What math can do for you
GUEST COLUMN | by Nigel Nisbet
“Why do we have to learn Algebra?” was the question a student asked me one day in the middle of class. I hadn’t been teaching very long so I wasn’t entirely sure what to say. I tried to ignore it but he asked again so I came up with some lame reasons like, “you’ll need it later”, or “lots of jobs use algebra every day”, but the more I looked at what I was teaching, the more unconvincing this sounded, even to me. I mean, when exactly would my students use the quadratic formula? Sure, in Algebra 2, but outside of education I don’t know anybody who uses it in their day-to-day job – actually that’s not entirely true, I do know one guy… my brother-in-law is an engineer at NASA and I’m pretty sure it comes up from time to time – but OK, out of 486 Facebook friends, 653 LinkedIn contacts and 97 Twitter followers I know one guy who uses the quadratic formula as part of his job… and he’s literally a rocket scientist!
Eventually, I caved in and gave my student the ultimatum used by teachers everywhere… “you need to learn the quadratic formula because it’s on the test!” And even as I said it, I knew I’d lost him. It was as though I’d officially made it OK for him not to care about math.
And he’s not alone, most kids have a very tenuous grasp on why they’re learning math. A few years ago a survey of elementary school students turned up some really interesting responses…
Why do you learn math?
- Because it comes after English class
- Because it’s in the Bible and George Bush says I have to
- Because my teacher will get sued if she doesn’t teach it
Wow!! So kids are confused about why they’re learning it, and teachers are teaching it because they have to… hardly surprising then that it’s the least popular subject in America, and overall, we’re not very good at it.
So why then should we all learn algebra?
It turns out, the big reasons for doing this are not actually about math at all, it’s really about learning… it’s really about upgrading your brain.
My son Cameron is 17 months old and his favorite toy right now is a wooden box with geometric holes in it (circle, square, triangle, octagon etc.) and a corresponding set of blocks to push through the holes – I’m sure you’re familiar with these. And he loves this toy… but there’s a problem — he’s not very good at it. He’ll push a block through a hole, then he’ll pick up a different block, and guess what… he’ll try to push it through the same hole again. Now this is a brilliant problem solving strategy, and one that’s worked well with other toys in the past, but now this game has a new rule he doesn’t understand: each of the twelve blocks is uniquely matched with one and only one hole… a one-to-one correspondence – but his brain didn’t come wired with that idea!
Uh-oh! Is this it? Am I going to spend the rest of my days saying “No Cameron, that’s a star not a square”?
Obviously not, because here’s the astounding thing, over the next few weeks and months, through trial and error, exploration and frustration, and a little subtle guidance, he will figure out this completely new idea for himself… His brain will literally re-wire itself, building new connections and networks of neurons where previously they didn’t exist! And, astonishingly, once built, this neural network for one-to-one correspondence isn’t just able to be used for this game, Cameron can apply this way of seeing and understanding the world to new, and completely unrelated situations…
Cameron is building an operating system – a system of ideas he will use to thrive and survive in the world around him… and from this simple game his operating system will upgrade itself with new networks with information about the attributes of twelve different shapes, and that rotating these blocks through two and three dimensions will produce different results, and of course the most important lesson… he’s learning is that he can figure big stuff out for himself – he is a learning machine!
Wow all that from playing a game with blocks!
So, imagine what algebra can do for you.
Prior to algebra, in elementary and middle school, math is basically about numbers — whole numbers, integers, fractions, percentages etc., and getting good at calculations with them. This is great, it enables you to understand, describe and interact with the world around in all sorts of useful ways — you can calculate the discount during a sale at the store, you can estimate how much gas you might need to drive on a long journey, or you can figure out what your share of a meal with your friends in a restaurant is — but no matter how good you get at this, most problems in the real world just can’t be solved by being good at mental math… what happens when you throw a ball in the air… how fast will a car be going after it’s accelerated for a certain amount of time… how do you build a rollercoaster? These problems require a whole new way of thinking – your brain needs an upgrade.
Learning algebra is the hardwiring of big new ideas into your operating system that gives you the confidence to say, I don’t know what the answer is but I have a way of figuring it out. The quadratic formula is part of an incredible connected system of ideas capable of analyzing and describing complex interactions between objects in the world, and the reason you have to pass Algebra 2 to go to a 4-year college – and why employers pay more money to hire people who are good at math – is not because you can memorize the quadratic formula but because you have internal operating system that knows how to use it.
So, why are you learning algebra? Because you are a learning machine and math trains your brain to think!
Nigel Nisbet is the Director of Content Creation at MIND Research Institute, where he leads a creative team designing interactive visual math games used by half a million students across the U.S. Write to: firstname.lastname@example.org
It’s sometimes useful to read the New York Times to give your questions a little..more…context: http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all&_r=0.
Andrew Hacker’s question is close enough to your student’s to make you pause a little more. And ideally to reflect much more: While there is every reason to understand mathematical reasoning, and the relationships between numbers or more generally quantities, there is even more reason to make those relationships more concrete, less abstract, more connected with real life, less distant and historical. And most, if not all, of those relationships are only algebraic as abstractions – a 15% tip at a restaurant doesn’t require algebra unless you want to generalize way beyond the experience of a buyer or seller.
This is not a process of “dumbing down,” by the way, but rather of “speeding up.” Look at how Montessori taught algebra to eight to ten year olds, and you’ll wonder why it slides to high school. For that matter, one of my favorite observations of k-16 educations was by Larry Cremin, the historian and quondam President of Teachers’ College at Columbia. He pointed out that the reason we have eight grades is that the contractor who built the first graded school in America, Boston’s Quincy School in 1849, assessed the site and found it best to build eight rooms. So much for traditional educational values!
Perhaps my somewhat inelegant prose above wasn’t clear enough, I agree 100% with your point. I am saying precisely that the mental math for figuring out tips etc is NOT algebra, and that we need Algebra to be able to figure out more complex situations (projectile, acceleration etc). The other angle I really didn’t get into her of course, is that unfortunately, the way Algebra is generally taught often obscures the bigger picture and students are left with te impression of a succession of unrelated topics, and no idea why any of it was important