A math-schooled mind is a chloroformed mind

Thursday, January 24th, 2019

For decades since Benezet’s time, educators have debated about the best ways to teach mathematics in schools:

There was the new math, the new new math, and so on. Nothing has worked. There are lots of reasons for this, one of which is that the people who teach in elementary schools are not mathematicians. Most of them are math phobic, just like most people in the larger culture. They, after all, are themselves products of the school system, and one thing the school system does well is to generate a lasting fear and loathing of mathematics in most people who pass through it. No matter what textbooks or worksheets or lesson plans the higher-ups devise for them, the teachers teach math by rote, in the only way they can, and they just pray that no smart-alec student asks them a question such as “Why do we do it that way?” or “What good is this?” The students, of course, pick up on their teachers’ fear, and they learn not to ask or even to think about such questions. They learn to be dumb. They learn, as Benezet would have put it, that a math-schooled mind is a chloroformed mind.

In an article published in 2005, Patricia Clark Kenschaft, a professor of mathematics at Montclair State University, described her experiences of going into elementary schools and talking with teachers about math. In one visit to a K-6 elementary school in New Jersey she discovered that not a single teacher, out of the fifty that she met with, knew how to find the area of a rectangle.[2] They taught multiplication, but none of them knew that multiplication is used to find the area of a rectangle. Their most common guess was that you add the length and the width to get the area. Their excuse for not knowing was that they did not need to teach about areas of rectangles; that came later in the curriculum. But the fact that they couldn’t figure out that multiplication is used to find the area was evidence to Kenschaft that they didn’t really know what multiplication is or what it is for. She also found that although the teachers knew and taught the algorithm for multiplying one two-digit number by another, none of them could explain why that algorithm works.

The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, “It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal ‘home schooling’ of children.”

It must be the supplementary informal home schooling…

We should drop arithmetic

Wednesday, January 23rd, 2019

Peter Gray makes the case for teaching less math in school:

In 1929, the superintendent of schools in Ithaca, New York, sent out a challenge to his colleagues in other cities. “What,” he asked, “can we drop from the elementary school curriculum?” He complained that over the years new subjects were continuously being added and nothing was being subtracted, with the result that the school day was packed with too many subjects and there was little time to reflect seriously on anything.


One of the recipients of this challenge was L. P. Benezet, superintendent of schools in Manchester, New Hampshire, who responded with this outrageous proposal: We should drop arithmetic! Benezet went on to argue that the time spent on arithmetic in the early grades was wasted effort, or worse. In fact, he wrote: “For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child’s reasoning facilities.” All that drill, he claimed, had divorced the whole realm of numbers and arithmetic, in the children’s minds, from common sense, with the result that they could do the calculations as taught to them, but didn’t understand what they were doing and couldn’t apply the calculations to real life problems. He believed that if arithmetic were not taught until later on — preferably not until seventh grade — the kids would learn it with far less effort and greater understanding.


In order to evaluate the experiment, Benezet arranged for a graduate student from Boston University to come up and test the Manchester children at various times in the sixth grade. The results were remarkable. At the beginning of their sixth grade year, the children in the experimental classes, who had not been taught any arithmetic, performed much better than those in the traditional classes on story problems that could be solved by common sense and a general understanding of numbers and measurement. Of course, at the beginning of sixth grade, those in the experimental classes performed worse on the standard school arithmetic tests, where the problems were set up in the usual school manner and could be solved simply by applying the rote-learned algorithms. But by the end of sixth grade those in the experimental classes had completely caught up on this and were still way ahead of the others on story problems.

Language in this exchange does not reflect Carolina’s values

Monday, January 21st, 2019

The same nonprofit that is suing Harvard University for racial discrimination — against Asians and Whites — is now suing the University of North Carolina:

In their filing, the plaintiffs said their analysis of UNC’s admissions data showed race is a “determinative” factor for many underrepresented minorities, particularly African-American and Hispanic applicants from outside the state.

In a 2003 ruling, the Supreme Court said universities can use race as a “plus” factor in admissions, but must evaluate each applicant individually and not consider race as the defining feature of the application.

