Copyright © 2015 jsd

Practice Does Not Make Perfect
John Denker

1  Practice Makes Permanent

Practice absolutely does not make perfect. If you are practicing the wrong things, practice is worse than nothing. It would be more nearly correct to say:

Practice makes permanent.

This should be obvious. We’ve all seen it a thousand times.

This has direct application to teaching, for instance in connection with so-called "guided inquiry". There needs to be a treeeemendous amount of guidance, especially at first. Otherwise students will become deeply entrenched in a morass of misconceptions, and there will be hell to pay trying to dig out from there.

The only thing that has ever made sense to me is the spiral approach. That is: introduce a bunch of new ideas, touching on each one lightly, and then spiral back, reinforcing each idea and connecting it to the other ideas. The spiral continues, around and around, introducing new ideas, reinforcing old ideas, and making ever-more connections. The connections are super-important, but they were not possible the first time around the spiral, because you cannot connect to an idea that has not been introduced yet.

If you think about it in these terms, you see that you cannot master an idea the first time you see it ... and you should not even try. Touch on it lightly, move on, and come back to it later.

There are some well-known educators who get this wrong. They won’t let students learn things out of order. They won’t let students "move on" to thing B until they ave provably mastered thing A ... according to some sequence that the teacher has decided is correct.

What’s worse is how the ideas of "practice", "automaticity", "mastery", and (gasp, choke) "beyond mastery" are used in the schoolhouse. Even if the last section of reference 1 is ambiguous, most of the people who use those terms are quite uncompromising. They demand immediate mastery (and beyond) in such a way that it becomes the opposite of the spiral approach.

  1. As a low-level example, being able to recite the alphabet or say the names of individual letters is absolutely not a prerequisite for learning to read. If anybody has questions about this, we can discuss it in more detail.
  2. At a slightly higher level: Knowing the times tables (aka short multiplication facts) is absolutely not a prerequisite for learning the long multiplication algorithm. You can do long multiplication just fine, even if you have to refer to a multiplication table and/or count on your fingers for each of the short multiplication steps. Forsooth, carrying out long multiplication gives you an opportunity and perhaps a reason to practice short multiplication skills ... whereupon the lower-level skill is seen as a consequence, not as a prerequisite.
  3. At an even higher level, neither speed nor accuracy with grade-school arithmetic is a prerequisite (or any kind of necessity) for doing higher math.

Willingham writes specifically:

>> The student who struggles to remember the rules of punctuation and >> usage (or must stop to look them up in a reference book) cannot >> devote sufficient working memory resources to building a compelling >> argument in his or her writing.

I once heard Tom Clancy address this point. Somebody asked him what sort of English classes one should take in order to become a novelist. He said

"None of that matters. The main thing a writer needs is a good story to tell. All that other stuff – spelling and grammar et cetera – is not critical. You can hire an English major for minimum wage to blue-pencil your draft if necessary."

He said his previous career as an insurance adjuster was good preparation, because he got to see lots of different people, strong ones and weak ones, and got to see how they behaved in various weird situations. He got to hear how they talked.

>> The student who does not have simple math facts at his or her >> disposal will struggle with higher math.

The part that is true is irrelevant to the topic of the paper, and the part that is relevant is untrue. Mastery and automaticity and endless practice with "simple math facts" is absolutely not required for higher math. Probably "most" professional mathematicians are "good with numbers" but some of them would have trouble balancing a checkbook without a calculator. Either way, the point is, it’s irrelevant to the job description. Mathematicians are allowed to use calculators. Why would anybody bother to do long division if they could use a calculator instead?


I have no idea what result Willingham and others are trying to achieve, but the actual result is that students are drilled, drilled, drilled until tears run down their cheeks, learning stuff that didn’t need to be learned, and all the while learning to hate school.

3) It is astonishing to see what Willingham does *not* discuss in any detail: Independent and critical reasoning, judgment, originality, creativity, integrity, professionalism, et cetera.

Automaticity is in many ways the opposite and the enemy of these things.

4) Automaticity is the characteristic of automatons, i.e. robots. Automaticity is important if you believe the purpose of the educational system is to produce a bunch of meat robots, i.e. to emphasize ritual, obedience, and conformity. Plenty of so-called teachers are in fact martinets who believe precisely that. I vehemently disagree.

Drilling, drilling, drilling produces automaticity. Another word for this is rote learning. Obviously rote learning counts as learning ... and for *some* purposes it is useful, occasionally life-critical ... but for most other purposes it is the least- valuable form of learning.

Again, it almost doesn’t matter what Willingham says in the body of the article; martinets will take the title and abstract and use it as a license to drill, drill, drill until the students can’t see straight.

5) Willingham talks about "Becoming an Expert". However, I insist that real expertise is nearly the opposite of automaticity. If I wanted automaticity, I would entrust the task to a robot, not to an expert. Automaticity allows you to shoot from the hip ... whereas true expertise often consists of knowing when /not/ to shoot from the hip. Anybody who had any real expertise would know that.

For example: Suppose I take a stack of documents to the patent lawyer. Do I expect automaticity? Do I expect him to write out a patent application "on the spot"? Am I going to hover over him until he does? You’ve got to be kidding. More likely he’s going to think about it for a week and then get back to me with a long list of questions. Does that make him unprofessional? I don’t think so. I’m not going to give automatic answers to his questions; I’m going to think about it for a week and then get back to him. Does that mean I am not an expert in the field? I don’t think so.

If you act automatically, any bad guy who knows how you were trained can manipulate you into making spectacularly bad decisions. There are in fact bad guys who specialize in this. Daniel Kahneman wrote a nice book discussing many of the bad things that result from over-reliance on automaticity. I heartily recommend the book. It’s well written ... but not easy to read.


