Political Animal


July 29, 2012 11:40 AM Is Algebra Really that Hard?

By Ryan Cooper

Over at the Times they’ve got a big piece on Almighty Algebra by Andrew Hacker and how it’s crushing our students:

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…
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.)

The obvious question here is just how far “algebra” reaches into “quantitative skills.” Hacker is somewhat unclear on this point. “My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus,” he says. But that represents three to four years of mathematics. If we’re talking advanced algebra, trig, and calculus, I agree, despite their massive scientific utility, those are probably outside the reach of the average student. But throughout the rest of the piece he’s talking just “algebra.” Even the simplest bit of quantitative reasoning—trying to figure out which credit card offer is screwing you the least, say—needs some variable work. Just where do we stop with that? Hacker isn’t clear.

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.

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? What do you think?

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Ryan Cooper is a National Correspondent at The Week, and a former web editor of the Washington Monthly. Find him on Twitter: @ryanlcooper


  • c u n d gulag on July 29, 2012 12:38 PM:

    Algebra proves that God does NOT exist.

    No all-knowing, all creating, entity, would let numbers and letters mix together.

    Letters need to be letters, and numbers need to be numbers.

    Algebra is an abomination to nature, to science, and to mathemtics, in that it integrates the two.

    And only man, not some Supreme Being, could think of something so nefarious and torturous!

  • c u n d gulag on July 29, 2012 12:40 PM:


    Here I am, bitching about mixing letters and numbers together, and I can't even spell "mathematics" correctly.

  • David Martin on July 29, 2012 12:56 PM:

    There's something unkosher about mixing letters and numbers as if they were wool and cotton? Actually, the letters ARE numbers. I guess the Romans must have done some calculus, no idea how.

    I, for some reason, skipped seventh grade math, trudged through high school, then spent much of my college freshman year trying to make sense of calculus, to the detriment of freshman chemistry and even biology. On the second try, calculus was an easy A, but the all-important grade point average never fully recovered. Later on, I got a good intro to statistics and much later, picked up a reasonable grasp of matrix algebra, which happened to be useful and relevant.

  • DAY on July 29, 2012 12:57 PM:

    Back in school (1950's) it wasn't the algebra that was so hard, it was having to memorize ALL the presidents! So, unfair; when the teacher was in school there not nearly as many.

    I say, now that we have Wikipedia, let's abolish school altogether. Plus, with teh Google, you doant even need to spell gud anymor.

    (And, Captcha is proof!)

  • leopoldvonranke on July 29, 2012 12:58 PM:

    Unless it's taught differently than it was taught 40 odd years ago, I can see student's difficulty. Back then, it was just about learning to manipulate the equations, with no practical applications. Manipulating the equations, for the "smart" kids, was no big deal. For most kids, the question of "why bother?" was preeminent. There are numerous practical applications of algebra, geometry, trig, and calc. Why don't teachers start with those, integrate them into the work with equations, and give the kids some sense that in working the equations, they are solving practical problems?

  • Objective Dem on July 29, 2012 1:01 PM:

    I think basic algebra should be required for almost everyone. But I would rather than spend time teaching people trig and calculus I would much rather see classes teaching more basic algebra using everyday situations. I also think it would be more useful to teach people probability and statistics. (But since Lottery money "helps pay" for education it may hurt in the long run)

  • schtick on July 29, 2012 1:01 PM:

    We need to make a better attempt to teach basics, like reading, writing, and arithmetic. Basic algebra would then fall in line along there, too.
    The chemistry and geometry sucked for me. I was out due to illness the first four months of classes and could never catch up with the rest and I'm not really sure I would have anyway. I had a real hard time with those classes and finally gave up.

  • martin on July 29, 2012 1:02 PM:

    Like so much we learn in school but don't "use", algebra is one of those things it is good to know, good to know it exists, and useful when you do need it. Algebra, statistics and public speaking we're, for me, the most useful classes I ever took.

  • joel on July 29, 2012 1:04 PM:

    I took algebra in 8th grade, too, followed by geometry, algebra II and trig, pre-calc, 4 quarters of calculus in college and a semester of biostatistics in grad school. I'm a full professor of biochemistry and molecular biology and have authored or co-authored over 70 scientific articles. The only math I need beyond simple arithmetic is algebra. Learn it. You won't be sorry.

  • Mikhail on July 29, 2012 1:05 PM:

    I'm with Leopold von Ranke here. Teaching practical applications would help a good deal, and perhaps a method of teaching that was less focused on rote memorization of formulae?

    My own math career was weird. I did abysmally in Algebra and pre-Calc, but Geometry, Statistics, and Logic (the last in college) were all easy-As for me. They seemed to be intuitive and have real-world applications, and I still use the knowledge from them some (confidence intervals show up a lot, for instance). But Algebra? "Memorize these twenty formulae by monday."

  • mellowjohn on July 29, 2012 1:05 PM:

    i teach in the chicago public school system. my kids are classified as "trainable mentally handicapped" – more modernly said as "moderately cognitively impaired." their IQs measure between 40 and 55.
    i had one of my students doing simple one- and two-step algebra problems last year.
    that said, i had bitch of a time with anything past that when i was in high school.

  • KP on July 29, 2012 1:09 PM:

    I cannot believe the New York Times allowed such rubbish to be displayed so prominently on their editorial pages.

    There are all sorts of things in school that aren't "necessary" in everyday life: Shakespeare, ancient Mesopotamian history, analogous color schemes in art, playing the oboe or some other instrument, writing research papers with correct citations, geometric proof, and so much more. But each of these things sharpens the mind. An athlete will run laps and lift weights. Lifting running laps weights and isn't part of a basketball game or a football play; however, these activities improve the body for whatever will happen in the game. In school, we learn many things that may not be directly applicable to one's life or career; but these things we learn strengthen the mind, increase one's imagination, and create an extra capacity of brain power to better handle what one does on the job and at home.

    Education is not the same as job training. The function of a school is not to shape youth into better servants and peons for the elites, but rather to maximize the potential of every individual. We don't know who will be our future engineers, political scientists, artists, or leaders. So we give every student a chance to find out what she or he can be.

    I have been seeing a lot of verbiage and codswallop about education in the public discourse lately. Maybe it is today's culture of punditry, but it would be nice if the writers in our editorial pages and on the talking heads on television actually know what they were talking about.

    (I am an actual public high school math teacher, and I teach in an urban school district at a school which is 100% "minority" --- if such a phrase actually makes sense --- and where nearly all of the students qualify for free lunch. I have taught at the college level. I enjoy fiction, as long as it doesn't pass for political discourse.)

  • leopoldvonranke on July 29, 2012 1:10 PM:

    Objective Dem

    Once had an interesting argument with a fundamentalist co-worker who "pointed out" that, "statistically" it was impossible for amino acids to aggregate in such a way as to produce DNA/mRNA. Turns out, I'd read the article from whence this notion sprung, and it was a melange of misunderstanding.

    The fun part was in pointing out the first rule of probability -- once something has happened, the chance of its having happened is 100%. He didn't get this.

  • bleh on July 29, 2012 1:15 PM:

    I don't care what his credentials are, Hacker is completely off-base, and his prescription is absurd.