The plaintiffs also say the school has violated Supreme Court precedent by failing to seriously attempt race-neutral alternatives to achieving diversity.

Lawyers for UNC said in Friday’s filing that race is not a dominant factor in admissions. UNC said it uses a holistic approach to admissions, with application readers scoring applicants in five categories: academic program, academic performance, extracurricular activities, essays and personal qualities, like “curiosity, integrity, and history of overcoming obstacles.”

The school said race has no numerical weight at any point in the review.


For applicants to UNC-Chapel Hill in 2012, the average SAT score for admitted Asian or Asian-American students was 1431, compared with 1360 for white applicants and 1229 for African Americans, according to the plaintiffs. They said that differential, as well as a similar gap in grade-point averages, shows the school gives an unfair tip to applicants of certain races or ethnicities, despite weaker academic credentials.

In Friday’s filing, the plaintiffs also said UNC admissions readers frequently highlight the applicant’s race, citing one reader’s comment that even with an ACT score of 26, they should “give these brown babies a shot at these merit $$.” Another reader wrote, “Stellar academics for a Native Amer/African Amer kid,” the plaintiffs said.

Steve Farmer, the university’s vice provost for enrollment and undergraduate admissions, said in response: “Language in this exchange does not reflect Carolina’s values or our admissions process.”

It’s proved itself over the past 113 years

Friday, December 28th, 2018

Because Taleb has a much higher IQ than Steve Sailer has, the only way Sailer can win an argument with him is by being right:

It’s almost as if the IQ glass is somehow both half empty and half full at the same time…

This doesn’t mean that IQ is a perfect measure above criticism, just that in an imperfect world, it’s proved itself over the past 113 years as one of the social sciences’ enduring accomplishments.

Manufacturing up-from-hardship tales to sell to the Ivies

Wednesday, December 26th, 2018

The T.M. Landry College Preparatory School seems like a predictable outcome of our current system:

Bryson Sassau’s application would inspire any college admissions officer.

A founder of T.M. Landry College Preparatory School described him as a “bright, energetic, compassionate and genuinely well-rounded” student whose alcoholic father had beaten him and his mother and had denied them money for food and shelter. His transcript “speaks for itself,” the founder, Tracey Landry, wrote, but Mr. Sassau should also be lauded for founding a community service program, the Dry House, to help the children of abusive and alcoholic parents. He took four years of honors English, the application said, was a baseball M.V.P. and earned high honors in the “Mathematics Olympiad.”

The narrative earned Mr. Sassau acceptance to St. John’s University in New York. There was one problem: None of it was true.

“I was just a small piece in a whole fathom of lies,” Mr. Sassau said.

T.M. Landry has become a viral Cinderella story, a small school run by Michael Landry, a teacher and former salesman, and his wife, Ms. Landry, a nurse, whose predominantly black, working-class students have escaped the rural South for the nation’s most elite colleges. A video of a 16-year-old student opening his Harvard acceptance letter last year has been viewed more than eight million times. Other Landry students went on to Yale, Brown, Princeton, Stanford, Columbia, Dartmouth, Cornell and Wesleyan.

Landry success stories have been splashed in the past two years on the “Today” show, “Ellen” and the “CBS This Morning.” Education professionals extol T.M. Landry and its 100 or so kindergarten-through-12th-grade students as an example for other Louisiana schools. Wealthy supporters have pushed the Landrys, who have little educational training, to expand to other cities. Small donors, heartened by the web videos, send in a steady stream of cash.

In reality, the school falsified transcripts, made up student accomplishments and mined the worst stereotypes of black America to manufacture up-from-hardship tales that it sold to Ivy League schools hungry for diversity.

Draw to remember

Monday, December 24th, 2018

A picture is worth a thousand words — when it comes to taking notes:

Fernandes and her colleagues first established what they call the “drawing effect” — getting people to draw quick pictures of words in a list (such as “truck” or “pear”) led to much better recall of those words than writing them out multiple times. Creating just a four-second drawing was also superior to imagining the items or viewing pictures of the words.

