Isegoria

A persistent error is a sign that learning has occurred, but the student has inadvertently learned the “wrong” way really, really well and needs to unlearn it:

Researchers at the University of Verona (Milanese et al., 2008) conducted a study of thirty 13-yr olds learning how to perform the standing long jump in three sessions spread out over a three week period.

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One group received instruction using an experimental teaching method called “Method of Amplification of Error” (MAE group). More details on this in a moment, but the tl;dr version is that this method involves doing things wrong on purpose, not just doing things correctly.

Another group received the traditional instructional method of verbal instruction (direct instruction group).

And the third group received no instructions at all, and just practiced on their own (control group).

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The kids who received no instructions at all performed pretty much the same at both tests. They jumped 158.9cm on the first day of training and 160.6cm on the final day of training. A difference which isn’t statistically significant, and is pretty much what you’d expect.

On the other hand, the students who received instruction and feedback during training did improve over the course of three weeks. They started out at 159.4cm, and improved to 162.3cm by the final test – a gain of 2.9cm. And though an improvement of just over an inch may not sound like much, this would have been the difference between medaling and not medaling in the men’s long jump at the 2020 Tokyo Olympics.

And how did the amplification of error group do?

Well, the kids who were coached using the Method of Amplification of Error improved by an average of 20.4cm, going from 159.5cm on the first day of training to 179.9cm three weeks later. This is almost 7 times the improvement of the regular instruction group, and would have been the difference between Gold and Bronze at the same 2020 Olympics. In the same exact amount of training time!

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On the surface, the Method of Amplification of Error training was not hugely different. The only difference was that instead of being instructed to jump with the correct technique, they were told to exaggerate as much as possible the main error that the instructor identified.

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It seems pretty counterintuitive to practice doing something the exact wrong way, but the researchers explain that this actually deepens our understanding of what not to do and initiates an internal search for a better way to perform the skill.

In a recent study, Arizona State University professor Rob Gray trained casual baseball player to hit a baseball the right way or the wrong way:

One group — the “right way” group — practiced hitting the ball the correct way. Their instructions were to “hit a hard line drive into fair play.”

And during their training sessions, a coach would observe and give them feedback on their technique and mechanics. And provide suggestions on how to improve their performance.

The “wrong way” group on the other hand, received no technical instructions and no corrective feedback during their training sessions.

And their hitting instructions changed from one training session to the next.

One week they were asked to “hit the ball as far to the right as possible.” Another week they were asked to “hit the ball as far to the left as possible.” Then they were asked to “try to pop the ball up in the air.” And then to “try to drive the ball into the ground.”

They were also asked to “hit a hard line drive into fair play” in one of their practice sessions, just like the right way group. But in five of their six practice sessions, they were asked to practice hitting the ball all the wrong ways.

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Well, as you would expect, the right way group that got coaching and practiced hitting into fair play improved their hitting in several key areas.

Their batting average improved, they struck out less often, and they hit more doubles/triples/home runs than they did in their initial test too.

But the wrong way group, which spent 5/6th of their time practicing hitting balls into foul territory, and other undesirable hits also improved their batting average, strikeout percentage, and slugging percentage.

And they not only improved in these areas, but improved by a lot more than the right way group did!

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The value lies in learning how to achieve specific undesirable outcomes, on purpose, with some consistency. Because it seems that purposefully doing things extremely wrong provides us with a lot more information about how to do things correctly, than trying to do things correctly and accidentally getting it slightly wrong.

Early floundering can lead to better learning:

Generally, teaching looks something like:

1. Explain how to do something (lecture)
2. Show students what it looks like in action (demonstration)
3. Fix their off-target attempts, to help them minimize “failure,” and reward them for their successes (feedback)

This sequence tends to emphasize getting to the correct answer as expeditiously as possible.

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A pair of researchers (Kapur & Bielaczyc, 2011) conducted a study of “productive failure” to see if early floundering would lead to better learning than the traditional teaching approach (“direct instruction”).

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The direct instruction class began learning about average speed with a lecture.

