The liberal world vouches for math: Yesterday, we did a post about Andrew Hacker’s opinion piece about algebra. (See THE DAILY HOWLER, 7/31/12. Scroll to the end.)
Drop-out rates are quite high, Hacker said. And uh-oh! “Most of the educators I’ve talked with cite algebra as the major academic reason.”
We don’t know how many kids drop out because of algebra. In 2006, we did a four-part series about a superb news report in the Los Angeles Times concerning this very problem.
We don’t know how widespread this problem is. But we were struck by the way some liberals couldn’t seem to grasp, or identify with, the problem Hacker described.
At the Washington Monthly, Ryan Cooper was doing the weekend shift, filling in for Ed Kilgore. Cooper graduated from Reed in 2008. To our ear, he didn’t seem to have any idea who Hacker was talking about.
After snarking at Hacker a bit, he offered this rumination:
COOPER (7/30/12): In any case, this got me wondering. Suppose Hacker really is talking about basic algebra. I did that in eighth grade. From there I went through the usual cycle, through geometry and calculus, and then a couple math classes in college required for a chemistry degree, which were by far the hardest classes I’ve ever taken, leading to existential panics and profound self-reevaluations. And that barely scratched the surface of college-level material, which in turn isn’t even close to the work that real mathematicians do.Hacker wasn’t discussing “the average person.” To our ear, Cooper didn’t seem to know who Hacker was talking about.
I would estimate that in my school career I made it about 5 percent of the way to an actual high-level understanding of some kind of mathematics (since of course no one person can be an expert in every sub-field). In turn, I would estimate that basic algebra represents about one percent of my understanding at its peak (now significantly decayed), or roughly 0.05% of a full math education. Is the average person really so rubbish at math that they can’t handle that? Or, perhaps our culture has such an inferiority complex about math that we hamstring ourselves?
For years, we’ve told you—the liberal world quit on low-income kids several decades ago. We prance around praising ourselves about our tribe’s vast racial greatness. But when someone like Hacker writes a column like that, we don’t seem to have any idea who he’s talking about.
Forget about a lack of empathy. We can’t even picture the people we’re supposed to feel empathy for!
Kevin Drum did a respectful post on the same subject, asking a semi-skeptical question about the utility of algebra. We reacted to the bulk of his comments much as we did to Cooper’s post. It seemed to us that most of his readers had little idea who Hacker was talking about. To check for yourself, click here.
Drum linked to Eugene Volokh, a UCLA law professor. Volokh isn’t a liberal, but he pretty much completed the rule of three:
VOLOKH (7/30/12): I’m on a family trip, and will be blogging little if at all this week; but I had a chance to look at a New York Times op-ed titled “Is Algebra Necessary?” and thought it was worth passing along to see what our readers thought of it.Volokh went on to discuss Fermat’s Theorem.
My own quick reaction to the op-ed is negative—though I’m not certain of this, I suspect that algebraic problem-solving teaches useful mental habits that both open up possible future careers and also help train people’s general problem-solving abilities—but I don’t have time to say more about it. So instead of substance, I thought I’d note this sentence...
Question: Did Volokh understand who Hacker is talking about? Hint: Most of those struggling kids won’t be having “careers.”
Liberals quit on these kids a long time ago, although we keep insisting we didn’t. We make up for it through our skill at saying that everyone’s racist.
The only way that I made it through algebra in both high school and college was via the long suffering tutorage of a brilliant daddy, siblings, and husband.
ReplyDeleteI'm for making this hurdle less universal in student life, and I'd argue for a vocational tract in high school, but I've been able to do the slightest thing technical or manual with any competency either.
What does Finland do about algebra? Or Japan, Germany or China? Are we suggesting our "struggling kids" are any less capable than theirs? Anyone who disagrees with Hacker, especially on first impression while recognizing it is a radical proposal that needs more serious thought, is not someone who properly may be insulted for "quitting" on these "struggling kids." Rendering an entire segment of society clueless and with a feeling of helplessness when confronting concepts grounded in basic high school algebra does not seem like an empowering move.