    His article is full of contradictions. For example, he says students should learn long division (a tedious algorithm that can be performed by any calculator), and it's okay to teach "machine tool math" (which can be nothing but a series of very specialized algorithms), yet it's inappropriate for students to spend time learning the algorithms of algebra. And he bemoans the lack of STEM graduates, yet says burdens should be reduced on "poets and philosophers," of which I have rarely found a lack on the average college campus.

    He also says students should be taught "quantitative reasoning," but he never says what that is, or how to teach it, and in particular he never addresses the crucial skill of mathematical reasoning IN THE ABSENCE OF KNOWN VALUE -- ie, use of "variables" -- that is the heart of high-school algebra and that is essential to very many practical applications.

    Rather than throwing away what has evolved over many many decades, we might instead try improving what we've got. One way to do that would be to PAY TEACHERS BETTER, so qualified people don't abandon teaching for the more lucrative jobs available to mathematically sophisticated people. And another might be to GET OVER THE MATH PHOBIA that Hacker so easily accepts; maybe if parents didn't say "oh yeah, it was hard for me too, that sucks" and shrug their shoulders, students might be more motivated to learn algebra instead of giving up.

    This is one of the wooliest-headed pieces I've ever seen in the Times.

  • joel hanes on July 29, 2012 1:15 PM:

    Mathematics requires thought and understanding and effort.

    You can't bullshit your way through a math test. You can't use tricks of irony, humor, or diction to make up for your lack of understandng. You can't make a big poster of some easy math concepts, attractively presented, to fix your grade.

    Most people hate to actually study and to think hard, and will avoid them when possible. Math requires both.

    Excellence in athletics requires hard training, which most people also avoid; but in our culture we shower those who excel at athletics with accolades, and many who will never excel find considerable satisfaction in the pursuit of athletic improvement.

    It's nice to imagine a culture in which excellence in thought and learning were as honored in American schools as excellence in football is honored today. We know it's possible: viz. Jaime Escalante.

  • Crissa on July 29, 2012 1:21 PM:

    How we teach most students how to approach and think of algebra doesn't match the uses in many ways, I think.

    He doesn't think it's useful because he doesn't know when he's using it.

    For me, Algebra was the point in time where my math test scores went from 'we should put this kid in remedial' to 'we should send this kid to the top engineering school.'

    By giving rote memorization for much of math teaching we bore them out of realizing it has any use.

  • James on July 29, 2012 1:26 PM:

    You can't learn to drive a car by having someone explain it and then watching someone do it. You have to actually physically get behind the wheel, coordinate the muscles, the vision, the hearing. You have to actually step on the gas and brakes, turn a corner, park a car, accelerate on the roadway. Then you know how to drive a car.

    It's a similar process with mathematics, specifically algebra. You learn how to evaluate and solve problems, logically, step by step by working through the equation and coming up with the indisputable answer. Mathematics, algebra, trains the brain in thinking logically to discover truth. You can't just learn that by someone telling you about it. You have to actually take it step by step, make mistakes and go back and find them, correct them, and finally get them right.

    It is the same with memorizing. It trains the brain and makes healthy connections. You learn Shakespeare or the true meaning of the Gettysburg Address by memorizing passages, you learn to write (well) by parsing sentences and conjugating verbs. You learn foreign languages by reciting the basics until you know them cold. One trains the left side of the brain through algebra, the right side of the brain through language and music.

    Yes, statistics is far, far more useful in ordinary life, as is trig and geometry. But you can't find use in these skills until you are able to think logically through a problem and solve it step by step. That's what you learn in algebra.

    Otherwise, one is defenseless against the kinds of garbage that the Republicans throw out there. I say we need MORE algebra. SOONER.

  • leopoldvanranke on July 29, 2012 1:30 PM:

    Crissa --

    Hear, hear. In my profession, mostly what I do is use basic spoken English to convince people of a certain proposition or propositions. But a basic understanding of mathematics is nevertheless often helpful. Reducing it to the spoken word is essential. You don't need to quit teaching it, you just need to make it pragmatic.

    Years ago, I helped an astrophysicist build a picket fence. The man wrote a computer program to determine how much angle to put on the stiles to optimize water run-off and minimize rot, as well as the optimal angle to place on the tops of the pickets for the same purpose, spacing of the pickes and posts, etc. A bit overboard, but nevertheless eccentric and charming.

  • Colin Day on July 29, 2012 1:38 PM:

    @c u n d gulag

    The letters in algebra are variables (perhaps it would be less confusing if we used something else for variables). The domain of the variables is usually the set of real numbers. The letters are a way of denoting any number from some set of numbers.

  • jjm on July 29, 2012 1:44 PM:

    Good grief! Just because something is hard to learn, and probably harder to teach, it's not worth learning??

    My high school algebra teacher was the coach (the math teacher had left the school suddenly), and he admitted he was just 'one page ahead' of us in the textbook. But the idea of systematically working through an equation was actually very inspiring, and it also seemed to me to have plenty of 'real world' applications.

    When I consider that algebra was an Arab invention and that it helped to put Arabs way ahead of the rest of the world in cultural progress maybe there is something to this complaint. The desire appears to be to have us return to a world devoid of all 'pernicious' foreign elements, just as the Germans, beginning in the 19th century, tried to purge all foreign-origin words from their language (particularly those from Latin).

  • David Martin on July 29, 2012 1:46 PM:

    The astrophysist's computerized design for a picket fence is not unlike what a grad student named Anthony Starfield did back in the late 1960s to figure out how to air condition South Africa's deep underground mines. His programming saved a huge amount of drudgery, and later he became an expert at modeling the population dynamics of big animals, which has done a great deal to improve decision-making.

  • Davis X. Machina on July 29, 2012 1:50 PM:

    I struggled with algebra in 9th grade, but took a couple of USCG Auxiliary navigation courses in the following two years, and learned it all in that context, right down to the spherical trig needed to do celestial navigation. Along the way I got my ham radio licence, and that came with a fair amount of math, too, including imaginary numbers for transmission line impedance, and stuff.

    Came back to Algebra II/Analysis/Trig as a senior, and aced it all.

    One vote for applications making a big difference....

  • T-Rex on July 29, 2012 1:51 PM:

    He missed the most important argument of all: Algebra is an ARABIC word! Obviously this is part of the Muslim Brotherhood's plot to infiltrate our government, corrupt and brainwash our youth. The only math kids need is in the Bible, where it tells them to multiply upon the face of the earth. (Not before marriage, of course).

  • Cranky Observer on July 29, 2012 1:53 PM:

    It is essentially impossible to get an entry-level job in a modern manufacturing plant without demonstrating proficiency through at least trig, and promotion to a journeyman level is going to involve skills (e.g. self-managing TQM analysis for a workgroup) that will require at least a bit of pre-calculus (formerly college algebra) math.

    So Hacker is essentially saying "let's outsource the last of our manufacturing ability to Germany and the PRC". Yeah, that'll end well.


    oldirese notes (4th try)

  • DAY on July 29, 2012 1:54 PM:

    The main- only?- goal of education is to teach students how to think.
    The rest, as Einstein said, you could "look it up."

  • Anonymous on July 29, 2012 1:55 PM:

    For the mathematically challenged, a primer on basic math and algebra:

    1. The natural numbers are 0, 1, 2, ... . They are nouns that describe quantity.

    2. The integers are signed numbers. You can interpret -10 as "10 dollars in debt."

    3. The rational numbers are fraction of integers. The express ratios. You can interpret 2/3 as two pieces of a pie cut into 3 equal pieces. They also express rates, as in miles per gallon.

