Teaching children to learn

I wrote it. American Thinker published it. I’m reprinting it here for you to read it:


I volunteer for a music organization in which my son is involved. Recently, through a community outreach program, my son’s group was augmented by some boys from economically disadvantaged backgrounds. These boys are really nice kids. They have no “attitude.” Instead, they’re just sweet little people, and they obviously come from caring homes. They’re also very pleased to be where they are, and are enjoying the cachet associated with this organization.

I have noticed something significant about these little boys during music theory class, though. Just as all the other boys do, they wiggle and chat — all the time. And, as with all the other boys, you have to demand and/or capture their attention (and the theory teacher whom I assist is good at this).

But unlike all the other little boys, however, these boys seem to have few – or at least different – tools for learning. They don’t respond to mnemonics, because they simply can’t grasp the relationship between a mnemonic and knowledge acquisition. Thus, neither the time-worn phrase “Good Boys Do Fine Always” for the line notes, nor the word “F A C E” for the space notes has helped them master note recognition. In this they differ from the other little boys who, from day one, were able to fall back on the mnemonics when they needed to.

When it comes to rhythm recognition, all the other boys, when prompted, will place their fingers under the relevant notes so that they can “read along” as a rhythm is clapped out. These visiting boys, when prompted, freeze. They simply don’t understand that concept, and I have to position their fingers under the notes every time so that they can see this principle at work. I know they’ll learn this technique. I’m just surprised that they don’t seem to have any concept of it now.

At the start of each class, the teacher writes on a white board the notes that are going to be highlighted in the workbook and gives them the relevant “do, re, me” labels. She does this because, in sight singing, these labels are not fixed. That is, “do” is “C” only in the key of C. In the key of G, “do” is “G.” This means that for any sight singing exercise, the boys need to know which note will be “do.” If the other little boys forget what “do” is in any particular exercise, they look to the white board, spot the note, and read its label. (“Aha! This time, ‘do’ is ‘C.'”) These new little boys, however, seem not to move their eyes back and forth between board and book. Even when prompted, they can’t seem to track the information on the white board and relate it to their theory book.

Having worked with these little boys for a while, I’ve concluded that they’ve never been taught how to learn. To the extent they have mastered academic skills (and they all read, and none are stupid or unwilling), they’ve learned by brute force repetition. How dull. How meaningless. These boys are a manifest reminder that learning itself is an art form.

To my mind, the perfect approach to teaching children how to learn is to enable them, whenever possible, to see the concrete principles behind what they’re being taught. To state that Pi equals 3.14 is dull and, to a young child, meaningless and irrelevant. To have the children measure the diameter of a circle and then visually compare it with the circle’s radius makes Pi have some context. Indeed it makes it very exciting (as you will see if you try this experiment yourself).

In the same way, when teaching children about number systems other than base ten, it’s useless just to announce the rules for adding or multiplying in, say, base 8. It’s much more exciting to look at how we tell time, and to explain that our system goes back to the ancient Mesopotamia, where they had a base 60 system. Children who are already practiced at turning 60 minutes into an hour, aside from being thrilled at this direct connection to ancient times, instantly grasp the abstract principle that there are bases other than 10, and will readily respond to lessons about how to apply this knowledge.

Likewise, when teaching children pattern recognition, how many more minutes does it take to explain why patterns matter? Thus, most teaching is simply limited to giving the kids techniques for calculating the next number in a series of numbers. This is usually based on determining the number of units between each number and the next. (Although, as I discovered, the sequence 0, 1, 2, 3, ___ actually yields two different predictive outcomes: the number 4, if you’re dealing in whole numbers; and the number 5, if you’re dealing in prime numbers.) However, it’s one thing to be told what to do and another thing entirely to be sent to the kitchen to examine the tile and see why it’s extremely important to predict a pattern (the tile would be chaos without), or to understand how Mommy can knit without a pattern, just by examining what came before.

Public schools — at least the quality public schools in our affluent community — operate on the assumption that children learn from play and repetition. (Although the games really are a repetition subset, since they’re not intended to deepen understanding, but simply to reinforce remembering.) Public schools like to break abstract knowledge into bite size pieces. They seem to forget that, whether the abstract information is a bite or a chunk, small children don’t do abstract. They may memorize it, but they can neither apply it nor can they extrapolate from it. It is meaningless information, stuck in an intellectual vacuum.

