Instead of algebra, ‘citizen statistics’

Is Algebra Necessary? asks political scientist Andrew Hacker in the New York Times.

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.

Inability to do math — specifically algebra — is the major academic reason so many students fail to complete high school, Hacker writes. He proposes “citizen statistics” as an alternative.

. . . it would familiarize students with the kinds of numbers that describe and delineate our personal and public lives.

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.

This need not involve dumbing down. Researching the reliability of numbers can be as demanding as geometry. More and more colleges are requiring courses in “quantitative reasoning.” In fact, we should be starting that in kindergarten.

I think it is dumbing down math — so far down that it will close the door on many careers. But it’s better to teach some math than stick unprepared, unmotivated students in dumbed-down classes labeled “algebra” and “geometry.”

Frustrated by huge failure rates in remedial math, some community colleges are teaching “quantitative reasoning” rather than algebra to students who don’t have STEM ambitions. That makes sense. But it’s an admission of failure.

Hacker also wants to see classes in the history and philosophy of math, which he thinks would draw more math majors.

Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet.

Maybe more people would major in math if it didn’t require learning math, but what would be the point?

A commenter recommends The Number Devil: A Mathematical Adventure, which sounds like a cool book.

Here’s how Times readers responded to Hacker’s essay.

Yes, algebra is necessary, responds cognitive scientist Dan Willingham.

First, it’s not true that otherwise talented students are dropping out because of algebra. Motivation, self-regulation, social control and a feeling of connectedness and engagement at school are as important as grades, and a low grade in English is as accurate a predictor of failure as a low grade in math.

Second, “the difficulty students have in applying math to everyday problems they encounter is not particular to math. Transfer is hard.”

The problem is that if you try to meet this challenge by teaching the specific skills that people need, you had better be confident that you’re going to cover all those skills. Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won’t transfer.

Well-educated people can learn on the job, Willingham writes. “Hacker overlooks the possibility that the mathematics learned in school, even if seldom applied directly, makes students better able to learn new quantitative skills.”

Kids who can’t understand math usually can’t read well either, writes RiShawn Biddle on Dropout Nation. “The very skills involved in reading (including understanding abstract concepts) are also involved in algebra and other complex mathematics.”

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Comments

  1. Even basic stats requires some background into basic algebra (when you look at the formulas for variance, std. deviation, chi-square, etc).

    This same article was posted on slashdot: http://www.slashdot.org

    And if you want to get to the nuts and bolts, insert where algebra is.

    Has our educational system gotten so bad in society that we cannot require students to master and pass at least pre-calculus (which if a student prepared properly in high school, and really MASTERED the material), should have ABSOLUTELY no problem passing (and pre calc is usually two 3 credit or one 5 credit course), or the student can pass it via CLEP.

    Excuse me while I throw up here folks…

    • We’ve accepted dumbed-down and math-phobic teachers for a couple of generations now, and other interests have shifted the demographics of the country toward ethnic groups which perform more poorly (though still better than in their countries of origin).  There is no easy solution to this; certainly none that can be done with the usual tactic of throwing money at it.

  2. I’m not sure why we think not having students take pre-calc is showing that schools are getting worse. My parents (born in 1950) graduated from high school in a small city (ie not a poor rural school). They talk about the smart kids who took algebra 2 in high school. I think my dad did, mom called it quits after geometry. They used to talk about how I had surpassed their math knowledge by the time I finished 9th grade.

    While we can talk about dumbing down of math, we have to realized that not everybody intends to go into those fields, or even college. A friend in high school took the vo-tech track – he could take apart an engine, and he worked as a machinist. As I was graduating from college, he was talking about taking a trig class at the local CC to learn the theory behind what he did. He said that it would have been wasted on him in high school. While I have no problem with diplomas signifying ‘college prep’ and ‘regular’ or some such, I’m not OK with denying a diploma to people who may be excellent preschool teachers, truck drivers, etc.

    • Barry Garelick says:

      We’re not talking about pre-calc or algebra 2. Just algebra 1. And the big question to ask which Hacker did not ask, is why students in high school and college cannot do basic addition, subtraction, multiplication or division. This might explain why algebra 1 is hard for some/many students.

      • tim-10-ber says:

        How much is related to K-8 teachers not having the math mastery needed to truly teach math to their students? I think this is a major part of the problem…look at the requirements for K-6 and sometimes K-8…just how much math is required?