This was proof of principle type work. The researchers next looked at whether drawing aids memory of more complex terms and concepts. They found that study participants who had a minute to draw an image representing “isotope” or “spore”, for example, were more likely to remember the meaning than people who were asked to copy out the definitions instead. “As with single words, we reasoned that drawing facilitates retention, at least in part, because it requires elaboration on the meaning of the term and translating the definition to a new form (a picture),” the researchers write.

In fact, there are various components to the process of drawing a picture of a word or concept, each of which seem to cumulatively aid memory. Getting people to trace over an existing drawing (so getting them to make relevant arm and hand movements, but not allowing personal elaboration), or to create a drawing which they were then not allowed to see (so allowing the physical movements and personal elaboration, but depriving them of the visual memory of the end result) both improved memory — but not as much as when all of these stages were allowed. “Memory scaled up as components were added to the encoding task,” the researchers note.

Fernandes and her colleagues went on to find that although older adults performed worse than younger adults at remembering words they had learned by writing, there was no difference between the two age groups in their ability to remember words they had drawn. Encouraged by these results, the team then asked 13 people diagnosed with dementia and living in a long-term care facility to either draw or write 60 words that were read aloud by an experimenter. The results showed a “massive” memory benefit for words that had been drawn rather than written. If it can be shown that drawing also helps with other sorts of memory — for where things are kept, perhaps — this strategy could be practically useful for people with dementia.

In some cases, the patients’ drawings looked just like scribbles. But how good — or bad — the drawings were didn’t seem to matter. In fact, in most of the experiments, the researchers assessed their participants’ ability to create vivid images and also their experience at drawing, and neither was correlated with memory performance. Even people who struggle to create a stick figure should, then, get memory benefits from drawing.

(Hat tip to Hans G. Schantz.)

Excellence is a compound effect of mundane actions

Friday, December 21st, 2018

Sociologist Daniel F. Chambliss wrote an ethnographic report on stratification and Olympic swimmers, which examined the mundanity of excellence:

Excellence here is defined as consistent superiority of performance.

1) Quality > Quantity: Excellence is a qualitative phenomenon. Doing more does not mean doing better. It is the quality of the work you do, not the quantity of the work you do, that makes the difference.

2) Talent is a useless concept. Varying conceptions of natural ability mystify excellence, treating it as the inherent possession of a few; they mask the concrete actions that create outstanding performance.

3) Excellence is a compound effect of mundane actions. Excellence is accomplished through the doing of actions, ordinary in themselves, performed consistently and carefully, habitualized, compounded together, added up over time.

When my friend said that they weren’t exciting, my best answer could only be, simply put: That’s the point.

Turning psychosocial discourse back toward the syncretistic, multicultural Jung

Sunday, December 16th, 2018

There are astounding parallels between Jordan Peterson’s work and Camille Paglia’s own, she says:

In its anti-ideological, trans-historical view of sex and nature, my first book, Sexual Personae (1990), can be viewed as a companion to Peterson’s first book, Maps of Meaning: The Architecture of Belief (1999). Peterson and I took different routes up the mountain — he via clinical psychology and I via literature and art — but we arrived at exactly the same place. Amazingly, over our decades of copious research, we were drawn to the same book by the same thinker — The Origins and History of Consciousness (1949), by the Jungian analyst Erich Neumann. (My 2005 lecture on Neumann at New York University is reprinted in Provocations.) Peterson’s immense international popularity demonstrates the hunger for meaning among young people today. Defrauded of a genuine humanistic education, they are recognizing the spiritual impoverishment of their crudely politicized culture, choked with jargon, propaganda, and lies.

I met Peterson and his wife Tammy a year ago when they flew to Philadelphia with a Toronto camera crew for our private dialogue at the University of the Arts. (The YouTube video has had to date over a million and a half views.) Peterson was incontrovertibly one of the most brilliant minds I have ever encountered, starting with the British philosopher Stuart Hampshire, whom I heard speak impromptu for a dazzling hour after a lecture in college. In turning psychosocial discourse back toward the syncretistic, multicultural Jung, Peterson is recovering and restoring a peak period in North American thought, when Canada was renowned for pioneering, speculative thinkers like the media analyst Marshall McLuhan and the myth critic Northrop Frye. I have yet to see a single profile of Peterson, even from sympathetic journalists, that accurately portrays the vast scope, tenor, and importance of his work.

