The chloroformed mind: the case against teaching math

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Erik Kain

Erik writes about video games at Forbes and politics at Mother Jones. He's the contributor of The League though he hasn't written much here lately. He can be found occasionally composing 140 character cultural analysis on Twitter.

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36 Responses

  1. Avatar Dan Summers
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    says:

    1) I think your link is broken.

    2) My math abilities are one of the few things in life I truly lament. There is such beauty and elegance with mathematics, yet my apprehension of such things seems permanently marred by my early exposure to long division. Plus, unlike such things as music lessons or foreign languages, I don’t see much by way of math appreciation classes for adults.Report

  2. Avatar Rufus
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    says:

    I don’t know what the trick to math is. I was terrible at it in high school and then enjoyed it in university after I’d studied a few languages and just started seeing it as another one.Report

    • Avatar Jaybird in reply to Rufus
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      says:

      We teach algebra before geometry?Report

      • Avatar Mike Schilling in reply to Jaybird
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        says:

        When I was in high school, the sequence was

        First-year algebra
        Geometry
        Second-year algebra
        Trigonometry
        Calculus (only for the most advanced)

        Now, my kids get

        First-year algebra
        Second-year algebra
        Geometry
        Pre-calculus (no idea, yet, what that includes)
        Calculus (for lots of kids)

        Very foolish, in a few ways. To begin with, much of the point of geometry is to learn how to do proofs, just as in Euclid’s day. This is being put off until too late. Second, a lot of the stuff in second-year algebra (e.g. basic trig functions) needs some understanding of geometry to motivate it. Last, calculus is being used as a credential, rather than as something available to kids who will actually use it when learning advanced math and physics in college.Report

        • Avatar T. Greer in reply to Mike Schilling
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          says:

          Both of the high schools I attended (in New Mexico and Minnesota) were organized as follows:

          Algebra (taken in 8th grade if you were smart)
          Geometry (also moved forward a grade for the AP kids)
          Algebra II
          Statistics, AP Statistics, and Pre-Calc (your choice).
          For those a year ahead of schedule, there was AP Calc.

          A smaller budget stopped the New Mexico school from offering statistics or its AP variant.

          So things are not half as bad as you seem to be saying – I only graduated a year ago.Report

          • Avatar Mike Schilling in reply to T. Greer
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            says:

            Perhaps my complaints should be limited to California, then.Report

          • Avatar Trumwill in reply to T. Greer
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            says:

            In an unnamed state in the south, mine went: Algebra I, Geometry, Algebra II, Precalculus. That last one was optional and in place of Algebra II or Precal, you could take Trigonometry & Statistics. I only know a couple of people that did that and both did it for mistaken reasons.

            Advanced/Honors students took Algebra in the 8th grade, though, and landed in Calculus at the end. You also had the option of skipped Precal and going straight into Calculus if you could get your Alg-II teacher to sign off on it (my teacher tried to convince me – I didn’t budge). Most of my regular-class peers stopped at Algebra II, though. I would have, too, were it not for parental pressure. Notably (and I don’t know if this speaks positively of my high school or poorly of my college), my placement exam allowed me to skip straight past college precal and Intro to Calc into Advanced Calculus.

            I graduated fifteen years or so ago. Supposedly they were going to up the requirements after I left. I don’t know if they did or not.Report

            • Avatar Alan Scott in reply to Trumwill
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              says:

              Around the time I graduated, my high school switched from Algebra I/Geometry/Algebra II to Algebra I/Algebra II/Geometry. The primary reason, according to the teachers I talked to, was that by the time kids got to Algebra II, they’d forgotten most of Algebra I. Since Algebra I was often taught at the junior-high level, they didn’t have any control over the quality of the Algebra I education–and by sending students straight into Algebra II, they could quickly find out who was doing fine and who needed help.Report

        • Avatar JBL in reply to Mike Schilling
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          says:

          I think the idea that a standard high school geometry course gives any sense of what mathematical proofs really look like is sorely mistakenReport

          • Avatar Yoshi in reply to JBL
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            says:

            They teach the thought process required for a proof to be done and read, not what it’s supposed to look like. Many times when I’m doing proofs, my last 5 or 6 rough drafts are in two column form, then my final product is a paragraph proof.Report

  3. Avatar Rufus
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    says:

    I don’t see why they would still do it, but yeah, my school went from basic arithmetic to algebra and then did geometry later. It does seem like a bad idea in retrospect.Report

  4. Avatar Francis
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    says:

    Speaking of continuous learning, one reason I’m around so much (and occasionally excessively obnoxious) is that I’m unemployed.