For my daughter, the main problem in this teaching method shows up with math. Just as it never worked for me so many years ago when I attended public school, it doesn’t work for her to be told a formula and then be expected to learn it by repeating it again and again. This holds true even when the formula is introduced through games, brightly colored objects, and gentle repetition. Instead, she learns by having the underlying principles and purposes demonstrated to her, whether she’s working on algebra, fractions or pattern recognition. Give her the “why” and she’ll master the “how.”

My son is one of the lucky ones who has a fairly intuitive grasp of mathematical principles, but he finds writing frustrating: especially the writing in public school that requires him to churn out a daily essay on a (usually) very stupid subject. For months, his essays came back with exactly the same criticisms on them. It only slowly dawned on me that the teacher thought that this repetitive criticism was the way to teach him how to write correctly. I stepped in and, in three weeks, while he still bitterly resents the mindless topics, his writing has improved dramatically, as demonstrated by the teacher’s effusive comments on his work. I have to laugh, though, when I think that my behind-the-scenes efforts probably mean that his teacher believes that, just by repeating the same criticism over and over, she has finally encouraged my son to do it right!

All of which gets me back to the nice little boys I introduced at the start of this essay. Neither in their homes, nor in their schools, do they ever seem to have been exposed to any learning techniques at all, whether the superior technique of ensuring understanding before embarking on drills, or the lesser, but still effective, memorization techniques used at a quality public school. The approach these boys have to knowledge acquisition is simply to sit there and let it wash over them, with the hope that something will periodically stick. This passivity is intriguing because, presumably, as public school attendees, they’re getting the same curriculum as my children — but they’re not learning how to learn.

I suspect that, for public school children, the big factor isn’t the school, it’s the home. That is, while there’s a huge difference emotionally and socially in requiring a child to go to a rundown, dangerous urban school, as opposed to a spiffy suburban school, the real difference in learning doesn’t take place in the classroom, but takes place with, or because of, Mom and Dad.

The parents in my affluent community are just like me: when they see the manifest gaps in understanding that a public school education leaves behind, they step in with lots and lots of help. If the teacher’s methodology didn’t, or couldn’t, explain the steps for adding fractions, Mom and Dad will step in, either directly, or by hiring a tutor. If the teacher, driven by a cast iron curriculum, doesn’t have the time to stop and teach principles of paragraph construction to the kid who didn’t get it the first time, she doesn’t need to worry, because Mom and Dad will take care of it. That’s not happening in poor, neighborhoods. Mom and Dad often aren’t around to fill in the gaps, and, even if they are around, they themselves don’t have the language or education skills to help out, and they certainly don’t have the money to hire a posh tutor.

None of the above is meant to be a criticism of the families in poorer neighborhoods. It is meant to be a criticism of the way we keep both throwing money at failing schools, and imposing more and more test requirements, in the belief that these things will magically fix the children’s learning deficits. I think the teaching methodology is inherently flawed, in that it stuffs children with facts and rules like geese being readied for the pate machine. Simply beefing up this fact-stuffing approach won’t matter in the poorer neighborhoods. What would matter, and what could be done without demanding ever more money, is to adjust the curriculum to help children understand what they’re learning and then to give them the tools to teach themselves. While they might master less material, they’ll actually learn what is put before them, and they will embark upon a lifetime of knowledge acquisition, no matter the situation in which they find themselves.

UPDATE: From gumshoe1, I learned something new:

Hope it’s not taken as a nitpick:

“To have the children measure the diameter of a circle and then visually compare it with the circle’s radius makes Pi have some context. Indeed it makes it very exciting (as you will see if you try this experiment yourself).”

comparing radius to diameter reveals a 1:2 ratio…
ie this is NOT Pi.

Pi is a ratio.

it is the ratio of the radius (OR diameter) of a circle


Apparently I’m able to rise only so far above my public school education and my math phobia!

UPDATE II:  Another reader informs me “0 and 1 are not prime numbers.”  There you have it.  That’s the difference between a real math education (his) and no math education at all (mine).  Still, what’s really sad is that I’m doing better than my kids’ teachers!