    4. Basic arithmetic involves operations on numbers: addition, subtraction, multiplication, division. Very helpful in balancing your checkbook or deciding how mucg flour to measure out for baking multiple pies.

    5. Algebra is basic arithmetic coupled with the idea of a variable (the dreaded letter x). If I want to build a fence that encloses 100 square feet and is twice as long as wide, how many feet of fencing material must I use? Answer: a variable to be determined.

    6. Algebra is used to determine the quantity of a variable. If the width of my fence is x and the length of my fence is 2x, then 100 = (x)(2x) = 2x^2 and so x is the square root of 50 (just over 7). Hence I need x + x + 2x + 2x = 6x feet of fencing material (just over 42 feet).

    7. Polynomials are arithmetic combinations of a variable, as in 2x^2 or 6x. We factor polynomials in order to obtain information about the variable they are expressed in terms of.

    8. You can't do much higher quantitative work in the sciences without algebra and calculus (the latter impossible without algebra).

    You're welcome.

  • dalloway on July 29, 2012 1:59 PM:

    A wee word here from the mathematically challenged. I'm fine at arithmetic, loved geometry (because it's visual), but sucked at algebra and higher math to the point where I had an embarrassing meltdown during a trig test. My SATs were hilariously lopsided in favor of the verbal score -- to the point where one guidance counselor asked me about brain damage. I got into a great college decades ago, but with the weight placed on the math SATs now, I wouldn't even be considered.

    Yet I've had a successful career (in a non-math field, of course) and managed my finances well enough for a very comfortable retirement. If I've used algebra, it must have been on such an unconscious level I didn't know it at the time.

    The point is that higher math is a talent. I don't have it. Those who do should be given all the math they can eat. Those who don't shouldn't be force-fed math they'll never use. If I'm a mediocre swimmer, sure, make me do laps to get better. But don't expect me to train like Michael Phelps.

  • Anonymous on July 29, 2012 2:14 PM:

    Far be it from me to force-feed you anything. But eat you must, and to withhold either vegetables from you as a child because you didn't like the taste of them, or to withhold teaching you basic mathematics (about which we're talking here) as a child (8th grade in my case), is to handicap you for the rest of your life.

  • Thymezone on July 29, 2012 2:18 PM:

    Algebra serves no purpose in ordinary everyday life. In some pursuits, yes, but I have held at least two dozen jobs in my life, technical, aeronautical, nontechnical, administrative, food service, janitorial ... I have needed algebra maybe five times in forty years. For this I suffered 4 years of high school and two years of college torture for no good reason.

    Slide rules, calculators, and computers have bailed me out of almost every math dilemma I have gotten into. I wish I had spent all that time in school wrangling with math problems instead working on solutions to basic relationship skills. That would have been useful. Also employment law, or maybe some meteorology. Anything but frickin' algebra.

  • Thymezone on July 29, 2012 2:26 PM:

    jjm, there is a difference between finding something "hard to learn," and just hating it.

    I hate advanced math. German was hard to learn, but I don't hate it. Flying upside down was a little challenging, but I don't hate it. In fact, I taught it to others. Hard to learn has nothing to do with anything. Hating something and loving something have a lot to do with everything that means anything. If a person hates math, then let them hate it. Some people hate Windows system admin, and it's a useful skill set, but why force people to learn it? And nobody needs advanced math skills to do it.

    People who insist that math is essential are just bullies. Fuck them.

  • Anonymous on July 29, 2012 2:26 PM:

    First, learning mathematics is not incompatible with learning how to relate to people.

    Second, the purpose of teaching algebra is not to train students to factor polynomials in the "real world." Just as the purpose of teaching a foreign language is not so that we can order from the menu in the appropriate native language. We teach algebra to train the mind in quantitative and abstract reasoning and to prepare students for the sciences if they choose to go that route. We teach Spanish or Latin to familiarize students with other cultures, other ways of thinking, and to increase the understanding and use of language.

    I love how people rail at ignorance daily on this blog but somehow it is acceptable to denigrate mathematics as if it is uncool and (most important) not necessary for the Good Life (defined as having a large retirement income).

  • PTate in MN on July 29, 2012 2:30 PM:

    Algebra requires thinking. It seems hard to students not because memorizing formulas is hard for young brains, but because they aren't used to thinking; they will learn to think better by doing math. Nevertheless, I agree 100% with Objective Dem: algebra, probability & statistics, more applications. God, for a population that is statistically literate!

    It astonishes me that it is socially acceptable in many otherwise cultured circles for people to say things like, "I don't need math" or "I just don't like math, and I never use it." There's even a certain cachet to being a math-phobe, as if it makes you supercool, part of the in-crowd (obviously, real poets don't need math.) To my ear, however, saying you don't like math is like saying, "I don't like to think, and I don't need to think. I'm proud of being thoughtless." Hacker's article is just a better written variation of the usual math-phobia.

    Wow, CAPTCHA. Five tries to post!

  • Thymezone on July 29, 2012 2:34 PM:

    Nobody is "denigrating" math. Math is what it is, let those who want it or love it have it. I am denigrating math tyranny as advanced by bullies who insist that their appreciation for the skills must be adopted by everyone. It's just baloney. Let people be who they are and pursue what they choose to pursue. Who the hell are you or anyone to tell people what they have to study? I once earned a living being a press mechanic, and enjoyed the work tremendously. Had I stayed with that pursuit, I'd never have needed any math beyond arithmetic. So what?

    My parents excelled in the law, in acting, as a legal secretary, and at portrait art, at various times. Advanced math would have been of little use to them.

    And your extrapolation of denigration of math bullying into "denigration of mathematics" is both stupid and dishonest, since mathematics will be appropriately valuable in some contexts, and not others, with or without your particular support for it. Don't puff yourself up please.

  • Anonymous on July 29, 2012 2:36 PM:

    Seems like you're the one doing the bullying here.

  • Thymezone on July 29, 2012 2:41 PM:

    Oh, the rubber-glue retort is way out of your league, friend.

    You're the bully, who asserts that my request to be left alone is "bullying." You remind me of the math teacher who told me that my resistance to calculus would cause me to never amount to anything. Go die in a fire.

  • rfb on July 29, 2012 2:46 PM:

    Forget about algebra, Americans are largely mathematically illiterate. In France the ground floor is 0 and underground floors are -1, -2, etc. In the US the ground floor on elevators might be G, L, M, or some other arbitrary letter. Below ground floors seem to have both random numbers and letters. Presumably this scheme accommodates those who can not comprehend the number 0.

  • c u n d gulag on July 29, 2012 2:49 PM:

    I was kidding in my earlier comment.

    I fully agree that something like algebra needs to be taught as part of someone's overall education.

    I had some terrible, and I mean REALLY terrible math teachers at my JHS and HS. They made the subject so boring and repetitive, that I watched the girls in the class more than I watched the teacher explain at the blackboard.
    I also had one or two bad history teachers. And it's tough to make history boring for me, because ever since I was a child, I LOVED history.
    How do you make history boring?
    Same as math: Ask kids to memorized things, instead of understand concepts, and not show the practical things that someone can do with that knowledge.

    And despite all of this, our HS was one of the top-rated ones in NY State.

