07 June 2007 @ 01:37 pm
Algebra  
Aaron posted a link to an article lamenting the LA BoE's requirement that all students pass algebra to graduate.

Far be it for me to defend the utility of algebra classes; everyone here knows how I feel about that. Nor am I really happy about any statement that says, "all students must learn X," since it usually translates to "all students must sit through a lot of talk on X, and spit back the appropriate answers on tests" and any actual learning is incidental. But this Richard Cohen guy's talking through his hat; he's using his employment as a writer to justify his ineptitude at math. "Because X is useful, Y must be useless."

(Before anyone gets on my case, how do you get through life without being able to calculate percentages? Sale! 30% off! This IS useful.) (And if he really needed a class to learn how to type...well, that's one wasted semester, is all I can say. Typing is useful--a semester of "how to type" is trolling for an easy A.)

This article in the LA Times gives a much more balanced view of the situation. It developed in part because the school adopted "tougher graduation requirements" without devoting effective resources to preparing students to meet those requirements. This isn't about math, except maybe the kind with dollars and no sense.

But if one feels for the hapless students forced to sit through hours of polynomial hell, it's also pretty hard not to feel for teachers like George Seidel, who "once brokered multimillion-dollar business deals but left a 25-year law career, hoping to find a more fulfilling job." Poor sucker, here's what he gets to deal with every day:

Only seven of 39 students brought their textbooks. Several had no paper or pencils. One sat for the entire period with his backpack on his shoulders, tapping his desk with a finger. Another doodled an eagle in red ink in his notebook. Others gossiped as Seidel, a second-year teacher, jotted problems on the front board.
Oh, and Gabriela Ocampo? "Gabriela didn't give Seidel much of a chance; she skipped 62 of 93 days that semester." At press time last January, she was working at Subway for $7 an hour.

Could passing algebra have changed Gabriela's future? Most educators would say yes. Algebra, they insist, can mean the difference between menial work and high-level careers.
No, no, no, people, how wrong can you be? Graduating high school means that difference. The algebra is incidental. Going to college means an even greater difference--where algegbra is, for some mystifying reason, required even for humanities majors.

A better question is, how much of Gabriela's repeated failures (6 times??) and subsequent dropping out was caused by stricter graduation requirements without real resources, and how much was caused by her own apathy? Even better: how much of her apathy was caused by that same lack of resources? "The strategy has also failed to provide students with what they need most: a review of basic math." Trying to teach alebra to a kid who never mastered long division is like trying to teach an illiterate to read Shakespeare (which may explain why so many students do so badly at literature, but I digress).

But now we come to the crux of it. What's it all about, then, really, when you get right down to it? What is algebra, really, for?

"If you want to work in the real world, if you want to wire buildings and plumb buildings, that's when it requires algebra," said Don Davis, executive director of the Electrical Training Institute, which runs apprenticeship programs for union electricians in Los Angeles...Analytical skills and formulas enable people to make sense of the world. Algebra can help a worker calculate income taxes, a baseball fan determine a pitcher's earned-run average and a driver determine a car's gas mileage.
Excellent! Wonderful! The real world! Teach me this stuff, it sounds great! Except that's not how we get taught algebra, is it? No, indeed, we get bogged down in a hopeless muddle of Xs and Ys and square roots. The real world can hardly compete with such a morass of abstraction.

Ironically:

Until recently, high schools offered a range of programs. Students seen as academically able were placed in college-prep classes. Others were funneled into vocational courses in which they learned such skills as auto mechanics and office technology.
Or maybe plumbing? So you mean to say, the old system meant that students considered "destined" for careers where algebra might have actually been useful were being steered away from it? Saints preserve us.

State Sen. Chuck Poochigian, apparently in an effort to deflect attention from his silly name, is responsible for the algebra graduation law, and it must be admitted that Senetor Pooch has a point: "We have a problem with a high dropout rate. You don't address it by making it easier to get through and have the meaning of the diploma diluted." True, but you also don't address it by tossing students and teachers alike to the sharks. Wake up and smell the blood trail, Chuck.