Out with the false idols and in with the true!

Saturday, December 15th, 2018

Secular humanism has been a disastrous failure, Camille Paglia argues:

As I repeatedly argue in Provocations, comparative religion is the true multiculturalism and should be installed as the core curriculum in every undergraduate program. From my perspective as an atheist as well as a career college teacher, secular humanism has been a disastrous failure. Too many young people raised in affluent liberal homes are arriving at elite colleges and universities with skittish, unformed personalities and shockingly narrow views of human existence, confined to inflammatory and divisive identity politics.

Interest in Hinduism and Buddhism was everywhere in the 1960s counterculture, but it gradually dissipated partly because those most drawn to ‘cosmic consciousness’ either disabled themselves by excess drug use or shunned the academic ladder of graduate school. I contend that every educated person should be conversant with the sacred texts, rituals, and symbol systems of the great world religions — Hinduism, Buddhism, Judeo-Christianity, and Islam — and that true global understanding is impossible without such knowledge.

Not least, the juxtaposition of historically evolving spiritual codes tutors the young in ethical reasoning and the creation of meaning. Right now, the campus religion remains nihilist, meaning-destroying post-structuralism, whose pilfering god, the one-note Foucault, had near-zero scholarly knowledge of anything before or beyond the European Enlightenment. (His sparse writing on classical antiquity is risible.) Out with the false idols and in with the true!

The Harvard grads are completely self-assured in their wrongness

Sunday, December 9th, 2018

Harvard Medical School dean George Daley has come out in favor of editing genes, and Steve Sailer notes that no child will be left behind without the Harvard grad glibness & self-confidence gene, as he shares this excerpt from A Private Universe:

Definitely watch the video.

(I’ll wait.)

Sailer’s point:

Both sets of people come up with the same wrong answer — because the earth’s orbit isn’t perfectly circular and so we are further from the sun in winter — but the townies are obviously ashamed that that’s the best answer they can come up with, while the Harvard grads are completely self-assured in their wrongness.

I’m sure there were some Harvard grads who gave the right answer and ended up on the cutting room floor, but they will probably end up working for the Harvard grads who were technically wrong but winningly self-confident.

The video actually has some interesting comments on Y

New York Times picks up signal in a world full of noise

Monday, November 26th, 2018

I don’t follow Shane Parrish’s Farnam Street closely, but I’m familiar enough to be pleasantly surprised that it got coverage in the New York Times:

Shane Parrish was a cybersecurity expert at Canada’s top intelligence agency and an occasional blogger when he noticed something curious about his modest readership six years ago: 80 percent of his followers worked on Wall Street.

The blog was meant to be a method of self-improvement, helping Mr. Parrish deal with a job whose pressures had increased with the growing threat of global hacking. But his lonely riffs — on how learning deeply, thinking widely and reading books strategically could improve decision-making skills — had found an eager audience among hedge fund titans and mutual fund executives, many of whom were still licking their wounds after the financial crisis.

“People just found us,” Mr. Parrish said. “We became a thing on Wall Street.”

His website, Farnam Street, urges visitors to “Upgrade Yourself.” In saying as much, Mr. Parrish is promoting strategies of rigorous self-betterment as opposed to classic self-help fare — which appeals to his overachieving audience in elite finance, Silicon Valley and professional sports. His many maxims cite Ralph Waldo Emerson, Bertrand Russell and even Frank Zappa. (“A mind is like a parachute. It doesn’t work if it is not open.”)


Mr. Parrish’s site has drawn the attention of some of the biggest names in finance. Dan Loeb, one of the more prominent hedge fund executives on Wall Street, is a big fan. And Ray Dalio of Bridgewater, the world’s largest hedge fund, recently did a podcast with him.


Mr. Parrish joined the Communications Security Establishment, a division of Canada’s Defence Department, straight out of college. His first day was Aug. 28, 2001, and he was soon promoted in the tumult that followed the Sept. 11 attacks. Suddenly, he was managing a large staff at the age of 24.

