Great. Another Non-Math Person Complaining About Algebra. - The Jose Vilson

Great. Another Non-Math Person Complaining About Algebra.

by Jose Vilson on July 30, 2012

in Mr. Vilson

Holy cow, Andrew Hacker. Shut up!

OK, that was a bit harsh. Warranted, but harsh. Say what you want to, but lower your voice a few decibels. Frankly, I didn’t care much for your rhetorical question, but you had to write it in the New York Times, adding a semblance of legitimacy (if not outrage) to your argument against teaching abstract math to kids. The crux of your argument, that we shouldn’t teach algebra except to those of us who want to get deeper into the math and that we should instead focus on useful life math, whatever that means. I won’t spend time debunking any of your claims because Dan Willingham did so rather convincingly today.

Rather, I’ll ask: if we taught the humanities (presumably English, arts, and yes, political science) in the same way you’re suggesting for math, how would that look like?

If you’re OK with English and language arts taught this way, then let’s focus 100% fully on non-fiction texts … like “How To Operate Your VCR” and “The Intricacies of Setting Up Your Passport.” Useful, and often complicated, these texts would surely be of worth post-college, especially for kids who never get out there. They’d have no need for Jon Steinbeck, William Shakespeare, or Julia Alvarez; their texts aren’t very relevant to what students actually encounter on a daily basis, so we’d leave it alone in the hopes that they don’t have to think abstractly.

If you’re OK with political science taught “with relevance,” you’d teach them about a few politicians here and there, their initiatives, and ow the media views the two prominent candidates. You’d never have to discuss political ideology, how bills are created, and about the Electoral College. About 58% of citizens of voting age actually vote anyways, and they don’t use with strategy in mind, but their message, and how their favorite news channel views the candidate. They’d never see The Federalist Papers, or the Emancipation Proclamation; all people need to know is that they’re free … so long as they’re not imprisoned. It doesn’t matter anyways, because that’s not very useful to the everyday citizen. Just the ones it affects.

If you’re OK with the arts taught this way, then … we wouldn’t have use for the arts, really. Unless you show a gravitation towards creativity early on in age, then everyone should get to paint the fruit basket with the shadow to show a level of mastery in the arts until they get to college.

Most math pedagogues would agree that we need to reexamine the way we approach math for our students, especially those who get taught math as a way of passing the deluge of tests at the end of the year. But you didn’t see that, Hacker. You chose instead to spew what I’m dubbing a humanities elitism that perpetuates attitudes this culture espouses about math. If you’re not interested in math, that’s really up to you, but don’t call for a disbanding of math if you don’t want anything to do with math. Instead, join us in saying that we need to infuse more mathematics into the socio-cultural discussion of civilization.

Because that’s a much more compelling argument. Every civilization’s greatest contributions involved math, from the architecture to medicine, fostering a love of math meant having an understanding of how society’s form, whether abstractly or otherwise. Don’t be the loser who asks us to dummy the math down to “usefulness.” Be a voice that asks us to transform the teaching of math.

Jose, who strives for relevance as a teacher …

{ 11 comments… read them below or add one }

John Young July 30, 2012 at 8:08 pm

Reminds me of a great TED talk:

[ted id=587]

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John Young July 30, 2012 at 8:08 pm
Shireen D July 30, 2012 at 9:24 pm

Thank you for so articulately putting down arguments against this ridiculous idea that I couldn’t quite formulate. I just got 2 out:
1. the kids that struggle with algebra are mostly also the kids that struggle with the basics of math. then what?
2. giving kids an “out” from hard math will strip too many kids of the chance of actually succeeding at something challenging that they may wrongly assume they can’t do.

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Patrick Delaney July 30, 2012 at 9:46 pm

Might we all take a breath here? Check out Tom Hoffman’s reasonable comments on the topic. I’d add, as I did to his posting, that “algebra for all” can wreak havoc on a large school’s master schedule, resulting in a weird form of tracking and subverting the political agenda of equity assurance that it claims for its own. The severely stretched analogy of math without algebra being similar to Lang Arts or English taught without literature is countered best by Mark Edmundson’s _Why Read?_

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Jose July 30, 2012 at 10:02 pm

Thanks everyone for your comments.