ReplyDelete(Apparently Finnish students start learning algebra in some form in first grade. Maybe the better answer is to teach it better.)
Urban Legend asks:
Delete>>>>>What does Finland do about algebra?... Are we suggesting our "struggling kids" are any less capable than theirs?<<<<<
"Less capable" is a loaded characterization. Therefore, before answering yes, emphatically, let's reword that second question a bit:
>>>>>What does Finland do about algebra?... Are we suggesting our "struggling kids" are far less likely to succeed in grade school than any substantial cohort of theirs?<<<<<
To that question one writer on grade school education issues would answer, "Yes, that's clearly the case."
>>>>>In fact, the United States is little like Finland. We have large poverty issues among all major population groups, even among the white population, which has always been culturally and politically ascendant. Beyond that, our brutal ancestors spent three to four centuries doing everything they could to stamp out literacy among one large segment of the population; Kozol’s famous, discarded book helps us see where matters stood just forty years ago, a blink of the eye in historical time.
The legacy of those brutal centuries can’t be wiped or wished away because we want to close our eyes and pretend that we’re just like the Finns—that we too are a small, middle-class, uni-cultural nation which has always valued literacy. (In fact, we are none of those things.)
Finally, this country stands at the end of several decades of high immigration. This has brought a lot of delightful, deserving kids to our schools, but many of these kids come from low-literacy, poverty backgrounds. And they don’t speak the language.
These factors produce large educational challenges. Flying off to the Finland station can’t make such challenges disappear. And by the way: When the rubes fly off to Finland, there are certain basic questions they can’t get answered there! They can’t learn how Finland dealt with the types of challenges American school systems face.
They can’t learn how Finland dealt with such issues, because Finland hasn’t dealt with such issues. Reason? The Finns never spent four hundred years brutalizing a racial minority. And Finland has no immigration.
Finland is Keillor’s Lake Wobegon. It’s a small, high-literacy, one-culture nation. The children are all above average.<<<<<
So what's the solution? Do we classify children according to whether their ancestors underwent hundreds of years of oppression and exempt them from algebra if they did? Or is the decision to be based on current levels of discrimination against a given ethnic group, or the income level of the child's family? How about other subjects? Are kids from poor neighborhoods who can't do algebra invariably competent when it comes to reading and writing?
DeleteThis whole debate is cockeyed. I could see discussing which math subject is appropriate for students at various levels of competency and how to raise the level of competency. Or we could discuss how schools by themselves can't make up for those hundreds of years of oppression. Instead, though, we're discussing how oppressed groups can't do algebra. Time to abandon this thread.
Dropping algebra from the curriculum of certain students might be a way, in the short run, of tackling some of the problem that is the 25% dropout rate among High School students. As you know, in his article Hacker wrote:
Delete>>>>>The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.
Shirley Bagwell, a longtime Tennessee teacher, warns that “to expect all students to master algebra will cause more students to drop out.” For those who stay in school, there are often “exit exams,” almost all of which contain an algebra component. In Oklahoma, 33 percent failed to pass last year, as did 35 percent in West Virginia.<<<<<
In the alternative, I guess we could assert the equality of man more vociferously than we do now as the method, in the immediate future, for dealing with that 25% dropout rate.
Bob is worth reading, but he twists almost everything to fit his own obsessions. So people who think it is important to expose all students to basic algebra are in Bob's mind people who must not care about the underprivileged. It all makes sense, in Bob's mind.
ReplyDeleteMost of us have some subject or field that we didn't like. I hated art and music and P.E., but would oppose anyone who said that people like me (non-musical, non-artistic, and physically klutzy) shouldn't have to take such subjects. The same is true of mathematics, foreign languages (come to think of it, I didn't like foreign languages either) and other topics.
When I started reading Hacker's piece I thought he was going to say we should be teaching non-math majors a different subject with more direct applicability to real life, like statistics. He made a few gestures in that direction, but he didn't stick with it. Of course, statistics beyond the very most rudimentary level requires some knowledge of algebra (and advanced statistics requires calculus and beyond).
