6 Things You Don’t Know (and Should) About How Math Is Taught

Okay, big news. Doug Ford is putting Ontario Math teaching “Back to the Basics.” Ho hum.

Now, don’t get me wrong. I loved teaching Math, and over the years, I developed some pretty decent lessons. Also, I know a lot of people who are passionate about their theories of Math teaching, and an even larger number of people who are equally passionate about the fact that they can’t understand Math. So why don’t I care about this attempt to drag education back into the 1950s?

Well, dear reader, there are a couple of things about Math and the teaching of Math that the general public doesn’t know, and I’m about to let you in on them.

  1. The Great Pendulum

You might have noticed; like most other aspects of the education system, Math teaching swings back and forth between two extremes: The Basics, which uses a lot of rote learning, and the more creative system (nobody has ever found a name that catches on) that focuses on teaching theories in a more intuitive method. Every ten or fifteen years some group of fanatics gets into power and imposes their system on the poor, unsuspecting public. Or tries to. It usually has some connection to whether the Left or the Right are in government and feel the need to play to their voter base. Hence Ford’s foray into idiocy.

But What Really Happens?

  1. Teachers Don’t Listen

That’s right, folks. When all those fancy new systems come rolling down from the administrators without proper training and support for the teachers, we all just smile and take the new equipment and textbooks, listen to the scanty training, look for anything in the program that might improve our teaching, and go right along teaching Math just like we always did. Why? Because we’ve seen it all before, and we know where it’s going. Nowhere. Plus, very few people have the Math skills to switch just like that. It’s sort of like you’ve been teaching guitar for years, and they come along and say, “The music program is going to be taught on trumpets from now on.”

And This Is a Good Thing. Why?

  1. Because Kids Don’t Learn Either Way

That is, some kids learn better with a lot of rote learning of techniques they don’t really understand, and some kids learn better with a lot of focus on the ideas, but less emphasis on practical application. And all the other kids fall into line on the continuum in between.

The conclusion any fool can draw from this is that if you’re a good teacher you try to present each Math concept both ways, so that you reach all the students in your class. But the administrators and academics don’t like that, because it leaves them with nothing to argue about, so on they go, battling it out to see whose system will win for the next decade.

Which Is Why…

  1. Teachers Don’t Listen to Academics (or politicians or rah-rah administrators)

I remember figuring one thing early in my Education classes. Don’t Listen to What These Fools Are Telling You.  Just smile and regurgitate whatever it is they’re feeding you, and wait until you’re on practicum with a real teacher to help you deal with a real class. That’s where you learn to be a teacher. NOT in university, and not from people who don’t actually teach children.

And here are a couple of examples of how idiotic this battle has been:

If You’re a Back to the Basics Type, Listen to This One.

  1. You’re Not Testing Math Correctly

That’s right. I only ever learned one big idea in all the Math Pro-D I took, and it’s that the Rote Learning folks are marking their tests wrong. I was, too. Let me explain.

A task like Long Division takes a series of steps. Let’s say ten. In order to get a correct answer, you have to complete all ten steps perfectly. But what if a child has one step wrong? He knows nine of the steps, but at step 7 he adds instead of subtracting. He’s going to get every single answer wrong and get zero on the test. So his report card will indicate that he has learned nothing about Long Division. In actuality, he has learned 90% of Long Division. So a Long Division test shouldn’t be twenty questions where the teacher marks only the answers. It only needs to be three or four questions, but the teacher has to give a mark for every step. Then the teacher will find out exactly how much the child has learned and will be able to report that accurately to the parents. More important, the teacher will have pinpointed any weakness and will be able to fix it easily.

And If You’re a Whole Math Type? Here’s One for You.

  1. Your System Doesn’t Work

That’s right. Studies have shown that when you use all those Math Manipulatives in the primary grades, for a lot of the kids the information doesn’t transfer to normal Math operations.

Why not? Probably because half the kids in every class don’t learn Math that way.

The Bottom Line

You Have to Teach Both Ways.

A little anecdote for you. I went to school a long time ago, when rote learning was the only way to teach Math. So I learned, for example, that when you were subtracting large numbers you had to do something called “borrowing.” I had no idea what that meant, but it was simple enough to do and it always gave me the right answer, so why would I complain? I learned to “borrow” From the “Tens column,” and give it to the “Ones column.”  Whatever those were.

And then I got to high school, and we had this Math teacher who was a genius. He was on the provincial committee that was bringing in the New Math System. Which, of course, focused on teaching the theory, rather than just the rote learning of the techniques.

And since the New Math was going to start with the grade that followed ours, he used us as guinea pigs and tried out some of the lessons on us.  Now keep in mind, this guy was a great teacher, so I’m sure they were fine lessons.

But I still remember the day he taught us the idea of Base 10. And Base 8, etc. Because not only did I understand it immediately, but I suddenly realized what I had been doing all along with the Ones column and the Tens column, and what I was borrowing and why.

So contrary to what you might think, instead of needing the theory so I could understand the process, I was taught the process first, and it helped me understand the theory. If I had been given the theory first, I’m sure I would have learned just as well. But until I had been taught both, my Math learning was incomplete.

Both Ways

So I humbly suggest to the politicians, the academics and the administrators that instead of getting their egos all in a knot about whose system is best, they start thinking about the variety of learning styles in the students they are supposed to be educating, and make sure the Math program has a balance of intuitive and rote learning experiences.

And for those of you in Ontario that are worried about your kids’ Math, don’t be. This, as well as Doug Ford’s brand of populism, will pass. By the time his initiative filters down through the education system, he’ll be out of power.

Now, I wonder if we can persuade him to create a “Back to the Basics” Sex Education Program. Wouldn’t that be interesting?





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