Gifted Issues Discussion homepage Forums General Discussion Is Algebra Necessary?

http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html
Is Algebra Necessary?
By ANDREW HACKER
New York Times
July 28, 2012

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.

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.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee. Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.

California’s two university systems, for instance, consider applications only from students who have taken three years of mathematics and in that way exclude many applicants who might excel in fields like art or history. Community college students face an equally prohibitive mathematics wall. A study of two-year schools found that fewer than a quarter of their entrants passed the algebra classes they were required to take.

“There are students taking these courses three, four, five times,” says Barbara Bonham of Appalachian State University. While some ultimately pass, she adds, “many drop out.”

Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math. The City University of New York, where I have taught since 1971, found that 57 percent of its students didn’t pass its mandated algebra course. The depressing conclusion of a faculty report: “failing math at all levels affects retention more than any other academic factor.” A national sample of transcripts found mathematics had twice as many F’s and D’s compared as other subjects.

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A related discussion here is at http://giftedissues.davidsongifted....sing_the_achievement_gap.html#Post118807 . I think it is reasonable to expect high school graduates to know Algebra I (for example finding the equation of a line given two points) and for college graduates to know Algebra II, but since I think a large fraction (maybe 50% or more) of the population cannot learn algebra, that means that lots of people are not smart enough to get a real high school education, much less a college one. The idea that a bachelor's degree is for the (at least mildly) gifted, not for everyone, is "elitist", but I think it is true.

That article appears to conflate "mastering algebra" with passing an Algebra 1 course (or passing an Algebra 2 course, in places). Is that a reasonable conflation, in the US system? In the UK, a student needs to get grade A-C at GCSE mathematics (exam taken age 16) in order to be counted in certain "success" statistics for the school, and in order to go to university (any subject). The GCSE syllabus includes a lot of what you call Algebra 1 or Geometry e.g. solve quadratics, do stuff with the equation of a straight line, work with exponents, calculate volumes and areas of various 3D shapes, prove simple things using circle theorems, etc. However, getting a C at GCSE is a pretty low hurdle, and by no means proves that you've "mastered" all that material.

I don't think it's unreasonable to expect high school kids to take Algebra. Algebra is not that difficult, frankly. I do think the bar is set super low in math in the USA. My son is doing a beginning alegebra boook at home, and he just finished third grade.
I think the USA needs to really wake up in math and science. I'm sure other countries have their high schoolers take Algebra, and they can do it. OK, I don't think everyone needs to take Calclus, but Algebra???

LOL! And what talent would this be?

With higher education collapsing, the non-productive degree departments will be reduced or eliminated. Art and most of the hyphenated departments will be gone. Only the ones requiring math will be left.

Many vocational programs like surveying, welding, machining, etc etc have a very high math component. Algebra and working knowledge of geometry are REQUIRED.

Maybe hair dressing and truck driving will allow someone to function without numerical literacy, but the higher certs in trucking do REQUIRE math skills.

The author of this article has no knowledge of how the real world works or any interest in providing a productive future for kids.

Based on my experience working with less conceptually intelligent people (and by this I mean those who are generally not able to deal with theoretical aspects of math in any classroom environment), many people seem to develop enough math skills to do the jobs they want to do.

So, for example, if you have a person who really, really wants to learn how to do machining, such a person will apply themselves and eventually learn enough math to perform their job well.

Remember, everyone is generally able to learn specific mathematical skills, it just might take them a long time.

And by long time, I mean 5 years to grasp something that I could grasp in about 10 minutes.

Often being on the job for years is an excellent way to obtain sufficient vocational training to perform jobs rather than any kind of more formal vocational training.

If someone knows what kind of job they like to do, they will generally find a way to work around or deal with any intellectual limitations.

Yup. I agree... 100%

It's like anything else - you get out of it what you put in to it. Gifted kids may be ready to learn it younger, but it's certainly not beyond the average student, assuming they're willing to pay attention and apply themselves (which they'll have to do with anything in life if they want any kind of success).

I don't think it's unreasonable to ask high school students to master an algebra class. BUT...

In my state, graduation requirements include passing Algebra 1, Geometry, then Algebra 2. Which is fine...for some kids. But we have to be reasonable and understand that not all kids are college material, not all kids are particularly bright, and that there simply *are* kids who will become cable installers, welders, and plumbers (and at the rates our plumber charges, I fail to believe I'm condemning these kids to a life of penury by saying so). Holding these kids to that particular standard is an exercise in failure, and to no real purpose. It hurts them, and it hurts their classmates, who must wait while the teacher tries to drag them along.
We need to go back to a multi-path secondary school program. It would mean more appropriate education for the students, a better use of the teachers' time, and be a more efficient use of our tax dollars.

You probably don't want to know, Austin, how very little math is required of the average health care degree program.

Indeed. Everything that eldertree just said, including the high school graduation requirements imposed by the state BoE, and the relative insanity of doing so.


I taught chemistry to pre-nursing majors (year-long survey course, otherwise known in the trade as the G-O-B course, for 'general-organic-biochem') and most of those students could not:

a) turn a simple real-world problem into a mathematical expression of any kind,

b) solve VERY simple equations, even those previously set up for them, of the variety; 3x = 21,

c) recognize the words "quadratic equation,"

d) correctly use simple proportions to solve for scaled quantities, or

e) work with metric units using dimensional analysis to perform unit conversions correctly.

My child could do most of those things by the time she was in second grade, and could do them with mastery by the time she was in 6th grade.


These were college students, recall. People who were studying to become nurses.

I weep for the future...

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My major comment re: the article is that, well, DUH-- maybe this just suggests that not everyone is that bright. Maybe not everyone is "college material" to start with.

Now, what I ultimately mean by that statement is-- maybe that's actually just reality and it's fine that not everyone can become proficient in everything.

Also unspoken is that not everyone gets what they want. Very few people (relatively) who want to become brain surgeons are capable of doing the job to begin with. It's not very nice to delude those students well into college-- better to let them get over their disappointment early and make other plans. At least that's my opinion.

Same thing goes for college in general. Maybe if you can't handle basic algebra, a university isn't the place for you, if you see my point. I hardly think that the reasonable thing to do is to lower the standards to make college more inclusive. Lowering barriers to access, I'm all for, make no mistake-- but lowering expectations, I'm dead set against.

The world needs skilled tradespeople, too-- and not everyone can learn to be highly skilled there, either. The difference is that nobody is trying to suggest that I should feel like a failure for my lack of ability every time I take my car to my mechanic.

Kind of makes me grumpy that we seem to have lost our minds completely in the past generation, at least re: what constitutes "success" educationally.

I'd even go so far as to argue that "making math mandatory" doesn't prevent us from discovering talent as much as removing the mandate does.

Because look, even if it were possible to 'remove' math requirements from fields like medicine, geology, or fashion design (hint: it isn't, because reality doesn't care about anyone's fantasies), maybe allowing people to call themselves professionals in those domains without actually, you know-- being competent at them--

gets in the way of those people discovering just where their talents actually lie.

Maybe they DO have talents. But maybe a high school or university/college classroom isn't where they're going to find them. If we participate in the fallacy, we are tacitly discouraging those people from doing the kind of exploration necessary for finding out where they ARE competent.

Sorry-- the article is just stupid. The logic there is abysmal.