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Spinning Dancer created by Nobuyuki Kayahara Spinning Dancer created by Nobuyuki Kayahara Spinning Dancer created by Nobuyuki Kayahara

Paradigm Shift In Education
by Luby Prytulak, PhD
You are at   www.twelvebytwelve.net/fundamentals/paradigm.html
Send comments to:   lubyprytulak@yahoo.com
First posted 16 Sep 2013 01:18am PST, last edited 12 Nov 2013 10:23am PST


I put three copies of Nobuyuki Kayahara's Spinning Dancer at the very top of the page the sooner to get them scrolled off the screen, else they are so distracting that it would be difficult to get any reading done.

The Spinning Dancers are of interest here mainly because they present a vivid and memorable example of alternative interpretations.  Say the viewer's first impression is that the dancers are spinning ClockWise (CW), and thus bouncing on their left heels; but if he watches long enough, they will suddenly appear to be spinning in the opposite direction, CounterClockWise (CCW), and thus bouncing on their right heels.

All dancers spin in the same direction, and so whenever direction reverses, it does so for all, this despite the fact that they are not identical in appearance.  Similarity seems to be enough.

I dedicated a few minutes to trying to see one dancer spinning CW and the others simultaneously spinning CCW, but couldn't manage it.  The Spinning Dancer is sometimes referred to as creating "bistable perception", because it can be perceived in two different ways.  Seems to me, however, that it would more rightly be considered "quadrastable perception" because it can be perceived in four different ways.  For example, in the "two frames/sec" version further below, I am able to see the dancer reversing her direction of spin every 180 degrees, so that her toe always points forward, toward the viewer.  I have not seen, but think that it must be possible to see, a reversal of spin direction every 180 degrees but with the toe of her extended foot always pointing away from the viewer.  In fact, I find myself sometimes being incapable of immediately shaking off this third mode of perception; it can become just as gripping, or one might say "stable", as the others.  A fascinating area of research, but not the focus of our interest at the moment.

The use of the three dancers to me right now is that they provide a vivid and memorable demonstration of how it is possible for a viewer to totally reinterpret the events before him.  It would be saying pretty much the same thing to point out that one viewer's perception might be opposite to another viewer's even though both are looking at exactly the same thing — that is, one viewer may be seeing all three dancers spinning CW while another sees all three spinning CCW.  And given that it's really a quadrastable image, it is even possible for four viewers to have different perceptions while looking at the same thing.

I am following the example of philosopher of science Thomas Kuhn who used a still image — the Duck-Rabbit on the left below — to make the same point, and who went on to extrapolate that point to the scientific revolutions that he calls paradigm shifts.  That is, just as we can be seeing the duck (with its bill pointing left), but then suddenly switch to seeing the rabbit (with its ears pointing left), so too can scientists start off interpreting the world from one theoretical perspective, but suddenly discover a better theory, and begin seeing the world quite differently.

The simplest such demonstration may be the Necker cube on the right below, gazing at which produces reversals between seeing the cube from above or from below.

Optical illusion: Duck and Rabbit   Optical illusion: Necker Cube

One difference between such optical-illusion reversals and scientific revolutions is that in the former, there is no right answer — seeing the dancer spin CW is no more right or wrong than seeing her spin CCW, the duck is no more a correct perception than the rabbit, no advantage accrues from perceiving the Necker cube from above rather than from below.  In science, however, the new paradigm is proposed, and ultimately recognized, as superior, and the old paradigm is relegated to history-of-science books.

At the same time, even though a paradigm shift in science may be unstoppable, it never takes place instantaneously, simply because most practitioners are incapable of abandoning the perception that they have grown used to over their entire lifetimes.  In the words of physicist Max Plank, "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it".

The same is on the verge of becoming true in education.  Even now the paradigm shift is in progress and its momentum is irresistible.  It only awaits the previous generation to go into retirement for it to become universally adopted.

The purpose of this essay is to describe that new paradigm, that different mode of perception, that new way of seeing which everyone is destined to eventually adopt.  Unless that new paradigm is described, many may not realize it exists, as happened to me with regard to the Spinning Dancer.  I had run across her several times on the Internet, but not realizing that her spin could be reversed, I merely glanced and passed on.  To experience a Spinning Dancer reversal requires either a long look together with the happenstance of a reversal being noticed, or, as happened in my case, requires having the possibility of reversal pointed out.

In the case of the Spinning Dancer, the perceptual shift affects not only the particular dancer being gazed at, but the other two as well, despite differences between them.  The paradigm shift in education is similar in that once the new paradigm is adopted, every one of hundreds of different classroom scenes becomes transformed by acquiring a different, often opposite, significance.  Classroom scenes that are broadly accepted today as showing best teaching will be recognized tomorrow as showing worst teaching, and vice versa.

And as is true in scientific paradigm shifts, the new education paradigm is not merely different from the old, it is better.  The justification for regarding the new education paradigm as better is that it graduates students scoring above the 90th percentile on all conceivable examinations, and often in the 99.99th percentile.  "On all conceivable examinations" means on all examinations whether they be written or oral or performance, and whether they be true-false or multiple choice or problem solving or essay writing, and whether they come represented as measures of intelligence or aptitude or achievement.  Any comparison that is possible to make shows students educated under the guidance of the new paradigm to perform not just a tad better, and not just noticeably better, and not just incontestably better, but vastly better and not-in-the-same-ballpark better.


With few exceptions, movies dealing with education, especially ones that reviewers greet as offering an idyllic view of superior teaching, not only fail to offer insight, but rather perpetuate fallacies and misconceptions, as for example the three films that I have reviewed so far on twelvebytwelve.net:  Goodbye Mr Chips (1939), Dead Poets Society (1989), and Good Will Hunting (1997).

And where one might least expect to find educational insight — in a movie such as Talladega Nights (2006), a vulgar comedy about NASCAR racing — out pops the most important educational insight of all within its first few minutes.

Talladega Nights poster

The Talladega Nights insight starts with its opening-credits statement, misattributed for comic effect to Eleanor Roosevelt — "America is all about speed.  Hot, nasty, bad ass speed":

Talladega Nights, Eleanor Roosevelt quote, TwelveByTwelve TBT

The action begins on Career Day, with schoolboy Ricky Bobby listening to a father of some classmate describing his dead-end job.  Ricky's mind, however, is elsewhere.  On his desk he inscribes "I wanna go fast":

Talladega Nights, Ricky Bobby inscribes desk, TwelveByTwelve TBT

Ricky's father, Reese Bobby, whom Ricky hasn't seen in ten years, surprisingly shows up for this Career Day, and after introducing himself, proceeds to give the children his vocational guidance:

REESE BOBBY:  And the first thing you gotta learn if you're gonna be a race-car driver, is you don't listen to losers like your know-it-all teacher over here.

Talladega Nights, Don 't listen to losers, TwelveByTwelve TBT

TEACHER:  OK, I think that's enough.

Talladega Nights, OK I think that's enough

REESE BOBBY:  Your teacher wants you to go slow, and she's wrong, 'cause it's the fastest who gets paid and it's the fastest who gets laid.

Talladega Nights, Your teacher wants you to go slow, TwelveByTwelve TBT

Reese's message strikes a sympathetic chord with the class:

Talladega Nights, Students cheer Reese Bobby's vocational advice, TwelveByTwelve TBT

REESE BOBBY:  Oh, yeah!  You know what I'm talkin' about.

Talladega Nights, Oh, yeah! You know what I'm talkin' about. TwelveByTwelve TBT

The sanitized message might be taken to be: children yearn for speed and society compensates and admires speed, which would be a happy fit did not teachers block speed.  And Reese Bobby cannot be talking only about NASCAR racing, as it is implausible to suppose that he is accusing the teacher of wanting NASCAR drivers to drive slowly.  Reese Bobby is accusing the teacher of suppressing speed wherever it threatens to erupt.

What Reese Bobby has just expressed is the core of the paradigm shift which has begun to usher in a new era for education.


Nobuyuki Kayahara's Spinning Dancer is made up of 34 images which can be presented at various speeds, including his normal speed of 34 frames per second which is the rate they were presented at above, and also in the last of the three versions below.  Unfortunately, the software I used to create the slower-moving versions limited me to 30 frames, so that the two slow versions will be observed to jump an unusual distance when they arrive at the gap, which defect if corrected, I think, would not change any of my conclusions.

My impression is that the Spinning Dancer becomes increasingly boring the slower she rotates.  And as her speed increases, there comes a point when the viewer sees something more than the same succession of images but a bit faster.  At speeds approaching 34 frames per second, the motion becomes smooth and natural, and the pleasure of watching increases dramatically.

One frame every three sec
(3000 msec per frame)
Spinning Dancer created by Nobuyuki Kayahara, 2000 ms per frame
  Two frames/sec
(500 msec per frame)
Spinning Dancer created by Nobuyuki Kayahara, 500 ms per frame
  Thirty-four frames/sec
(29.4 ms per frame)
Spinning Dancer created by Nobuyuki Kayahara, 29.4 ms per frame

An understandable sentiment upon learning the figure of 34 frames per second is awe at what a great volume of very complex information, and arriving at very high speed, the human brain is able to process, and that would go for even very young brains too.  At the same time, the boredom that begins to build from watching the slower versions seems absent when watching at 34 frames per second.  Thirty-four frames per second, then, may be regarded as a natural speed, or as the speed that gives pleasure because it is the speed at which the human brain was designed to function.

What is definitely not the case is that the viewer experiences 34 frames per second as requiring a burdensome amount of mental labor to process.  Burdensome better describes the boredom of processing at far less than 34 frames per second.

Of course I do not conclude that speed is preferable to all viewers under all circumstances.  A slomo replay of a football fumble may be appreciated for clarifying what happened, but perhaps nobody would want to watch the entire game in slomo.  I would expect, too, that if fans of any sport were able to view a game either at normal speed, or else a bit slower, or else a bit faster — always assuming that any overlaid speech remained intelligible — then few would opt for slower and many would opt for faster.  The speed that we hunger for is often a speed that the real world fails to supply.


By "cerebral speed" I mean thinking speed, and more particularly problem-solving speed, as exemplified here by math-problem-solving speed.

