I have sworn upon the altar of God eternal hostility against every form of tyranny over the mind of man. -- Thomas Jefferson

Thursday, September 17, 2009

Tyranny vs. Chaos: The False Dichotomy of “Progressive” vs. “Traditional” Education

Alfie Kohn has a revealing essay* posted on Education Week, currently available for free to the public.

Kohn is a well-known advocate of “progressive” education and his article exhibits nicely the basic error that “progressives” make, as well as the opposite error made by far too many advocates of “traditional” education.

On the one hand, Kohn criticizes the traditional teacher-as-lord-and-master approach as consisting of “mandates handed down from on high… where test scores drive the instruction and students are essentially bullied into doing whatever they’re told.”

I think that is a fair rap.

“To divide fractions, invert and multiply.” (Why?)

“Democracy is the best system of government.” (Then why not carry out open-heart surgery democratically?)

“Humans are descended from fish.” (How do we know this?)

To simply order children to believe the “right” answer causes them to accept that one can only learn the truth from authority, and that they, and humans in general, lack the ability to reliably determine the truth for themselves.

And, if kids ever start to wonder how the “authorities” learned the right answer, since the authorities themselves also are mere humans, the kids may fall into a naïve skepticism, thinking that no human can ever really know any truths at all.

But, sadly, Kohn offers, as a false alternative, the old “progressive” solution of giving kids the “opportunities to discover answers to their own questions,” i.e., the “constructivist” approach where kids have to create knowledge for themselves rather than systematically being taught what humans have discovered, at enormous effort, during the last three thousand years.

That really would be a swell approach – if kids had a spare three thousand years to work out everything, and if all kids were as bright as Euclid, Einstein, etc.

So, how to avoid the false choice of “progressive” vs. “traditional” education?

The answer should really be obvious from everyday life.

In real life, we explain to kids that you need to brush your teeth because you will otherwise get cavities, you need to wash your hands because there are germs on your hands that can make you sick, etc. We give explanations.

The idea of giving rational explanations, as opposed to the false dichotomy of either issuing irrational commands or forcing the students to discover everything for themselves, is really not that complicated!

E.g., why “invert and multiply” to divide fractions?

Well, division is the inverse operation to multiplication: if you multiply by some fraction and then wish to undo the multiplication, inverting and multiplying will indeed undo the original multiplication.

Liping Ma, in her brilliant Knowing and Teaching Elementary Mathematics, a “must-read” for all homeschooling parents, goes into much greater depth on this issue of dividing fractions: this is one of the toughest things to explain clearly in elementary mathematics.

But it can be explained. It is unrealistic to expect kids to discover for themselves how to divide fractions, or to fully understand on their own why it works, even if they do stumble upon it. However, it is also not necessary to teach the standard algorithm as an arbitrary rule imposed, for some mysterious reason, by adults.

As Ma explains, if one wishes to use division as the inverse of multiplication, if one wants division to be a means of carrying out repeated subtractions, if one wants the “cancellation law” to apply to division, one has no choice: there is only one right answer, the one given by the standard algorithm.

Ma advocates a “profound understanding of fundamental mathematics”: i.e., both a serious conceptual understanding of elementary math, as well as a practical mastery of the elementary math facts and the standard algorithms.

That indeed should be the goal in all academic (and non-academic) subjects: a conceptual understanding of American history combined with detailed factual knowledge of dates and historical events; an understanding of the experimental bases for scientific theories as well as detailed knowledge of the important scientific facts; etc.

As a practical matter, it is sometimes necessary to say to a student, “We will see the justification for this next month or next year.” Sometimes, one cannot fully understand the evidence for a theory until one has grasped exactly what the theory is. And, it would be foolish to slavishly imitate all the false starts and errors made in the historical development of scientific theories, in the historical creation of various concepts in economics, in the historical discovery of various methods in mathematics, etc.

A student’s learning need not and should not recapitulate the historical process by which knowledge was originally discovered. The whole point is to make it easier for the student than it was for the original discoverer.

Often, the historical experiments or reasoning that led to a discovery are relevant: this is true, for example, of Rutherford’s discovery of the nucleus. But the important thing is to present the best proof and justification we possess today for a particular piece of knowledge.

The other error to avoid, which tends to be shared by both “progressive” and traditional approaches to education, is the false belief that kids have to wait until they are mature to be told of discoveries that the human race only stumbled upon in the last century or so.

It may have taken humans a long time to discover the Big Bang, the fact that humans are descended from fish, etc. But a six-year-old can grasp those ideas – they are not that complex. Even the basic evidence for those facts – e.g., the fossil record, the fact that the galaxies are expanding outward – can be explained at a simple level to six-year-olds.