Here’s another example, namely US Airways flight 1549, the one that ended up in the Hudson River. This is a case where we can sharply compare automaticity versus expertise and professionalism.

There actually were some automatons in the cockpit, notably the autopilot, the ground-proximity warning system, and the alpha-protect system. In contrast, there were also a couple of professionals in the cockpit. Take a guess: Who saved the day? The automatons, or the professionals????

a) The autopilot was not turned on at the time of the bird strike. The First Officer was hand-flying the plane. The pilots could have turned on the autopilot, but they didn’t bother, and it would not have made much difference either way. It would’ve taken about the same amount of effort to tell the autopilot what do as to just do it by hand. If they had switched it on, they would have had to switch it off about a minute later.

b) The GPWS was turned on by default, as usual. It got left on. All it did was generate unhelpful nuisance warnings. In the aftermath, the NTSB recommended adding to the emergency checklist an item about turning off the GPWS. That’s serious business. You don’t lightly add items to an emergency checklist.

c) The alpha-protect system was on and could not be turned off. The A320 is a fly-by-wire aircraft, and the computer gets the final say. It made things worse: In the last seconds of flight, the pilot commanded the plane to raise the nose another degree or so and the airplane did not respond, because the alpha-protect system would not allow it.

In summary, I score the automatons 0-2-1: No wins, two losses, and one tie.

Now what about the pilots? Do you think they were trained-trained-trained to achieve "automaticity"? If so, you really don’t understand the job.

Sure, they were trained to know the emergency checklists by rote ... but they were also trained to understand the same issues at a much deeper level. The two types of learning are not mutually exclusive. All of the rote stuff the First Officer knew was unnecessary in this case, because he had the Quick Reference Handbook to follow. What’s more, virtually all of the QRH was irrelevant! The engine-restart procedures assumed the engine quit at altitude, allowing plenty of time for a restart. Step 3 on the checklist involved waiting for 30 seconds. Think about that. The total time from bird strike to touchdown was one minute and 15 seconds. The First Officer skipped the 30- second wait step. An automaton would not have. On the other hand, he never made it past step 4, because both engines were completely ruined. (He had no way of knowing they were ruined, so it made sense to attempt the restart.)

They crew didn’t even make it as far as step 0 of the ditching checklist ... and wouldn’t have been able to complete the checklist anyway. And no automaton could have done better. An automaton can only do what it is programmed to do, and nobody had ever contemplated making a ditching decision on such short notice.

So this is why you need professionals. They went off-script. Waaaay off-script. I’ll concede the pilots exhibited "some" elements of more-or-less "automatic" behavior. For example, the autopilot could have kept the aircraft right-side-up, automatically. The pilot was able to do the same thing, subconsciously, "automatically" if you will ... but that’s not the interesting part of the story. The interesting part is all the non-automatic stuff he was doing at the same time.

Sure, those guys were experts. They were well trained. However, the objective and result of the training was not automaticity. Not even close.

I’ve got a million stories like this. Ask me about the Thévenin equivalent story sometime.


My suggestions:

*) Let up on the rote drilling, drilling, drilling. There are a *few* situations where rote is the right approach, but presently we are overinvested in rote by many orders of magnitude.

Let up on the automaticity, mastery, beyond-master, conformity, subservience, and Kadavergehorsamkeit.

*) Instead cultivate independent and critical reasoning, judgment, originality, creativity, professionalism, integrity, etc.

*) Rely on the spiral approach.

*) Rely on personal responsibility. I tell my students very explicitly: I cannot teach you more than a tiny percentage of what you need to know. My job is to get you started in the right direction, to motivate you to set high standards for yourself, to help you learn how to learn, and get you to a point where you can safely teach yourself the rest.

Many of them achieve mastery, but they do it on their own, and I’m usually not around to see it. Sometimes long afterwards I get to see it or hear about it, which gives me a big smile.

If practice were the sole determinant, or even the main determinant, we wouldn’t need teachers or coaches.

On 07/23/2015 04:03 PM, ’Michael Gresko’ via Chemistry Education Discussion Group wrote:

> Singing, playing musical instruments, acting, sports of any kind and > science or math have the same requirements for competance: practice.

A fair number of people believe that. Some of them really, really believe that. In particular, there are probably about a million high-school students who believe that they don’t need to go to chemistry class, or any kind of class. All they need to do is spend more time shooting hoops. If they practice Practice PRACTICE more than everybody else, they will automatically become the next Kobe Bryant, and get paid 25 million dollars a year. Or so they’ve been told.

Imagine their surprise when they find out there are only about 14 thousand pro-sports job openings per year total, and only a few hundred in the NBA ... so more than 98those million kids will be left on the outside looking in. And the lucky ones who "make it" discover that the median salary for sports players is /less/ than for high school teachers. http://www.bls.gov/ooh/entertainment-and-sports/athletes-and-sports-competitors.htm http://www.bls.gov/ooh/education-training-and-library/high-school-teachers.htm

I’ve seen some bad schools and some good schools, including some that are quite literally better than most people can imagine. At the bad schools, the motto is speed and accuracy, speed and accuracy, time on task, practice Practice PRACTICE. At the good schools the motto is pretty much the opposite: "Let me show you a clever trick that will let you solve the problem in one tenth the time."


2  Identifying Fallacies

I’ve always had a morbid fascination with fallacious arguments. It’s amazing to see the sort of arguments people use to "prove" things that cannot possibly be true.

For example: Just because something is proverbially true does not make it actually true.

3  References

Daniel T. Willingham,
“Practice Makes Perfect–but Only If You Practice Beyond the Point of Perfection”

Copyright © 2015 jsd