The videos of students working math problems at what in conventional schools would be regarded as high speed are not warmly received by all.  Many regard the videos as presenting a sight that they have never participated in or witnessed in a conventional school, and they think that if it was worth doing, then conventional schools would be doing it.  Mainly, it looks to them like it might be painful to perform, and certainly painful to learn how to perform.  But that attitude is the old-paradigm view, the view that today drags education downward.  Let us take a closer look at these math videos and see if they are capable of evoking any different evaluation.

The six math-deck videos on the TwelveByTwelve (TBT) Pilot Study page permit anyone to calculate that the three students are solving math problems at rates ranging from 10 to 17 solutions per minute.  Extrapolating the observed rates to decks of 50 cards gives us the times to completion shown in the right-hand column:

MARKO PRIMES    17     2.9
Get That ANGLE 10  5.0
ALEXA Solve For X 11  4.5
Solve for WHATEVER   10  5.0
KIRSTEN Get that AREA 15  3.3
Get that EQUATION 11  4.5

Because the mean of the right-hand column is 4.2 minutes, and the maximum in the column is 5.0 minutes, we will consider 5 minutes as the time within which a TBT student comfortably completes a 50-card deck.  And if a student completes a dozen different decks each day, then he solves 50 times 12 equals 600 math problems each day, and doing which takes him a total of 5 times 12 equals 60 minutes.

How many problems are solved per minute depends, of course, on problem difficulty.  When the problems are elementary (limited to, say, the integers 2 to 13, as for example 7+9 in an ADD deck, or 11-3 in a SUBTRACT deck, or 4*9 in a MULTIPLY deck, or 26/2 in a DIVIDE deck), and if we look not at typical performances, such as those in the above table, but at each student's personal best, as shown in the table below, then problems solved per minute is much higher, sometimes approaching one per second, which in the table below would have appeared as 60 problems solved per minute:

Student age when setting personal best (yy:mm)
STUDENT               ADD           SUBTRACT       MULTIPLY        DIVIDE    


Let us now compare to what traditional-school student John Doe is doing.  John, we imagine, averages six math problems a day.  Why six?  Because it synchronizes nicely with my figures so far — it has the TBT student solving one hundred times as many math problems each day as John.  And six is chosen also because it strikes me as an exaggeration of John's average daily math practice.  I'm sure I never came close to averaging six math problems per school day through elementary and high school, and none of the children that I have ever been acquainted with since have averaged six math problems per school day either.

In calculating the work a conventional-school student actually does, it would be misleading to look at the volume of assigned homework for the reason that the student is likely to arrive at school the following day with less than the assigned amount completed, and with some of the portion that has been completed wrong, and with some of it completed only with the assistance of parents or other students, and from what I have seen, with much of it completed not merely with assistance, but by means of uncomprehending copying of some fellow-student's work.

The Coles Books chain used to publish solutions for all problems in all Grade 13 textbooks that I studied from when Grade 13 was the last year of high school in Ontario.  And the university textbooks that I am familiar with all have Solutions Manuals purchasable by anyone from the publisher.  These two observations alone are enough to convince me that no one knows how often the solutions to homework problems assigned from textbooks are simply copied.

Now if accepting the 100-to-one ratio is going to be a problem, then you'd better let me know, because I can convince you absolutely that it is a conservative estimate, if only because a TBT school day included vastly more than a single hour of math.  I think the true ratio may be closer to 500-to-one, and in any case, all my arguments would be unchanged even if the true ratio were discovered to be only 10-to-one.

And so the very conservative conclusion that TBT students get one hundred times the practice of conventional students readily explains the leading claims made on behalf of TBT, and brings to mind other benefits as well:

(1) Faster Progress

It may reasonably be supposed that one hundred times the practice will easily guarantee progress through the curriculum at the TBT-mandated rate of 1.7 times the conventional rate.  That is, completing Grade 12 while still 12 years old would be completing it while nominally still in Grade 7, and completing 12 years of work in 7 years is the rate 12/7 which equals approximately 1.7.  At the end of Grade 1, then, the TBT student completes not only Grade 1 but also 70% of Grade 2.  By the end of Grade 2, he has completed 1.7 + 1.7 = 3.4 years of the curriculum, and so on.  Seven years of this gives 7 * 1.7 = 11.9 years of the curriculum completed.  Anyone who wants to end up with exactly twelve years of curriculum completed instead of 11.9, can employ in his computations the exact 12/7 as the expected rate of progress instead of the rounded, but more convenient, 1.7.

(2) Greater Fluency

But one hundred times the practice is so vastly in excess of what is required to proceed at 1.7 times the normal pace that much of the practice goes not toward speeding through the curriculum, but rather goes toward acquiring mastery, or one might say fluency.  At one hundred times the practice, the TBT student learns to do mentally and accurately and rapidly what the conventionally-schooled student can do only with pencil and paper, and bumblingly, and slowly.

(3) Stronger Foundation

Deep mastery builds a strong foundation for further study, and so the TBT student finds himself fully equipped to assimilate new material and so he advances to it with confidence, and so he discovers the new work to be easy.  The conventional student, in contrast, proceeds to new work usually having only imperfectly assimilated the old, and so is beset with trepidation, and finds the new work difficult.

(4) Broader Curriculum

And one hundred times the practice is still so far in excess of what is required to achieve the above that the TBT student is able to simultaneously broaden his curriculum.  He advances to the 90th percentile compared to students five years older than himself not only in Mathematics and Physics and Chemistry and Biology, but also in English and two Foreign Languages, and also in History and Music and Art and Athletics, and more, and all owing primarily to the fact that he benefits from one hundred times the practice in all these other subjects as well.

(5) Less Homework

And one hundred times the practice is still so much more than is needed to accomplish all the goals laid out so far, that still another benefit can be guaranteed — that the TBT student will be assigned almost no homework.  Yes, he does a lot more work overall, but the work is squeezed into much less time, and so can be completed at school.  Unlike the conventional student who is expected to spend a good chunk of his evenings on homework, the TBT student's after-school hours are largely his own, with the sole exception of having to write in his journal a one-page-or-so account of some curious or revealing or amusing event of the day, to be read aloud to the other students over lunch on the morrow, and to be graded only implicitly by the interest and enjoyment that the author senses his writing has been able to arouse in his listeners.  That single journal page can be written in ten minutes, in bed just before lights out, and doesn't feel like homework.  It feels like preparing a Garrison-Keillor performance, calculated to edify and amuse tomorrow's lunch partners.

One benefit of such journal keeping is that the TBT student daily compares journal readings that succeed to ones that fail, both his own and those of others, and so sharpens his appreciation of what he needs to write in the future in order to hold the attention and win the appreciation of his audience.  More generally, it can be said that whatever skills are worth acquiring need to be practiced daily, and as both writing and public speaking are valuable skills, a daily reading to others from one's journal is one of TBT's indispensable components.

The need to contain homework is discussed further

(7) More Joy

Because most people have experienced schoolwork as painful, they readily imagine that one hundred times the practice means one hundred times the pain, and so turn away from TBT with revulsion.  The reality, however, is that the sense of onerous labor is a product of conventional schooling.  Pain typifies conventional-school activities because they are slow; gratification typifies TwelveByTwelve activities because they are fast.

And a word of elaboration concerning the origins of joy.  All human capabilities exist because they have proven conducive to the survival of the species, and nature has guaranteed that every skill that is conducive to that survival not only exists but is put into frequent practice by making it pleasurable.  For example, for the species to survive, its members need to eat.  But if individuals merely had the capability of eating but not the desire, then many would starve.  To prevent such loss to the species, nature builds in a punishment for too-infrequent eating — that punishment is the pain of hunger — and it also builds in a reward for eating — that reward is the pleasure of eating.  The same for drinking.  The same for procreation.  If any capability is conducive to survival, then the animal variant that will survive best is the one which enjoys exercising that capability, that is attracted to practicing it, that finds joy in giving it expression.

And surely the principle extends beyond eating, drinking, and procreating to every behavior that promotes the survival of the species.  Surely thinking, for example, is conducive to survival, especially rapid thinking, and surely nature punishes us with pain when we are starved of fast thinking — the pain of boredom — and rewards us with a sense of elation as a reward for fast thinking — perhaps something like the Eureka! sensation.  The Tom Cheney cartoon below expresses exactly this vital educational truth — that complex cerebral activity, I imagine rapid, can be deeply gratifying:

Tom Cheney Cartoon showing that math can be thrilling
Tom Cheney, New Yorker, 13 May 2013, p. 43.

Reese Bobby in Talladega Nights, then, was right.  The only people who balk at the acknowledgement that speed thrills seem to be teachers in their classrooms.  Everyone else views the connection as obvious.  For example, I open up the London Review of Books, and out pops reference to

a cinematic fad of the early 1900s.  Cameras and cameramen were hitched to the buffers of trains, and latterly trams, and filmed the track and scenery as they hurtled along.  [...]  Punters craved exoticism as well as velocity, though the thrill sometimes consisted in seeing familiar spaces at speed: there were phantom rides through Ealing, Leeds, and Southampton, and in 1910, A Trip on the Metropolitan Railway from Baker St to Uxbridge and Aylesbury.

Brian Dillon, London Review of Books, 4 July 2013, p. 16.  Blue emphasis added.

The familiar becoming thrilling merely by the addition of speed is more than a description of a psychological regularity, it is a formula which enables the teacher to transform exercises from familiar into thrilling.


Measures of what is being accomplished per minute can be taken not only of mathematical problems, but of several of the activities described on the TwelveByTwelve Pilot Study page.  The three right-hand columns below show personal best rates, and the Watchable on Video column shows rates that the reader is able to verify simply by watching the videos with a stopwatch in his hand, or perhaps by relying on the clock display that may be visible on his screen, but with the seconds showing in addition to hours and minutes.

Identifying 62 features of the HUMAN SKULL, and identifying 54 WOOD SPECIES, are shown on the video as group activities, whereas normally a student would run through the identifications in a set order and alone, which is to say with only a monitor present to handle the stopwatch and verify that all identifications were being made, which solo performance made it possible for the student to set personal bests.

Starting at the bottom line of the table below, we see that identifying 54 wood species, where the samples are presented in randomly-ordered stacks, gives rates resembling those obtained doing the elementary math decks which we encountered above — which is to say rates approaching the ceiling of one per second.

