Another day, another education-themed TED talk.
And this time, it’s all about math!
This Conrad Wolfram fellow thinks we put too much emphasis on teaching kids to do math by hand when what is truly important is to teach them mathematical thinking skills.
After all, he says, computers can handle the calculation part quite well. Calculating by hand has been obsolete since the advent of the pocket calculator. There is no point in teaching kids an ancient technique left over from the days when solving by hand was your only option and knowing basic mathematics was actually a very valuable job skill, one that could, in fact, make a whole career as a clerk.
Obviously, those days are long gone, and the argument can be made that calculating via the old paper and pencil method is a useless skill in these days when you can get a calculator at a dollar store that can handle all the addition, subtraction, multiplication, and division that you will ever need.
Not only that, but every cell phone is a calculator, as is every desktop computer, laptop, tablet computer, and so on.
The odds of you being in a situation where there are no computers around to do the calculating are diminishingly small. So why teach kids to do things the old way?
And when I look back at my own mathematical education, I have to wonder myself. The idea that I did not do anything but the most basic algebra until Grade 10 strongly suggests that we are spending a hell of a lot of money and time teaching kids calculation when they could be learning real math.
It makes me wonder what the heck we were doing in the years between Grade Five, when we learned long divison, and Grade Ten. What is there to learn between those two?
So in Conrad’s world, you would get a calculator in first grade, and right away, the teacher could be teaching you what is happening when you press buttons on it and what the number you get as a result means.
Potential problem : it might well turn out that no matter whether they are using calculators or not, kids before a certain level of cognitive development just plain cannot understand the concepts we would like to start teaching them that early.
I am not saying that would definitely be true. And if it was true at first, a diligent educator could develop a different teaching method for mathematical concepts that takes their level of cognitive development into account.
I am picturing teaching Grade 3 students basic algebra using pictures of animals for the variables. “Now children, solve for Frog. ”
Now I know that the idea that we could start teaching algebra in Grade Three will strike a lot of people as absurd, unrealistic, and perhaps even dangerous.
But if you take learning pencil and paper math out of the equation, what is left? And who knows, maybe if we learned algebra in elementary school, it would be a lot less painful for people.
And speaking of algebra, I am not exactly sure how you could teach that without using pencil and paper. I have tried doing algebra on a computer and it is a serious pain in the ass. The paper method is way simpler and easier. Maybe that is just because that is how I was taught to do it, though.
But having third grade students doing algebra is not my most pressing concern when it comes to math education. Wolfram hints at what I am looking for when he talks about people learning mathematical reasoning and hits it on the head when he talk about teaching people that they can attack a seemingly impossible mathematical question and, through applying the tools they have learned and a little creativity and forehead sweat, slay the beast and solve the problem.
For a long time now, I have been pondering why some people are comfortable with math and why others view numbers with fear and suspicion. Like it or not, math impacts people’s lives, and not just in the ways Wolfram mentions like figuring out if a statistic is bullshit or not.
Where math becomes vital is in the realm of money and finance. Everyone has to think about money in their life, and money runs on math. If you are not comfortable handling numbers, you cannot possibly figure out a budget and stick to it, let alone plan your retirement or avoid being scammed by financial hucksters who are counting on your unwillingness to deal with the quantitative world in order to rip you off.
So I am far less interested in teaching people calculus in middle school than I am in changing the way we teach math so that more people feel comfortable dealing with numbers and hence make themselves less likely to be victimized and bamboozled by people who just happen to be slightly more comfortable with math than they are, or at least can pretend to be.
In practical terms, most of us will never use anything beyond basic algebra. It is entirely reasonable to limit mathematical education for the average student to just the things they will have a practical use for in their adult lives, and leave the more advanced stuff as optional, for the kids with a genuine interest in math or in subjects where more advanced math will be needed.
I know that is blatant heresy to math teachers, who secretly think math is the greatest thing in the world and that everyone should be like them and love it for it’s own sake, and if they do not, they should be punished for it.
But I think that if we just relax our preconceived notions and look at math from a different perspective, one where it is treated like a fun game or as a useful skill, we might find that we can find all kinds of things to teach the kiddies that we would never have even glimpsed if we had stayed on the same old path.
I think math can be a lot more than what we teach today.
I think it can be a wonderful and powerful tool for understanding your world.
But it will never be that if we do not learn to teach it the right way.
Basic arithmetic is probably a good skill to have as a foundation on which to build other mathematical skills. I would still recommend learning it and then let the students use a calculator after that.
I was OK at arithmetic, algebra, and geometry. All other forms of math were too hard.
In grade seven I took some sort of special exam for smart students. It was totally optional. I guess I did it out of ego. I thought I was smart enough. I could not handle the math questions for one of two reasons.
1. Because they were the kind of thing that required knowledge that was not given anywhere and that you had to be lucky enough to have discovered by yourself through curiosity and observation. Example: two impossibly large numbers that have to be multiplied. Multiple-choice question: select one of four numbers. To get the answer by straightforward arithmetic would take forever. The trick is knowing that any number, no matter how large, ending in 7, multiplied by any number, no matter how large, ending in 3 will always result in a number ending in 1. This was not stated anywhere on the exam or even anywhere else in my entire school experience. You simply had to have noticed it on your own at some point, which depends on you being inherently interested in math and observant and able to recall at the moment of the exam that this is where to apply that particular piece of trivia.
2. So-called “story” problems. I felt particularly betrayed by these because the name implies that there is some sort of narrative solution, but in fact it’s exactly the opposite. From a deliberately obfuscated cloud of information you have to distill the problem down to a mathematical operation. The archetypical example is the “two trains” question. Note that the problem here is not doing the arithmetic, it’s knowing what arithmetic to even do. And again, there’s no way to know that without already knowing it. You can’t figure it out by rereading the question more closely. No-one teaches it to you. You just have to have won the genetic lottery.
In grade nine or ten we learned about matrices, and I had to fudge my way through that, guessing at the answers through intuition more than reasoning. Somehow I managed to pass.
Same with grade eleven math. I faked my way through that, enough to pass. I skipped grave twelve math, which was optional, but then that meant I had to take first-year university math, and I completely failed that. I could not grasp probability or linear (ha!) equations.
A few years ago I thought about taking a night school math course or two. I was shocked to discover that the things today’s students have to know to pass even grade nine math would be impossible for me. It’s no wonder so many people don’t graduate. It’s not because kids today are dumb or distracted by TV and computers. It’s because they’ve apparently been making school harder and harder.
The education system needs to recognize that a large number of us are just plain not smart enough to understand most math. Getting people comfortable with numbers, and teaching them, on a very basic level, how to look at problems, would be good, but it would mean actually spitting out the secret knowledge they keep from us so they can punish us for not knowing how to decode a cryptic math problem, so I don’t see it happening any time soon.
In a recent Opuntia the editor was criticizing fans for saying that the world of money was too complicated to study, yet we can remember “the name of the actor who played the third Klingon on the left.”
But complexity is not the same as storage capacity. Just because he finds economics as easy to understand as Star Trek trivia does not mean that everyone does.