    My math grades generally sucked, yet, on standardized tests, I could almost always figure out the correct answer - ditto on NY State Regents exams, where I did well on choosing one of the 4 answers, but lost a lot of points on the practical part of the exam, where you had to show your work.

    One HS Guidance Counselor explained to me that I certainly had the aptitude for math, and could take all sorts of higher level math classes, and do very, very well.
    Instead, though now I love reading books for laymen about physic's, the first day of class, I saw the amount of math in that course, got worried, and took Earth Science instead.

    I wish someone had made math as much fun as my English teachers made books, and plays, and poems; and my good history teachers, who said that while dates were important, the causes and effects were just as important - and who showed the human sides of historical figures, and how the average Joe's and Jane's were affected by what was going on around them at that time.

    Instead, I was told to memorize endless strings of formula's, which was as boring as watching paint dry.

    And then they wondered why I was bored, and hated their classes.

  • TCinLA on July 29, 2012 3:01 PM:

    I was "bullied" as a child in math by the fact that my Original Creative Genius father could do calculus in his head. Of course, he expected me to follow him into a similar scientific/technical field, for which I had no aptitude or talent whatsoever. In the Navy, I met an old Chief who gave me the best piece of advice ever: never compete with an expert on their own turf. It took awhile to convince dear old dad that I wasn't going to follow him in my college course work after the Navy, but having that attitude let me get through the math I had to do in lower-division classes. And then becoming the one thing the Original Creative Genius wanted to be and couldn't be (since he had no talent for it) - a writer who paid the bills with writing only - pretty much led to us working all that out. It is funny to realize that once you are not "competing" lots of scientific/technical things are not so hard to understand.

    What mathematics does is teach logical thinking, and that is something that is in dire need to being expanded, given that the Illogical is now dominant in society. Logical thinking allows critical thinking, allows one to learn to detect the presence of bullshit.

    Actually, Thymezone, you're right that it doesn't take a knowledge of algebra to fly upside down (I've done it too), but it does help when figuring out weight and balance, or doing navigation to be sure one has sufficient fuel to arrive at the chosen destination, you know, those little things that allow you to fly again the next time?

  • Bob on July 29, 2012 3:05 PM:

    Many, many students are not successful at algebra because they never learned the multiplication tables, nor, in many cases, the addition and subtraction tables. This material is usually learned around the third grade, and algebra is just about impossible if you don't know it.

    I have taught and worked in all types of k-12 schools and in community college. This is what I have seen. Children living in poverty seem to be most affected by this.

  • golack on July 29, 2012 3:06 PM:

    Parody? Snark? Inside joke between Hacker and himself?

    Or just another attack on science and technology?

    It would be great if, in most math classes, they provide real world examples--compound interest anyone? How about a good understanding of real statistics (not the random survey/push poll done for politics)--say what the 50% chance of showers really means for you? Or how does insurance really work?

    Ok, maybe this is really arguing for Home Economics in the 21st century....

    and I certainly agree with many of the comments here--and yes, teachers do matter

  • RL Alitheia on July 29, 2012 3:14 PM:

    Judging from the budget understanding and economic proposals of today's Republicans, we need MORE math, not less.

  • Walker on July 29, 2012 3:14 PM:

    Algebra is one of the first mathatics courses that is not rote computation. Innumeracy is a major problem in our society and you are advocating making it worse. All of the higher level quantative concepts depend on it. This is not Calculus, which is completely optional and often senselessly pushed on to the top students. There is no statistics and no modeling without algebra.

    It is entirely sensible to say that algebra is taught badly. But removing it from the curriculum is societal suicide.

  • jd--Central Florida on July 29, 2012 3:16 PM:

    The worst taught subject (by far) in high school and college was math. It existed, apparently, to be memorized and had no use in real life, was just as boring to the dull teachers as to most of the students.

    Hacker has a point--that most careers outside of the technical areas--require little beyond arithmetic. Unless, of course, if the point is to make students suffer for the sake of their character development.

    Another lopsided GRE (mine) : two tests in 99th percentile, math in 3rd percentile (that was for ignoring it, points for putting my name on). Followed a bit later by a Ph.D. in the humanities.

  • JM917 on July 29, 2012 3:21 PM:

    Back in the Dark Ages when I took junior-high and high-school math (the late 1950s), algebra was a source of terror and humiliation for me. It was all memorization of dry formulas; I had no idea of what all the a's and b's (not to speak of the x's and y's) were all about, and quadratic equations totally floored me. Later, I took the required geometry course, and I loved all those neat, logical axioms and the deducing of proofs. But based on my bad algebra grades, I was barred from going on to trig. That was the end of my math; in college I took logic and philosophy courses rather than math and so became a history major, up to the Ph.D. I learned statistics on my own.

    The algebraic scales fell from my eyes only when I had kids in school and the pre-algebra teacher gave a "refresher" for parents so we would be of help. She used graphs! I was fascinated: so this is what the x's and y's mean! But why was this news to me? I looked back in the algebra book I'd used in school and was amazed to see that every reference to graphing was labeled "optional," and (because I'd made no notes in these sections) obviously my teacher had skipped it all. She was evidently a one-trick pony who ground us through the dry manipulations of symbols but never related them to anything that could be represented on graph paper. No wonder I had hated it, been frustrated and bored by it, and had retreated into reading history books rather than try to learn what I was convinced was incomprehensible gibbrish. (It didn't help that my father had forgotten all his algebra and told me it didn't matter at all; his highest aspiration for me at the time was that I get a post-high school job selling nuts and bolts in a hardware store.)

    My wife, no intuitive mathematical genius either, had likewise never been exposed to graphing; but she'd had m more sitzfleisch than I as a h.s. student and so dutifully memorized the algebra formulae in order to meet the NY State Regents' Exam criteria. (I went to high school in Colorado and could get by with far skimpier math requirements.)

    Both of our kids excelled in math and science in high school, got 5's on their AP calculus exams, and majored in sciences at the college level. My daughter is now finishing med school and my son has been a naval officer (nuke service) and is going into grad school in meteorology.

    Yes, math can be terrifying and humiliating if it's poorly taught by a teacher who just goes through the mechanical motions. Struggling with math sent me into what was probably prolonged depression as a kid, from which I could escape only by learning to excel in something totally unrelated. And now I realize how much my life was stunted and crippled by blocked-off opportunities. (In school I'd wanted to be an architect, but my algebra troubles forestalled that.) Given good teachers, our two kids (who of course inherited our genes) took to math like ducks to water.

    The Hacker piece, which I read with mounting frustration this morning, totally misses the boat when it comes to the issue of teacher quality. A good teacher should be able to find some pathway into math that virtually any normally intelligent child can follow, and the math needs to be taught with direct application to the other subjects (especially science and technology) that the student is encountering in school. There is no greater gift that any teacher can give than relative ease with elementary mathematics, extending up to statistics (a much-underrated branch) and calculus. Our entire world is built of elements of mathematics. I've discovered that too late in life for any practical application, but it is criminal to allow teenagers to go out into the real world without that power at their command.

    One of the many things this country needs is a large corps of good public-school math teachers. (And, I would add, history teachers too.)

  • exlibra on July 29, 2012 3:53 PM:

    I was terrible at all three branches (algebra, geometry and trigonometry; in my day, calculus was considered college level math and, since I studied English, I never had to touch it, praise be!) of math, and never thought I'd use any of it, once I left school. And, except for figuring out how large a circle to cut out for the waist of a full circle skirt, I never did.