In the line second from bottom, we see 62 features of the skull being named and pointed to at rates far exceeding one per second, but this is only because the features are being identified in a standard order.  Had the features been presented for identification randomly (not easy to do when they are embedded within a replica of the skull), the one-per-second ceiling would undoubtedly have held.

The seemingly fantastic rates in the uppermost line, reaching as high as 290 identifications performed per minute, are made possible by such expedients as naming the five metatarsals by saying "First to fifth metatarsals" and indicating them with a sweep of the pointer.  Had the 29 foot bones instead been presented for identification individually and randomly, then the one-per-second ceiling would undoubtedly have been discovered to be impenetrable here as well.

Task  Watchable On Video   Kirsten 
personal best
personal best
personal best
Identifying 29 articulated foot bones in fixed order  Kirsten   124 290 249 218
Identifying and assembling 29 jumbled foot bones  Kirsten    17  28  13  15
Blind assembly of five scrambled lumbar vertebras  Alexa      8  10  12    9
Identifying 62 features of the skull in fixed order  group activity  83  72  48
Identifying 54 wood species presented randomly  group activity  40  54  29

If anyone wonders what is the use of such detailed knowledge of anatomy, then one answer is that it smooths the path not only for the study of first aid, which every high-school graduate could be expected to be proficient in, but also removes one of the major stumbling blocks to the successful study of medicine that is described in relation to Charles Darwin:

In addition, he never learned human anatomy.  Hatred of this essential but dull, difficult, and exhausting business is the biggest single reason why medical students give up or fail their course, today as then.  So Darwin's omission was not surprising.  Nevertheless, ignorance of anatomy was always a handicap in his career.  Indeed, his failure at Edinburgh to learn more about the human body was the reason why, as a student of organic life, he was always stronger on flora and fauna than on people.

Paul Johnson, Darwin: Portrait of a Genius, Viking, New York, 2012, pp. 20-21.

Not only does TBT teach its students a good chunk of what they would be expected to learn in medical-school anatomy, thereby lightening their load should they find themselves studying it, but TBT also strips them of the emotion of "hatred", and the feeling that anatomy is "dull, difficult, and exhausting".  Arousing such feelings and attitudes is not inherent in anatomy, it is the by-product of the bad teaching of anatomy.  Unburdened of such demoralizing and destructive emotions, the TBT graduate might be expected to not only breeze through medical-school anatomy, but to breeze through it cheerily and to find its more advanced study fascinating.

We turn now to two other activity types that are conducive to the survival of our species, and that contribute most to that survival the faster they can be executed, and so which deliver pain when we are blocked from indulging them, and deliver pleasure when we are permitted to indulge in them — the two other activities being discussed under the headings ORAL SPEED and MANUAL SPEED.


Fast Speech Is Twenty Oral Movements Per Second

As part of learning the circulatory system, the TBT students traced how Toxocara canis — the common roundworm of the dog — gets from the human alimentary canal to the human brain.  The students were aware that, contrary to popular belief, Toxocara canis does invade the human body and that it can settle in the brain.  To get to the brain, a favorite path is the blood stream, through a series of one-way streets and past certain key signposts.  The students had studied a chart of the pathway, and carried an image of it in their minds.  They recited, "Alimentary canal, portal vein, liver, hepatic vein, inferior vena cava, right auricle, tricuspid valve, right ventricle, semilunar valve, pulmonary trunk, pulmonary artery, lung, pulmonary vein, left auricle, bicuspid valve, left ventricle, semilunar valve, aorta, carotid artery, brain."  And for no particular reason that I can recall, they began to recite it quickly, and to have their times noted.  Recitations in which any phonemes (distinct sounds) had been mispronounced or elided were not credited.  The record for this recitation was eleven seconds, and the number of phonemes in the recitation is 216, which gives a rate of 19.64 phonemes per second, and which rounds to the more memorable 20 phonemes per second.

It is not difficult to determine if you are able to talk at this rate yourself.  Sit by a clock or metronome that ticks every second, or set your computer's clock display to show seconds, and in the latter case of a visible but inaudible display of the passing seconds, begin to nod your head or tap your hand to correspond.  Then begin repeating "Yer gonna get the funny money" in synchrony with the beat.  If you can do this every second then you are speaking at 20 phonemes per second.  If your recitation is fast enough that it leaves you with a silent interval at the end of each second, then you are speaking faster than 20 phonemes per second.  You might find it not terribly difficult to keep on reciting once per second even after adding the three additional phonemes in the word "not" by reciting "Yer not gonna get the funny money", which would be speaking at 23 phonemes per second.  It may be hard to do any of this for long, but being able to do it for just a few seconds should convince you that such a rate is realizable.

We can infer too that if a child is able to listen to speech streaming in at 20 phonemes per second, and catch that the speaker has changed "Yer gonna get the funny money" to "He's gonna lick the runny honey" or "She's gonna pat the bunny, sonny", then the listener must be processing and comprehending audible phonemes at the rate of twenty per second.

The rate of 20 phonemes per second is not offered as a typical or desirable speaking or listening rate, but only as a rate children are capable of both speaking and understanding over a short burst.

The three TBT students did enjoy their own recitations, and those of others, because they were fast.  That such enjoyment was not a peculiarity of our small group is evidenced by two patter performances showing fast singing delighting large audiences.

The patter song is characterized by a moderately fast to very fast tempo with a rapid succession of rhythmic patterns in which each syllable of text corresponds to one note (there are few or no melismatic passages).  It is a staple of comic opera, especially Gilbert and Sullivan, but it has also been used in musicals and other situations.

The lyric of a patter song generally features tongue-twisting rhyming text, with alliterative words and other consonant or vowel sounds that are intended to be entertaining to listen to at rapid speed, and the musical accompaniment is lightly orchestrated and fairly simple, to emphasize the text.  The song is often intended as a showpiece for a comic character, usually a bass or baritone (with or without choral interjection).  The singer should be capable of excellent enunciation in order to show the song to maximum effect.

Patter song, Wikipedia    en.wikipedia.org/~

  George Rose, Modern Major-General, TwelveByTwelve TBT
George Rose VIDEO

George Rose performs "Modern Major-General" from Pirates of Penzance

Worth noting on the video is that the Pirate King, presumably expressing the sentiments of the other Pirates within the play, and as well the sentiments of the audience watching the play, asks to hear the patter a second time, and conveys also that it is the speed which is amusing by asking that it be performed even faster than before:  "Can you do it one more time?  And can you do it really fast?"

Restricting attention to the last two verses when the Major-General repeats them at his maximum speed, my calculation is that the first of these verses ("In fact" to "sat a gee") contains 320 phonemes and is spoken in 14 seconds, which is 23 phonemes per second, and that the second of these ("For my military" to "Major-General") was 154 phonemes spoken in 6 sec, which is 26 phonemes per sec.  However, one can hear that at such high speeds pronunciation becomes somewhat slurred or indistinct, and that perhaps some phonemes get dropped, so that speeds substantially beyond 20 phonemes per second may be considered to be speeds at which speech begins to deteriorate.  Recitation this sloppy of the Toxocara canis path would not have been credited in the TwelveByTwelve Pilot Study.

  Tom Lehrer, The Elements, TwelveByTwelve TBT
Tom Lehrer VIDEO

Tom Lehrer Performs "The Elements" in Copenhagen, 1967

Tom Lehrer brings down the house by merely embedding the chemical elements within the Modern Major-General melody.

The rate calculation for the first verse ("There's antimony" to "thallium") is 288 phonemes spoken in 14 seconds equals 20.57 phonemes per second, though crediting Lehrer with this rate might require the overlooking of occasional slurring.

In Tom Lehrer's case, however, counting spoken phonemes does not fully measure his level of activity, as he's also playing piano, and none too slowly, so that a fuller description of the degree of his activity could include not only how many phonemes he articulates per second, but also how many notes he is playing each second at the same time.  One could go even farther — his feet are probably simultaneously following the pedal instructions which the score dictates.  Might the sum of his substantial oral together with manual activity combined with some pedal activity be approaching some sort of overall-activity ceiling?  What additional activity could conceivably superimpose on what he is already doing?  Perhaps, for the hearing-impaired, blink out a Morse-code version of the lyrics with his eyelids?

George Rose's Modern Major-General and Tom Lehrer's Elements, then, corroborate the TwelveByTwelve Toxocara canis recitation by indicating that the top rate at which people can speak and be understood appears to reach a limit at around 20 phonemes per second, and the higher a rate goes beyond this, the more does the quality of the speech deteriorate.

Of particular interest here is that performance at such a rate holds the attention of a large audience, and that the audience responds with laughter and vigorous applause.  May we conclude that words, which if spoken slowly would be painful to listen to because of their lack of significance, become fascinating when speeded up?

Normal Speech Is Ten Oral Movements Per Second, And Slow Speech Is Five

Also useful to have some idea of is the rate of typical, unrushed speech.  The TwelveByTwelve Pilot Study shows eight declamations that are delivered at something close to normal rates, and which are presented in the table below.  This data suggests that student normal speaking rate is around 10 phonemes per second.  Small dips below that rate are sometimes caused by a deliberate slowing and pausing for the purpose of enhancing intelligibility and heightening interest.  Larger dips are more likely caused by distraction: one Kirsten declamation dips to 8.05 phonemes per second because she is simultaneously distracted by climbing a tree, and one Marko declamation dips to 5.78 phonemes per second because he is simultaneously absorbed in turning over rocks.

And here's a small piece of evidence on the rate of speech in the British Parliament:

Lloyd George was an inspirational leader on the Welsh preacher model.  He thought and spoke on his feet, and expected the House to interrupt, to participate, and so to inspire sallies, jokes, splashes of venom, and apothegms.  He created dramatic pauses and raised hubbubs.  So his speaking rate was slower measured in words delivered per minute — 85 to Churchill's 111, with Gladstone's 100 as the standard.

Paul Johnson, Churchill, Penguin Books, New York, 2009, p. 29.

If we assume an average of 3.18 phonemes per word for all three of the above British Parliamentarians, a figure borrowed from the Winston Churchill quotation declaimed by Kirsten which starts "If you will not fight for right", then we are able to compute a phonemes-spoken-per-second rate for each of the three Parliamentarians and summarize their talking rates (see table below) by saying that a Parliamentary speaker may hold the floor, but nevertheless be slowed to around 5 phonemes per second by the sort of audience interruption and participation that is alluded to above.