Here's one problem with cutting out algebra. 14 year old kids don't necessarily know what they might be interested in later, and if a student reaches college and decides he wants to study engineering or the physical sciences or economics or some other area which does use algebra, it's pretty damn difficult to make up the gap in college. You'd be starting two or three years back from where you should be. In practice, if you don't know algebra when you reach college you're not going to go into a field that requires some level of mathematical proficiency. But hey, maybe only those upper class kids should have such opportunities.
Opportunities?
DeleteHello! It's not a question of making Algebra UNAVAILABLE to kids who want it, need it, can do it.
It's a question of forcing kids who can't do it, aren't prepared for it, and won't be prepared for it by graduation time to accept that they therefore CAN'T HAVE A HIGH SCHOOL DIPLOMA.
Yeah, 7:00 PM anonymous, I read the article. First off, you missed my point. You really want to say that kids should know by age 14 whether they will ever need algebra? Seriously?
DeleteAnd I disagree with the solution, which is to remove a subject from the curriculum if kids "can't" do it, aren't prepared for it, and don't graduate because they fail. Most kids can do it if they are prepared, unless of course Americans are just dumber than the rest of the world. The debate should be on why kids aren't prepared and what we can do to prepare them, not on which subjects we should delete. There isn't some magical difficulty in algebra and I'll just repeat that I felt the same way about art, music, foreign languages and even sports. Personally, I wish physical education had taken into account the shy nerdy unathletic kids like me--we needed encouragement to be physically active and not humiliation, but I don't think the solution to this would be to remove P.E. And that's not a trivial problem either, given the ever-expanding waistlines of Americans.
I went to an inner city school for one year, as part of court-ordered integration. And it wasn't just algebra some of these kids couldn't handle. I remember one kid in the ninth grade who was asked to do a report on Latin, and he came back with a report copied word for word from an encyclopedia on "Latin America". Some of these kids were 14 years old and weren't prepared for any subject at all. So maybe we should "help" them by removing all portions of the curriculum. And as for writing, I have friends who teach at college and what they say about student writing would be amusing if it wasn't so depressing. And these weren't underprivileged kids--most are middle class suburbanites.
Some of the positive reaction to this story comes from people who hated algebra and somehow in some strange way feel validated by a recommendation that we remove it --oh, in order to help the underprivileged, of course. Plenty of people hate history, English, grammar, reading, art, music, foreign languages, shop class, P.E., etc.... Maybe we could validate everyone by handing out diplomas for passing those courses people are willing to take.
Well, that's a strawman as well. Every year, millions of kids without aptitude in algebra receive high school diplomas. That's because high schools offer another math track for those who are less than whizzes.
DeleteTake my own kid for example. He is now studying at a pretty well renowed university conservatory to be a classical musician. His brain simply wasn't wired for high school algebra, particularly "word problems", even though the kid gets the strong connection between music and math.
So in order to satisfy his math requirement, he was put in a "consumer math" track in which all the work was done at the board in class (a relief from homework to him given the hours he was spending practicing and in private lessons), in which he learned the math that he really needs in the real world -- balancing a checkbook, measuring volumes and distances, dividing, multiplying. None of this "A train leaves New York travelling at 60 mph. At the other end of the same track, another train leaves LA travelling at 65 mph. Where do they meet?" crapola.
Well, if you are going to drag your kid into this, I don't think education policy for the student population as a whole should be set by the fact that there might be some kids who honestly can't do algebra. I'd be skeptical about that with most people though. 14 year olds don't necessarily know the direction they are going to take if they get to college and if they don't have a background in algebra there are whole fields that are eliminated for them, unless they want to spend seven years getting their bachelors degree. But sure, if some kid can demonstrate that he or she can't understand algebra to save his life, then he should be able to take "consumer math" and graduate that way. But I'd be afraid of way too many kids claiming to have that problem when they don't.
DeleteNow, what do we do about students who can't write, who hate history and can't memorize, or who hate music or art or P.E.? It's not a strawman. You probably can find people who lack the ability to pass one or more of the above. Do we set educational policy for most students based on the difficulties of those who can't learn particular subjects?
