Saturday, September 13, 2008

Algebra--It's Everywhere

While I don't believe everything in this article--for example, I believe so-called discovery learning is a horrendous way to learn math--it certainly gives a lot of food for thought.

This part is true:

Algebra, says Devlin, is a language, a very precise language written in symbols, and it's everywhere: in nearly all electronic devices, every statistic and each Internet search engine - and, indeed, in every train leaving Boston.

"You can store information using it. You can communicate information using it," Devlin said. "Google has made billions capitalizing on algebra."

What we need is curriculum that is both interesting and comprehensible so that we can show students the applicability. Otherwise, they're closing doors on themselves before they ever leave high school.

How has Google made billions using algebra that lower-level math students can understand?

How is algebra used in electronic devices?

How does Boolean algebra work?

Help me out with these types of tools--this may come as a surprise, but I don't know everything--and let's see if we can get even more kids learning.


rightwingprof said...

Ah, that would be the business school model, which is all about teaching students how to use tools in real world situations. If I ever get Office 2007 installed on this laptop ...

Darren said...

I'm not one who thinks that math should be taught that way. Oh, there's nothing wrong with showing examples and demonstrating applicability and such, but we do a disservice to students when we teach them that the only benefit of knowledge is practical utility. Learning how to think, how to analyze, how to synthesize by drawing on all the information you have--those skills require you to have some basic knowledge to begin with. And they're not necessarily taught explicitly but they *can* be learned.

Ellen K said...

But then you have the parents who want their kids to pass at all costs, even if it means your job. So they whine and moan and choices end up being either to water down the curriculum or to simply pass everyone. And people wonder why so few American kids major in technology fields.

David said...

I do think most kids would be more interested in algebra (and other stuff) if they were given some idea how it is used.

To pick off one of your questions: Boolean algebra deals with symbols representing "true" or "false" conditions rather than with symbols representing numbers, and hence is useful in dealing with the elementary operations of digital computers, such as "and," "or," and "not."

In designing an electronic device, Boolean algebra might be used to find that a particular configuration of elementary operations could be replaced by another, simpler (and hence, cheaper) configuration which will always perform the same way as the more complex/expensive approach.

allen (in Michigan) said...

I agree with David about demonstrating importance but for some realms of learning it just won't work.

Math is entirely conceptual and only shows utility in its application. In other words, you can show what math is used *for* but you can't show math in the sense that you can show the force of gravity or the laws of genetics.

The real problem with discovery learning, like every other edu-fad, is that in order for it to work it assumes a professional environment in which teaching ability is rewarded and that's not the public education system. Smart or dumb, concerned or un, competent or incompetent, it's all the same to the vast sausage-grinder that is the public education system.

Darren said...

That's not the problem with discovery learning. The problem is that we expect teenagers to discover what it took the greatest minds the human race has to offer millenia to figure out.

Aristotle was a pretty bright guy, but it still took all of humankind a couple of thousand years to come up with a Newton to show he was wrong.

Robert Talbert said...

It's certainly good to give students in the beginning phases of post-arithmetic math (such as algebra) a sense of where this is all headed. But on the other hand, the applications that are really compelling in the real world are not low-hanging fruit. You can talk about how algebra is used to communicate information, but if you really want to understand communication from a mathematical perspective then you first have to learn algebra, and a whole lot more. It's very hard to explain the "how" questions behind these applications other than in a brutally oversimplified way to beginning algebra students; and if you want it *not* oversimplified you have to learn the basics first.

There's a tendency, once it becomes clear that an understanding of applications helps keep student interest level up, to make the subject all about the applications. In some fields (business) that makes sense, but in math, I don't think so. When you emphasize application at the expense of learning the rudiments behind the application, the subject devolves into a feel-good session. The best approach seems to be to give students a sense of the breadth of application but to be honest with kids too, and tell them that for now, they will need to master the rudiments of factoring and long division before the AES cryptosystem or Hamming codes make sny sense. The real applications are a reward for having learned the technical aspects of the subject with mastery.

rightwingprof said...

Oh sure, but we can only teach this way because students know all of the necessary math skills. And what we do isn't "discovery learning." We'd be in class for years if it were. But it is real world in the literal sense, as opposed to the sense in which ed people seem to use it, which seems to be using crayons instead of actually learning anything. I'm contrasting it with, say, learning math in the math department, where it appears in the abstract. Call it applied.