    I’m transitioning from land use lawyer to patent lawyer. (Not as far a stretch as it sounds, as both primarily involve working well with experts and regulators.) In order to qualify to take the patent bar, I need (at age 45) to take 2 semesters of college chemistry. And in order to qualify to take college chemistry at the local community college, I need to pass a qualification exam that demonstrates I’ve completed a solid high school chem. class. I’ve got about 6 weeks before registration starts and I need to take the qual. So I’m sitting at home with a high school chem. textbook open on my desk, procrastinating.

    Actually, chem’s kind of fun, once you get into it. But it’s very weird needing to read this textbook in order to get back to practicing law.Report

  5. Avatar historystudent
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    says:

    I think your labeling of this idea as “counterintuitive” is correct. Teaching basic math skills to children introduces them to number manipulation, and it is good mental training generally. We’ve heard other suggestions from educators and others that such-and-such a subject ought to be taught later. It seems to me that children in the U.S. are already coddled too much; we shouldn’t be looking at curriculum changes that make school less challenging and arguably unbalanced. What they need to spur their learning is not postponement but challenge and engagement. Certainly, language should play a major part in school at all levels, including the primary grades, but it is not necessary to concentrate on that and neglect numerical skills.

    However, it probably would be a good idea to take another look at math books. I think some of their presentations of mathematics beyond the basics leave a lot to be desired. Also, in my experience what can turn youg people off math is when they learn concepts that are not properly anchored in applicability. It is often easier for people to learn something permanently (as opposed to just long enough to pass a test) if they really understand how it is used in the real world. And I don’t mean the often silly word problems. The teachers need to be able to demonstrate and explain how math really is the basis for so much of our technological society and have the students work on problems underlying science, statistics, etc. This can be done elementarily even for primary grades.Report

  6. Avatar Josh
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    says:

    You know, I’ve been working on a newspaper feature about a guy who’s considered a minor deity in gaming and tech circles because he was one of the first people to build cool shit (he put together a portable PlayStation three years before Sony released the PSP) and he builds it well. He just built a pinball machine, and it is not a simple affair—it’s got audio and animation and 13 modes; it’s mind-boggling—and he had to know math and woodworking and electronics and programming and art design and just a shitload of stuff to do it.

    Anyway, naturally, he did a semester of college and dropped out, and that was, like, 15 years ago. And he dropped out because while he obviously has the ability to learn, he isn’t good at learning something that he doesn’t have a reason to learn. I’m pretty sure he’s not alone. I kinda hated school because of that, and I wonder how many kids who get tagged as suffering ADHD aren’t great at sitting quietly when they’re working on something they’re into.

    I mention this book all the time in blog comments (I’m sure I have here before, even), but it really is, I think, the smartest thing ever written about our education system and why it doesn’t work. Our schools are built to be one-size-fits-all—they’re based on exactly the same paradigm that mass production has its roots in—and all that really matters for purposes of succeeding in them is that you fit.

    That’s getting a little afield, and in the book, Neil Postman and Charles Weingartner don’t necessarily focus on it; but they do focus on creating a system of education centered on helping kids learn how to learn. Their plan revolves around taking the natural curiosity of the most curious members of our species, children, and then showing them how to approach the questions they’re interested in answering. As you say, E.D., it’s about context.

    And I’m not even sure it has to be about language coming way before math. I think the main point is to teach kids that asking questions can be stimulating and fun, and that they can learn ways to find answers; it seems like once their interest is piqued, there’s no reason they couldn’t start figuring out the mechanics.Report

  7. Avatar Alan Scott
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    says:

    On the contrary: I think arithmetic education is one area where our nation really excels. American students score well on math tests in early grades–it’s the later grades where they start to lag behind. I think this is a problem of real-world applications vs. abstract concepts–Americans start to fall behind right around the point where problems can no longer be expressed in terms of how many apples you keep and how many you give to a friend.