Patrick, I get Tom’s points, and trust me when I say, we need a reformation about the way we think about math being taught. I just have a problem with the foundation of Andrew’s argument, which is: “These poor kids drop out, so let’s not teach them algebra. Instead, let’s make algebra more useful for every single one by only giving them enough math to do their jobs.” That’s an argument I’ll never buy. Since his argument is so stretched, I simply offer a rejoinder that assumes his “stretch” is true and follow suit.

Also worth noting: from what I’ve read on the synopsis of Mark’s book, it seems to me that he’s trying to say what many of us Hacker critics are saying: let’s reform the math sequence, not get rid of lit completely, but use it to improve our lives. I feel the same way about algebra. And all types of maths.

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ASTRAKA July 30, 2012 at 11:27 pm

We are regressing as a society. Arguments against Algebra remind me of those made against Geometry (10th year Math). It is infuriating to me to see political discourse, marketing, and Ed-reformers, taking advantage of our citizens’ inability to think logically. Everyone has their own definition of what a proof is. Most cannot understand that the converse of a statement is not always true. I can go on and on….I teach elementary statistics in college. Many of my students have majors related to Nursing and other health fields. Those who are weak in algebra have difficulties in doing basic statistics. Algebra is “useful life math”.

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Mike Thayer July 31, 2012 at 9:06 am

Getting back to your original point about “what if we taught the humanities in the same way…”, I had a thought:

I feel that the way we teach kids math in elementary school, in the main, is that we give them more difficult versions of the same problem to solve, over and over. For example, we go from adding two one-digit numbers, to two-digit ones; we teach times tables, and then extend that to multiplying two-digit numbers; etc. I’m not convinced that the students DO anything with this knowledge other than, well, learn the algorithms. Oh, and let’s not forget the test-prep aspect: students often aren’t allowed to learn new things in math until they demonstrate proficiency at the old things (e.g., can you add 50 pairs of 2-digit numbers in 120 seconds? If so, great, on to adding 3-digit numbers; if you only got 47 pairs, sorry, more practice for you.)

So, if we taught kids to read that way, we’d be teaching them, say, how to read 3-letter words, then 4-letter words, then 5-letter words…and we wouldn’t let them read actual books until they’d “demonstrated proficiency at reading 5-letter words” or whatever. Patently ridiculous. Learning to read isn’t an end goal – it’s a door, on the other side of which is an opportunity for a kid to learn about whatever the heck they want to.

Our problem is that we don’t teach arithmetic in such a way that it’s a door to bigger and better things that can often be self-directed – we teach it as an end unto itself. Which means that when our students take algebra 1, they’re used to the idea that it’ll be simply another set of procedures disconnected from anything real in their lives. We haven’t given them any hints that math is abstract, either, really, until algebra 1.

The way I read Hacker’s article, one of his major fallacies is assuming that the students who are failing algebra 1 are doing so while having a real fluency with arithmetic. He doesn’t reflect at all on the mental context that math lives in for many students by the time they get to algebra 1, and he thinks that by offering to students the “backdoor” alternatives he describes, the students will overcome that context and develop quantitative literacy.

Mark me down as skeptical about that.

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Jose August 5, 2012 at 9:19 am

Agreed wholeheartedly, Mike.

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Sue Jones July 31, 2012 at 3:35 pm

Thanks for the very apt connection from algebra to other things we’re not nearly as terrified about getting abstract with. I clicked in expecting a repeat of “but learning algebra can teach deeper learning skills!”
I share *some* of the skepticism about students overcoming the context … but I have to say that it’s more likely to happen in the “math you need” type classes Hacker advocates, simply because it’s more likely to be considered as more than just an algorithm.
I also find that Willingham takes two things for granted. Students do *not* have to become all that fluent in the basics that are embedded further along. Rather, they hope that the calculator enables ‘em to get enough partial credit to pass the course. Secondly, that ” possibility that the mathematics learned in school, even if seldom applied directly, makes students better able to learn new quantitative skills” is a very remote possibility. What happens more often (in what I see) is that it makes students more averse to even attempting to think about quantitative things, because they’re “not good at math.”

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David November 16, 2012 at 5:55 pm

Well, I agree. Except that I also agree that the teaching and assessment of pure mathematics is in fact stifling real learning. The assessment movement is only moving us further into archaic notions of mathematical representation and expression, thus further alienating the way students think. Check out Bret Victor’s blog. There is a section called kill math that is awesome. We need more math people to speak up and less hackers, for that only ruins the conversation. http://worrydream.com/

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David November 17, 2012 at 11:57 am

Change the interface.

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