Patter Songs
In fact, when I know
what is meant by
0:06   39 154 3.95 390.00 25.67
For my military
knowledge, though
0:14   92 320 3.48 394.29 22.96
There's antimony,
arsenic, aluminum
0:14   52 288 5.54 222.86 20.57
TwelveByTwelve Pilot Study Toxocara Canis Path
Student Alimentary canal,
portal vein, liver
0:11   37 216 5.84 201.82 19.64
TwelveByTwelve Pilot Study Declamations
Kirsten If you will not fight
for right when you
0:24   83 264 3.18 207.50 11.00
Marko Even my short
experience with war
0:31   75 303 4.04 145.16   9.77
Alexa In the end it is
attention to detail
0:44 112 418 3.73 152.73   9.50
Marko As far as my
experience goes the
0:59 157 550 3.50 159.66   9.32
Alexa The discipline of the
ship requires every
0:50 126 441 3.50 151.20   8.82
Marko The fox and the cat
as they travelled
1:44 236 850 3.60 136.15   8.17
Kirsten Talk is by far the
most accessible of
0:19   40 153 3.83 126.32   8.05
Marko Perhaps the most
valuable result of
0:36   60 208 3.47 100.00   5.78
Parliamentary Discourse
1:00 111 353 3.18   111   5.88
1:00 100 318 3.18   100   5.30
1:00   85 270 3.18     85   4.50

We may note, incidentally, that words spoken per minute is a poorer measure of speech rapidity than phonemes spoken per second.  For example, consider that Kirsten holds the record in the TBT Pilot Study for most words spoken per minute (207.50), and yet this is for her unrushed recitation of Winston Churchill's "If you will not fight".  This seeming anomaly results from the words in that passage being short (3.18 phonemes per word), and her phonemes per second rate of 11.0 reveals that she is in fact speaking close to the normal rate which our working assumption pegs at 10.

Our working assumptions so far, then, are that 20 phonemes per second is fast speech, 10 is normal, and 5 is distracted or interrupted.  Instances of indistinctness in the patter songs suggests that exceeding 20 phonemes per second tends to be accompanied by quality deterioration.  And we are reminded again that speed brings joy, and perhaps that at the normal talking rate of 10 phonemes per second was already speedy enough to add pleasure to the memorized declamations.


TwelveByTwelve Pilot Study Students Could Type At Eleven Keystrokes Per Second

TBT students typing "The quick brown fox jumped lightly over the lazy sleeping dogs" (intentionally longer than is necessary to qualify for pangram status) peaked at 10.5 keystrokes per second (the space bar counting as a key), and which rounds to 11 keystrokes per second.  The timing was performed not by an observer holding a stopwatch, but by the computer program which was monitoring the typing.  The speed seemed to be a leading reason why typing was experienced as more like entertainment than schoolwork.

Two Instances Of Fascination With Fast Piano

A characteristic of Marko's piano practice was that he occasionally took pleasure in playing pieces at the highest possible speed, revelling in how quickly he could sound all the notes without even giving notes of longer duration any more time than the minimal he gave to what should have been the briefest notes.

And Marko's example, placed alongside that of pianist Jeremy Denk below, suggests the hypothesis that youthful craving for maximal piano speed may not be unusual:

"USE METRONOME."  This heartless device is invoked constantly: "Metronome!  You need an outside policeman every time the inner policeman breaks down"; "Use Metroyouknowwhat"; and on and on.  Anyone who has taken music lessons knows the indignity of emulating a machine until every last human vagary vanishes.  The clicking monster was also part of Leland's cunning scheme to prevent me from playing everything as fast as I possibly could.

Jeremy Denk, EVERY GOOD BOY DOES FINE: A Life In Piano Lessons, The New Yorker, 08-Apr-2013, p. 41.

A Measure Of Piano Top Speed

Alvino Yang, who in his
VIDEO did play as fast as he could, calculated that he played 233 notes in 12 seconds, giving him a rate of 19.4 notes per second, a number strikingly similar to the 19.6 phonemes per second spoken by TBT students.  However, according to an alternative method of calculation, because Alvino Yang played 233 notes with each hand, he really played 466 notes in the 12 seconds, which credits him with a rate of 38.8 notes per second.

Anticipating criticism for having played an exercise faster than it was meant to be played, Alvino Yang writes under his video:

How fast can human fingers move?

Note: please do not comment on how this isn't the way this exercise is supposed to be played or how bad it sounds, because the point of this video is to show how fast someone can play this exercise.  Thanks.

Alvino Yang did not subject his "slow" playing, which might more properly be considered his normal or proper playing, to the same measurement, but I clock it at 27 seconds, and so that credits him with a normal playing rate of 8.6 notes per second using his method of computation according to which he played 233 notes, but credits him with 17.3 notes per second if he is considered to have played 466 notes, which is the calculation I prefer.

Racing Through Chopin's Minute Waltz

Wikipedia says that the "Minute" in Chopin's "Minute Waltz" has the stress on the second syllable, and so conveys the meaning "Tiny Waltz" or "Short Waltz", which makes sense because when the Girl in Pink (age 10) below plays it, it sounds right and is very fast, and yet it takes her 1:37, which is much longer than one minute.

However, possibly because some tend to read "Minute" (stress on the first syllable) "Waltz" as meaning the "Sixty-Second Waltz", they do try to play it in one minute:  "I could also run off Chopin's Minute Waltz (minus the repeats) in 43 seconds, a world record, as far as I could ascertain" Nicolas Slonimsky, Perfect Pitch: A Life Story, Oxford University Press, 1988, p. 20 .

But why does Slonimsky skip the repeats?  If people play different fractions of the piece, it becomes difficult to compare speeds, and inappropriate to claim a world record.  In any case, Slonimsky's is just a claim which cannot be verified.  His autobiography is filled with jokes, and perhaps this is one.

But a
VIDEO exists which shows an anonymous pianist seeming to play the entire Minute Waltz, repeats included, in under one minute.  Of course the pianist is butchering the piece, but what great fun he's having, and what great fun to watch!

I Measure The Girl In Blue's Normal Speed

Eight-year-old Girl in Blue plays Chopin


It is necessary to emphasize that such quantification of piano-playing speed as is performed here is not being offered to either performers or their teachers or their listeners — none of these have any use for such measurements.  But such measurements are, or should be, of interest to educators, because they facilitate comparison of activity rates between various student activities.  It should also be clearly understood that no one advocates striving for maximum speed.  Some pianists may do it as a lark, and Alvino Yang did it out of curiosity, but it is understood and agreed that music almost always needs to be played slower than the fastest possible.

To get an idea of notes-played-per-second during regular performance and not while racing, I timed at 31 seconds the eight-year-old Girl in Blue playing the
first page of Fantaisie Impromptu in the video that can be watched further below.

The number of notes on that page is 443, and which over 31 seconds works out to 14 notes per second.  Again, we are not looking for any kind of a record here.  We seek only a rough idea of note density during a single normally-paced performance.

As was mentioned in the discussion of Tom Lehrer's patter recitation of The Elements, that a fuller measure of his rate of activity would have added to his phones-spoken-per-second both the piano playing he was doing with his hands and the pedal engagements and releases that he was performing with his feet.  It can be said similarly that a fuller measure of the rate of activity of the Girl in Blue would include her use of the pedal, and whose engagement and release are indicated in the above score by "Ped" and the asterisk-like character which follows.


Below are videos of pre-teen piano prodigies, spanning ages from 4 through 12, a small selection from the many that are readily available.

My own reaction to these performances is one of shock.  Children this young should not be able to do the things that I see them doing.  I am shocked even though I have been preaching for decades that child learning is voracious.  And I continue to be shocked even though I have watched these videos innumerable times.  Drawn to what shocks me, I can't get enough of watching them.

My fascination with these performances results from three old-paradigm-shattering perceptions that I carry around with me.

First New-Paradigm Perception.  I view these piano prodigies as resulting mainly not from innate talent but from effective training.  Innate talent does play some role here as it does in all human behavior, such that we can be certain that not every last child who receives effective piano training will rise to the prodigious height evident in the videos, but the power of effective training is so great that perhaps one in ten will.  If there were four million twelfth-graders in the US, then effective instruction would see 400,000 of them graduating as piano prodigies each year.

Second New-Paradigm Perception.  Each Piano prodigy below has a Math prodigy counterpart somewhere on earth who does not come to our attention because Mathematics is not a performing art.  So we might be able to say, for example, that Marko writing the university Calculus exam Math 140 at Age 10 is equivalent to the Girl in Pink below playing Chopin's Minute Waltz at Age 10, and Marko writing the more challenging university Calculus exam Math 101 at Age 12 is equivalent to Tiffany Poon below playing the more challenging Chopin Polonaise at Age 12.  And if there isn't a math prodigy to match every piano prodigy, there could be one and there should be one.  In any case, to the 400,000 Piano prodigies graduating from Grade 12 each year, I add 400,000 Math prodigies.

And the same with Chemistry, Physics, Computer Science, Biology, and so on.  Chalk up 400,000 more prodigies in every conceivable field of study.

Third New-Paradigm Perception.  Marko's example shows that it is possible to complete university courses — and I don't mean college courses, I mean heavy university courses at a university that rejects a healthy proportion of applicants for admission — in Mathematics, Physics, Chemistry, Computer Science, French, and Ukrainian while still a pre-teen.  Therefore, among the millions of graduating prodigies that I have been envisioning above, it will be commonplace to find ones who have achieved prodigy status in several areas.

Two background points that I do not forget.  First, that effective education does not merely produce one prodigy for every ten children, while abandoning all the rest to mediocrity.  What effective education does is graduate students who in all their subjects range from impressive at the bottom to prodigious at the top, and with the category just below prodigious being magnificent.  The nine out of ten that I happen to be paying no attention to at the moment will demonstrate performance that ranges from impressive to magnificent.

At the same time, those falling below prodigious are to be treated with the utmost respect, for the simple reason that the world's great advances are going to come mostly from their ranks.  This is a phenomenon related to the concept of regression toward the mean, and which is universal and inescapable, and which can be found explained in my Companion to Correlation.  I do not forget, while momentarily giving the top ten percent my exclusive attention, that the bottom ninety percent deserve unstinting support because our hopes for the future depend largely on them.

