September 17, 2010

"Drill, Baby, Drill"

Virginia Heffernan writes in the NYT Sunday Magazine:

The word “drill” has come to define bad teaching. The piercing violence that “drilling” evokes just seems not to belong in sensitive pedagogy. Good teachers don’t fire off quiz questions and catechize kids about facts. They don’t plop students at computers to drill themselves on spelling or arithmetic. Drilling seems unimaginative and antisocial. It might even be harmful.

“In educational circles, sometimes the phrase ‘drill and kill’ is used, meaning that by drilling the student, you will kill his or her motivation to learn,” explains Daniel Willingham, a University of Virginia professor of psychology who has written extensively on learning and memory. “Drilling often conjures up images of late-19th-century schoolhouses, with students singsonging state capitals in unison without much comprehension of what they have ‘learned.’” ...

Oh, those schoolhouses — with the hickory sticks and the dunce caps. “Harrisburg! Salt Lake City! Montpelier! Tralalalala!” That does sound kind of fun — I mean, authoritarian. And drilling hardly has a better reputation outside academia. On message boards, students complain bitterly about Kumon, the extracurricular Japanese system of worksheet drills that many also admit has made them superb at math. Only unsportsmanlike parents hellbent on raising valedictorians, it seems, require their kids to do such rote work. At the same time, parents dismiss cutesy, flashy apps and Web sites that drill students using elaborate animation (like PopMath for arithmetic, iFlipr for custom flashcards, Cram for custom practice tests) as superficial edutainment, on par with children’s TV. 

Willingham also approves of drilling as a way to measure what you’ve learned. “Testing yourself is really good,” he told me. “It actually leads to better learning than studying” — e.g., reading passages over and over, sometimes with a highlighter. He explained, “You can’t be proficient at some academic tasks without having certain knowledge be automatic — ‘automatic’ meaning that you don’t have to think about it, you just know what to do with it.” For knowledge that must be automatic, like multiplication tables, “you need something like drilling,” Willingham wrote. He also warned, “You’d hope to make it a little less boring for the student.”

Here’s something I’ve found that makes drilling not boring: colorful, happy apps. 

By the way, the family of the Mr. Kumon who founded Kumon in Osaka in the 1950s now owns $400 million dollars worth of Kumon stock. The funny thing about Kumon is, last I checked, it is resolutely low-tech: it was completely paper and pencil drilling. You fill in a huge workbook of problems, then you give it to the Asian lady who owns the franchise, she grades it by flipping through the pages at amazing speed, then she gives you either a higher level workbook or one of their endless supply of additional problem sets at the same level.

Computers can make this more efficient by grading tests automatically. Moreover, they can shuffle questions on the fly so if you are doing badly, the computer can lower the difficulty until you get the hang of it.

The big question is whether math drilling programs can do what a first-rate tutor can do: figure out why you are making a recurrent mistake and explain it to you in a way you'd understand. In theory, it doesn't sound impossible, but here we are, in 2010, and I've never heard of anybody in Silicon Valley getting as rich off math tutoring as Mr. Kumon did.


Tanstaafl said...

Khan Academy

Anonymous said...

All for free:

Steve Sailer said...

Yes, Khan Academy is wonderful because Mr. Khan is a terrific teacher. But the experience is like taking a lecture course at college in an auditorium of 400 from the most engaging lecturers on the faculty.

If Khan gets enough money from donors, it wouldn't be hard for him to fill out his courses with homework and tests.

The final stage of development, however, would be some sort of artificial intelligence system that would recognize patterns in mistakes on drilling and suggest semi-customized ways to fix characteristic errors, the way a good human tutor does.

KissTheGoat said...

A system that figures out what you're doing wrong does exist; Ken Tilton has one:

He did a presentation (now gone) on it (look for 'Tilton', here: where he explained that it models students' errors. I haven't used it, but it's free for a while if you want to play.

But it does seem strange that no-one thought of doing that before this lone semi-genius. In fact I'm trying to keep my eye open for some other area to do the same thing for. Suggestions welcome :)

Anonymous said...

Considering the 'Dunce's cap', that traditional English instrument of child abuse, it was actualy named after a real historical individual one Duns Scotus, a mediaeval theologian, who was mocked and reviled for his heretical views.
Similarly the traditional English word 'buggery' (meaning active homosexuality), whch is still the correct English and legal term for such acts, is derived from a mediaeval term for 'Bulgarian'. You see in the middle ages various gnostic 'heretical' religious sects in Bulgaria were more than suspected of 'buggery' as part of their belief systems.

nsam said...

