Concrete learning

[velvetpage]

Part of my job involves making sure kids can draw or stack blocks to represent the number 100 000. That's as high as grade fives in Ontario are expected to be able to understand.

Well, here's a much bigger number, represented in stacks of $100 bills.

Probably the most difficult thing about math, either scientific math or advanced economics, is the understanding of quantity that comes with it. One trillion dollars is really hard to visualize. Nobody will ever hold that much cash in their hands, or even in their warehouses. It's 10 to the power of 12, and it's just at the limit of how big something can be and still be relatively simple to represent visually (as this website did.) Once you get past that, it becomes a lot easier to compare it to something else: like, one in ten trillion is one drop of water in an Olympic-size swimming pool, for example. (Note: I don't know if that's true.) I think a big part of the reason most kids have trouble with math in the higher grades is quite simply that nobody takes the time or the energy to draw those comparisons for them in such a way that they understand the concept of "orders of magnitude."

Math gets hard at exactly the rate that it gets abstract. Make it less abstract, and most people can do a lot more of it. The problem with the traditional methods of teaching math has always been that it left math as an abstract concept long, long, long before most people were ready to think, "I can manipulate these numbers in certain ways without thinking about what the numbers actually mean at every point along the way."

Anyhow. An economic visualization and a little plug for concrete methods of teaching mathematics, at the same time.

Comments

[daednu.livejournal.com]

I don't know if it's just my brain, or the way I was taught math. All math is abstract to me. It's something I just cannot feel my way around. The fastest way to make me feel stupid is to throw math at me. Particularly surprise math. Like when I'm working a cash and someone gives me a twenty to pay for a $1.79 coffee (no problem!) but then changes his mind 4 different times about what money his paying with.

[velvetpage.livejournal.com]

It's probably the way you were taught - as though numbers had no meaning off the page. Your kids are probably going to grow up with a better understanding than that because their teachers are expected to teach using manipulatives, so they're likely to get to high school without ever being asked to learn a math concept without representing it visually in some way - with blocks or at least with drawings and most often with both.

When you're never asked to think about what the numbers mean but only about how to make them move around to become more abstract answers, you never learn the key thing about math: it's a language used to describe the world. Absolutely anything can be described with numbers, and every math question is describing something that exists in the real world.