UPDATE III:  Just today, I read this in an AP story reporting on the fact that more and more American colleges are allowing homeschoolers to enter directly, rather than forcing them to attend community colleges and rack up some grades:

David Sample lives in Redlands with his parents and three younger siblings, who are also homeschooled. He got acceptance letters from colleges in Illinois and Texas but wanted to attend UC Riverside, the local university.

Now a freshman, he is adjusting well to college classes and shrugs when his peers complain about the way a professor teaches.

“You are already used to teaching yourself,” he said about homeschooling. “Forget the teacher, forget the class, I am just going to read the book and figure it out myself.”

Apparently David spent some time at home learning how to learn, and I’m willing to bet that’s true for many other (most other?) well-taught homeschoolers.

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  • http://ymarsakar.wordpress.com/ ymarsakar

    Brilliant. The point I should have made before in a discussion with a professor.

  • gumshoe1

    hope it’s not taken as a nitpick:

    “To have the children measure the diameter of a circle and then visually compare it with the circle’s radius makes Pi have some context. Indeed it makes it very exciting (as you will see if you try this experiment yourself).”

    comparing radius to diameter reveals a 1:2 ratio…
    ie this is NOT Pi.

    Pi is a ratio.

    it is the ratio of the radius (OR diameter) of a circle
    to its CIRCUMFRENCE.



  • http://ymarsakar.wordpress.com/ ymarsakar

    Apparently I’m able to rise only so far above my public school education and my math phobia!

    I know what you mean, I never tried to figure out the geometric proofs and correlations of a circle either. I just use the equations.

    In a sense pi is a number that is counter-intuitive. Meaning it is almost like physics, instead of geometry. A perfect circle or sphere after all is something created in null-gravity. It is not something we created that was only a math abstraction, it actually exists. I mean by counter-intuitive because we don’t see it, the rate of change, or even know why it should change at that rate as the circle curves. A square, we see a line, and we can measure or even approximate. But a circle curves, and that is calculus level derivatives.

  • Kurt

    Some of what you’re talking about I recalled from my calculus days in junior college. We were given the formulas and expected, through repetition, to understand how to apply them to a given problem. This worked fine for the first 40 problems in a chapter. But it was largely worthless for the remaining 15 problems at the end…which were intended to throw curves to everyone.

    We had three Vietnamese students in our class…who had been taught an entirely different way to go about math. Different than the brute force method. They actually understood the reasons and theory behind what were were doing. They ahd a hard time understanding why the final problems in each chapter gave the rest of the class so much difficulty.

    It always seems to me that because they actually knew what they were doing, the ‘harder’ problems didn’t represent any difficulty. While the rest of us, having memorized using the formula in an ideal situation, were stumped.

  • http://ymarsakar.wordpress.com/ ymarsakar

    second and third derivatives, anti-derivatives, for trigonometric ratios, Kurt?

    I took an online class in calculus, and it was basically “figure it out for yourself” while they give you the solutions. It was nice in that there was a basic kind of problem, and after I figured out that one, they would change it, then I would have to figure out the new one. I realized that if I could do the first problem reliably without the solution, just from memory, I could understand and do the second variation of the problem easier and faster. So it kind of builds. You get a sense of what they are asking and how things change as the variations of problems changes. And I did not need 40 problems of one or 3 kinds. Just 3 examples of one kind of problem is enough, with the solutions of course.

    A lot of the problems I see is that the instructors tell you how to do things or they do it for you, or they ask you to do it for them, but the problem was always, everyone has individual hurdles to pass, and until they figure out what their problems are for themselves, they won’t get pass it. Regardless of what the instructor can say to you, he can’t read your mind, so he doesn’t know why you don’t get it.

    The problem with people memorizng a pattern, is if you change the pattern on them, they are stuck. They become confused. But if you learn by figuring out why things change and adapt to those changes, so any new changes, you at least won’t have hit a brick wall. It is not all that certain a person who recognizes what he should do on the hard problems, will get it right. After all, he can make a mistake. But at least he knows in a general sense, what he is supposed to do based upon what he has done before. So it helps, since advanced problems rely upon the basics, presumably. If a person didn’t master the basics, he might have a problem.

    Big time constraint too.