And not to be forgotten is that following mastery of Grade 12 by Age 12, I imagine almost all the students continuing their studies, and at the same rapid pace and with the same depth of mastery, through university graduation, and through graduate school.

And so what?  What good will it do anyone if our society is inundated with probably snotty and self-important prodigies, bragging about how fast they can play the Minute Waltz, challenging their elders to solve incomprehensible math riddles, reminding us all that they better understand the history that we lived through before they were born than we ever understood it?

Among other things, it seems to me that the rate of scientific progress will be immensely accelerated.  Non-polluting and cheap energy will run our factories and speed our cars and feed the hungry and reverse global warming — all as our air and water become cleaner.  Cancer will be cured.  When the killer epidemic strikes, it will be detected early and contained totally.  When the killer asteroid approaches, we will know about it years in advance, and we will deflect it.  When ICBM H-bomb warheads come showering down on the United States, all will get shot down.  Whatever the sorts of blessings science has brought us in the past will flow in faster than ever before.  The arts and the humanities will enjoy a renaissance.

In my discussion of patent protection for educational innovation, I cite Eric Hanushek estimating the dollar benefit of raising US education up to the level of Canada's to be seventy trillion dollars: "If we could, for the whole nation, be up to the level of Canada, it would be worth perhaps seventy trillion dollars in present value [...]."  But the new-paradigm perception is that Canadian and American education are almost identically ineffectual, and that TwelveByTwelve soars miles above both.  So that if as trivial an improvement in US education as that of equalling Canada's might be worth seventy trillion dollars, what might be the worth to the US of soaring high above the Canadian standard, and indeed soaring high above every standard on earth?

Well, on to the piano prodigies.  The New-Paradigm perception is that these children are free, and the children sitting silent and immobile in their classrooms, and silent and immobile in front of their TVs at home, are in bondage.  The piano prodigies have escaped being enmeshed in passivity and are absorbed in exercising the powers that evolution has bequeathed them.  The conventional children have been taught to find it natural to live with their hands tied behind their backs and with their mouths gagged.  The cultures that produce the piano prodigies will dominate the earth economically and militarily; the cultures that produce the couch potatoes and the schoolroom potatoes will supply the world with unskilled labor.

Four-year-old Tsung Tsung plays piano

Age 4    Nominally in Pre-School
Tsung Tsung plays piano

Of all the piano prodigies presented on this page, none except Tsung Tsung have sheet music in front of them, and he never looks at his.

It is possible that Tsung Tsung's youthful love of speed rides roughshod over metronomic constraints, particularly in his first piece to such a degree that it might be wondered whether he is learning bad habits that will prove to be troublesome to unlearn.  From the opposite viewpoint, however, it may be wondered whether a premature demand for slowdown and metronomic conformity may not sometimes dampen enthusiasm, even incite aversion, such that it might be better to end up in later years with a student who continues to be enthusiastic and only begins to tolerate metronomic constraints than a student who submits to the metronome early but dreams of dropping hated piano.  In any case, when at the end of his video Tsung Tsung replays his first piece, it becomes evident that it did not take years for his inner metronome to begin to exert tighter control over his playing.


Age 4    Nominally in Pre-School
Aimi Kobayashi plays Clementi Sonatina Op. 36

Five-year-old Tiffany Koo plays Chopin

Age 5    Nominally in Kindergarten
Tiffany Koo plays Chopin, Nocturne #20 C Sharp Minor

Tiffany Koo will be presented again below, two years older.

Six-year-old North Korean girl plays red piano

Age 6    Nominally in Grade 1
Yu Pyol Mi plays the North Korean composition "The General and the Children"

A valuable insight might be gained from the introductory bars of this performance — they deprive the listener of the speed which he craves so that he will be all the more grateful when it is delivered just a few seconds later.

Seven-year-old Gavin George plays  Bumble Boogie

Age 7    Nominally in Grade 2
Gavin George plays J. Fina, Bumble Boogie.

Seven-year-old Tiffany Koo plays duet with Dr Mikhail Korzhev

Age 7    Nominally in Grade 2
Tiffany Koo practices a duet with her teacher, Dr Mikhail Korzhev

Tiffany Koo, whom we have already seen above at the age of 5, provides for us here a rare view of a prodigy practicing with her teacher, and in a relationship which deviates radically from any seen in conventional schools.  Here we see a student who is fully active, not merely doing a little something now and then, but actually cramming into each second of time more motion than the conventionally-schooled child will be called upon to make in an hour, and recalling from memory a longer sequence of movements than the conventionally-schooled person will be asked to perform over his lifetime.  The high resolution of this video also gives us perhaps the clearest view of a piano prodigy's hands in motion that is to be found on the Internet.

Seven-year-old Anastasia Rizikov plays primo in duet at Vladimir Horowitz competition in Kiev 2006

Age 7    Nominally in Grade 2
Anastasia Rizikov plays primo in duet at Vladimir Horowitz competition in Kiev 2006, and is heard from again below at Age 12.  Two further videos reproduced here mainly to demonstrate her fluency in both Ukrainian and Russian also contain some excellent piano.

Eight-year-old Girl in Blue plays Chopin

Age 8    Nominally in Grade 3
Girl in Blue plays Chopin, Fantaisie Impromptu

This is the Girl in Blue who was clocked above playing the first page of her piece at the rate of 14 notes per second.

Eight-year-old Danylo Shvedko plays Chopin, Myashkovsky, Chopin, Prokofiev

Age 8    Nominally in Grade 3
Danylo Shvedko plays Chopin, Myashkovsky, Chopin, and Prokofiev

Nine-year-old Girl in Black plays Chopin

Age 9    Nominally in Grade 4
Girl in Black plays Chopin, Waltz in B minor Op. 69-2

Nine-year-old Varvara Kutuzova plays Chopin

Age 9    Nominally in Grade 4
Varvara Kutuzova plays Chopin, Waltz No. 14 in E minor

Ten-year-old Ivan Bessonov plays Czerny Etudes

Age 10    Nominally in Grade 5
Ivan Bessonov plays Czerny Etudes

Ten-year-old Girl in Pink plays Chopin

Age 10    Nominally in Grade 5
Girl in Pink plays Chopin, Waltz No. 6 Op. 64 No. 1
The Minute Waltz

This is the Girl in Pink who was timed above playing The Minute Waltz in 1:37.

Ten-year-old Marusia Matveyeva plays Chopin

Age 10    Nominally in Grade 5
Marusia Matveyeva plays Chopin Waltz in E-minor

Ten-year-old Ray Ushikubo plays Chopin

Age 10    Nominally in Grade 5
Ray Ushikubo plays Chopin Etude Op. 25, No. 11 in A minor "Winter Wind"

The same trick that the six-year-old North Korean girl played on us — a few bars almost painfully slow, but then a cascade of notes that is not to be believed, in this case a Winter Wind.

Eleven-year-old George Li plays Liszt

Age 11    Nominally in Grade 6
George Li plays Franz Liszt, Hungarian Rhapsody, No. 11 at Carnegie Hall

George Li begins to play about one-third of the way through this video.

Eleven-year-old Benjamin Grosvenor plays Scarlatti and Balakirev

Age 11    Nominally in Grade 6
Benjamin Grosvenor plays Scarlatti, Sonatas in D minor and B minor, and ending with Mily Balakirev, The Lark

Twelve-year-old Tiffany Poon plays Chopin

Age 12    Nominally in Grade 7
Tiffany Poon plays Chopin, Andante Spianato und Grand Polonaise Brilliante 2/2 in a solo recital at Paul Hall, Juilliard School for the Performing Arts.

Twelve-year-old Miranda Shum plays Chopin Polonaise

Age 12    Nominally in Grade 7
Miranda Shum plays Chopin Polonaise in G# minor, Op. Posthumus

Twelve-year-old Anastasia Rizikov plays Liszt

Age 12    Nominally in Grade 7
Anastasia Rizikov plays F. Liszt, "La leggierezza", from Three Concert Études, S. 144

Benjamin Grosvenor and David Gray horse around

The same Benjamin Grosvenor that we saw performing at Age 11 above is joined by David Gray in demonstrating that commitment to the pursuit of excellence does not mean that you give up horsing around, though it might mean that your horsing around tends to be conducted on an elevated plane.

Roman Boldirev plays Rachmaninoff Italian polka

We are waiting for young Roman Boldirev to appear and ask the show host for an autograph.


Piano is only one of many musical instruments that it is possible for a child to dedicate her creative energies to.  Kang Eunju, for example, a student in Shin Hung Kindergarten, Hamhung, North Korea, shows the product of childhood dedication to the concert guitar by playing a tune from the children's movie, "Boy Commander" which is captured on VIDEO.

To the parade of child genius there is no end.  I'll make this North Korean percussion trio the last for now.  That the little girl who looks initially like she's mainly a tambourine thumper will surprise you in the end is reason enough to watch this VIDEO.


A model that certainly works in Chemistry and Physics and Biology and Medicine: everything that is discovered in the laboratory is examined for potential applications, and if any are found, and some usually are, the machinery of production is set in motion and that discovery begins to benefit mankind.  And it is sometimes assumed that education works the same way: research continuously discovers the principles of human learning, the new findings are published in hundreds of professional journals, and eventually find application in the classroom.

Now at the time that I was teaching Marko, Alexa, and Kirsten in the TwelveByTwelve Pilot Study, I happened to have unusual access to the principles of learning that had been discovered in psychology laboratories.  I had a BA in Experimental Psychology from the University of Toronto, and a PhD in Experimental Psychology from Stanford University, and I had taught for eleven years in the Department of Psychology at the University of Western Ontario.  My shelves groaned under the weight of Psychology textbooks.  From each of a sample of ten of these, I
show a haphazardly-selected graph conveying the results of some learning experiment or other.  The exact significance of each result is of no relevance here, as I am at the moment only trying to impress the reader with the wealth of information that exists in this field and that was available to me.  In the second of these books I was surprised to be reminded that the Author Index listed pages on which my own small contributions had been cited.