The teacher explained the concepts, worked through some examples, encouraged questions, and had students solve practice problems.

Then they reviewed the problems and discussed the solutions.

For homework, they were assigned similar problems in their workbook.

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The productive failure class was split up into small groups, and each was tasked with solving two complex problems…

They were given these problems with no teacher support or guidance, but simply allowed two class periods to try to solve each problem (4 classes total).

There was also no homework, though they did receive extra problems to work on individually when the group problems were complete (2 class periods).

After 6 sessions of working on their own, the class spent their final class session sharing their solutions and strategies with the teacher and each other.

Only then did the teacher finally explain how to solve these problems the “correct” way, and help the students go through their previous work, fix their mistakes, and ensure they could arrive at the correct answer.

Ultimately, the productive failure group spent 7 class sessions working on calculating average speed, just like the direct instruction group. But they spent most of these classes floundering on their own, and doing many things wrong. It was only during the 7th and final class that they learned the correct way to approach these problems.

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As you can probably imagine, the direct instruction group did waaaay better than the productive failure group in the early stages of learning.

The direct instruction group averaged a score of 91.4% on their homework.

Meanwhile, the productive failure group performed miserably on their unguided attempts to solve the complex problems. Only 2 out of the 12 groups (16%) arrived at the correct solutions. And when they had to work on the problems individually, their average score of 11.5% was even worse.

But a very different picture emerges when you look at the groups’ performance on the post-test.

On the final test, the performance between the two groups flipped, and the productive failure group outscored the direct instruction group by a significant margin.

On the simple problems, the productive failure group earned an average score of 84.8% (vs. 75.3% for the direct instruction group).

And on the complex problem, the productive failure group earned an average score of 59.7% (vs. 42.4% for the direct instruction group).

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However, in much the way that spaced, random, and variable practice lead to worse performance in the short term, but better performance in the long term, it seems that the goal of productive failure is not to get the correct answer faster and more easily via shallower learning (“unproductive success”), but instead, to cultivate a deeper understanding of the fundamental principles and various ways of arriving at a solution even at the expense of short-term performance.

For more effective practice, try…longer…pauses:

Several researchers have looked at something known as the “inter-trial interval” or “post-KR delay” (KR stands for Knowledge of Results). This is the amount of time that elapses between one practice attempt and the next. For instance, if you’re practicing a tricky shift, you could just execute the shift over and over with no pauses between attempts. Or, you could try the shift, pause, and then try again. That pause between attempts is the inter-trial interval.

Thinking back, I’m not sure I ever made time for even the slightest pause between practice attempts when I was a kid. I totally piñata’d my way through every practice session. Heck, even in lessons I’d often cut my teachers off while they were still talking in a rush to play the passage again and get it right.

I always assumed that learning happened during the time my muscles were moving. The idea that some of the learning might take place in the time between practice attempts never occurred to me.

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A 2005 study (Bock et al.) in the journal Experimental Brain Research yields a few clues.

35 participants were split up into six groups, and given one practice session (and 25 practice attempts) to learn a tricky motor task.

The only difference between groups was the amount of time each was given between practice attempts. One group received a 1 second pause between attempts, while the others were given either 5, 10, 15, 20, or 40 seconds.

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Everyone improved with practice, but the participants who received only a 1-second pause between practice attempts consistently performed worse than the others, and weren’t as accurate in their efforts to hit the target.

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A 2007 study (Huang & Shadmehrin) in the Journal of Neurophysiology also reported on this phenomenon.

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Anyhow, the researchers in this study replicated the findings of the other study, observing that the longer delay of 14 seconds between practice attempts led to more rapid improvements than a shorter 4-second delay.

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Take your time between repetitions. Pause. And don’t just count to five or 7 or 11, but use that time to ponder or reflect on what just happened, and why it happened. Plan your next move. Give it a go.

People understand in the abstract that they can read a lot of books — that a book a week adds up to thousands over a lifetime — but they don’t seem to realize, Dwarkesh Patel suggests, what exactly it would mean to have read thousands of great books:

David Deutsch points out in The Fabric of Reality that contra conventional wisdom, it actually is possible for a single person to understand most things — not in the sense of memorizing the names of ant subspecies or the GDP of different Asian countries, but in the sense of appreciating the main explanatory theories in each field.