One of the things that bothers me about your post is the anti-intellectual tone and that phrase "the real world". You really can't understand very much about vast aspects of the world if you can't do basic algebra. People should understand something about interest rates, mortgages and basic probability and statistics and enough basic science to be able to follow at least some of the discussion that occurs with global warming , nuclear energy, population growth etc.... An interesting discussion would be what sort of math class everyone should take to understand "the real world" and that would include basic statistics. And you'd go far enough into the subject so that you'd start to see where simple algebra comes in handy. And that "crapola" about the trains--any child who might ever go into the physical sciences or engineering had better be able to handle that "crapola". (And yes, I know, your child had no intention of being an engineer.)
"Now, what do we do about students who can't write, who hate history and can't memorize, or who hate music or art or P.E.?"
DeleteGood question. What about the skinny, little clumsy kid who is no good at P.E.? Do we demand that he not receive a high school diploma until he masters basketball as well as the school's best players? Or is able to run a mile in 4:30 like the track team?
Of course not, but at the same time, you can teach that kid the value of exercise and physical fitness within the limits of his abilities.
Likewise, you can teach the concepts of basic algebra, which my son learned very well in his "consumer math" classes, while still maintaining a rigorous curriculum for those students who demonstrate talent in math.
You know, part of the problem with the teaching of "algebraic logic" is that you truly have to suspend all logic and common sense to learn it.
For example, the kid was posed this supposedly "real world" problem as homework which I will never forget:
"Ann and Beth together have $58. Ann has $7 more than twice as much as Beth. How much to each of them have?"
I showed him step by step: B = Beth. 2B + $7 = Ann. B + 2B + $7 = $58. 3B + $7 - $7 = $58 - $7. 3B = $51. B = $17. 2B + $7 = $41.
You know what he said? "Why don't you just ask them what they have? And how do you know they have $58 together if you didn't do that already?
Sorry, but mastering basic algebra is not in any way comparable to running a 4:30 mile. It's more like jogging an 11 minute mile. And yes, there are kids with health problems who couldn't do that and they shouldn't fail P.E. if that's the case.
DeleteAs for the Ann and Beth example, now you're just getting into the details of how to teach the concepts. I doubt anyone would be fascinated by that particular problem, but what that problem is meant to teach (translating the information given in words into 2 linear equations with 2 unknowns and solving them) is one of the most important ones in mathematics. They should be exposed to this. And yes, if they can't master something as simple as that, then send them to the consumer math class.
Why should your son have to know history? It's really depressing how you keep quoting what you think your son would say as a guide to educational policy. Children will always have objections to learning material they consider boring, whether it is grammar, history, math, science, music, art, and so on. For that matter, some adults never grow up. I sympathize--I'm pretty lazy myself on some things, but I don't take my likes and dislikes as models of what education policy should be or we wouldn't have spent five minutes learning grammar, art, music, and a few other things.
Somerby's point wasn't that Hacker didn't care about kids who are not privileged, but that he doesn't have a clue about them.
ReplyDeleteThat's not what Somerby says about Hacker at all. In fact, a careful reader of Somerby such as yourself should know that he has long advocated pretty much what Hacker is advocating now -- a way of teaching basic concepts to kids with varying degrees of talent.
DeleteBob S. frames the range of responses to the Hacker piece very strangely, it seems to me. Let me recommend Timothy Burke's post (and the comments):
ReplyDeletehttp://blogs.swarthmore.edu/burke/2012/07/30/hacker-job/#comments
I particularly was intrigued by the software engineers example of the necessity of algebra in real life by posing the following question:
Delete"But every time you face a question like, 'my car gets 32 MPG, and I’ve gone 300 miles, and I have an 11 gallon tank, so am I in trouble yet?' you’re facing algebra, aren’t you?"
To which my son the musician would answer: "You've got a gas gauge, don't you?"
So your son can't multiply or divide? The problem with that software engineer's example is that an elementary school kid should be able to do it without algebra.