Wanting to improve his decision-making skills, Mr. Parrish found inspiration in Charlie Munger — Warren Buffett’s longtime investment partner. Mr. Parrish quickly became an acolyte, drawn to Mr. Munger’s thoughts on multidisciplinary thinking and mental models.

He pored over Berkshire Hathaway annual reports and became a regular attendee of Mr. Buffett’s yearly meetings in Omaha. The name of his site is another tribute to the billionaire investor: Berkshire Hathaway’s address in Omaha is 3555 Farnam Street.

Last year, Mr. Parrish left intelligence work to tend to the site full time. He wouldn’t disclose how much his various projects were making.

A proposal for an archive revisiter

Thursday, November 8th, 2018

In his long list of statistical notes, Gwern includes a proposal for an archive revisiter:

One reason to take notes/clippings and leave comments in stimulating discussions is to later benefit by having references & citations at hand, and gradually build up an idea from disparate threads and make new connections between them. For this purpose, I make extensive excerpts from web pages & documents I read into my Evernote clippings (functioning as a commonplace book), and I comment constantly on Reddit, LessWrong, HN, etc. While expensive in time & effort, I often go back, months or years later, and search for a particular thing and expand & integrate it into another writing or expand it out to an entire essay of its own. (I also value highly not being in the situation where I believe something but I do not know why I believe it other than the conviction I read it somewhere, once.)

This sort of personal information management using simple personal information managers like Evernote works well enough when I have a clear memory of what the citation/factoid was, perhaps because it was so memorable, or when the citations or comments are in a nice cluster (perhaps because there was a key phrase in them or I kept going back & expanding a comment), but it loses out on key benefits to this procedure: serendipity and perspective.

As time passes, one may realize the importance of an odd tidbit or have utterly forgotten something or events considerably changed its meaning; in this case, you would benefit from revisiting & rereading that old bit & experiencing an aha! moment, but you don’t realize it. So one thing you could do is reread all your old clippings & comments, appraising them for reuse.

But how often? And it’s a pain to do so. And how do you keep track of which you’ve already read? One thing I do for my emails is semi-annually I (try to) read through my previous 6 months of email to see what might need to be followed up on10 or mined for inclusion in an article. (For example, an ignored request for data, or a discussion of darknet markets with a journalist I could excerpt into one of my DNM articles so I can point future journalists at that instead.) This is already difficult, and it would be even harder to expand. I have read through my LessWrong comment history… once. Years ago. It would be more difficult now. (And it would be impossible to read through my Reddit comments as the interface only goes back ~1000 comments.)

Simply re-reading periodically in big blocks may work but is suboptimal: there is no interface easily set up to reread them in small chunks over time, no constraints which avoid far too many reads, nor is there any way to remove individual items which you are certain need never be reviewed again. Reviewing is useful but can be an indefinite timesink. (My sent emails are not too hard to review in 6-month chunks, but my IRC logs are bad – 7,182,361 words in one channel alone – and my >38k Evernote clippings are worse; any lifestreaming will exacerbate the problem by orders of magnitude.) This is probably one reason that people who keep journals or diaries don’t reread Nor can it be crowdsourced or done by simply ranking comments by public upvotes (in the case of Reddit/LW/HN comments), because the most popular comments are ones you likely remember well & have already used up, and the oddities & serendipities you are hoping for are likely unrecognizable to outsiders.

This suggests some sort of reviewing framework where one systematically reviews old items (sent emails, comments, IRC logs by oneself), putting in a constant amount of time regularly and using some sort of ever expanding interval between re-reads as an item becomes exhausted & ever more likely to not be helpful. Similar to the logarithmically-bounded number of backups required for indefinite survival of data (Sandberg & Armstrong 2012), Deconstructing Deathism – Answering Objections to Immortality, Mike Perry 2013 (note: this is an entirely different kind of problem than those considered in Freeman Dyson’s immortal intelligences in Infinite in All Directions, which are more fundamental), discusses something like what I have in mind in terms of an immortal agent trying to review its memories & maintain a sense of continuity, pointing out that if time is allocated correctly, it will not consume 100% of the agent’s time but can be set to consume some bounded fraction.