    As I understand it, arithmetic was presented much more abstractly in the early part of the century, which may explain why Benezet’s 6th graders did so well against their peers: All of their math education had focused on story problems. But if you start teaching the story problems to first and second graders, what’s to say they couldn’t beat the pants off of those Benezet’s group by the time they were in 6th grade.Report

  8. Avatar Trumwill
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    says:

    this is as strong a case as I can make against a national curriculum or national standards, I think. We will lose all of our ability to experiment and innovate and find new and better

    To me, this is one of the better arguments in favor of school choice (even if just in the form of charters, magnets, and so on). I l0ve experimentation. I am less enthusiastic about my kid – without regard my opinion – being used to test some theory with no measurability or to have to move in order to avoid that. This isn’t my way of saying “I love experimentation but not on my kid.” I might sign my kid up for such a program if it was something I thought would work and Bezenet’s idea sounds much more appealing to me than the by-the-numbers approach. I just wouldn’t want my kid signed up for it by virtue of the neighborhood we live in. Because while I am intrigued by the Benezet method, the same cannot be said for a lot of other innovative education ideas particularly when it’s success or failure cannot be measured.

    I’d also add that the basis by which we believe that Benezet’s methods may be better is by… testing.Report

  9. Avatar T. Greer
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    says:

    I sent this note to a smart friend who is a Math BA and aspiring Education PhD. His reply is worth repeating for the larger readership here:

    “Ah, but there are a few flaws with this article:

    – First and foremost, one (or even several) studies doth not educational gospel make. The conditions of the study are understandably limited. This, in turn, leads to limited generalizability. I actually doubt that it would pass a review board today. Additionally, often the result of long term studies across years are not simply the result of one single cause. To assume so would be invalid. I’m going to optimistically hope that this suspect conclusion is the fault of the article and not the study itself.

    – Second, according to the article, the study doesn’t say to not teach math in those early years. It simply says not to teach drill and kill arithmetic. These are not the same thing. The truest teaching of math addresses all of the concerns brought up in this article. Measurement, number sense, logical discourse, etc. are all fundamental math skills.

    -Third, the article hits on what I consider to be the bigger problem. Teaching math to children isn’t the problem. Those who are teaching math to the children are. I bet if you had the same inept teachers who had taught the other kids all along teaching those kids in the sixth grade , they would not have performed as well as they did. On the flip side of that, I bet if an effective teacher had taught the early grades, those kids with have the same math skills as those sixth graders or better by the fifth grade.

    These are just my almost professional opinions (give me a few more years to wrap up the PhD), but we’ll get to see if I can back up my words when I eventually open my own elementary school.”

    Report

  10. Avatar Ian M.
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    says:

    My son just turned six and loves his kindergarten math. He’s good at it and it gives him confidence and satisfaction whereas he struggles with his reading. This goes to your greater point of nationalization of education being the wrong course. I would go farther – it should be tailored to each kid based on what the teacher is seeing. But we send Max to a private school and the math teacher rarely teaches out of a book.Report

  11. Avatar Björn
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    says:

    I learned maths and was able to solve story problems in elementary school. Also, maths was one of the few subjects I enjoyed, therefore I don’t see a point in removing it from the curriculum.

    Maybe alternative school forms might work, where pupils can choose for themselves what they want to work on at any particular moment (ie Montessori, popular in Germany at least).Report

  12. Avatar monika hardy
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    says:

    i would love insight on this latest idea… even if it’s: that’s ridiculous…
    http://monkblogs.blogspot.com/2010/03/foreign-language.htmlReport

    • Avatar Rufus F. in reply to monika hardy
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      says:

      It sounds reasonable to me. I found Spanish a lot easier to learn in Kindergarten than college. Unfortunately, they stopped after two weeks in Kindergarten, so I only learned a little then and the rest later. In general, I think it makes more sense to start with the foreign languages much earlier than they do and build on them, because indeed math is another language, and foreign to many people.Report

    • Avatar JG in reply to monika hardy
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      says:

      Simply learning early is enough. Earlier the better. Immersion is best. My brother and his wife spoke only Spanish at home since they were babies and let them simply osmote English through everyday life outside of the home. Result: they are all 8-10 yo and all are perfectly and unconsciously fluent in both languages.

      My fiance speaks English, Spanish and Chinese (Mandarin). When we have kids, she will speak Spanish, I will speak English (I’m USian) and they will osmote Chinese (we live in Taiwan). I’m pretty good at Spanish already. I’m taking Chinese classes (I’m 48 – it is my 6th language). Odds are we’ll have trilingual (minimally) kids as a result. It’s the way it works in Europe already.Report