DeleteBurke's piece itself was superb and I'm glad mch linked to it. Maybe there should be a real debate about what we should be teaching in high school math classes, but the Hacker piece was utterly incompetent. Bob could have used it as yet another example of what is wrong with the NYT, but instead Bob thought it was a rare exception to what is usually written there.
DeleteOf course my son can multiply and divide, and add and subtract. That doesn't mean, of course, that the software engineer's example of the necessity of knowing algebra isn't pretty doggone stupid. Which is one reason the kid was totally turned off by algebra. The problems given to him simply bore no relation to anything he could relate to.
DeleteBut suppose you give a kid this problem:
"LeBron James scored an average of 23.2 points in his first 15 games. In his 16th game, he scored 35 points. What is his new scoring average?"
My kid could do that one in his head.
"The problem with that software engineer's example is that an elementary school kid should be able to do it without algebra."
DeleteNo, the problem with the engineer's example is that if you rely on math instead of the gas gauge to tell you how much gas you got left, you're beyond help.
For instance, suppose you only think you're getting 32 mpg. Suppose you have a low tire. Or a plug not firing completely. Or wind or weather or road conditions lowering your mpg that day to, say, 28 instead of 32. Or suppose you only put 10.5 gallons in and didn't top off that 11-gallon tank.
So if you ignore your gas gauge and do the math that the software engineer suggests, you're good for another 52 miles, correct?
Now you tell me who is going to wind up by the side of the road. The non-math inclined who pays attention to the gas gauge, or the software engineer whose done all his careful calculations.
Brilliant, there, 10:07anonymous. So you've just established that all that book larnin' involving multiplication and division is worthless when compared to some music major using horse sense and a gas gauge that is always reliable. Well, I guess that showed us all.
ReplyDeleteBut wait--it turns out that all that was wrong was that the example should have involved sports. So maybe that multiplication and division is useful after all.
For anyone actually interested in substance, go read the Timothy Burke piece that mcha wrote. This is just becoming one of those chest-thumping threads (and yes, I'm participating.)
Assuming that you still want to have a serious discussion, the point I am making is NOT that algebra is useless. It's that the way it is being taught actually requires the student to shut off the critical thinking skills and problem solving techniques that algebra can teach very well.
DeleteNow if Hacker is correct, and we have millions of kids struggling with algebra, then perhaps instead of assuming that today's kids are too lazy and dumb to learn it, maybe we should examine the way we are teaching algebra these days.
That's the problem I had with the Burke piece -- the popular assumption that the problem is that algebra isn't rigorous enough, that the reason kids aren't learning it is because they aren't trying hard enough.
Please note that in the Drum piece Somerby linked to, Kevin Drum -- who I think we will agree is a fairly intelligent person -- is questioning whether the lessons learned in algebra really apply in any other areas of life beyond mathematics.
Now I would consider that the skills taught in algebra to solve problems by breaking them down into parts and applying mathematical rules to those parts to reach a solution would be self-evident.
But not apparently to Kevin Drum. Which leads me to believe that when you are given nonsensical problems to solve that defy common sense, it is difficult for even an intelligent person like Drum to see the value in that.
Incidentally, I did not mean to imply in my LeBron James example that it would work for EVERY kid. It would certainly work for my son.
DeleteAnd you know why it would work? Because it would be FUN for him!
Ooops! I just said a bad word! We all know that education shouldn't be FUN! It should we WORK, WORK WORK until we have beaten the joy of learning out of kids.
The problem with algebra is it is the point where the pretending stops. The school can no longer pretend that the student knows arithmetic, ratios, estimating. Because if the student does know these things then he can learn algebra.
ReplyDeleteI've taught algebra. Every time I've had a student who couldn't get started with algebra, who just didn't get it, that student also didn't know those basics. Every time we (the student and I) had the chance to work together and learn those basics learning the algebra followed right along.
Maybe this is too much. Maybe to reduce our drop out rate we need to drop the algebra requirement. Only let's not kid ourselves: we aren't just saying algebra isn't needed, we are also saying you don't really need to understand arithmetic.