    Fast forward 17 yrs, and my 8yr old brings home -- once again! -- one of those stupid "guess and check" problems. Something to do with dimes and nickles and what he can (or cannot) buy with them. The sheer inefficiency of that method just made me mad enough to try and reduce the problem to a couple equations. I explained some basic rules, and what I did not remember, I asked my husband to help out with (he was way farther removed from school than I but, OTOH, he actually *enjoyed* math in school. Shudder).

    Much to our surprise, the little one was enchanted and asked for more. He enjoyed both reducing a verbal problem to an orderly equation and manipulating the numbers within. He even went back to school and kindly informed his teacher that her guess and check method was inefficient and offered to teach her this revolutionary thing with "unknowns" (she told us, barely able to hold laughter, at a regular parent/teacher meeting).

    Since it turned out that math was his strength (he ended up studying computer science in college and he's writing software for a living), I don't begrudge those 11yrs of torture I went through in school, struggling. If I hadn't learnt the wee bit I did, it wouldn't have occurred to me to spring it on an unsuspecting 8yr old, who didn't know he was supposed to hate it. And then, who knows how long it would have taken him to discover the aptitude for it on his own?

  • DavidNOE on July 29, 2012 4:02 PM:

    I've found my school experiences considerably at variance with most people I know, in that my high school math teacher was excellent and interesting; the subject where I never had a good teacher in high school was English. Sophomore year I had one who was mediocre and boring; the other three years I had a woman who was not only boring but ignorant of practically everything about English, from grammar to literature. As someone who loves to read and is very interested in the workings of language, I found it torture, because I couldn't argue with her even when I knew she was wrong without getting marked down.

    Algebra was a revelation to me when I first began it; I'd always found arithmetic a crashing bore, because by the end of 4th grade I'd learned everything I needed to know about it and the next four grades were essentially all repetitive drills, aside from the occasional neat little trick like how to extract a square root manually - useless for all practical purposes, but sort of fun for a couple of days. Algebra, on the other hand, was actually interesting, and there was something new at least once a week. Geometry, trig, and calculus were even more interesting when I got to them, but algebra was the first interesting math class after I learned how to manipulate fractions in 4th grade. (I went on to get a degree in physics, make Phi Beta Kappa, and make an excellent living as an optical engineer for 30-odd years.)

  • Keeping Track on July 29, 2012 4:13 PM:

    Algebra gave me a unique experience. I could come
    up with an answer I totally believed was right, only to find out it was wrong.
    I took that to heart. No matter how strongly I feel I'm right, I remember I could still be wrong.
    Now when I see people sincerely spouting nonsense, I think, "probably flunked math" by which I mean Algebra.
    The neat part was when I started going back over my work, by plugging in my answer for x.
    If I simply repeated the work I'd done, I'd come up with the same wrong answer. By substituting for x I could theoretically score 100%, every time.

  • PTate in MN on July 29, 2012 4:18 PM:

    JM917: excellent comment!

    Also, commenting on your observation that "Struggling with math sent me into what was probably prolonged depression as a kid..." My impression is that this happens fairly often, alas. Many people who are attracted to teaching are themselves math-phobes who are uncomfortable teaching math so they become bad math teachers. It is a vicious cycle of bad teaching/alienated students who become bad teachers. It's a crying shame.

    Thymezone's response to those (like me) who think math is important for clear, logical, abstract thinking is the emotional fury of "...Go die in a fire." which more or less illustrates our point. In fact, individuals can be successful in life without all sorts of skills and abilities (consider our previous president.) Individuals can succeed, for example, while being marginally literate. The success of some without literacy doesn't mean we should stop teaching reading and writing. Ditto math. Yes, some people can succeed without math skills--bravo to them--but teaching math is still important.

  • Brooklynmom on July 29, 2012 4:25 PM:

    The problem with that article is that "Algebra" means different things to different people. My child just took the NY State Regents in Algebra, which is typically something students take in 9th grade, and sometimes 8th grade for advanced learners. I'm very good at math, but what counts as "Algebra" today is nothing like what most adults understand it to be. Basic Algebra is taught in the first 2 months. The rest is what we used to call Trigonometry, graphing quadratic equations and inequalities, not to mention probability, box-and-whisker plots, and other things that most adults have forgotten if they were ever taught it in the first place. Most people commenting on the article think of Algebra as basic algebra, but it encompasses much more than in decades past.

  • N.Wells on July 29, 2012 4:34 PM:

    I often had a hard time with math (the ways it was taught almost never clicked with me), but I teach it (as parts of other stuff) to students today. I actually like teaching math to math-scared college students, because all but two students in my experience were able to do far far better than they thought, and I like seeing the lights turn on.

    My worst math experience (of many) was page one of my Calculus book: about ten lines in it said, "Let f(x) represent some function of x. Let g(x) represent f(x)." The first sentence was fine, but I just freaked out about why one would want to substitute letters for other letters.

    I use trig and statistics a lot, with algebra as a base that I don't think about too much. The trig is particular to what I do in science, but the statistics seems critical for everybody.

    Some days it seems like the single most valuable subject I learned in school was Latin. Learn that, forget most of it, and you've got a good working understanding of English that makes more sense than most lessons in English spelling, grammar, and rhetoric. But I had a great Latin teacher who had a really motivational method of teaching. Plus it's an unbelievably unfair advantage on SAT and GRE tests.

  • JMS on July 29, 2012 4:35 PM:

    I got through calculus in high school, one calculus class in college, and then it dawned on me that as an English major, nobody would ever force me to take math again. Hooray! I can honestly say that since then, I've never been in a situation where I've had to use math beyond about the ninth grade level. And yet.

    If we say that we want to produce the type of innovative yet disciplined minds we need to take on "knowledge worker" type jobs--even those that have little to do with STEM, intellectual cross-training seems just as valuable as scales for musicians or weight training for an athlete, even if they don't do those things when performing or competing. So yes, poets should learn math up to a certain level (one that certainly includes algebra). Even if they don't use it directly, I suspect it will make them better poets.

    But beyond that, math literacy is so generally poor that we could raise intellectual standards if we could just maintain the adult population at about the sixth grade math level.

  • joel hanes on July 29, 2012 4:38 PM:

    Elementary-school reading is often taught by confident and accomplished readers, by people who value the world of books and well-chosen words.

    Elementary-school math is almost always taught by people who themselves have not had much math, and don't much enjoy it. Imagine if reading was taught primarily by people who were unable to read at the level of the mean college freshman.

    I hated arithmetic, made many mistakes, hated drill problems and wouldn't do homework, and my middle-school math was indifferently taught (forgive me Mr. Burke; I know the beauty in the patterns was clear to you, but to a 14 year old boy, you were the epitome of fusty irrelevance). At the end of compulsory high-school geometry I vowed no more math. I started college all humanities.

    But I got drafted, and exited from the Army with a different perspective and some experience, and went back to school. Trigonometry, five years after my previous math class, was agony and I had to repeat it. The "differential calculus for engineering students" was a revelation: here was the explanatory beauty that I'd heard about and missed, where trig and algebra became the essential tools in describing the world in ways that matter because they're true and exact.

    Also I discovered that I have no particular talent for higher math, and that I had to do homework thoughtfully, and work hard at it, to see the patterns being taught.

    I didn't get very far in math, but what understanding I retain has enriched my life enormously -- not so much materially, but in providing interesting things to think about.