That the human race had to be “mature” to discover such things does not mean that young kids cannot understand those discoveries.

An educational approach based on giving rational explanations, as opposed to the false dichotomy of either issuing irrational commands or expecting the students to discover everything for themselves, is really not that hard to grasp. Both progressivism and the traditional approach to education are wrong.

We need to teach our kids that humans can and do have a rational understanding of reality. Neither the “progressive” nor the “traditional” approach to schooling really achieves that.

Our kids deserve a "content-rich" approach that teaches them, at an early age, the marvelous and amazing facts that human beings have discovered about reality.

____________

* Thanks to Barry Garelick at Kitchen Table Math for bringing Kohn's essay to my attention.

12 comments:

  1. Will you have a reading list of the materials you are using with your kids?

    I have been reading KTM for several years and I have taught math in public school. I was recently not re-hired due to budget cutbacks and my aversion to fuzzy math. The county just adopted CPM for all middle school students. I had said that I didn't believe in it.

    My daughter is only 6. I had a lot of trouble teaching her math, ironically. So we are enrolled in Kumon. Reading was easy to teach using Siegfried Engelmann.

    She is currently enrolled in a montessori school and they love to teach the cosmic story. But I don't know how we will get from here to wherever she needs to go.

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  2. One quick note. I agree with you that Alfie presents a false dichotomy in the way you describe. It's also false, however, in mischaracterizing traditional teaching as ALWAYS being dictatorial (if that's what you were saying, forgive me). What I mean is that while the teaching in the past had its problems, (traditional education done poorly) the teaching in the past had its merits as well (traditional education done well). One has only to look at the literacy and math skills of people in my generation (baby boomer) when we entered college with those entering college now to see a vast difference. Whatever was working back then wasn't failing, even if some improvement was needed.

    You might be interested in an article I wrote on traditional math that was in Ed News:
    Part I Part II Part III

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  3. Exactly! I cannot figure out how people can keep their face straight and tell you that kids should "construct" all of the knowledge there is. It took great scientists their whole *lives* for each prat... but my kids should just do this in an hour a day? Uh... no?

    We sort of follow The Well Trained Mind, but I do not follow science by just introducing concepts as they were discovered through history. We cover scientific historical figures in order, but for "science class" we go in a more rational order -- which is actually to start with physics, then chemistry, then biology, etc.. (I mean, there is a mix, but waiting on atoms and physics until later seems silly. How do you understand chemistry if you don't know any physics??)

    My kids are 6 and 3, and we're currently enjoying Nebel's Building Foundations of Scientific Understanding (for grades K-2).

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  4. Barry Garelick wrote to me:
    >It's also false, however, in mischaracterizing traditional teaching as ALWAYS being dictatorial (if that's what you were saying, forgive me). What I mean is that while the teaching in the past had its problems, (traditional education done poorly) the teaching in the past had its merits as well (traditional education done well).

    Oh, sure.

    In some ways, I was creating a “false trichotomy”!

    And, of course, I do not mean to suggest that Alfie Kohn was intentionally lying in creating a false dichotomy. I merely think there is an alternative that avoids some of the negatives often present in traditional teaching and that also avoids some of the negatives in his own approach, and that Alfie ignores that alternative.

    On the other hand, I do think that some of the “progressive” criticisms of a lot of traditional teaching (“drill and kill,” “the sage on the stage”) do have some merit. While some degree of rote memorization is indeed necessary (multiplication tables, foreign language acquisition), it is certainly possible to mindlessly and pointlessly push rote memorization when there are better alternatives.

    Someone on Kitchen Table Math a while back (Catherine, perhaps?) pointed out that there is “natural” memorization (none of us have to memorize who the current President is or when the attack on the Twin Towers occurred), and “unnatural” memorization (memorizing meaningless, unconnected information or memorizing important information without the context that causes it to make sense).

    My point, and I think one of E. D. Hirsch’s points, is that a content-rich education leads to a lot of memorization being of the “natural” kind, which is certainly more pleasant than the alternative.

    Similarly, I took two classes as an undergrad from the Nobel laureate Richard Feynman. It was cool: Feynman really was a true “sage on the stage”: intellectually brilliant and personally engaging: he went to a great deal of trouble to make his lectures a true experience (the homework, alas, was terrifying!).

    However, in my experience, that is very rare, even more rare at the university level than the high-school level (I can think of a handful of high-school teachers whose teaching skills were comparable to Feynman’s – and I suspect that I may have been more fortunate in my high-school teachers than most students nowadays).

