Concrete learning
Mar. 12th, 2009 07:48 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpagePart 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.
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.
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Date: 2009-03-13 03:46 pm (UTC)(no subject)
Date: 2009-03-13 03:53 pm (UTC)You can't build on knowledge you don't have, and memory is very closely tied to how well we understand the connections between concepts. If you don't understand how to connect math concepts to each other or to the real world, then it doesn't matter how well you can manipulate them - you're not going to be able to apply them outside of contrived situations and you're going to have trouble remembering them after the impetus of the exam is gone.