    I still make a lot of mistakes.

  • leopoldvanranke on July 29, 2012 5:40 PM:

    So. One sees a lot of agreement here that the best way to teach mathematics is to make it relevant to the quotidian world in which most of us live and work. That is, teach practical applications as the formulae are being taught. joel hanes' comment being a prime (no pun intended) example.

  • GP on July 29, 2012 6:54 PM:

    Granted, I loved math in high school and started out as a math major in college. Math remains central to my work and my understanding of the world. The core math I learned in high school, including calculus, is something I consider as important as the study of history or biology or a foreign language. So, I admit I am predisposed to find the premise ludicrous.

    Bailing out on math education is the most profoundly stupid idea I have heard in a long time. It's an admission that we should willingly produce two different classes of citizens. It's as if we accepted that only a higher class of citizen needs to know how to read. It's a capitulation to the fear that we don't know how to teach math. It's proof that the author never really understood why math education is necessary. It really is the soft bigotry of low expectations.

    I have done volunteer tutoring in high school and seen kids struggle with algebra, particularly that first big hump in analytical geometry, the humble linear equation. Every student I've had time to work with one-on-one has made it through that, but it takes patience from a tutor and perseverance from the student.

    There is nothing about that level of algebra that cannot be absorbed by 90% of the population, except perhaps for those that wait until after 9th grade to start. By then they're often too distracted to focus on it, and more apt to dismiss its importance because by then they (believe they) already know everything, but that's no excuse for letting them off the hook.

    Teach algebra in 8th grade in every school. More importantly, have kids ready to learn algebra by 8th grade in every school. Just do it.

  • Ron Byers on July 29, 2012 7:06 PM:

    Jesus H. Christ on a popcycle stick. We are about to live in the world of quantum computers and "learned" people are preaching algebra is too hard for most kids so we ought to quit teaching it. Maybe the Republicans are right. We are so dumb we will fall for anything.

    If America is going to compete in this 21st century we have to teach our kids more not less. We have to teach them harder not easier. We don't have a kid to waste.

  • David on July 29, 2012 7:29 PM:

    I'm #56 on the comment list so I doubt if anyone will read me, but here goes.

    Is Hacker really objecting to algebra per se or to its current incarnation in the schools? It's true that many math teachers have lost their way, and teach rote methods with no apparent practical utility. But Hacker's argument misses the point. True, his example of an algebraic proof may seem sterile and useless - but it's perfectly reasonable to expect a high school student to expand a 2nd degree polynomial, which is all the 'proof' requires. It's pretty easy and good, useful examples are to be found everywhere. Also, consumer price indexes are pretty complex and require understanding of weighted averages, which you only get from studying a lot of algebra. Maybe Hacker didn't think it was algebra, but it was.

    So Hacker isn't objecting to algebra at all - if anything, maybe what he's really arguing that there should be more of it, just taught better.

  • rick on July 29, 2012 8:13 PM:

    Try this simple test of math education. Sometime in October or November, when the new school year is well underway, ask any random junior or senior high school student two questions: 1) What are you studying in math now? and 2) What is it used for?

    Math is treated as an end rather than a means. The way that it is taught has defeated its own purpose.

  • thalarctos on July 29, 2012 8:30 PM:

    1. Count on a political scientist to advocate for more ignorance among the hoi polloi.

    2. The most crucial aspect of teaching algebra is, IMHO, teaching abstract thought. Yes, this _should_ be connected to real-world examples; this really is the point. Being able to go from "a circle" to x^2 + y^2 = r^2; being able to go from a concrete, tangible thing to an abstract representation of that thing is FUNDAMENTAL to developing abstract reasoning skills--and that's what separates us from the monkeys.

  • DKDC on July 29, 2012 8:38 PM:

    I can understand the deep sense of frustration of those who think that they are incapable of learning algebra, geometry, or statistics.

    Math is poorly taught in America, but some level of knowledge is essential. We would never allow someone to claim that reading isn't for everyone. We call it what it is, illiteracy. The same should apply for math. We should never accept the idea that math is not for everyone.

  • Big River Bandido on July 29, 2012 8:45 PM:

    When gutting education is your primary goal, why stop at music and arts? Mathematics is next on the list for the Neanderthal caucus.

  • obadiah youngblood on July 29, 2012 9:19 PM:

    The point is not that algebra should be canned because it is difficult, and the weakness of Hacker's argument is it can be seen as an argument for dumbing down math education, which it is not. If you read the whole thing, what he is really arguing about is the highly abstract garbage which is taught as algebra in our schools, not the practical, useful algebra we use in daily life. He goes on to say much the same of calculus, a truly worthless course, for most people, even for most scientists. But Hacker is a professor of government and he's interested in policy and educational reform so he belabors the point on teaching abstract math and its effects on society.

  • Vvano on July 29, 2012 9:50 PM:

    I studied mechanical and electrical engineering so I breathed algebra and calculus for years. Now I work in IT and I do support and development for accounting (yeah I know I tell my kids I'm a nerd squared).
    For all commenters here who say you dont need algebra in life, I beg to differ. Any office worker who needs to use spreadsheet in their work has to use algebra. I can see how painful it is for some of them. They cannot figure out how to use excel because they cannot abstract what they are trying to do and cannot figure out what the formula is to accomplish for them what They are trying to do.
    I can tell you that most people cannot figure out how to use pivot tables or v-lookups even if their life depended on it. So in office work, most people DO need algebra, even if it isn't what it's called

  • John Sully on July 29, 2012 10:05 PM:

    I still remember the "math team cheer" from high school some 40 years ago:

    b2 - 4ac punch them in the function key! Go team!

    b2 - 4ac is the discriminant in the quadratic formula and determines whether or not an equation has a real or complex solution(s). I never had any real aptitude for math yet I made it all the way through two semesters of Calculus. The trick was taking the time to do the homework. If I didn't do that I flailed. Algebra was comparatively easy and for some reason i found Trig/Pre-calc pretty easy. I probably flailed at calculus because it had been 6 years since I had done anything remotely resembling math.

  • Jamie on July 29, 2012 10:12 PM:

    algebra isn't hard, but it is often tought poorly to students who are told that this course will be too hard for them

  • jd--Central Florida on July 29, 2012 10:59 PM:

    What I find interesting in the comments (I'm pretty far down at 3:16 p.m. today) is how angry some of the defenders of algebra/math are. Somehow it's the student's fault for wanting the easy way out, it's all about dumbing down.

    I was and am an intelligent person capable of dealing with abstraction. Yet, in no way was I ever exposed to more than memorization of stuff I didn't understand in math. A plane geometry class in high school: I turned in homework every day that was every day wrong and got credit for it. Should I have failed or did the teacher fail? She taught to the two girls in the room (twins) who understood, ignored the 25 others.

    In Algebra II I had the first and only good math teacher. I could see that there was something to it that I couldn't quite grasp but that was more than I had been able to see previously. She told me, years later, that I had come to her too late; by then, I had no foundations to build on.

    It's not only practical use in real life that is a question. Perhaps an explanation of the nature of math, the philosophy of math that might have given some substance to the routine stupidity of math teaching.