  • http://jackalope.blogspot.com Nancy Coppock

    Okay, poor bookworm is not a math genius, but folks y’all are missing the main idea (former remedial reading teacher) of the piece. What is happening is that things that should be rote learned — multiplication tables, spelling words –are being “fuzzied up” and the joy of learning, the “A-ha!” process is being rote taught. That’s the point of the piece and a good point it was!

  • Marvin

    Bookworm, the problems with public education run deeper than what you perceive (though it doesn’t mean that the flaws you perceive are not correct).
    Take the number patterns you mentioned. The whole question of “what is the next number in sequence …” can only be posed by somebody that doesn’t really understand math. There is an *infinite* amount of number sequences that start with 0,1,2,3 (or any other sub-sequence). Forcing the kid to provide an answer simply teaches him to look for an answer the teacher has in his tiny mind rather than to think.
    About every other thing public schools teach children are the same kind of misguided brainless crap that turns them into educated morons that are willing to beleive any kind of ridiculous ideas about anything (human induced global warming for example).
    What I personally do with my kids is to teach them that
    a. Teachers are mostly stupid but unfortunately have power to hurt you.
    b. Make sure you understand the issue teacher is talking about and evaluate it regardless of what the teacher says.
    c. Then figure out what techer wants you to answer and give him the answer he expects. Make the big powerful moron happy and enjoy that you know better.
    d. Read a lot but don’t beleive everything you read either.

    b. and d. are hard and require my constant help. However, it works. By now my kids are considered gifted and are absolutely loved by the teachers. We laugh at them in the privacy of our house.

  • http://ymarsakar.wordpress.com/ ymarsakar

    We all knew book didn’t like math. At least the regulars.

    Technically, a good teacher can make bad administrative policy, effective. While a bad teacher can make good administrative policy, bad.

    So it becomes a recommendation of, use Book’s teaching techniques, but also find the teachers that appreciate such efficiency.

    Learning how to read is very important, and that at least, gets better the more you practice it. But not on the same book, please.

    Some of the heavy literature stuff was hard to get excited about. After all, it is hard for a young person to relate to these things. Even a simple thing such as telling you the bio of the author and then relating how certain things in the poem/novel reflects the person of the author, would be more interesting. Discussing abstract ideas and what not, is pretty boring and stale. People could get it, but it is easy to forget or ignore just because it doesn’t feel as real as a real person.

    Julius Caesar (Shakespear), combined with the 2nd Punic Wars, analysis of the battle of Cannae, would be interesting.


    Why would a student care about Julius Caesar, play or no play? In his life, he has seen no assassinations, although he may have seen some serious political disagreements on tv. In some cases, the Senate has wanted to stab Bush for a long time. A good reason for the secret service.

  • Paul Merling

    I have read what you wrote about education. You sound like John Dewey to me. Beginning learning is difficult for most children. So what else is new. Your romantic approach is a detriment to the education of many children. Enough dreaming. Let’s get to work teaching the old fashioned way.

  • Marguerite

    I have a feeling that a President Clinton would soon find a way to ‘discourage’ home schooling. Interesting piece on yesterday’s American Thinker about a home schooled girl across the pond who has been locked up in a psych ward for public ‘school phobia’. Every single one of my friend’s home schooled grandchildren run rings around government schooled children – in scholastic and social skills – and it is very difficult to talk about due to the number of government teachers in my social groups. And I come from a family of teachers.

  • Al

    A certain amount of memorization is required when starting to learn something unknown or not experienced. Memorizing the ABCs, memorizing the positions of the keys on an piano. But after that, the higher technique of learning needs to be taught. Bravo, BW.

  • highlander

    I agree, Al. In some cases it works best to memorize something first and then learn the logic behind it afterwards. The multiplication table is a good example. Which to do first is a judgement call, and may not be the same for two different children. In any case, I think it’s important to do both.

    Excellent post, Book. It builds a strong case for those of us with the time, and the inclination, to do some volunteer tutoring for children in less advantaged situations. And we might learn something of value ourselves, too.