So you could imagine some sort of software along the lines of spaced repetition systems like Anki, Mnemosyne, or Supermemo which you spend, say, 10 minutes a day at, simply rereading a selection of old emails you sent, lines from IRC with n lines of surrounding context, Reddit & LW comments etc; with an appropriate backoff & time-curve, you would reread each item maybe 3 times in your lifetime (eg first after a delay of a month, then a year or two, then decades). Each item could come with a rating function where the user rates it as an important or odd-seeming or incomplete item and to be exposed again in a few years, or as totally irrelevant and not to be shown again – as for many bits of idle chit-chat, mundane emails, or intemperate comments is not an instant too soon! (More positively, anything already incorporated into an essay or otherwise reused likely doesn’t need to be resurfaced.)

This wouldn’t be the same as a spaced repetition system which is designed to recall an item as many times as necessary, at the brink of forgetting, to ensure you memorize it; in this case, the forgetting curve & memorization are irrelevant and indeed, the priority here is to try to eliminate as many irrelevant or useless items as possible from showing up again so that the review doesn’t waste time.

More specifically, you could imagine an interface somewhat like Mutt which reads in a list of email files (my local POP email archives downloaded from Gmail with getmail4, filename IDs), chunks of IRC dialogue (a grep of my IRC logs producing lines written by me +- 10 lines for context, hashes for ID), LW/Reddit comments downloaded by either scraping or API via the BigQuery copy up to 2015, and stores IDs, review dates, and scores in a database. One would use it much like a SRS system, reading individual items for 10 or 20 minutes, and rating them, say, upvote (this could be useful someday, show me this ahead of schedule in the future) / downvote (push this far off into the future) / delete (never show again). Items would appear on an expanding schedule.


As far as I know, some to-do/self-help systems have something like a periodic review of past stuff, and as I mentioned, spaced repetition systems do something somewhat similar to this idea of exponential revisits, but there’s nothing like this at the moment.

Students don’t know how they study and learn best

Wednesday, November 7th, 2018

Some progressive teachers take pride in allowing students to choose how they study and learn best, but there’s a serious flaw they overlook: students don’t know how they study and learn best:

Karpicke, Butler, and Roediger III (2009) (1) explored study habits used by college students. They surveyed 177 students and asked them two questions. For the sake of this post, I will only focus on question one:

What kind of strategies do you use when you are studying? List as many strategies as you use and rank-order them from strategies you use most often to strategies you use least often.

The results? Repeated rereading was by far the most frequently listed strategy (84% reported using) and 55% reported that it was their number one strategy used. Only 11% reported practicing recall (self-testing) of information and 1% identified practicing recall as their number one strategy. This is not good for student-choice of study. 55% of those surveyed intuitively believed that rereading their notes best utilized their study time…assuming students intended on using their time most effectively. This is just not so.

A phenomenon known as the testing effect indicates that retrieving information from memory has a great effect on learning and strengthens long-term retention of information (2). The testing effect can take many forms, with the most important aspect being students retrieve information. A common saying in my room is to make sure my students are only using their brain…if you’re using notes, the textbook, or someone else’s brain, you’re not doing it right. While many correctly see this attempt as a great way to regulate and assess one’s knowledge, the act of recalling and retrieving strengthens long-term retention of information.

This is not so with repetitive rereading. Memory research has shown rereading by itself is not an effective or efficient strategy for promoting learning and long-term retention (3). Perhaps students believe the more time I spend studying, the more effective the learning. Is it correct to believe that the longer I study something and keep it in my working memory, the better I will remember it? No.

Stop when you’re almost finished

Friday, November 2nd, 2018

Performance psychologist Noa Kageyama recommends harnessing resumptive drive, or the Zeigarnik effect, to get yourself to practice when you don’t feel like it:

Bluma Zeigarnik described a phenomenon way back in 1927, in which she observed while sitting in a restaurant that waiters seemed to have a selective memory. As in, they could remember complicated customers’ orders that hadn’t yet been filled, but once all the food had been served (or maybe when the bill was paid?), it’s as if the order was wiped from their memory.