Another endless cause and effect loop rears its head when the article brings up the subject of the math teacher shortage:

The Center for the Future of Teaching & Learning in Santa Cruz found that more than 40% of eighth-grade algebra teachers in California lack a math credential or are teaching outside their field of expertise; more than 20% of high school math teachers are similarly unprepared...At Cal State Northridge, 35% of future elementary school instructors earned Ds or Fs in their first college-level math class last year.
Are there not enough math teachers because no one learns math well enough to teach it? Or does no one learn math well because there aren't enough teachers?

Chicken, egg, chicken, egg, round and round and round, and who gets caught in the middle? George Seidel, Gabriela Ocampo, typing giant Richard Cohen, and me.

 
 
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abovenyquist[info]abovenyquist on June 7th, 2007 11:38 pm (UTC)
That was a superb post!

Thanks for finding the article, too. Yeah, I don't have too much sympathy for someone who fails a subject when they skip 2/3 of the classes. But, as you point out, she must have been wondering why she had to be there at all.
Steve Eley: microphone[info]sfeley on June 8th, 2007 02:56 am (UTC)


(from xkcd, the Webcomic of higher geek truth)
Jeff[info]mastacool on June 8th, 2007 03:47 am (UTC)
I so love xkcd! :)
Jeff[info]mastacool on June 8th, 2007 03:00 am (UTC)
But this Richard Cohen guy's talking through his hat; he's using his employment as a writer to justify his ineptitude at math. "Because X is useful, Y must be useless."


I'm glad you posted that. I was thinking something similar when I read the article after Aaron's post, but I couldn't really be the one to say it. Not only is algebra (along with a few forms of even higher math) an essential piece of the theoretical base that helps me be a good engineer, I actually _enjoyed_ algebra. Especially word problems. So, I'm not exactly unbiased. Even so, there was a defensive "I told you so" tone to that article that reminded me of the busker-blogger that responded to the piece on Joshua Bell. It also produced a similar reaction in me: I didn't necessarily disagree with his basic point, but his reasons and his motivation are likely to turn off the very people he seeks to convince.

As for the usefulness of algebra... I am skeptical of the implication in the LA Times article that people in trade-oriented careers (like electricians and plumbers) are handicapped without full instruction in algebra. Certain concepts that come from algebra are certainly useful, but you can teach those concepts in the framework of a program not designed to prepare for higher-level math. For example, a framing carpenter doesn't do a trig problem every time he figures out how to build a roof to the appropriate angle of pitch. He uses a "distilled" form of that math along with tools:
http://roofgenius.com/roofpitch.htm

So why is this one subject such a hot potato? Hang on for the ride on this one. You're going to think we're on different sides, but we're really not. At some point it comes down to the concepts of evaluation and prediction. If you are interviewing someone for a job or picking out the limited number of students that are going to be admitted to your college, your goal is to efficiently and accurately predict the performance of each applicant. I've done this before. It's HARD. So, most people in that position use common reference points that have a decent (but not 100%) probability of predicting performance. GPA, standardized test scores, level of achievement in certain academic areas... despite where I'm going with this (I promise!), these things are useful predictors.

The real problem, of course, comes in when the point of education becomes not teaching people what they need to know, but preparing them to perform well for these predictors. That's driven further by other people who focus on using the predictors to the exclusion of all else in order to evaluate people. Talk about vicious circles!

Algebra... we were talking about algebra. High performance in algebra is quite a good predictor for certain types of thinking skills which are useful across a whole lot of jobs (many of which don't necessarily involve working a lot of algebra problems). The problem is turning that around and saying that in order to do well in these jobs, you have to know algebra.

I don't know how to fix it. In an ideal world, the kids would all know exactly what they want to do, and they would have the individual help necessary to pick exactly the right training to prepare them for that. When someone figures out how to accomplish that for even a bare majority of children, this world is going to instantly become a better place. In the absence of that individual self-motivation (look at those kids that didn't show up for class) and the resources to provide such individual and expert assistance... I don't think there's a single solution for the equation to balance the necessary compromise. But I do agree that doing things like blindly requiring algebra for graduation is a disservice to a lot of kids.
Joyce[info]joyeuse13 on June 11th, 2007 08:25 pm (UTC)
"I told you so" tone to that article that reminded me of the busker-blogger that responded to the piece on Joshua Bell

Yes, very good comparison!