  • http://ymarsakar.wordpress.com/ ymarsakar

    But Al, you said the same position that my professor friend said. Which I will add what I should have said to him. Which is, if you use Book’s techniques, people will learn faster than rote memorization. It is memorization. If something is unknown, the best way to integrate it into the brain’s net of neurons is to connect it in some way to existing knowledge. While this is not effective for young children, given they don’t have too much memories to go on in the first place, it isquite effective for 2nd graders at least.

    I hated the multiplication table. I memorized it and then forgot about it, until I learned the logic, then if I forgot, I just backwards engineered it from base principles. And this was back in what, 2nd grade?

  • indga

    I’m in the public school system and about to leave it. This I do without regret. Before I entered the system, I used to think the kids were being held hostage. Having been in the system, I think much of what you say has merit if the child is willing to participate. It’s not that kids aren’t being taught how to think; they are. They reject having to think for themselves. Any hands on, structured effort to help them develop the thinking skills necessary for success, they don’t want to know about cuz it’s too much work. The kids want the outcomes of work, but they do not desire to participate in the process which yields those outcomes. In this, they are supported by the administration of the schools, from the building principal up to the superintendent, and their parents. For some principals, regular attendance merits a D–no, no work is required. You see, the principals and the upper administration are playing a numbers game in which it’s bad form to fail those who are unwilling to learn or outright refuse to learn. Some of the parents, too, don’t care how or why the kid is failing (refusal to work) as long as the kid passes so he can graduate.

    The other thing is that rote memorization should not be sneezed at. In order to think about a thing and make connections, a kid must have a database of information which he can access easily. That’s database is the human memory. It seems to me that kids in the public schools memorize nothing–apart from rap lyrics. Consequently, they have very little comprehension of basic texts, much less for more complicated ones for vocabulary is essential to comprehension. If the kid cannot access elementary denotations without a dictionary, then one cannot address connotations.

    If I had a dime for every method tried to help kids think and for every method rejected with a head down on the desk, I’d be rich.

  • Al

    indga, it’s a shame you’ve been abused by the public “education” system. My wife Jo spent six years in ours, and all the horror stories are true, but you know that. If the parents or “guardians” do not motivate the kids to learn, it’s more than an uphill battle. Most little kids really do want to learn. I mean prior to Kindergarden. That’s where you’ve got to get them. There also may be a dietary issue. Diets high in the essential fatty acids seem to aid in neuro-development. The marine Oriental societies have more than twice the levels of essential fatty acids as Americans.
    Math has a logic which can be recreated if necessary. I am slowly teaching myself to play the piano. I know which note on the staff refers to which key on the piano, but I have to constantly practice, ie. memorize, to train my proprioceptive memory where in space each one of my ten fingers are in relation to the keys so I can strike them reliably each time. My basset starts howling if I am especially off key. It gets interesting.

  • http://ymarsakar.wordpress.com/ ymarsakar

    The piano is a muscle memory thing, Al. Not abstracts. Since after all, soldiers can disassemble and reassemble their weapons in the dark, simply because of muscle memory. The act of doing, without thinking.

    It is the opposite with such things as abstract math. Thinking, in order to do. Or specifically, thinking to remember, and then to do based upon the memory.

    A basic question is, why do geniuses often times are able to remember things faster and more completely than those of average intelligence? I think it is due to how fast their brains work in connecting different pieces of data to what they are trying to remember, because they do not remember so much as they associate things into a pattern. Geometric or otherwise. They see this pattern in 3d or even higher dimensions for mathematical savants. To relate this to the common theme, why do children remember rap lyrics but not others, is it solely because of repetition? I don’t tend to think so, simply because a person can listen to rap, but they can totally tune out the lyrics. You have to actually go to extra lengths to get the lyrics, and to understand what they are saying. People go to extra lengths because for some reason, they are motivated into doing so. It matters to them, not on an abstract level, but on a level that they can see, because it is connected to other things in their life.

    But the point is, intelligence of this sort is simply a speed advantage. It is nothing that hard work cannot emulate, at least for the majority of results.

  • Al

    I must agree with you, ymarsakar. Doing without thinking applies to both field stripping and turning notes on a score into sound. Though there is room for creative interpretation in the production of the sound. And yes, an indicator of intelligence is the speed with which information can be processed. Another indicator if intelligence is the quantity of information available for processing. And maybe a third indication of intelligence is the ability to retain and process different types of information, and their subsets.