One consequence of living in The Great Stagnation is that there is relatively little turnover in these fundamental ideas. Quantum mechanics, that nascent branch of physics which elicits the sense of woo woo from popular culture, is about a hundred years old. So is the theory of computation. The neo-Darwinian synthesis is over 50 year old.

So you don’t have to be scouring through the newest papers on Arxiv in order to know the most important things. A dozen or so textbooks even from a few decades ago contain about 80% of legible scientific knowledge.

The creative mindset pairs a high need for certainty with a low need for competence:

You find a problem that you really, really want to solve. At the same time, you work on developing a tolerance for not knowing the solution — yet. Both dispositions are necessary to move the creative process forward.

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But this need for certainty, which is the engine that drives creativity, can easily propel us in the wrong direction. Say we have a high need for certainty and a high need for competence — for feeling like we know what we’re doing. Then, write Güss and his coauthors, we are likely “to engage in anything that could restore competence quickly, rather than in explorations of a new domain.” If we can’t deal with our temporary lack of competence, the need for certainty will drive us toward safety-seeking behaviors that make us feel competent again, right now in the moment — but that steer us away from creative solutions.

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“Even when he worked in a new domain, such as flying, da Vinci could rely on his vast knowledge and skills. He had successfully created numerous inventions, drawings, and paintings and could rely on his successful strategy to divide a big problem into tiny problems that could be mastered. He had not only epistemic competence (i.e., enormous knowledge and skills) but also heuristic competence (i.e., trust and confidence in his own ability to master new situations and problems successfully).”

In other words, a sense of confidence about our global competence (“In general, I’m pretty good at this, and I know how to move toward getting this done”) allows us to tolerate the temporary feelings produced by situational incompetence—permitting us to remain open to new possibilities even as they take their time crystallizing into satisfying solutions.

Reading as we know it is engaged in an epic battle it has all but lost, Doug Lemov argues:

No matter where you are, Device is there with you, stowed in your pocket, at your behest, chirping away pleasantly. Check in with a colleague or the kids? Play Candy Crush? Find a baseball score? All while in line at Target or sitting through the 10 a.m. strategy meeting? Of course, Master. It would be my pleasure.

Suddenly Device must always be with you. You check it 150 to 200 times a day, studies tell us. You switch media sources (for instance, from Web browser to email) 27 times an hour. Your average duration of sustained focus on any digital task is just over two minutes.

Clever Device! Once it was the servant; now it is the master.

Poor Dickens. Poor Toni Morrison. They cannot compete with that. So we read less and less. But more importantly, we read differently. This is the subject of Maryanne Wolf’s profound new book, Reader, Come Home.

On the digital screen we read fleetingly, flittingly. Our brains have what scientists call “novelty bias.” We are predisposed to attend to new information; from an evolutionary perspective, what’s new, bright, and flashing could contain survival information. It gets priority. Reading on screens sets up a cycle of expectation and gratification. We are repeatedly distracted by whatever pops up, rewarded for each distraction with a tiny surge of dopamine. This attraction to “the new” crowds out reflection, creative association, critical analysis, empathy—the keys to what Wolf calls the “deep reading process.” We read in a constant state of partial attention. And, Wolf points out, this is as much cause as effect. Human beings developed the capacity to read relatively recently, over the past 5,000 years or so. The brain has no reading center. Rather, when we learn to read, we call upon multiple areas of the brain, exhibiting a cognitive quality known as neuroplasticity.

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We made ourselves modern via a collective rewiring when writing and later print emerged and spread across vast strata of society not so long ago. Reading taught us to sustain and logically develop ideas, to enter the minds and perspectives of others through their words. As societies, we became less impulsive, violent, and irrational. Wolf quotes Nicolo Machiavelli reflecting on how he lost himself in a book, conducting an inner dialogue with the author and reading for four hours without interruption. When was the last time you did that?