        • Teachers with sufficient subject knowledge are very important, but the quality of the curriculum and the effectiveness and EFFICIENCY of the instruction are also very important. Spiral curricula like Everyday Math are inherently flawed because nothing needs to be mastered before the student advances. In a strongly hierarchical discipline like arithmetic, the fundamentals need to be mastered in a specific sequence. Solid curricula like Singapore Math are structured to ensure this. Many schools use various group-work, discovery methods of instruction, which amounts to kids pooling their ignorance. Even if you believe such methods work, and I don’t (on any scalable basis), they are highly inefficient. Direct, teacher-centered instruction, combined with sufficient practice, is much more efficient and effective. Kids who don’t establish a sound foundation in ES will struggle thereafter and are unlikely to make up their deficiencies.

  3. Over 6 years ago there was one of these set-the-algebra-world-on-fire articles posted, and I responded then. This current article is no better than that one, so the response is easy:
    http://rightontheleftcoast.blogspot.com/2012/07/is-algebra-necessary.html

    The 6-year-old post is at http://rightontheleftcoast.blogspot.com/2006/02/what-is-value-of-algebra.html

  4. My old Algebra I teacher in 9th grade said it best:

    You guys and gals have no problems doing algebra, you just can’t add, subtract, multiply, and divide…

    Words to live by for any student who wants to succeed in higher level math :)

  5. Richard Aubrey says:

    Something to be said for being able to see through the stats constantly thrown at us, from Lancet and Iraqi casualties to AGW to GM’s profits.

    • This is why the elites of the world (which come in conservative and liberal flavors, before this gets miscontrued as a polticial post) don’t want the general public to be good at Math, or have any advanced Math skills; then they can get away with anything! (and they are)

      The K-12 schools aren’t failing in their mission; they’re succeeding beyond the elite’s wildest expectations…

  6. Cranberry says:

    As a school subject, mathematics is very effective. It’s easy to ascertain if a student knows how to graph x = y + 2. Ask her to graph it. If she can’t, you can be certain she doesn’t understand it. As mathematics is cumulative, she’s unlikely to understand parabolas if she can’t graph straight lines when given the formula.

    It’s harder to ascertain if he understands the Lend-Lease Act in WWII. It’s easier to pretend to find equivalent work — hey, how about a book jacket project for the kid who can’t read the book on World War II! Some of the kids submitting art and crafts projects on assigned books read and understood the books. Some didn’t. It’s much harder to determine a student’s difficulties in English and Social Studies, especially if the school sets assignments which don’t rely on reading comprehension or background knowledge.

    In short, banning algebra is the equivalent of shooting the messenger.

    I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures. Why not mathematics in art and music — even poetry — along with its role in assorted sciences? The aim would be to treat mathematics as a liberal art, making it as accessible and welcoming as sculpture or ballet. If we rethink how the discipline is conceived, word will get around and math enrollments are bound to rise. It can only help. Of the 1.7 million bachelor’s degrees awarded in 2010, only 15,396 — less than 1 percent — were in mathematics.

    The point of awarding degrees in mathematics to people who can’t master Algebra I would be? I’m at a loss to understand it. Ballet and sculpture may seem accessible to the passive viewer, but practicing artists undergo rigorous and pitiless training regimens. The liberal arts, properly taught, should be demanding courses of study, not preparation for a life as an arts aficionado. A bachelor’s degree in “math appreciation” courses wouldn’t be a bachelor’s degree in mathematics. The problem with mathematics isn’t math.

    • He thinks ballet is accessible and welcoming? Oh my goodness.

      Thanks to Cranberry’s quote I’m almost starting to wonder if this article wasn’t a practical joke.

      “The point of awarding degrees in mathematics to people who can’t master Algebra I would be?”

      I’m having trouble with that, too.

  7. The problem is that high school students have no idea what job they will have in their 30s and 40s. Things change too fast, their future job may not have been invented yet. I’ve had about three careers, so far.

    We seem to have been able to teach algebra in the past, shouldn’t we be looking for the problem that prevents us from teaching it now, instead of just throwing in the towel…

    • When I was in a small-town HS (class of 67, 29 in class), only the college prep kids took algebra. The secretarial and general kids took Math 9, which I think (IIRC) had some algebraic concepts but had more financial literacy stuff (which college prep kids also need to know). Up to HS, we all had the same classes, with some extras added for those who could handle them. My FIL was the principal of a technical HS and many of his kids took algebra, geometry and more, depending on the specific program. Those in the cosmetology and secretarial programs took less; those in the practical nursing (LPN) program took more, as did the tool and die-maker kids, the auto mechanics and the sheet metal workers.

      As I said above, the algebra/math problem starts in ES, with the failure to teach arithmetic to mastery. That needs to include fractions, ratios, proportions and decimals.