Salman Khan is brilliant/intense/crazy and caters to a wide range of folks. There is a part of the site that has adaptive software, I believe. The fellow at is a 1-person operation that is commercial. There are social aspects of face-to-face tutoring that can't as yet be replicated online. Often its not about getting the right answer but struggling to deal with a tough problem in multiple (often deadend) ways. That gives better insight than getting the right answer using some formula. Ms. Lindquist is there as an online algebra tutor and this supposedly teaches understanding. Amazing online resources for the right side of the IQ distribution. Great time to be a teenager or for that matter an older learner.

carol said...

It's always the same old math bugaboo, isn't it? This is getting old. Drilling works. Talking about number theory and playing with cutouts do not.

The experts can bitch about drilling all they want, but the only way I got through college was by drilling with a self-paced Algebra II workbook I picked up at a JC in Texas. If students would review and practice before each semester they would have a lot less trouble. I'm no math genius but HS and lower level college math doesn't require that.

coldequation said...

A place like a Kumon center, or even going someplace quiet with a pencil and paper, has the advantage over computer drilling that there's no temptation to become distracted by the internets.

Dextrology said...

So this is why Asians overperform relative to their IQ. The Asians drill like crazy; the Whites try to come up with safe, student-appeasing teaching methods that encourage "out-of-the-box" and creative thinking. And then the NAMs don't really do anything as far as studies go.

Anonymous said...

When I first came to California I worked for a year as a driving teacher. One of the central elements of the curricula was parallel parking. Being a cerebral sort of fellow I developed elaborate explanations of the geometry and the velocity of the car backing into a space. I made diagrams of the positions of the wheels and the car at the various stages.

After a while it was clear that my students weren't learning. I asked an older (and wiser) driving teacher for advice. He said, "You think they know what the steering wheel does". His point was that most of the women (nearly all were women) had no idea that the front wheels went side to side and the rear wheels didn't.

I radically changed. No more theory, diagrams or explanations - just drill. I put up two poles in a parking lot and had them drive around them in a figure eight - backwards. It sounds crazy but any experienced driver can do it. Students after a bit of drill found parallel parking trivial.

Some students benefit from a theoretical explanation - sort of like Placido Domingo. But many, maybe most students are like Luciano Pavarotti - they can't read music so they need a pianist (repetiteur) to bang the notes out over and over.

If you don't think drill works listen to Pavarotti on YouTube. But I warn you criticizing Luciano invites more death threats than a cartoon of Mohammad.

Currently I'm writing some software to help voice students learn music. No theory just drill. I'm creating a robot repetituer.


790v, 400m (old SAT) said...

Oh how I wish that there had been a Kumon franchise in my town, and that my parents had sent me to it. I might actually have learnt math instead of floundering for years, mostly failing that subject.

Math teaching in the 70s and 80s, at least at the public schools I went to, was 'New Math'. Only as an adult, taking a community college course, was I finally able to understand such simple things as factoring, dividing fractions, use of exponents, etc.

Anonymous said...

I took my older daughter to Kumon in the 90s. She hated it, it was inconveniently located, and expensive (for a single mother.) Looking back, I think I could have gotten a lot more bang for my buck by buying her a couple of third-grade consumable textbooks at a teacher's supply store and PAYING HER a small amount of money for each page she filled in perfectly.

I was a total failure as a child at piano lessons, and to a large extent it was because I never actually learned to read music. I knew all the rules, and could slowly figure out what each note meant, but I never got to the "automatic recognition" stage. I've heard that there are now computer games designed to teach beginning musical notation, and I wish those had been around in the olden days.

I will say that both of my children were successful at piano lessons, partly because they had some degree of natural ability, but partly because by the 90s the loathsome John Thompson series of music books had been replaced by various series of books with a much more gradual learning curve.

Truth(er) said...

Has anyone tried this software?

Looks awesome, but I do not know if it has been updated at all.

Dextrology said...

To 790v, 400m (old SAT)

Have you ever considered the possibility that you may have a learning disorder? A gap that big between verbal and math scores usually indicates something serious...
I doubt poor teaching methods alone would cause a 790v scorer to get a 400m.

Anonymous said...

This will never happen, because you will get an EEOC lawsuit the moment you start charging money or getting any traction. Department of Ed won't like it and you will be assaulted by every college prof and teacher in the country.

Anonymous said...

