By the numbers

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.

What you can learn from Khan

What can you learn from Khan?

Turns out, damned near anything.

First, let’s get this out of the way. I am not talking about this guy :

Nor am I talking about this guy :

No, I am talking about Salman Khan, otherwise known as this guy :

I just watched that Ted talk recently, and it really has my mind abuzz with thoughts about education.

For a long long time, I have thought we do education wrong. We strap our kids down and force-feed knowledge to children like it is a bitter pill they absolutely must swallow, and then regurgitate, and then wonder why kids hate school, hate reading, hate learning, and hate their teachers.

Children inherently want to learn. Everything they do as play is a result of this instinct to learn, explore, and understand. They are born insatiably curious, and it only by diligent long-term torture that we beat that out of most of them.

Our model of education has not changed since the dawn of the Industrial Revolution, and it is very much an assembly-line model. Get the kids into one place, give them the information, ring a bill, everyone goes to the next information station, and at the end of work periods, quality assessment.

But children are not machines. The mind of a child is not some kind of tabula rasa just waiting for us to write on.

Children are living breathing human beings who desperately want to learn how the world works, but want to do it in an active and interactive manner that can accommodate all the different learning styles. Individualized learning is what is called for, and yet, teachers say they just don’t have the time.

Enter Salman Khan. His idea of education is remarkably like the one I have had since I formulated it way back in my college days when dinosaurs walked the earth and I took a course called the Philosophy of Education at UPEI.

But what he adds to the picture is this notion of “flipping the classroom”. That means that watching a Khan lecture on a subject is not the lecture, it’s the homework. All the kids show up to school having already has the lecture on the subject, and at their own pace, with as much backtracking and rewinding and looking things up as necessary to boot.

This frees up the teacher to spend all the class time actually helping the kids do the thing they have been taught. The teacher can circulate in the classroom and see who is struggling, and offer them help when they need it, but otherwise leave the kids to figure it out either by themselves or with the help of their friends.

For a long time, I have thought that our ancient model of education reduces the role of the teach to basically being a piece of audio-visual equipment. They are just there to broadcast the curriculum at the students and then test them on it. Helping them learn it and do it is a luxury squeezed in between lectures. For the most part, they just there to lecture.

And here’s the thing : lecturing is actually the least important part of education. It is the part of the job that is the most menial, repetitive, and unpleasant for both teacher and student.

Teachers hate repeating the same things year after year, and students hate being forced to sit still and do nothing but listen for hours on end. Nobody is happy. And yet we put up with it because it is “normal” so we do not even think about it.

But if you automate the lecturing, suddenly the teachers are free to truly teach, and the individualized learning model is not just possible but preferable.

Full disclosure mode : Admittedly, I would have thrived in a system like that. I was ridiculously bright and learned extremely fast. If I could have done the learning and testing on my own, I would have zoomed through my education at light speed, instead of spending 90 percent of class time bored out of my mind and wishing I was anywhere else.

Heck, I would have found work that actually challenged me. Imagine that.

But I also think all the other kids would have benefited from that kind of education as well. The slow kids would have gotten tons more teacher time to help them get through the rough parts. The bright kids like me would have been happy to zoom along on our own most of the time. And the average kids would greatly benefit from a system that lets them learn at their own speed and in their own way.

The great thing about a system like that is that it rewards curiosity and initiative, and thus harnesses children’s inherent curiosity and enthusiasm instead of punishing it like out current system does.

It’s a little like food. The child can always have more when they want more, and stop when they are full and need to digest what they have just eaten.

And if they get indigestion from something, they can always go to the teach for…. um, nevermind. That metaphor is best ended right there.

I hope that these experimental programs scattered hither and yon that use the Khan “flipped classroom” approach will inspire an entire educational reform movement that sweeps the world and finally puts an end to this terrible, outdated, inefficient, inhuman, inhumane, and above all wrong system we have all over the world now.

Don’t get me wrong. Even out current broken-down system of education is far better than no education at all. And I am most vehemently not saying that we should replace all teachers with computer monitors.

But the history of human technological progress has been a story of people coming up with ways to automate the part of the task that is most menial and repetitive and that takes the least amount of intelligence, and thus freeing up human potential to focus on the higher order parts of the task,.

There is no reason why we cannot do this for education with the technology of today.