mathematical intuition, like some people have a good ear for music.
For those of us who aren’t athletes, discovering physical things that we can do for fun and fitness is very important. I found out I can downhill ski, ride a mountain bike, and play slo-pitch softball with sufficient competence that I make time to do all of them. Lots of people do this. Music is another thing I stink at. I’ve got no sense of rhythm. I can sing in a choir because I can listen and match my voice to the notes I hear, but I can’t start a song because I don’t hear the note in my head. But I listen to music, read and learn about music, and pester my musically talented friends to show me things I’m curious about. I even took Music Appreciation in college.
What’s this all to do with maths? Well, do you hear of anyone taking Math Appreciation? Do you talk to your friends about which new math you are going to try to learn? Do you go to the math club to tone your math muscles? No, of course not. Math, for most, is something to endure. Then forget. Which is a shame, as mathematics is not only one of the great accomplishments of civilization but it is fundamental to the natural sciences, engineering, and economics. You can’t do those things without math. Math is also powerful and beautiful for it’s own sake. People sometimes make music for no other reason than the joy it gives them. Believe it or not, math can be that way.
But we don’t have the time, inclination, or infrastructure to develop a larger pool of mathophiles. I do think we could reduce the pool of mathophobes, and that would be a good thing. People who aren’t good at sports don’t necessarily hate sports. They might even like sports. People who don’t make music don’t generally hate musicians, and most enjoy hearing other people make music. But people who find out they “aren’t good at math” run away from math and never come back.
How to fix that? And why? I contend that mathematical illiteracy, or innumeracy, is a bad thing. We are asked to look at quantities and rates all the time and make personal, financial, and political decisions based on these things. If we don’t have some mathematical competence then we are crippled in our ability to think clearly and we will make poorer choices. Some basic facility with maths is just as crucial to the big ideas of the modern world as being able to read critically. It’s also important to fight innumeracy because math phobia closes doors. Kids who are willing to get through advanced math classes have more choices later on.
I think we ought to figure out what kind of maths kids can learn even if they are lousy at math. That is, if they can’t stay on the algebra-to-advanced-algebra-to-calculus treadmill that doesn’t mean they can’t learn something. Lots of people learn a workable Spanish so they can travel around Central and South America. They may never read One Thousand Years of Solitude in the original but they can function in a foreign land. That’s quite a skill. Can’t people learn some useful, operational math like that? Just because you can’t do differential equations doesn’t mean you can’t do other stuff.
So I would say to prospective math teachers and to the next generation of schoolmasters not to neglect the rest of the people. Not just in math, but everywhere. Kids who get cut from the ball team still like to play. Find a way so they can. Kids who aren’t going to be chemists can still learn a lot of interesting chemistry. There are many mathematical skills and ideas that lots of students can learn, retain, and appreciate if given half a chance. The way things are set up now we’ve got plenty of scientific and/or technical people who learned enough math so they can do their thing. But it’s the non-scientists and the non-technical types who are increasingly being asked to grasp and act on scientific and technical, that is mathematical, notions. Wouldn’t it be a good idea to bring them along?