When I was a kid, I absolutely loved the Wizard of Oz stories, but even at nine years old, I realized they were fantasy. Apparently, not everyone got the memo. Take Professor Wogglebug, who had invented education pills. All students needed to do was swallow his pills and they had all of the knowledge they needed.
There are still plenty of people in the education field – administrators, teachers, curriculum developers and software designers – who believe that you can learn math without math class. We’ll have students draw maps and they will magically understand the idea of proportion and scale. We’ll read histories of famous mathematicians and that will teach children math because they will have role models and be motivated.
In developing educational resources for 7 Generation Games, I review a lot of lesson plans and most of those for math are awful. This is not universally the case. Last month, we posted 10 Interesting Math blogs, and they had some really terrific material. Unfortunately, these types of resources are the minority
Also, last month, I read The Smartest Kids in the World, a really interesting book comparing educational systems in the U.S., South Korea, Poland and Finland from an insider’s view – through high school exchange students. I found myself nodding in agreement when one of the students from Finland, studying in the U.S. said,
“Not another poster!”
She couldn’t believe how much time was wasted in classrooms in math (and history and literature) making posters. Learn the equation for a line? Graph it and make a poster. Learn the formula for the volume of a cone? Make a poster about it.
Maybe I’m just bitter because back in middle school I aced algebra and flunked art. Maybe. At least I know the difference between algebra and art.
Here is something I learned on my way to becoming world judo champion 30 years ago – success doesn’t come easy. If you want to be good at something, you need to work at it. I had friends who tried mental conditioning, aerobics classes and running a few miles a day instead of judo practice. All of those things are good for you and are good supplements to judo practice. If you want to get good at judo, do judo.
Math is the same way. Biographies of famous mathematicians who are the same race, gender or sexual orientation as you might make you more interested in pursuing a career. Jumping over a pit might teach you about physics, calculus, gravity and deceleration. It might, but I don’t believe it will any more than I believe taking Emilia to the Lorikeet exhibit will have her discovering ecology of the rain forest (or wherever it is lorikeets come from).
Some people argue, “It isn’t that simple.”
My answer would be that if you think teaching children math is simple, you’ve never done it.
Then there are the magic hand-wavers,
We don’t know how it works, but we have children wander around, explore the world and they discover mathematics.
This kind of thing makes me want to scream and swear. Math is amazing. I’m teaching a course in multivariate statistics next term and lots of things from logarithms to Euler’s number to inverted matrices invoke wonder in me that people figured this stuff out. One person didn’t figure it all out. Lots of people did, over thousands of years. How crazy and inefficient is it for us to expect children to figure it out all by themselves or because they drew some pictures.
After thirty years of teaching, here is how I think people learn math (and probably most other subjects)
- Problems are posed that they find interesting.
- They wonder about how to solve those problems.
- They acquire facts and procedures that will help, either by reading a book, watching a video, getting hints.
- They try to solve the problem.
- If they can’t solve the problem, they try something else.
In all of those steps, teaching happens. Just today, I was looking at a problem that asked,
The girls went out from the camp to meet their brothers coming home. They agreed to meet at a spot where the boys were 3/4 of the way back to camp. How far FROM the camp would the girls walk? Drag them to the correct spot on the number line.
The player can click on a link for a hint that explains how you would find 3/4 of the way back to the camp and why it is not the same as 3/4 of the way from the camp. There are also explanations of common denominators and equivalent fractions in this same level, so that you know that the spot that is 6/8 of the way back is the same as the spot that is 1/4 of the way from the camp.
If you are ever meeting up with anyone, that would be useful information to know. What we did NOT do was expect them to wander around inside the virtual world and intuit a knowledge of equivalent fractions.
The other thing we didn’t do is have them draw a number line with a picture of the camp, a picture of the boys, a picture of the girls. You may think I’m kidding but I’ve seen far too many math classes that had one problem like this with five minutes of math and forty minutes of drawing. That’s not math class. It’s art class.
Maybe you’ll learn math by studying art. I think it more likely, you’ll learn math by studying math.