Slashdot Mirror
Promoting Arithmetic and Algebra By Example
Capt.Albatross writes "A couple of months ago, the New York Times published political scientist Andrew Hacker's opinion that teaching algebra is harmful. Today, it has followed up with an article that is clearly intended to indicate the usefulness of basic mathematics by suggesting useful exercises in a variety of 'real-world' topics. While the starter questions in each topic involve formula evaluation rather than symbolic manipulation, the follow-up questions invite readers to delve more deeply.
The value of mathematics education has been a (recurring issue on Slashdot)."
Aside from the obvious ones in engineering, where few kids will participate...
There is the issue of "how much paint will I need to paint my house?"
Doing the math will save you money.
The reason is not algebra's application to daily life. The reason you teach algebra is because algebra teaches symbolic manipulation. Learning math teaches you not just how to add two numbers. Addition is almost unnecessary in daily life (we do have calculators). Learning algebra is critical because it teaches us to think in terms of abstractions, of models. We do not teach mathematics to teach you how to add, we teach mathematics to teach you how to solve, to teach you how to think.
"Siri, how much is 400 grams in some fucked up imperial measurement?
Andrew Hacker and nearly everyone else is missing the point.
Taking an algebra class for many students is not about the algebra, it's about learning to think. Even if you never use algebra again, the process of learning algebra is mental exercise that improves the mind. Taking a foreign language, studying biology, learning economics, studying history - it doesn't matter what the subject is, merely the more you learn the better a learner you are, and the better thinker you are.
In sports we see athletes perform all kinds of exercises that help develop skills used in their sport, but are never used directly. Ever see footage of a football player stepping through tires? Ever see one do that during the game? Ever see footage of a quarterback or pitcher throwing the ball through a hanging tire? Ever see them do that in a game? Athletics is filled with examples of training exercises done to hone one's skills for a game, yet we have difficulty accepting that mental exercises hone skills we need for life.
I've been a developer for about 16 years, and have had a pretty spotty math education. I've generally taught myself what I need to know as I needed to know it - 3D programming? What's a matrix? How do I rotate things with it? Developing animate graphical charts? How do I scale from business coords to pixel coords, and animate? Draw box an whiskers charts etc...
Recently, I've decided to stop doing the corporate developer gig and to go to school. As part of that, I've needed to take math a lot more seriously, so I've bought some books and been going through a more rigorous program.
One thing I've discovered through this process is that I *really enjoy it*. I'm not being pressured to learn something for a test, I'm not worried about a grade. Instead, I take my books to a coffee shop and relax and think about fascinating things, like trying to visualize the complex plane, and what the value for i really is, and what dividing by zero really means.
Instead of memorizing the quadratic equation, I spent some time learning how to derive it from basic principals. Instead of memorizing that the vertex of a parabola can be found by -b/2a, I noodled around and tried to visualize the determinant (sqrt(b^2 -4ac)), it's effect on an equation, and what happens if you zero it out.
I spend a leisurely afternoon coming up with a visual proof of the Pythagorean theorem, and was pretty excited when I finally had it, and was even more excited when I googled it and saw the same basic proof has been derived by students for a really long time - I loved the notion that I was connected back through time with a whole bunch of other people who were going through the same mental steps.
This stuff is great! And I'm only scratching the surface. I'm in baby algebra - and I'm excited to keep going.
My point is - we go about this stuff all wrong. Forcing kids to memorize equations so they can pass an exam is absolutely pointless, if not masochistic. Exploring really interesting concepts about numbers, and what they mean - this stuff should be recreation. It's great!
I see my older son struggling through his algebra course, and he hates it. He doesn't care, and hates doing the homework. But when I get excited about some math problem I'm studying, he'll come over to look over my shoulder to see what I'm doing, and we'll puzzle it out together. He forgets that we're doing math, instead we're talking about concepts and challenging each other. We'll spend an hour or two going over something that's really cool, and we both have a great time.
Ask him about math, however, and he immediately relates it to school, and he'll tell you how much he hates it.
Drinking habits can be dangerous. You can choke on the cloth and the nuns will wonder where their clothes are.
I suspect that algebra has value beyond its immediate application and utility. I think this is often overlooked in debates like this. When learning algebra, you are in effect modifying your brain in a particular way. You are training yourself to think a certain way. You can gain a feeling of mastery if you learn it well. And implicitly, you are taught the value of reason and logic. The very fact that you are asked to learn algebra carries the message that logic and rational thinking are valuable skills, and that people who are good at such things are particularly valuable to society. The pursuit of a topic like algebra encourages discipline and structure in the way you think about many other things.
To focus only on the immediate applications of algebra is small minded and unwise, in my opinion.
This and no other is the root from which a tyrant springs; when first he appears as a protector - Plato (423 to 327 BC)