And had I wished to consult the world's leading experts on what learning research had managed to come up with, I could have started by approaching the authors whose names appear twice in connection with the ten tomes below — Gordon Bower, whom I knew from his having sat on my Doctoral Thesis Committee at Stanford, and Ernest Hilgard, whom I knew from having spent a summer working at the Stanford Laboratory of Hypnosis Research of which he was Director.  I will have more to say about hypnosis later in this essay.

To repeat, I was in the strongest imaginable position to begin applying in my TwelveByTwelve Pilot Study the rich knowledge concerning learning that had for decades been pouring out of psychology laboratories.

In fact, however, while conducting the TBT Pilot Study, I consulted my many textbooks exactly zero times, and I conferred with my more senior and more expert colleagues exactly zero times.  Thus, I seemed to be not at all following the precedent apparent in Physics and Chemistry, and so on, of putting laboratory discoveries to use.  And why not?

The answer was that I knew by heart what was the single most powerful, and most reliable, finding to come out of all the learning research, and I was able to apply that one supreme principle, the First Rule of learning, and was able to see its breathtaking results.  As the application of the First Rule was already taking up all my time, I had none left to comb the learning literature for other rules that might find application, and as I was already applying the laboratory-proven strongest and most dependable method of promoting learning, I had small motivation to even begin thinking about applying weaker and less dependable methods.

And even though the ten graphs above all deal with different questions, nevertheless the First Rule — that supreme and unequalled principle — is nevertheless evident in every one of them — and that First Rule is that learning increases with number of trials.  The more you practice, the better you get.  Practice Makes Perfect!  The learning researcher and the educator are unable to forget this rule because they see documentation of it everywhere they turn, just as we have seen that documentation in the collection of graphs above.

The First Rule is so well established and so ubiquitously broadcast that the psychology student is not kept waiting until he is able to read such advanced texts as the ten above — he learns it in his first psychology course, as I did in 1963 reading Clifford T. Morgan, Introduction To Psychology (second edition, 1961), with one of its many learning-curve displays being the following:

Clifford T. Morgan Introduction to Psychology textbook

Learning-curve display in Clifford T. Morgan's Introduction to Psychology textbook

And one does not need to take introductory psychology to know that learning increases with practice.  Everybody knows it.  A cave man who had no better way of bringing down small game than hurling rocks at it knew that the speed and accuracy of his throw improved with practice.  When his toddler son threw his first pebble, the cave man engaged him in stone-throwing games because he saw the connection between practice and survival.

And I conjecture that absolutely no one who read at the beginning of this essay that one hundred times the practice produces better learning thought, "How clever!  Who would have thought practice was needed for learning!"  My expectation is that every reader did think, "Of course! How obvious!" and so I count every reader among the cognoscenti who believe in the First Rule.


Well, and what research findings are the teachers applying in conventional schools?  No need to look far, as they aren't even applying Rule One.  More practice, to the teachers, is more material that needs to be marked.  Less work for the teacher to derogate practice as "rote" learning and skip it as much as possible.

And let us not forget the Great Clash.  The teacher's overriding goal is to create a classroom of children all eager to devour each day the tiny morsel that she comes prepared to feed them, to accomplish which homogeneity she needs mainly to rein in the leading students.  And for the teacher to be reminded of the miraculous learning that students are capable of is for her to be reminded that she can't compete with them.  If the students are let loose from their restraints, then every class will have several students who play piano better than the teacher, and several more who are racing through university math and several more who are racing through university physics, and so on, when the teacher is unable even to comprehend what the students have learned, let alone teach them more.  To give the students freedom to practice is to engulf the classroom in chaos, and the teacher in embarrassment.  What the teacher needs to ward off this chaos and this humiliation is student passivity, and so the skill that she primarily teaches is passivity, and she teaches it well.  By the time the teachers get through with them, almost all the students will have earned an A in passivity.

In my educational-movie review of Dead Poets Society, I portray John Keating as striving to maximize passivity, and show him twice proudly calculating particularly high Passivity Index scores following what he considered to be particularly successful classes, meaning classes in which the students had been particularly passive.

Keating's first Passivity Index calculation: after his read-kick class, he estimates that each student engaged in educational exercise for only 6 of the 3,600 seconds available in the hour, which worked out to a Passivity Index score of 99.83%.  Someone who valued activity, however, and who therefore preferred high scores to signify commendable performance, would translate that into an Activity Index score of 00.17%.

John Keating calculates a second Passivity Index score by noting that whereas his Poetry Workshop students had the potential of speaking 240,000 words in an hour, only 27 words of poetry were actually recited, which gave him a Passivity Index score of 99.99%, and which, again, could be translated into an Activity Index score of only 00.01%.

Although such extreme scores might be taken to be jokes, in fact I intended them to be taken seriously.  The percentage of available time spent in academic exercise is a plausible measure of activity, as is the amount of practice performed as a percentage of the practice that could have been performed.  I see nothing wrong with John Keating's calculations, and think that education would benefit from all teachers making similar calculations for all their classes.

A wrong that I do see is nobody else noticing, let alone measuring, the sparseness of activity taking place in John Keating's classrooms.  Movie reviews of Dead Poets Society tend to regard John Keating as an inspired teacher of the sort that we have too few of, and not a single review that I have read has expressed concern at how long were the stretches during which Keating's students said nothing and wrote nothing and did nothing by way of academic or athletic exercise.  Come to think of it, similarly-low Activity Indexes could probably be calculated for every classroom scene ever shown in any movie, and I expect at the same time that perhaps no movie review ever written has expressed disapproval of the mind-destroying passivity that can be seen everywhere depicted.  Ubiquitous acceptance of classroom passivity seems to be the rule.

The reason for such reviewer tolerance of movie-depicted passivity is that reviewers have known nothing else, and consider it normal.  A roomful of students sitting silent and motionless and staring blankly at a teacher has become universally accepted as the immutable core of the educational experience.  So essential is the silent and motionless student to education, that if he fails to attain the requisite passivity in response to normal school coercion, the school will dose him up with Ritalin.

The new paradigm foresees Activity Index scores being regularly computed, and then nudged upward until they reach the high nineties, the way that John Keating nudged his Passivity Index scores into the high nineties.


Living out in the country as I do exposes me to a sort of animal behavior that some consider to be animal hypnosis, and which reminds me of when I was a graduate student in Stanford's Department of Psychology, and one summer worked in Stanford's Laboratory of Hypnosis Research which at that time was under the direction of Dr Ernest Hilgard and was lodged in Hawthorne House.

What to me will always be Hawthorne House has today added a wheelchair ramp and is known as Bolivar House, and is home not to the Laboratory of Hypnosis Research but to the Center for Latin American Studies.  I understand that after my time at Stanford, the Laboratory of Hypnosis Research moved from Hawthorne House into Jordan Hall, along with the entire Psychology Department which in my day had been housed in Cubberly.

Hawthorne House today is Bolivar House

Below is the covering page of a research proposal that I submitted to Dr Hilgard:

Luby Prytulak note to Hilgard

And below is the first page of the Hawthorne House Research Memorandum that resulted from my proposal:

Hawthorne House Research Memorandum #112

During my summer at Hawthorne House, I was given permission by Dr Hilgard to conduct further hypnosis research of my own, quite different from the above, and one of my experiments, in fact conducted in the room whose second-story window overlooks the front door, but which was never written up in a Hawthorne House Research Memorandum, has considerable relevance to education, and will be the subject of my future writing.

I am reminded of my days at Hawthorne House by several of the animal behaviors that I see around me being indistinguishable from trances.  By "trance" I mean a state of being benumbed, unusually still or even immobile, highly passive, unresponsive.  The same, or similar, animal behaviors have been discussed using other terminology, as for example "tonic immobility (TI)" or "thanatosis" meaning "feigned death".

A Tranced Rabbit

Here's an example that appears in the movie Eternally Yours (1939).  Escape artist and magician Arturo (played by David Niven) puts a rabbit into what he would have called a hypnotic trance so that it will stay quiet while stuffed into its hiding place until he magically produces it during his stage performance.  Although in the first still below, David Niven is shown picking up the rabbit, the scene cuts to a close-up where it is probable that it is the hands of a professional animal hypnotist that we are seeing.

David Niven picking up a rabbit to be hypnotized
David Niven picks up a rabbit.


The hypnotist grasps the rabbit's ears
The hypnotist's left hand slides up from the nape of the rabbit's neck to grasp its ears.  The right hand, meanwhile, grips the rabbit's hind legs and keeps them pressed against its body.

The hypnotist covers the rabbit's eyes
The left hand moves to cover the rabbit's eyes.


The hypnotist releases the rabbit's hind legs
The hind legs are slowly allowed to straighten, and are then released.

The hypnotist uncovers the rabbit's eyes
The rabbit's eyes are uncovered.


The rabbit lies motionless in its trance
The rabbit lies motionless in its trance.

Tranced Birds Galore

I am often reminded of animal hypnosis out here in the country because I keep seeing it all around me.  For example, birds fly into either the truck garage shown below, or into the little greenhouse attached to the garage on the left, and then they can't get out.  They lack the intelligence to simply go out the way they came in, and instead exhaust themselves trying to fly through glass, which impresses them as a promising strategy, I suppose because through that glass they can see blue sky.  If they are not rescued, they will die at the foot of the window which they have committed themselves to flying through, and so I rescue them.  Whenever I see a bird in this predicament, I pick it up, carry it outside, and toss it into the air, where it instantaneously takes flight.  I've saved mostly hummingbirds, a few swallows and robins, and once a hawk, in deference to whose sharp beak I for the first time donned gloves, but he gave me no more trouble than the non-raptors.

Bird-trapping garage

The flappers visible in the photo, installed only recently, have as their purpose to keep birds out.  When the air is still, the flappers form a uniform wall; when the wind blows, they go into the bird-scaring commotion shown.  They do help, but some birds still manage to find their way in.

It didn't occur to me until just recently that my bird rescues have implications for education and should be recorded — but better late than never.  However, a really good collection of photographs is going to have to wait until next summer, as the hummingbirds retreated southward weeks ago, and only a few of the swallows remain.  In any case, I think it's new arrivals who haven't learned the lay of the land that are most likely to wander into buildings, and new arrivals are most plentiful in the spring.