There is always the "Quest to Learn" method of playing lots of video games in class. America, your future is bright!


adfasdfasdf said...

Shouldn't it be

Driru baby Driru?

Anonymous said...

"Drilling works. Talking about number theory and playing with cutouts do not."

Way too simplistic of a model there.

Drilling works for dumber kids. The kids who will never need math in their jobs.

Those with a natural aptitude (the kind that are heavily represented in the SWPL focus groups which come up with theories) prefer to understand the theory first. There's no one-size-fits-all solution, which frustrates liberals to no end.

Don't crush the spirit of eager learners with endless drills, and don't try to force stupid kids to learn a bunch of abstract theory.

beowulf said...

This group has the entire California K-12 curriculum (and for some reason, pre-med and medical school too) online as electronic flashcards.

Its free to use unless you want to sign up for school credit (accredited but alas, not for med school). :o)

none of the above said...


Yep, that's the "culture" part of the equation. Similarly, Jewish and Yankee culture both put a premium on learning, and there is a corresponding advantage. And similarly, blacks and hispanics tend to have the opposite sort of culture, with opposite effects.

Especially for second generation immigrant kids, there's a huge problem there. To a first approximation, everyone who was born here went to school, even if they didn't get much out of it. Even someone who never had any reason to consider college probably learned to read and to do their multiplication tables, and has some experience studying. Now, when their young kid comes to them with problems on their homework, they can at least give them some kind of help. By contrast, if your parents are illiterate campesinos from El Salvador, they can't give their kid any help, not even as a 2nd or 3rd grader. Not even "what does this word mean, Daddy?"

none of the above said...

Anonymous (drilling works for dumb kids):

I don't know any way to get multiplication tables but drilling. Similarly, when I had calc years ago, you could understand the concepts without drilling, but if you wanted to get decent grades on the tests, you damned well had to memorize a big table of differentials/integrals, rather than trying to work out d/dx sin(x) on the fly as needed. Drill baby drill.

And in general, even when you don't have big tables of facts to memorize, you have to work a lot of problems to get the algorithm for how to work them nailed solidly into your mind. Those become tools you can use to do more intersting things (solve real-world problems, work out proofs, etc.) later.

adsfasdfasdf said...

"The Japanese have an expression: The nail that sticks out gets hammered down."

So, is this like "the screw that sticks out gets drilled in"?

Lucille said...


It's perfectly possible to have a dedicated computer connected only to a LAN, or not set up for networking at all. It's not a given that a computer will have internet access.

As for Kumon, though? It's fine for busy parents, but parents who have the time to spend with their children would do better just to have them worth through a practice-heavy text like Saxon math at home. Far less money.

CuChulainn said...

Frankly, much of what needs to be learned through grade school, even well into college for many majors can be obtained by rote memorization and drilling. American schools were better before they started trying to come up with creative and expensive ways to try to get around expecting people to put in the "elbow grease".

PRCalDude said...

Essentially, doing your math homework is a form of drilling. I don't see what's wrong with it. If you want to develop and intuition about the theorems you're learning, you need to practice using them. It's amazingly uncomplicated, when you think about it.

In fact, drilling works for everything else also. Perfect practice makes perfect. It's not reparations, though.

Anonymous said...

John Saxon, a retired Air Force Officer, developed a very old fashioned method of teaching math by drill methods. It was popular only with many teachers who found it worked. William F. Buckley interviewed him to leak the word about "realism" in education.

meep said...

My kids do Kumon. The couple who own our local franchise are East Asian, to be sure (the Hsus). But they hire their best students (mostly white in this area) to be the junior tutors.

And they do go over your worksheets with you. If you make a mistake, you're made to correct, but they also go over why you're making mistakes. My kids doing this are 5 & 7. The 5 yr-old is doing addition (up to 15 + 5), the 7 yr-old is doing 2x1 and 3x1 multiplication.

It's a good system. You can't go onto the next level until you master the previous.

meep said...

speaking as a "smart kid" - drilling worked for me, too. i had to do it in calculus, actually. I'm a whiz at taking derivatives due to the amount of practice I had.

Of course, I was doing it for fun....

David said...

PRCalDude has a good phrase: "Develop an intuition".

Instead of calling it "drilling," call it "INTUITION DEVELOPMENT."

A spoonful of sugar helps the medicine go down.

Cara said...

Teacher supply stores are filled with flash cards and books filled with worksheets that promote drills. I don't think that it is horrible. Repetition is part of the learning process. Students need to be exposed to a variety of learning strategies.