  • Steve P on July 29, 2012 11:11 PM:

    If we taught auto repair the way we teach Algebra, students would spend two years on combustion theory and power ratios before they touched a wrench.
    But they don't, so our cars get fixed.
    Problem is, people who were good at math teach Math. We need math teachers who were bad at math, and who finally got it after hard work; they know what it's like for the kids in the seats.
    But what we'll probably get is Chicago Math 2.0.

  • Rich on July 29, 2012 11:31 PM:

    One of the dumbest op-eds in memory. PoliSci is known as the weakest of the social sciences--a lot of dumbed down sociology and history. Political writing is a good showcase why a little higher mathematics wouldn't hurt a lot of people---pundits and political "reporters" endlessly yammer about polls but don't know the slightest about interpreting them (which is pretty simple). I'd imagine most of them assiduously avoided math in college.

  • castanea on July 29, 2012 11:59 PM:

    I'm sure every student in India or China (or any other country eager to launch down the pathway to economic success) who buckles down to learn algebra and calculus is heartened to see that America has so many anti-math whiners.

    Honestly, people who complain that their math teachers just didn't make the subject "practical" enough for them sound a bit prima donna-ish.

    For the typical student, the critical thinking skills associated with learning algebra probably are far more useful in life than learning how to diagram a sentence or memorizing a particular poem.

  • Evolouie on July 30, 2012 12:44 AM:

    And this my friends is what is wrong with school today.

    5. Algebra is basic arithmetic coupled with the idea of a variable (the dreaded letter x). If I want to build a fence that encloses 100 square feet and is twice as long as wide, how many feet of fencing material must I use? Answer: a variable to be determined.

    This has no real world application. It is just not done this way. No one sets out to build a fence this way, it's laughable actually.

  • Beijixiong on July 30, 2012 1:28 AM:

    This may be one of the most depressing posts I have read recently. I am appalled that people (that think they are) commenting on current affairs can think that algebra is all the Math you need to know (if even that). The only thing that public policy can have on things like job creation, national debt etc is on their second derivative. This is simply Newton's 2nd law, which applies in some form to all systems with inertia (and economies certainly have inertia). Anyone who cannot evaluate the sign of the 1st & 2nd derivative from economic has has no business trying to interpret it. The fact that people remain ignorant of these concepts (from Calculas 101) is why Romney can blame the job losses and debt accumulated in Obama's first few months in office on Obama and get away with it. (Romney, a successful business man, so he understands derivatives -- probably by some other name -- and thus, undoubtedly, knows better.) On the other hand, our political commentators remain ignorant of this, or at least pretend too. And worse, most voters, the people who control our fate, seem happily unaware of the mathematical concepts that are, in fact, the ABC's of economics and economic policy. Posts like this one indicate that this will probably continue, on and on and on...

  • Alix on July 30, 2012 2:16 AM:

    I never did "get" algebra (and my father was a math professor!). And it's never actually hurt me in life. I mean, I can't think of the last time I used algebra (while I realize I use geometry and physics every time I pull into a parking lot).

    I think "consumer math" or something like that would probably be more useful for most of us.
    However, years after graduation, a friend who was good at math said something offhanded about "algebra is just a sentence with numbers," and I realized that context, utility, story might have helped me understand algebra. That is, teaching might affect understanding. I had an ancient algebra teacher who just taught numbers. My friend had a teacher who really explained the meaning of the numbers. She loved algebra and saw it in almost every aspect of life, like music, cooking, finance.

    I'm not interested enough to try algebra again, but I would be interested in more explanation of the meaning of algebra.

  • cathymac on July 30, 2012 3:14 AM:

    My experience (after tutoring algebra to lots of middle schoolers, some high schoolers, and a few adults over the last 10 years) is that, as with language development, there's a brain readiness factor. The problem is that math readiness seems to be more individual than language readiness. Some students are ready in 6th grade, some by 8th, some in high school, and lots of people not until adulthood. Compounding the problem is the fact that math knowledge is cumulative - each level depends on understanding the previous level. Many (most?) kids are presented with basic algebra before they're ready to understand it; they get to high school without that foundation in place, and with the idea that math is hard, and they fail because what else can they do?

    Still, as adults they all figure out how sale prices work - where they could afford one unit before, they can now afford two. That's algebra and they aren't afraid of it. Maybe if we called it something else, like foundations of shopping, it wouldn't be so alarming.

  • Ron Byers on July 30, 2012 8:15 AM:

    Seventy two comments on the Algebra post and 10 comments on Dick Cheney. If Ed and Ryan had any math skills they would realized Dick Cheney is old news.

  • rick on July 30, 2012 8:22 AM:

    Many of you are confusing practical algebra with most of what students are saddled with: abstract algebra; a form of math in which numbers have NO meaning. Google "NYSED integrated algebra regents exam"and take a look at what ALL 8th or mostly 9th graders are required to pass in order to graduate HS.

  • mark on July 30, 2012 8:57 AM:

    All we need to teach our children to succeed in today's business world is: "If the customer asks for a cheeseburger, press the button with a picture of a cheeseburger on it. If the customer asks for a cherry Squishi, press the button with a picture of a cherry Squishi...
    The important thing to do is to place the kids in the correct track early on, so those from good families can learn what they need to know to get into college, while those who are "those people" can be tended until they are ready to enter the unskilled labor force.

  • JM917 on July 30, 2012 9:26 AM:

    @ mark:

    Snark, I assume... If this is indeed snark, then you are absolutely right in reading the intentions of the 1%--which is to keep the American "proles" dumb and pacified.

    I suggest re-reading Orwell's 1984 for the picture of how Big Brother's and "the Party" rule the proles. Keep 'em dumb. Let 'em live in squalor. But divert them with the lottery, astrology, fundamentalist religion, porn, movies, sports, and celebrity scandals. That way, they don't even have to be kept under surveillance (unless some of them really get uppity; then they get secretly bumped off.)

    It's how the Koch Brethren and Karl Rove intend to rule.

    Start teaching the proles math, and some really will begin to start thinking analytically. Robert Moses, back in the Civil Rights days, got it absolutely right. Remember, he was a Harvard mathematician who saw it as his mission to into the segregated black communities and initiate kids in the empowering mysteries of math.

    We need to go back to Moses' vision.

  • K Wilson on July 30, 2012 10:26 AM:

    Basic algebra is necessary to function effectively in the modern world. Basic statistics is at least as important. One can teach them in a way that is less oriented toward going farther in mathematics and more oriented toward practical applications, but the skills themselves are essential to being a fully functioning citizen. Neither is all that difficult.

    Geometry is not as useful in itself (unless one will be building things), but the introduction to logic it contains is invaluable. The greatest "AHA!" moment in my entire education was in 8th grade when I was introduced to the concept of a geometric proof - premises and steps, each with the supporting reason, all lined up showing the argument in breathtaking clarity. Amazing! I ended up as a mechanical engineer, and what little skill I have in logic I attribute to geometry.

    A Modest Proposal - all high school students should take math through algebra - more theoretical for students who will be going on to calculus, more practical for everybody else - basic statistics, and a basic logic course (verbal as well as mathmatical). Public discourse might improve a little.

  • leopoldvonranke on July 30, 2012 11:13 AM:

    Really enjoyed the post by ecolouie, supra., arguing that "no one" uses mathematics to build a fence. Seems I know this astrophysicist who actually wrote a computer program to design a picket fence, built it with the assistance of a wood worker who knew about the dimensional characteristics of pine, hemlock and douglas fir (math required with regard to variables such as moisture content, type of saw cut -- e.g. slab or quartersawn, etc.). The fence was built in 1994, is still standing and has never had a component replaced due to rot. Damn thing is on my way to work, and I see it five days a week. My own picket fence, well, I replace wood every year.