      • the algebra/math problem starts in ES, with the failure to teach arithmetic to mastery.

        The problem is that this immediately creates politically troublesome and visually obvious statistical disparities in results.

        This isn’t going to change without repeal of the core of one or more civil rights acts, specifically those which find liability for disparate impacts and outcomes.  I would love to see enough political momentum behind repeal to do that, but I’m not expecting it.

  8. Richard Aubrey says:

    Rob. When “studies” show changes, the first thing to do is look at the methodology.
    Back in the day, there was the college prep track and there was the other or others.
    Commercial or vocational were not, when I was in HS, formally labled. However, the classes you took made it pretty clear. Algebra, even A1, wasn’t necessarily on the non-college list.
    First question, then, is whether we’re testing the same cohort now as then.

  9. Roger Sweeny says:

    Hacker’s article is wrong in lots of ways. But he has seen a basic problem with our educational system.

    In grades 1-8, students are supposed to learn to read, write, and do basic math. In high school, they take what are essentially simplified college courses (“biology” “algebra”). For most students, most of what they are taught in these courses will never be used outside of another school. So we have to ask ourselves, honestly and brutally, “is this how young people should be be forced to spend their high school years?”

    Once students have a basic understanding of math–fractions, decimals, and yes, basic algebra–it may make a lot more sense to have them get an understanding of statistics than to slog through algebra 2 and trigonometry, or the more advanced parts of algebra 1.

    Right now, we have accomplished the seemingly impossible. Lots of students leave high school having taken algebra 1 and beyond, but without a usable understanding of basic math.

    Too often when we talk about school, we pretend that taking and passing a course means a student understands the material in it and can use if once the course is over. It is a pleasant delusion, but it is a delusion. Making policy based on it means that we make bad policy.

    • Mark Roulo says:

      ” In high school, they take what are essentially simplified college courses…”

      Except for math.

      Algebra is not a simplified college course. And at places like San Jose State they offer Algebra (Math 003A and 003B), but the units do not count towards graduation.

      But, yeah, in general high school courses are simpler/slower/easier versions of college classes.

  10. Anyone who thinks to substitute statistics for algebra doesn’t understand either statistics OR algebra. Why does anyone listen to this doofus?

  11. Perhaps people listen to him because he is a doofus :)

    The problem lies in the foundation of math that these students receive in grades 1-8…

    If a student hasn’t mastered Add, Subtract, Multiply, Divide, Fractions, whole and real numbers, place value, etc…they’ll NEVER be able to make it through algebra, and in many (if not all) colleges, algebra is not a course which is counted towards a degree or entry to any major program of study. Just like any course less than English 101 would not count towards a degree.

    Momof4 has it correct…piss poor preparation in ES/MS (along with the math programs in use) has ruined the ability of countless students who MIGHT have otherwise excelled in math. (gack).

    • A regular parent commenter on another ed website says it’s now likely, even in the affluent, highly-educated leafy suburbs, that only those kids who have had tutoring (parent, Kumon, private etc) are really prepared for 8th-grade algebra. He’s talking about bright kids who should all be ready for that, and most should be ready in 7th or 6th. Without outside help, those kids fail the placement test for 7th-grade pre-algebra, because they haven’t mastered basic arithmetic. They’ve never been asked or expected to do so. As long as “enough” kids make the cut, the schools don’t want to know how they did it.

      I do know that parent pressure forced the Scarsdale, NY (highly affluent Westchester County) schools to switch to Singapore Math a year or two ago. The director of the local Kumon was quoted as saying that they would have to adjust their message. I also read that MoCo is changing their ES curriculum to something with Pearson publishing that sounds highly questionable. Unfortunately , Scarsdale is a small system (only 1 HS), so it’s easier for parents to apply pressure. MoCo is huge and does exactly what it wants to do.

  12. Well, if only I could pass certification exams so easily that I didn’t have to understand basic concepts :)

    Not likely to happen, however, since the concepts only keep getting harder and harder (or I forget more and more as I get older) :)

    hehehehe

  13. The original author is a fool, and (as another commenter said) apparently doesn’t understand statistics OR algebra. And Dan Willingham is exactly right!

    The minimum requirements for a high school diploma in the U.S. should be PreAlgebra, Algebra I, Geometry, and then either Algebra II or Financial Math. With PreCalculus and Calculus added for the advanced students. Can’t meet these minimum requirements? Then no high school diploma for you. Period.

  14. Here’s someone who is just smart enough not to know he’s stupid. Read up on IQ.