    So, I think we should give the devil his due and admit that many of the “progressive” criticisms of a great deal of traditional teaching are quite fair, even though there are of course traditional teachers, such as Feynman, who were and are fantastic.
    CONT.

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  5. CONT.
    Barry also wrote:
    >One has only to look at the literacy and math skills of people in my generation (baby boomer) when we entered college with those entering college now to see a vast difference.

    I’m in the post-Sputnik age-group. Our science textbooks (high-school level) were much better than our parents’, and New Math was actually much better (for the top half of the class) than is commonly claimed. On the other hand, there were a decent number of stupid, uninspiring, incompetent teachers even back then. And, even back then, most parents cared little about their kids’ learning anything beyond the three Rs and a bit of propagandistic US history.

    Of course, the scary thing now is that so many kids don’t end up with even the minimum of the three Rs or even a superficial knowledge of history.

    Anyway, I do think we need to emphasize that merely “back to the ‘60s” (or the ‘40s or 1900 or whatever) is not enough, even if it would be an improvement over the current situation. At least in my grade school back in the ‘60s, we did the “fireman is my friend” and such nonsense in the early grades. We should have been reading about mummies, knights and castles, etc., which are both significant and interesting.

    Similarly, today’s grade-school kids should not be reading about roots, stems, and leaves but about DNA, evolution, the Big Bang, extrasolar planets, and black holes, which are after all both more interesting and more important than roots and leaves.

    So, I really do think we can advocate an alternative that is better than both progressivism and traditional approaches.

    I’ll check out your article – thanks for the link.

    All the best,

    Dave

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  6. Hi, silvermine!

    You wrote:
    >We cover scientific historical figures in order, but for "science class" we go in a more rational order -- which is actually to start with physics, then chemistry, then biology, etc.. (I mean, there is a mix, but waiting on atoms and physics until later seems silly. How do you understand chemistry if you don't know any physics??)

    Somehow, I think you knew that you would not find me disagreeing with teaching physics as early as possible. (Incidentally, we’re not systematically going through the history of science in chronological order, but the various science books we use, not public-school textbooks, tend to have a fair amount of history. I also explain a fair amount of the history of science orally, since I am interested in it and know a decent amount about it.)

    The problem with giving a full coverage to physics is, of course, that you cannot fully understand physics till you know calculus (Newton after all, invented calculus to understand physics), and it’s hard to get very far in physics at all without some algebra.

    On the other hand, I really do think that if you cannot explain an idea in some form to a six-year-old, you do not understand the idea yourself.

    So, I entirely agree with you that the basic facts about atoms can be taught at a very early age: if six-year-olds can understand the idea of the solar system (and they can), then they can also understand the idea of the atom being like a miniature solar system with the electrons whirling around the nucleus.

    Of course, that is not quite right, and kids should be honestly told that exactly how the electrons are moving is a bit unclear: indeed, as a physicist, I am still not clear exactly what the electrons are doing (this has been a subject of rather intense debate among physicists for over eighty years now).

    But the fact that six-year-olds (and physicists!) cannot fully understand quantum mechanics does not mean kids cannot be told basic facts about atoms.

    I have found that kids can grasp quite early that opposites attract and that this is how the protons hold the electrons. I’ve also found that the idea that chemical bonds are due to sharing of electrons between atoms is easy to grasp.

    On the other hand, I’ve found that the idea of electron shells, the tendency of atoms to try to complete their shells, etc. is harder to grasp.
    CONT.

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  7. CONT.
    We’re currently reading Fred Bortz’s series of short books on subatomic particles: “The Electron,” “The Photon,” “The Quark,” etc. I’d consider these fourth-to-sixth grade reading level, for good readers and with the parent reading with the child (i.e., the child reading out loud, and the parent helping with anything confusing). Bortz keeps making a chronological error about de Broglie’s contribution, but otherwise the books are generally accurate: he makes a very strong effort to take complex ideas and explain them in a comprehensible form.

    I just bought Gamow’s “Gravity,” which I’m hoping to read with the kids in the next few months: I consider this fifth to seventh grade level (under the same conditions as above).

    One other physics book I recommend is Irving Adler’s “The Wonders of Physics” – probably fourth to sixth grade level (under the above conditions).

    I’ve experimented with explaining to my grade-school kids some fairly complicated ideas such as the curvature of spacetime, the angular-momentum thing that ice-skaters do, some basic ideas about statistical mechanics, etc.

    They didn’t seem to get the ice skater thing (though I think I myself understand it better!). I think they did get a little sense of what is going on with microscopic randomness tending to increase (i.e., entropy) and with spacetime being curved (Einstein’s theory of gravity), though of course they cannot understand these at a sophisticated level.