But I did manage to get photos of one recent rescue of a swallow.  I climbed a ladder to capture it against the high window visible in the photo.  Like all birds, it flapped its wings as my hands approached, and struggled upon being caught, but within maybe two seconds, convinced that it could not escape, it went into a trance — it lay motionless not only when enclosed in my hands, but when I uncupped them as well.  My intention had been to get photographs of my rolling the swallow over onto its stomach without awakening it, something I had accomplished previously with other birds.

Swallow being tilted, but still in hypnotic trance

But I hadn't gotten much farther in rolling this swallow over than can be seen in the photo above when it took flight.  Some trances are deeper than others, and this one was not very deep.

Swallow awakens from hypnotic trance

The survival value of the trance for birds is clear.  Their first priority is to not be captured, which requires the beating of wings to effect an escape, but once captured, their frailty makes further resistance futile.  Their only chance of survival is to play dead, thereby sometimes lulling their captor into inattention.  If their subsequent dash for freedom comes too soon, then the captor may still be too near and too vigilant, and so they continue in their trance even though sensing the removal of restraints.  Of course delaying awakening too long brings the danger of the captor deciding to begin its meal, if that's what it's after.

A Tranced Garter Snake

Can a snake be tranced?  Nothing had been further from my mind when I saw exactly that happening, quite by accident.

The story begins with my coming across a garter snake out in the bush, and immediately picking it up and carrying it home, thinking to keep it for an hour or two for the entertainment and education of the family, and then releasing it back where I found it.

When I got home, I could not readily see any container that I might put the snake into, so I put it in the shower stall, closed the glass door, and went to look for a container, but finding nothing suitable, decided to simply leave the snake in the shower stall for the duration of its visit.  Upon looking in on the snake a while later, I saw that it had defecated, and thinking to clean up the mess with least bother, I turned on the shower, setting the temperature to tepid, aimed the shower head, and left thinking that the longer the water stayed on, the more certain it would be that all the feces would be washed away, and that the snake would get rinsed too, in case it needed it, in preparation for my intending to soon pick it up again to return to its habitat.

Having let the shower run for many minutes, I returned and saw that the feces had all been washed away as I had hoped, but what surprised me was the attitude of the snake — it had pressed itself vertically into a corner with its head as high as could be maintained given that there was nothing to hold on to, and in any case no hands to hold on to anything with, and in this erect position the snake sat, or rather stood, or rather leaned into the corner while the water from the shower beat down around it.  Every snake that I had ever seen previously had been on the move, most often in rapid retreat out of fear of my presence, or when unaware of my presence, then always at least slowly sliding forward.  Snakes are usually in motion because they are usually hungry, and they find more food if they travel in search of prey rather than waiting for the prey to come to them.  Or if it is not food but escape that is uppermost on their list of priorities, then they will be on the move searching for that escape.  When I had first picked up the snake, it did not lie motionless in my hands; it kept writhing as if trying to free itself, and when I put it into the shower stall, it moved about.  But now with the water raining down around it, it was motionless.

Well, I thought, there you have again the very phenomenon that has been occupying my thinking, and it is entirely understandable.  Snakes, after all, do tend to live in subterranean nests and tunnels, and these do sometimes come to be flooded.  The snakes that have survived such flooding over the millions of years of their evolution are the ones that did the right thing whenever they found the water level rising around them — which is, first, to struggle mightily to find a way out, but when no way could be found, then to place one's head as high as possible, and to calmly and patiently wait for circumstances to improve.  To continue struggling once it had been proven there was no exit, was to deplete oneself of energy that might be needed to win liberation should any avenue of escape be opened up.

All living things have learned the same lesson — learned it as a species through the mechanism of survival of the fittest, the fittest having among other gifts the capacity to sometimes enter a quiescent state — learned the lesson that in addition to responding appropriately to situations that required high activity, most notably fight or flight, there existed also opposite situations requiring stillness and passivity.  My friend the garter snake had shown me that snakes are like all other animals in also sometimes needing to fall into quiescence for the purpose of increasing their chances of survival.

A Tranced Mouse

It is first necessary to understand that in winter, field mice are busy constructing cities under the snow, as is revealed in spring when the snow melts:

Melting snow reveals Mouse City

The sub-snow mouse cities have exit holes, through which the occasional mouse sometimes emerges into the winter air, and sometimes wanders off just a bit too far and doesn't know how to find its way back through the featureless white wonderland.

Making my way along a country lane in the dead of winter, I came across a mouse lying in a tire-track in the snow, seemingly intact and yet motionless.  Given the bitter cold, I thought it must be dead, and touched it with the tip of my skiing pole.  To my surprise, the mouse leapt up and bounded out of the rut, heading toward the forest lying some twenty feet away, and which offered some chance of survival as there were areas under every tree that were snow-free and that might give access to a sub-snow mouse city.

What must have happened, I thought, is that the mouse had emerged through an exit hole, and wandering too far had become disoriented and eventually got stuck in a rut, and found that no matter how far it travelled, the walls of snow on either side were too high and slippery to climb, and feeling exhaustion coming on, hunkered down to await a miracle, and that miracle did arrive in the form of an energizing touch of my ski pole, which produced such terror as to make the mouse run in leaps and bounds, and one of which happened to carry it out of the rut.  When it had originally decided to try quiescence, then, it still had a reserve of energy which was triggered by my touch, and which prolonged its life.

A Tranced Fawn

Our party was running down to the creek when Maryanne said she thought she had glimpsed out of the corner of her eye something peculiar in the grass.  We walked back to investigate.  Fortunately I had my camera:

Motionless fawn

It was June 9.  The fawn must have been born that spring, and being as yet too young to outrun a bear or a wolf or a coyote or a dog or a fox — none of which are in short supply hereabouts — opted for trying to make itself invisible instead.  We lingered over it for a minute, exchanged a few words, I bent down and clicked away with my camera, with the fawn all the while choosing to ignore our bustle.  A deer will normally turn its head to look at anything moving in its environment, but the tranced fawn snuck no peak nor blinked an eye.  And a deer will normally aim its ears toward any new object of interest, but the fawn's ears did not so much as twitch.  Its natural curiosity concerning intruders, normally so essential to its survival, on this occasion had been suppressed.  Only a barely-detectable movement of its rib cage told us it was breathing.

And the size of those ears!  Those ears which must have informed the fawn, and its mother too no doubt, that we were imminent even while we were still distant.

And so we may conjecture that the deer's prescription for survival upon the approach of possible danger is to run if you're mature enough to run fast, but curl up into a ball and freeze if you're too young to run fast.  Freezing includes abandoning natural impulses to look, to listen, to scratch, to munch on the grass, to flick flies off your ears.  If this weren't a good survival policy, its practitioners would have become extinct.

Tranced Pigeons, Chickens, and an Alligator

A fragment of a BBC video shows pigeons, chickens, and an alligator being similarly tranced:

BBC alligator to be hypnotized

We might hypothesize, then, that all animals are capable of states of high activity as well as high passivity.  I witness it in all the animals around me — even the mosquitoes and the spiders and the frogs.  I've seen a tranced moose.  What triggers the trancement, and what are the characteristics of the trance produced, differ from animal to animal.  And man is an animal that is subsumed under the same rule.

Tranced Humans

Man too has needed states of passivity to survive.

Like most animals, he sleeps.  Sleep is a state of very high passivity which throughout man's evolution assisted his survival through the dark phase of the diurnal cycle.  That is, men who stayed active after dark tended to die out.  For one thing, their accident rate was higher — it was harder to see one's step in the dark, easier to fall and break a bone or crack a skull, and easier to walk into a broken-off tree limb and lose an eye.  And carnivores with better night vision had an immense advantage over him.  And even if no misadventure befalls at night, the return on nighttime hunting and gathering is smaller, and the men who expended their energy for smaller return would be more prone to die out than men who expended their energy for greater return.  The men who survived, then, would tend to be those who found a safe place to pass the dark hours sleeping.

And man discovered that a passive trancelike state was conducive to survival sometimes during daylight hours, by which I mean that the human species in a sense discovered it through the mechanism of natural selection.  Man noted, for example, that animals have very large ears, and which they keep aiming in the direction of the smallest sounds, and so that sneaking up on them was usually impossible.  The most reliable way to get close to them was to find a place of concealment — a hunting blind — and wait for animals to come to them.  Hunters unable to keep still for hours at a time died out because they failed to bring home the bacon.  It would not be good enough to fall asleep in the hunting blind — this was a deeper trance than was needed.  It resulted in animals passing the blind unnoticed, or being scared off by snoring.  And since warfare was unavoidable, the same skill would have proved serviceable in ambush, or in sneaking up on the enemy, or when in hiding from pursuers, like the fawn.  What man needed in many such circumstances was a waking state in which all habitual inclinations to talk or move were stilled.

Another circumstance calling for trancement may have been the presence of an aggressive alpha male, of the same species and even of the same tribe and even of the same family, but ready to maul any individual who seemed to be challenging his dominance, and as the quiescent did not seem to be vying for dominance, they were left alone and so survived.

The people who survived, then, were the ones who spent most of their day in activity, and yet who had the capacity to occasionally enter into a trance.

If the frequency of English words which appear to describe a trance state is suggestive of the frequency with which such a state can be observed, then the trance state may be suspected of being not uncommon.  For example:

cataplexy — a medical condition in which strong emotion or laughter causes a person to suffer sudden physical collapse though remaining conscious
fascinatearchaic (esp. of a snake) deprive (a person or animal) of the ability to resist or escape by the power of a look or gaze
freeze — become suddenly motionless or paralyzed with fear or shock
mesmerize — hold the attention of (someone) to the exclusion of all else or so as to transfix him
paralyze — render (someone) unable to think or act normally, esp. through panic or fear
petrify — make (someone) so frightened that he is unable to move or think
transfix — to become motionless with horror, wonder, or astonishment

And it seems to me that the above names refer to trances and which are much the same as the hypnotic trances that are commonly induced in today's psychology laboratories.

And one more detail.  Man has some capacity to extend or contract his active and passive states, as circumstances require.  Research subjects who are repeatedly hypnotized, for example, become receptive to being hypnotized, can enter the trance more quickly and more deeply, and stay in it longer.  And the same if it is passivity that is demanded in their everyday lives, people become habitually passive, and find themselves weighed down with lethargy when called to action.  And on the other hand, if it is activity that is demanded in their everyday lives, people become habitually active, and find themselves overwhelmed by restlessness when asked to keep still, a restlessness which if it occurs in children, stands some chance of being deprecated as attention deficit hyperactivity disorder and suppressed with Ritalin.