  13. Avatar J. Cathers
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    says:

    I think some of the commenters are missing the point E.D. Kain is trying to make based on what he/she has inferred from Peter Gray’s evaluation of L.P. Benezet’s initial hypothesis and subsequent research. Kain seems to be reinforcing Benezet’s intuition that the rigor of the antiseptic and dreadfully repetitive, and many times laborious, arithmetic processes associated with practicing mathematical calculation as a youth has a significantly counterproductive social effect that deters children from developing a socially meaningful appreciation of the language of mathematics; Essentially, I sense that the lack of compassion shown toward individual students by sacrificing a child’s sense of curiosity with the physical world in exchange for a “you’ll see why this is important later” stifles the learning process in a way that prevents it from being stimulating and rewarding enough to sustain any continued effort toward seeing it through to comprehension, robbing students of the ownership of an earned appreciation for what the language of mathematics is purposeful toward, robbing them of a meaningful and awarding appreciation of just how elegantly and beautifully the language of mathematics harmoniously interweaves all of their curiosity about the physical world with the process of discovery; Understanding that the language of mathematics is, in fact, *not* just somebody else’s arithmetic labor that needs to be performed before being granted freedom to explore but the Rosetta Stone that seemlessly integrates all disciplines of Scientific philosophical thought in a way that will later be continuously reinforced by their more conceptually/constructurally-based understanding of reality that will be much less difficult to integrate and associate with the pre-existing body of knowledge they’ve somehow managed to retain…

    It seems to me that montessorie schools have developed their approach to education using this very same mode of logic, and I happen to agree that this approach seems to be superior, if not simply more conducive to lasting happiness, toward developing a passion for the learning process within individuals. I base this opinion on my own personal experiences in public schools in America, having spent a significant amount of time re-educating myself on such basics after developing a finer appreciation for the Sciences later in life as well as resenting my inevitable predisposition to having been surrounded by institutions that failed to recognize the importance of such careful consideration.Report

  14. Avatar Kaleberg
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    says:

    They should also stop trying to get kids to read stories in the lower grades. I never could make head or tale of fictional narrative until I was in my mid-20s. Novels, especially, were just meaningless sequences of event descriptions to me. I never could put everything together or into any kind of context. Then, well after I got out of grad school, fiction suddenly started to make sense. It was a real revelation.

    As for foreign languages, they can also wait. I barely squeaked through Spanish in high school, but when I hit my 40s I found it easy to learn French. My Spanish has even improved! Maybe I’ll be able to “get” music someday, if I live long enough. I gather from my more musically enabled friends that it has some serious rewards, but I have no sense of what they are now. It’s something to live for.Report

  15. Avatar JG
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    says:

    It’s not the “what” (math itself) but the “how” that is flawed.

    The way math is taught in the USA, usually with people who didn’t even major in math itself or a math-intensive subject like science or engineering, is what is flawed.

    The teaching simple is doomed and teaching to a standardized test makes it even worse. I had several elementary school math classes taught by jocks with only physical education degrees! I only managed to learn math despite these clowns and the administrations that chose them on the cheap. Now I’m an engineer and engineering manager, working on leading edge technologies. I do not count my elementary math classes as being key to this accomplishment – they were barriers to success mostly.

    Standardized testing and the resulting pedagogy akin to teaching English classes only to a particular novel of Dickens (and pick the least interesting one! That would be “Michael Slater” according to Amazon) and nothing else. Now your “English test score” is based on how well you can remember the characters or themes of that particular book. You aren’t really learning English literature, or math, with standardized testing and teaching to the test; you are learning how to game a bureaucratic system absent of any real knowledge or learning. That’s a complete waste of time.

    Part of why it will be a cold day in hell before any child of mine steps foot in a US public prison (I mean, school).Report

  16. Avatar Yoshi
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    says:

    The thing that got me into math today was the fact they pounded it into me during my school years. I never made the accelerated math courses, but I loved math, and because of that, I waited patiently while taking precalculus three years in a row just to get to calculus.

    I took it three years because I already knew the stuff, and so I never did homework. I have a strong incentive not to do things I already know (re-invent the wheel). College rolled around, and that third year didn’t require homework, so I passed, and now I’m happily chugging through calculus.Report