    So, I view teaching our kids physics as on ongoing experiment. Since they are not being formally tested on any of this, if they fail to get some concepts, I back off and plan on coming back to it later.

    My own mentor in physics, the Nobel laureate Richard Feynman, went out of his way to teach undergraduate classes, even freshmen, although, as a Nobel laureate, he could have taught only graduate seminars if he had wanted to. He once told us that he did so partly because you are forced to understand something really well yourself when you have to teach it at a beginning level.

    That’s my experience, too. As a physicist, I am of course learning a great deal about biology with the kids (I avoided biology in school as much as possible). But, I am also learning a fair amount about both math and physics through trying to explain them to grade-schoolers

    Strangely enough, being a homeschooling dad seems to be making me a better physicist.

    All the best,

    Dave

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  8. Anonymous wrote to me:
    >Will you have a reading list of the materials you are using with your kids?

    Yeah, that was actually the primary purpose for starting this blog. I’ve got notes on paper of everything we have used back to kindergarten, and my grand plan is to enter it all on the Web.

    I’ve of course benefited from information provided by other homeschoolers: for example, a homeschooler from Massachusetts who has a masters in chemistry, GeekMom, very strongly recommended “Essential Biology with Physiology” by Campbell and Reece. I checked into it, and I’ve come to agree with her that this is probably the best text for advanced middle-school or intro high-school biology.

    I know that a lot of homeschoolers have stumbled across valuable resources, but there is a bit of a tendency to avoid mentioning everything you have done to other homeschoolers because it may seem that you are trying to insist that they use exactly the same resources you have used.

    The Web seems a good solution: post all the info and everyone is free to use anything that works for them. I’m hoping that lots of homeschoolers (and “afterschoolers”) will do this also, so that we can all benefit.

    You also wrote:
    >I have been reading KTM for several years and I have taught math in public school. I was recently not re-hired due to budget cutbacks and my aversion to fuzzy math.

    You have my sympathy. Our high school’s strongest department was the math department, and I owe the department chairman a real debt for helping me in my education – she saw that I had the ability to go far beyond the formal classes in our school, and she went out of her way personally to help me do that.

    As to your daughter, obviously I am positive about homeschooling, and you are certainly qualified to do that. But, in the end, everyone’s family situation is different, and so of course I cannot tell you what to do.

    The one big concern that I have about out-of-home schooling is the time factor. We tend not to value children’s time very highly. But, reading on the Web (e.g., at KitchenTableMath) about all the parents doing “afterschooling,” it is clear that there just is not time for kids to get a full education at home if their time in school (over a thousand hours a year normally) is largely wasted.

    And, of course, kids do also deserve to have time to think and wonder about things of their own devising, not assigned by parents or teachers: I’m not convinced that kids need time for Wii, TV, or video-games, but they do need time for daydreaming.

    So, if you cannot homeschool, I would urge you to look for a school that will not waste your daughter’s time. Ultimately, all we have in life is our time, and childhood is the period of life when we are best able to use that time for real learning.

    Thanks for dropping by – your asking me about fully posting info about the books we’ve used will help encourage me to get to work on it.

    All the best,

    Dave

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  9. Dave,

    Appreciate all your comments (particularly the allusion to the "fireman is my friend" which I had in social studies in second grade). At the risk of beating the same drum, my concern is in vilifying traditional education and in the process throwing out the baby with the bath water. While one can find examples of traditional education done poorly, there are certain attributes of traditional education that were and are effective and we shouldn't throw those out. In my look at the older math textbooks in use way back when, I don't find much of the "rote learning" that people seem to think existed. Instead I find fairly good explanations. That teachers chose to teach poorly is not the fault of the textbooks in use.

    Vern Williams, a middle school math teacher who was on the National Math Panel (and is my neighbor) uses Dolciani's "Structure and Method" series for teaching algebra and Moise/Downs "Geometry" for his geometry classes--both products of the new math era. The Dolciani book he uses is from 1986. Dolciani's book is similar to the algebra book I used, written in the 50's, though hers is better. We have gotten away from what needs to be taught in math classes and dumbed things down. So there is some value in going back to see what we did right and, as you suggest, improving on it and eliminating whatever was bad from those days.

    In terms of science, I agree that kids need to learn about DNA, etc, but my daugher's biology course in high school last year, in my opinion, had too much information. It was information overload. Start simple, start slow and build--sequencing and pacing is key. There is a lot more information to teach than there was 50 years ago, that's for sure, but there is some basic information that is unchanged that I felt got short shrift to make room for the new stuff.