Back in her lab, she found that indeed, participants were much more likely to remember tasks they started but didn’t finish, than tasks that were completed (hence, the Zeigarnik effect).

Another form of the Zeigarnik effect — and the one more relevant to what we’re talking about here — is the observation that people tend to be driven to resume tasks in which they were interrupted and unable to finish.

Researchers at Texas Christian University & University of Rochester ran a study on this form of the Zeigarnik effect.

Subjects were given eight minutes to shape an eight-cube, three-dimensional puzzle into five different forms. They were told to work as quickly as possible, and given three minutes to complete the first two puzzles as practice.

Then they were given five minutes to solve the last three puzzles.

The researchers deliberately made the second practice puzzle difficult — one that was unlikely to be solved within the time available. And just as they had hoped, only 6 of the 39 participants solved the difficult puzzle.

After their time was up, the participants had eight minutes of free time to do as they wished while the researcher running the experiment left the room to retrieve some questionnaires they accidentally forgot to bring, saying they would be back in “5 or 10 minutes.” This was all a ruse, of course, to see what the participants would do when left alone.

Despite there being other things in the room to do (e.g. a TV, magazines, newspaper, etc.), 28 of the 39 participants (72%) resumed working on the puzzles.


Of the six who completed the difficult puzzle, only one (17%) resumed working on the puzzles (and did so for one minute and 18 seconds).

Of the 33 who did not complete the challenging puzzle, 27 (82%) resumed working on the puzzle, and on average, spent more than two and a half times as long (3:20) working on the puzzles.

So, when interrupted in the middle of a task, not only were participants more motivated to resume working on that task, but they also continued working on it for much longer.


So instead of thinking about practicing for an hour, or having to work on 10 excerpts, or memorize a concerto, just tune your instrument. Or play a scale really slowly. Or set the timer for five minutes and pick one little thing to fix. And if at the end of five, you don’t feel like continuing, put your instrument away and try again later.

Don’t feel like studying? Just crack open the book. Work on one math problem. Write three sentences of your essay. Create two flash cards.

Second, once you’ve finally gotten yourself into the mood to practice or study, try stopping in the middle of a task. Meaning, if you’re working on a tricky passage that has you stumped, test out a few solutions, but leave yourself a few possible solutions remaining before taking a practice break. Stop when you’re almost finished solving the math problem. Or in the middle of a sentence.

It’s not what you know, but whether you use it

Thursday, November 1st, 2018

Two researchers from the City University of New York did a study of basketball players to discern a difference between the practice habits of the best free throw shooters (70% or higher) and the worst free throw shooters (55% or lower):

Difference #1: Goals were specific

The best free throw shooters had specific goals about what they wanted to accomplish or focus on before the made a practice free throw attempt. As in, “I’m going to make 10 out of 10 shots” or “I’m going to keep my elbows in.”

The worst free throw shooters had more general goals — like “Make the shot” or “Use good form.”

Difference #2: Attributions of failure were specific

Invariably, the players would miss shots now and again, but when the best free throw shooters missed, they tended to attribute their miss to specific technical problems — like “I didn’t bend my knees.” This lends itself to a more specific goal for the next practice attempt, and a more thoughtful reflection process upon the hit or miss of the subsequent free throw. Far better than saying “I suck” or “What’s wrong with me?” or “Crap, I’m never going to get this.”

In contrast, the worst performers were more likely to attribute failure to non-specific factors, like “My rhythm was off” or “I wasn’t focused” which doesn’t do much to inform the next practice attempt.

It’s not what you know, but whether you use it

You might be thinking that perhaps the worst performers didn’t focus on specific technical strategies because they simply didn’t know as much. That perhaps the best performers were able to focus on technique and strategy because they knew more about how to shoot a free throw with proper form.

The researchers thought of this as well, and specifically controlled for this possibility by testing for the players’ knowledge of basketball free throw shooting technique. As it turns out, there were no significant differences in knowledge between experts and non-experts.

So while both the top performers and the worst performers had the same level of knowledge to draw from, very few of the worst performers actually utilized this knowledge base. Meanwhile, the best performers were much more likely to utilize their knowledge to think, plan, and direct their practice time more productively.