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

[merlyn4401.livejournal.com]

That's scary.

[velvetpage.livejournal.com]

I'm not so sure. I think the piece that you and I are missing, now that we have a visual, is the piece to tell us where that money comes from. I know just enough about economics to know that money is created by other money. The government is shoring up businesses with money that exists because the government says it exists, or will exist by the time they pay it. It's all an exercise in fantasy-world generation, where the world they're creating is one that has this trillion bucks in it. The world didn't have that money until the American government decided to plop it into the financial industry.

You read in the paper that world markets have lost 20% of their value, or some such, since September. But what does that actually mean? Did 20% of the food that was growing suddenly stop growing? Did 20% of the machinery that was being used suddenly stop working? The fact is, that wealth was paper wealth to begin with (or computer wealth.) It had whatever value the bankers and money-market people said it had, because it didn't represent anything concrete.

Now of course, sooner or later it gets tied into something that feels concrete - like a mortgage on a brick-and-mortar house, or a new car coming off the line at GM. Still, those things are worth what the market says they're worth, no more and no less - so the ability to pay for them is determined by the same folks who are telling us that 20% of the world's wealth has disappeared in the last six months.

We're not being given the visuals to represent what's really going on, in part because there are no visuals. It's like the cheshire cat - "When I use a word, it means exactly what I mean it to mean - neither more nor less." Part of the way to solve the crisis may be to actually link money to concrete wealth again. I don't know. But I do know I'm not willing to let myself be drawn into how scary it is without a better understanding of exactly what it means.

[merlyn4401.livejournal.com]

I think whether it is tied to concrete wealth or paper wealth, it's still scary. That's an obscene amount of money.

[sassy-fae.livejournal.com]

0_0

*nodnod*

velvetpage, I think I'm going to repost that link on my LJ. (Though I don't think I'll use this icon, as you've ended up using it more than me, and everyone will think it's you posting! *giggles*)