  17. Avatar Megan
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    I wish I could share with all of you the studies about Montessori, but let me just say that the whole thing was a big experiment back in the early 1900s. Dr Montessori set up these environments, and observed what the children were interested in and what they did. She found time and again that the materials she presented to children were fascinating to the *younger* children. She observed that they have sensitive periods for certain kinds on knowledge, when they are the most interested in that area of learning. AND she found that children learn, under age six, because they are driven to do so. They just learn through their senses – they don’t have a reasoning, abstracting mind yet and need to have concrete materials to work with. This was confirmed with children all over the world, in all different socio-economic groups, and all different races.
    Much of what Montessori discovered by observation is now being confirmed by neuroscience. The answer isn’t to teach it later *or* to teach it earlier, but to teach it in a way the child can learn it, i.e., to connect the child with materials that he can use to teach himself, through physical manipulation of the material.
    For those who aren’t familiar with Montessori education, the typical age children start to write is age 4, followed by reading around 4.5. Math starts around 4 and in a good program they can do multiplication and division of large numbers (7 digit) by age 6 or 7. The teacher doesn’t force any of it – the children are interested, and can do it whenever they want to, so they do. Then they check their own work and if they want to they can do it again. The teacher just shows them how to do it, and gets out of the way. They have complete control over their “study” and they enjoy doing it (though of course the teacher observes to see if they need help or another lesson and provides it if needed).Report

    • Avatar tom van dyke in reply to Megan
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      The oft-asked for list of famous Montessori graduates strikes me as rather thin. But that could be a function of numbers.

      I like Marquez. The internet dudes are cool. The rest, though— certainly many colleges and even some high schools have produced equally impressive lists, with fewer minds and bodies to work with, and without uniformly involved and got-bucks parents.

      Jeff Bezos (Founder of Amazon.com)
      Larry Page and Sergey Brin (Co-founders of Google.com)
      Jacqueline Bouvier Kennedy Onassis (Former U.S. First Lady)
      Prince William and Prince Harry (English Royal Family)
      Anne Frank (Famous Diarist from World War II)
      Chelsea Clinton (Former U.S. First Daughter)
      Katharine Graham (Owner/Editor of the Washington Post)
      Sean ‘P.Diddy’ Combs (RAP Mega-Star)
      Gabriel Garcia Marquez (Nobel Prize winner for Literature)
      T. Berry Brazelton (Pediatrician and Author)
      Julia Child (Chef, Star of many TV Cooking Shows, and Author)
      Friedensreich Hundertwasser (Austrian Painter and Architect)
      Report

      • Avatar Megan in reply to tom van dyke
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        I admit that there aren’t as many studies as there should be, but what that list doesn’t take into account is how many very successful people there are who *aren’t* famous. And as for it being a function of numbers – absolutely. So many people don’t even know that Montessori exists, let alone have the option of their child(ren) attending. In addition, not all schools that have Montessori in the name actually follow the principles. There’s no law preventing Joe Blow from opening a “Montessori school” in his living room without any training at all, so I could argue about your “fewer minds and bodies” statement. I’d also like to mention that we ask parents to commit to three years and often they pull out the third year so their child can go to public school kindergarten and socialize with the group of children they’ll spend the rest of their educational journey with. That limits the benefits because the third year ties together all of their previous work.
        Montessori education is often private and expensive, but it isn’t always. The very first classroom (around 60 children under 6 with one adult and a teenage assistant) was for children whose parents both worked to make ends meet, and there are some (though not enough) schools today for low income families, all around the world. They have the same outcomes – children spontaneously learning to read at four and a half years old, even if they came from illiterate families, and similar advances in other areas. Montessorians just need to get off our rear ends and document it more scientifically – and then make the findings known.Report

        • Avatar tom van dyke in reply to Megan
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          says:

          Thx for the response, Megan. Head Start shows similar gains, which unfortunately tend to disappear come 4th grade or so. The real world takes over, despite the elegant and worthy “head start.”Report

          • Avatar Megan in reply to tom van dyke
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            says:

            Montessori is all about the real world. The very first lessons are practical life activities such as hand washing and sweeping. The children don’t just memorize facts, they work with concrete materials and completely internalize what they’ve done – whether it’s practical life, work with the sensory materials, language, or mathematics. I assure you the advantage doesn’t disappear after fourth grade.
            I also am a bit resentful about Montessori education being compared to Head Start – they are not at all the same in either process or outcome. One of the basic tenets of Montessori philosophy is that we respect the child enough to let him guide his own education. All we do is provide the means.
            How much do you really know about Montessori? I’d love to share with you all that I know about how and why it works (and why the results couldn’t possibly disappear) but there’s just too much information that you have to understand in context with itself. Here’s a resource with a little bit of information – I’m linking you directly to a study that shows it has a reflection into the high school years at least.
            http://amiusa.org/wp-content/uploads/2010/06/amiusa-outcomes2.pdf
            The rest of the site has more information about Association Montessori International, which is the organization Dr. Montessori and her colleagues of the time established, and the Montessori Method specifically.Report

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