Certain concepts that come from algebra are certainly useful, but you can teach those concepts in the framework of a program not designed to prepare for higher-level math.

Which is exactly the problem, and it's not just with math. So much of high school is based on preparing students for the kind of classical education more in keeping with the era when only the children of the upper classes went on to higher learning. We are attempting to educate a much vaster portion of the population (ie, all of it) than a classical education was designed for. Teaching algebra to every student simply as a means to prepare them for higher-level math which they may never see, let alone use, is an exercise in futility.
Joyce: Math[info]joyeuse13 on June 11th, 2007 08:29 pm (UTC)
Also, also:

High performance in algebra is quite a good predictor for certain types of thinking skills which are useful across a whole lot of jobs (many of which don't necessarily involve working a lot of algebra problems).

I think you say that bc you are good at both the numbers and the reasoning behind them. I seem to completely lose track of the numbers, but if you give me the concepts verbally, with lots of examples, I have no trouble understanding them. Tell me a story about how the world works, and I'm with you. Give me a sheet full of numbers and I'm lost. To me, logic has nothing to do with math. I can see the relationship, but only if you tell me it's so.


Jeff[info]mastacool on June 11th, 2007 11:14 pm (UTC)
I think you say that bc you are good at both the numbers and the reasoning behind them.

I don't disagree with that.

I do disagree, however, with what I think you're implying about my statement. Just because I say that high performance in algebra is a good predictor of certain kinds of thinking skills does not mean I think that those who do not do well in algebra necessarily do not have those skills. That's why depending solely on any single predictor is a dangerous thing. That, however, also does not invalidate the predictor.

As Mr. Miyagi said, "Must have balance, Daniel-san." :)
JP Sugarbroad[info]taral on June 8th, 2007 04:42 am (UTC)
I know I've only met you once, but :( anyway.

ObPost: Yes, educational systems are screwy. I still don't know how to fix them.
Joyce[info]joyeuse13 on June 8th, 2007 04:19 pm (UTC)
Er? Why do I get a :( ?
JP Sugarbroad[info]taral on June 8th, 2007 11:21 pm (UTC)
2007/06/08: Unfriended by: joyeuse13
Joyce[info]joyeuse13 on June 11th, 2007 08:39 pm (UTC)
Oops, so I did. Sorry, periodic purging of the friends list...I coudln't remember where we'd met. :) Judging from the mutual friends, I'm guessing Fencon?
JP Sugarbroad[info]taral on June 12th, 2007 12:02 am (UTC)
Indeed! I was with Jazz and Andrew and we had a wonderful time. I'm looking forward to seeing you this year too!
(Anonymous) on June 8th, 2007 01:02 pm (UTC)
Beauty and Grandeur of Algebra
What a thoughtful and valuable post!

First, to get it off my chest - you are so right to lament Richard Cohen's use of ignorance to defend ignorance. Classic bad rhetoric. Shame is, if he had honed his mind with algebra, he would be able to avoid such simple logical gaffes.

Or maybe not.

Your observations have lead me to a lot of thoughts, most of which are too long to post here.

I am fairly new to blogging (to any extent) and am not sure of the etiquette. I hope it's not too presumptuous to link to a post in my blog that is inspired by your post. If so, please delete this and let me know the best way to go about this.

The link is to the The Math Mojo Chronicles at
http://mathmojo.com/chronicles/2007/06/08/why-learn-algebra.

Thanks so much for your insightful writing,

Yours truly,

Brian Foley

(Anonymous) on June 17th, 2007 04:40 pm (UTC)
Enjoyed this post
I really appreciated much of what you had to say. However, I think your typing comment was slightly off target. I had to drop typing at semester because it was killing my GPA :-)