    By the way, I was a big fan of Gamow; his books for kids are great, though by no means easy. He was a professor at George Washington University, I just found out.

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  10. Barry Garelick wrote to me:
    >Vern Williams, a middle school math teacher who was on the National Math Panel (and is my neighbor) uses Dolciani's "Structure and Method" series for teaching algebra and Moise/Downs "Geometry" for his geometry classes--both products of the new math era.

    Have you compared and contrasted some of Dolciani’s books from early in her career with ones from near the end of her career? I think I see a dumbing down in the later books, mandated by the publishers, I suspect, because of the defeat of the “New Math” movement.

    Incidentally, “New Math” illustrates the concern I have about referring to “traditional methods”: while it had some flaws (basically poorly trained teachers and the fact that it was tough for the bottom half of the class), yeah, “New Math” was in many ways superior to what came before or after. But, in my experience, very few people think of “New Math” as “traditional” math. At the time, it was derided as radical nonsense from a bunch of academic eggheads. An awful lot of people still lump “New Math” in with “fuzzy math,” when, of course, they are diametric opposites.

    I’ve recently found that the decline in math teaching may go back far further than we imagine. I recently bought G. Chrsytal’s “Textbook of Algebra,” originally published in 1886. The subtitle is “an elementary textbook for the higher classes of secondary schools and for colleges.” It seems to have been intended for what we would now think of as AP-level classes.

    Chrystal’s book has material that I myself did not learn until after I got my Ph.D.: for example, the theory of continued fractions, and the general theory of symmetric functions, including Newton’s theorem for the sum of powers of roots of an equation.

    I have actually used the two topics I just mentioned in practical engineering applications (correcting digital errors in satellite communication systems and estimating the raw transmission error rate in those systems), so these subjects are not just old-fashioned, out-dated material. Yet, I had never even heard of them through my entire formal education, up to and including my Stanford Ph.D.

    Something is wrong here.

    Incidentally, there seems to be a bit of a “back to the future” trend among some academic mathematicians to recover some of the late nineteenth-century math that was viewed as uninteresting through most of the twentieth century, partly because a lot of it is proving useful in various computer-science and engineering applications.
    CONT.

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  11. CONT.

    Barry also wrote:
    >In terms of science, I agree that kids need to learn about DNA, etc, but my daugher's biology course in high school last year, in my opinion, had too much information. It was information overload. Start simple, start slow and build--sequencing and pacing is key.

    Yeah. That is part of the reason I want to see real science, basic but hard-core, taught through the five or six years of grade school. You can’t expect a six-year-old to grasp Hardy-Weinberg equilibrium, but, if kids learn a fair amount about Mendel and his peas in grade school over an extended period, then, by high school, Hardy-Weinberg will be a piece of cake.

    The same is true for chem, physics, etc. For example, I don’t think most adults understand at all why we refer to astronauts who are in orbit as being in “free fall”: the answer, of course, is that they are indeed really falling, but in an arc such that the earth curves out from underneath them at just the right rate to keep them the same distance from the center of the earth. That is not a mathematically complicated idea, yet, few people ever learn it at all.

    A similar point can be made for the heliocentric theory: everyone has been taught to believe that the earth moves around the sun, but I have found almost no Americans who know what the strongest evidence is for that fact (it’s rare for anyone to know any evidence at all for the heliocentric theory).

    Both of these points apply not just to current science education, but also to your and my and our parents’ and our grandparents’ education.

    When “traditional” education was indeed better than the present, as in Dolciani’s books, and, rather spectacularly, in Chrystal’s book, should we return to those “traditional” standards?

    Absolutely.

    But is “traditional” good enough, is it the real goal?

    No. The real goal should be to expose kids to the very best knowledge humans now possess of nature, of the conceivable structures of reality (i.e., math), and of the nature of human beings, as well as the best works of sensory imagination created by humans (music, art, literature, etc.).

    I don’t see that tradition is a good thing in and of itself. But excellence is.

    All the best,

    Dave

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  12. Good points; thanks. I am for excellence as are you. I believe that in certain periods, educational content (and delivery) was excellent.

    Your point about new math is well taken. It certainly was a departure from "traditional".

    I think there is math taught well, and math taught poorly. In the latter case, it may be because of bad teaching by the teacher, or the textbook or both. The term "traditional" carries baggage and is confusing for the reasons you've stated.

    (I also agree with you that Dolciani's later books were dumbed down--I don't like them.)

    I think for many of the textbooks and programs today, whether you dub them traditional or progressive, the textbooks and/or curricula material is such that the math is inherently taught poorly.

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