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Looking for the Hows and Whys

In her continuing struggle with the Algebra II class that she’s taking this year, Post staff writer Michael Alison Chandler blogs about her quiz last week.

The topic was solving systems of linear equations and while she thinks she understands the process of doing matrix arithmetic, Chandler is confused about other factors.

It’s difficult to describe how or why math works. It’s easier to just write the formula and say, “Do this.” Several readers have commented on this blog that what’s often missing from math education is more of a focus on why certain applications work. I agree. It’s harder to remember what to do, if you don’t have some sense of why it works.

Knowing why the formula works would be excellent, although Chandler is probably in the minority among high school Algebra II students in wanting to move beyond the basic mechanics of getting the task done.

However, even more important would be if she and the rest of her class were learning how people actually use this process to solve real problems.

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2 Comments

  1. The problem is that matrix algebra is taught as just a technique to solve systems of linear equations that exist in the abstract. One illustration is 3D geometry, and there are tons of great illustrations in computer graphics (and games!) — but, it would take even longer to teach it will all of that attached.

    So we just teach the formula and leave the real applications for some future time.

    Matrix algebra was invented before computers, so it’s a bit like taking students through a history of math. I think it’s archaic, and has simply been ossified into the curriculum. Just like logarithms, they are simply a way to solve complex problems without computers.

    No one uses this process anymore to solve real problems, seriously. Everyone uses computers.

  2. Dave

    This should be such a great time for motivation in math class. All you have to do is point out the problems in the economy and the pretty much universal consensus that those problems were largely caused by people getting loans they couldn’t afford. Then you point out that a lot of those people probably thought they’d never see a real-world application of what their math classes covered. And you know what, they were right: they never saw it coming.

    It’s got to be right up there with the compound interest lesson showing how easy it is to be a millionaire, if you can save a little each month and leave it alone in an account for a while.

    Sylvia: Who programs the computers? Who is able to check whether those programmers did it right? Who is able to get vital work done if the computers don’t work? People who understand the math. It’s the difference between being a replaceable cog in the machine, and the person companies can’t live without.

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