And so here we have been discussing the means by which teachers are able to induce the tranquility and passivity that renders their classes manageable.  The trance is the teachers' chief weapon in their fight to suppress upstart students who write on their desks "I wanna go fast" and who yearn to be talking at speeds ranging from 10 to 20 phonemes per second, and typing at speeds of 11 keystrokes per second, and playing instruments at speeds ranging from 10 to 40 notes per second, and watching motion at a rate equivalent to 34 frames per second, and solving problems, as in mathematics, at the rate of ten per minute, or as in creek walking or rock climbing at the rate of 10 repositionings per minute — but schools require them for days at a time to say nothing and to do nothing in a room in which very little is happening.  The longer a student can be kept in such passivity, the more habituated he becomes to it, and the more he comes to prefer it.  In the end, his hours of staring speechless and motionless at a television screen at home transforms him into a couch potato, and his hours of staring speechless and motionless at a teacher in a classroom transforms him into a school potato.

The mass trancement of entire classrooms of students is further elaborated on The Zombie Hypothesis page.


The above discussion of speed of practice amounts to setting the goal of occupying the student in academic exercise at high speed so as to increase both her pleasure and her learning.  But how, practically speaking, is this to be accomplished?  How, for example, is it possible to teach anyone to type while maintaining throughout a typing speed not too far below what seems to be the ceiling of 11 keystrokes per second?  Or how to teach a student to identify 54 wood samples, the whole time maintaining a rate not too far below 60 identifications per minute?  How to maintain such high speeds throughout learning, and yet without confusing and frustrating the student, and without burdening her with a sense of oppressive labor?

Several such methods are available, among them being the Personal Best Method which I used extensively in the TBT Pilot Project.

Among the obligations that a TBT student would satisfy each day was to achieve a personal best on something like thirty tasks.  A personal best was defined as either completing a task at the same level of difficulty as previously, but faster, or completing the task at a higher level of difficulty, no matter how slowly.  It was always left up to the student to choose which of these paths she would pursue.

It must be understood, incidentally, that the student being expected to come up with something like thirty personal bests every day constituted only a fraction of her productivity, as many of her tasks were not amenable to the Personal Best Method, as for example her daily drawing or her piano or her shorthand or her declamation or her working through old Canadian Mathematics Competition papers.

Let's take a look at how the Personal Best Method was applied.

Learning To Type At 11 Keystrokes Per Second

The TBT students became proficient touch-typists by setting as their initial goal the rapid typing of "the quick brown fox jumped lightly over the lazy sleeping dogs", and where Level 1 was considered to be typing the first word, "the".

Of course the students had earlier been instructed on correct fingering.  Their keyboard keys had been taped over so that they would be less tempted to look down at their hands.  A picture of the keyboard identifying the keys lay beside them for consultation should they need that information.  In the initial stages, students tended to disobey instructions by using whatever finger seemed convenient to reach a needed key, and therefore needed to be monitored to prevent the acquisition of bad habits.

And so the very first time she types "the", the computer informs her of her typing speed in keystrokes per second, and saves that speed in her file.  As it is her first time ever, it is considered to be a personal best in typing, and whenever a student earns a personal best, she is free to move on to some other activity — but of course she doesn't.  She considers her achievement too paltry and wants to see if she can do better, which of course she easily can.  As she types "the" over and over, her speed increases, and she accumulates more and more personal bests.

When she returns to typing practice next day, she may find it easiest to simply stay at the previous day's level of difficulty, which is typing only the word "the", and earn personal bests simply by increasing speed.  And just increasing speed might go on for a day or two, or longer, but the instructor doesn't care how long, because the student can be depended on to eventually realize that she is typing "the" so fast that going any faster is not going to be easy, and in any case wants to become a typist able to type something more than the word "the", and so is sure to eventually decide to earn her next personal best by choosing to work at Level 2, which is to say by typing "the quick", and whatever her first speed, it counts as a personal best at Level 2.

And after that, repeat the cycle — after learning to type "the quick" at lightening speed, move on to Level 3 which is "the quick brown", and so on.

After that first sentence has been mastered, further sentences come laden with capitalization and punctuation.  After that, sentences can become enriched and meaningful, and incidentally cover spelling practice and vocabulary expansion and complex syntax, and so on.

Identifying 54 Wood Varieties At Almost One Identification Per Second

The student is asked to pick out a few wood blocks which seem to her to be interesting or memorable, perhaps five, and examines them, and reads their names, perhaps choosing ebony because it is so black and heavy, and balsa because it is so white and light, and purpleheart because it is purple, and zebrawood because it is striped, and red oak because there is a red oak floor in the room she is working in right then.  She starts at Level 5 because any lower level seems too easy for her, and being new to the task, is unsure she can handle Level 6.  A younger student could pick out three blocks to start with, and a still younger one might be happy with two.

The student studies the blocks, and when ready to be tested, the blocks are stacked in a neat pile with the species name that is printed on one edge facing away from her and readable by the monitor sitting across the table from her, and then the student says "ready," and a few seconds later the monitor says "go" as he starts the stopwatch, and times her identification.  If the student makes an error, she is asked to correct it right then, and if she can't then she is told the answer, which she repeats, and in any case the block is placed off to the side to be redone after all the others are finished, the time required for that second identification being added to her total time.

Having earned her first identifications-per-minute score, she will be told "You've already won a personal best just by identifying the five wood blocks for the first time.  You can stop now, or else try to increase your speed, or else you can continue to be tested after adding one or more blocks to your pile.  What do you prefer to do?"

No student quits at this point — she will try for higher speed, and she will delight in seeing that speed trend upward, and as the days go by, the number of blocks being identified expands, with the speed of identification always hovering just below 60 per minute, and the identification of all 54 species that initially seemed almost impossible, is taking place daily and at high speed.  Note, too, that whenever the student wants to move on to a higher level, she gets to choose not only how many blocks she adds, one being sufficient, but also which block or blocks it will be.

More Generally

Any flash-card deck can be attacked in the same way.  For example, even the very youngest student can be timed on an ADD deck consisting of three cards whose problems are: 1+1=, 2+1=, 3+1=.  When time to complete this deck gets fast, this youngster might choose to add a card or two, as for example 4+1= or maybe 2+2=.  From such small acorns as this grow mighty oaks.

Or, even a very young student can begin a PRIME FACTORS deck by starting with perhaps these five cards: 2 is a prime, 3 is a prime, 4 is 2 times 2, 5 is a prime, 6 is 2 times 3.  In the case of PRIME FACTORS, better to add cards ordinally rather than allowing the student to select.  The next card for the student we are considering should be 7 is a prime.

Some Benefits Of The Personal Best Method

The Personal Best Method gives equal recognition to fluency and to advancement.  Acquiring fluency in what you have already learned is as meritorious as learning something new.  Learning something new may not be commendable if what you think you already know is shaky.

The student consults her own feelings as to whether to increase speed or to advance to a new level.  If she yearns to leap ahead, nothing holds her back.  If she feels insecure, nothing drags her to advanced work for which she is unprepared.  And so the Personal Best Method also accommodates different student personalities, some students revelling in speed more than in advancement, and others revelling in advancement more than in speed.

No matter at what level of difficulty the student works, she usually works rapidly, being slowed only briefly following each advance to a higher level of difficulty.

The student is permitted to advance by as many levels in one jump as she wishes.  For example, in typing she might start at Level 2, typing "the quick", and might next jump to level 4, typing "the quick brown fox", but for her next advance, might choose to add only one word, and so work at Level 5, typing "the quick brown fox jumped", and so on.

Boredom is impossible, since each day the student is able to earn her personal best on any task in a matter of minutes, and will continue working longer only if she feels like it.

There is deep gratification in seeing evidence of daily progress in thirty different tasks.  A day's improvement in any particular task may often be infinitesimal, and yet it continues relentlessly day after day, and over time goes from unmistakable to admirable to astonishing, and after that sometimes has a good chance of passing on to prodigious.

One of the most profound and uplifting benefits of the Personal Best Method is that it teaches a radically-different interpretation of individual differences.  A radically-different interpretation? — Well, yes, that qualifies as a paradigm shift, in fact the very heart of the grand paradigm shift in education that lies before us, a paradigm shift to be experienced by the student and by her parents and her teachers as well.  But leave the others aside for now, right now we are talking about the student.  What is this paradigm shift that awaits her?

In conventional school, a leading student will appear to her classmates to be mysteriously and gratuitously and even supernaturally gifted, to possess capacities which others lack, and to be permanently stationed in a higher sphere.  Students working under the Personal Best Method, in contrast, see their own learning curves charting their improvement over time, and see the learning curves of others as well, and are able to experience a sort of epiphany upon recognizing that the leading pupil at one time performed as they perform today!  The laggard is able to extrapolate her learning curve and see all that separates her from the leader is exactly so much practice over exactly so much time.  In other words — eureka! — individual differences amount to finding oneself at different positions on the same learning curve.  The laggard realizes that if she intensifies her efforts, she will begin to close the gap between herself and the leader, and if she intensifies her efforts long enough, the standing can be reversed — she will begin to lead and the leader will begin to lag.

This wonderful paradigm shift is the recognition that we do not live entirely in a caste system in which academic and social and economic standing is fixed for life, we live also in a meritocracy in which standing is the reward for exertion.  There is no greater inhibitor of action than the belief that others are inherently better, and forever will remain better.  There is no greater spur to exertion than the perception that it closes gaps and reverses them.

But is the great pain of that great exertion worth the reward?  What great pain?  Oh, yes!  The great pain felt by those whom society has rendered passive, those who have become habituated to trances from which all activity seems painful?  Well, granted!  To those who have been held in their trances so long that they cannot snap out of them, this manner of perceiving individual differences is unhelpful and unwanted.  The tranced do indeed live in caste imprisonment.  But I was referring to those who have not yet been utterly ruined by conventional education, those young enough that they can be rescued from the clutches of the mesmerists.

Beyond The Personal Best Method: The Reciprocal Presentation of Mini-Lectures

The Personal Best Method was only one of several employed in the TwelveByTwelve Pilot Study, and in university-level studies was largely replaced by the
Reciprocal Presentation of Mini-Lectures.

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