  • paul on July 30, 2012 12:06 PM:

    Not only do we need algebra, we need calculus. Everything interesting has a derivative (rate) and an integral. But zowie it's the few who get taught that way.

  • Danny on July 30, 2012 12:17 PM:

    From the American Mathematical Society webpage (http://www.ams.org/news?news_id=1573), a short response:

    "Is Algebra Necessary?"
    Monday July 30th 2012

    That's the title of an opinion piece that ran on the front page of the Sunday, July 29 New York Times's opinion section. The author, Andrew Hacker, a retired political science professor, answers with a definite No. He does think that students need quantitative skills, but feels that algebra blocks the progress of many otherwise capable students, causing them to drop out of high school or college. Hacker ends his opinion piece with: "Think of math as a huge boulder we make everyone pull, without assessing what all this pain achieves. So why require it, without alternatives or exceptions? Thus far I haven’t found a compelling answer."

    AMS President Eric Friedlander and members of the AMS Committee on Education responded to this piece. President Friedlander's letter follows.

    To the Editor:
    Mathematics is a key piece of the skills-set required of so many in modern society. Mathematics is pervasive in much of our increasingly complicated world. Mathematics teaches students there can be a right answer and a wrong answer, prepares students for the precision that is often demanded in the real world, encourages students to learn through concentration and effort. We seek to enable many more students to succeed.

    The answer to the recent Op-Ed piece in The New York Times entitled "Is Algebra Necessary?" is resoundingly YES! Without algebra, students are excluded from a whole range of careers and interest. The entire edifice of science and technology rests upon an understanding of basic algebra; especially those who work in STEM disciplines need a facility with algebra. Our discussions should be focused on how to enable many more students to understand, appreciate, and use mathematics.

    Yours sincerely,
    Eric M. Friedlander
    American Mathematical Society

    Comments on the article are no longer being accepted at the Times's site but people can write a letter to the editor or comment on the AMS Facebook page.

  • Jonathan Stiegler on July 30, 2012 12:45 PM:

    There are several commentators above who claim that very few jobs and careers require math beyond arithmetic. Maybe, just maybe, that's why the US is finding itself in a perpetual recession. We have an economy today full of Outlook paper pushers and middle managers who sit in meetings after meetings half asleep and adding little real value. But this gravy train can't possibly last forever. I wouldn't tell your kids that "math doesn't matter" if I were you. This pyramid scheme we've been running all this time is about to run dry.

  • TheAporetic on July 30, 2012 1:35 PM:

    I was never abe to pass algebra--failed it in 8th, 9th and 10th grades. Finally they crafted some kind of remedial math program for me so I could graduate highschool. Now I'm a 50 year old college professor with three books published. I have no idea, to this day, why I find math, and algebra in particular, so excrutiatingly hard, but I do. I admire those who can lern it, but I could no more master algebra than I could leap off the roof and fly.

    The experience of being made to renact your inability, over and over, is deeply warping. It's Kafka-esque and sadistic. If you continually ask a one-armed man to play the guitar, he'll either come to hate himself or hate you. I think it should be required, but "lightly required."

    I made a blog post about it: http://theaporetic.com/?p=3935

  • It's not that hard on July 30, 2012 2:11 PM:

    If you can't solve for x to a basic linear equation, your opinions count for squat in the 21st century and you only have a job through the surplus labor of others.

  • Mike O'Malley on July 30, 2012 2:29 PM:

    "If you can't solve for x to a basic linear equation, your opinions count for squat in the 21st century and you only have a job through the surplus labor of others."

    Wait--are you saying your opinions DON'T count for squat, or are you saying that they DO count for squat? Becaue if they count for squat, then they count, and you're not quite making sense. Maybe you should have paid less attention to solving for x and more to english class.

  • Jason on July 30, 2012 3:01 PM:

    "Algebra has its dwelling place only in a mind. We can not even say, as we can of our power of language, that algebra exists in the mind. It can live only in a mind that creates it anew for itself. That's why I can't really teach you algebra, and why I am, as you seem to have figured out, a bit of a fraud... I can show you some tricks, but you must do the teaching. And, no matter what they tell you in the slippery world of pliable convictions and values, you will have it in your mind that you can know something--truly know it, and not just believe it, or be informed of it--and maybe, since that is so, you can truly know something else. It's interesting to wonder what such a something else might be.

    I think you should learn algebra, because I wish you well, as a teacher, even a bit of a fraud teacher, should, and not because I want you to solve algebra problems. You will find that algebra shows you some truths. The first great truth is that there can be something real, and complete, and harmonious, and even, in some strange way, absolutely perfect right in your own mind, and made by you alone. You will see that you have a wonderful freedom not mentioned in the Bill of Rights, the freedom to decide what your mind will contain and how it will work You don't have to copy the rest of the world.

    Algebra tells sad truths too. Where there is no balance, there is no truth. What is equal is equal, and between the equal and the unequal there is no conference table, no convenient compromise. In this terrible law there is a hinting question for all of life. Are there other things like that?

    Algebra will show you the inexorable, the endless and permanent chain of consequence, the dark thread of necessity that brought you to a wrong answer because of a tiny little mistake back in the second line. I know how unfair that seems, and how scary that what seems unfair is nevertheless justice. Is life like that too, as all of nature seems to be? How then shall we live? What are the laws of the algebra of our living, and where do they exist, where created? Who can show us how to learn them?" - The Underground Grammarian, RIP

  • David E. Ortman on July 30, 2012 3:55 PM:

    Mathematics, which includes algebra and computer programming, is another form of language, and should be viewed as such.

    Our education system would be much better off if there was less focus on trig and geometry, and much more focus on statistics. The failure of most people to understand statistics leads to costly financial errors and wrong assumptions about information presented in the press and by politicians.

    But, then what are the chances of that?

  • Matt on August 01, 2012 10:32 PM:

    Fascinated by how fascinating you think your superior high school math skills were, and surprised by how dumb you must be to not catch the fact that your math skill have now significantly deteriorated. Perhaps that suggests that the emphasis and time you spent on math were truly a waste.

    And we all get that the average people are rubbish and you are (or were) some sort of superior scholar. So superior you use words like rubbish. However, get off your high horse and acknowledge that in America we don't say"rubbish", we say shit. As in, isn't that sanctimonious asshole full of shit.

  • paula miller on August 07, 2012 3:43 AM:

    math is not essential. Many people get along just fine without 'higher' math. Love is essential, kindness is essential. It is a conceit on the part of those who proscribe math as essential. Generally, these are people who love math and to whom it comes as second nature. I raised 4 children (all of whom love math) and grandchildren and am considered math deficient. So there.

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    of geography?
    of religion?
    of art?
    of music?
    of sports?
    of science?
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    of mathematics???

    Most people have read at at least something outside of classwork requirements in most subjects...except for mathematics. If you've never studied a subject outside of school, then what makes you think that you will have a chance of becoming competent in it? Why do educators expect students to become mathematically competent if they know that most of those students don't read anything about mathematics beyond what is assigned in school? We surely expect that our students will have read something about history besides their history text books. It's the same with other subjects. Why is our expectation of their mathematics reading so much lower?