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Fundamentals of TwelveByTwelve
Chapter 1: Voracious learning and student heterogeneity
lead to the great clash

by Luby Prytulak, PhD
You are at   www.twelvebytwelve.net/fundamentals/fundamentals-01.html
Email comments to:   lubyprytulak@yahoo.com
First posted 16 Apr 2013 03:07pm PST, last edited 09 Nov 2013 02:05am PST


Growing up as I did in an immigrant neighborhood of Toronto, almost all my friends came from immigrant families, and in whose homes I observed a phenomenon that strikes me today as having immense relevance to education — that my classmates and I all spoke an English that was indistinguishable from the English spoken by our Anglophone friends, but our parents spoke an English that was impoverished, error-ridden, and delivered in a heavy accent.

The observation seemed to be one that was generalizable to all foreign languages — I observed it in homes that were Finnish, German, Hungarian, Italian, Lithuanian, Polish, Romanian, Russian, Ukrainian, and Yiddish.  Since then, I have remarked the same generational difference in Korean-run Taekwondo classes, in family-owned Chinese restaurants, in Vietnamese-owned stores.

The difference did not seem to be attributable to level of education, as in some cases parents might have been doctors or lawyers or engineers or teachers back in their home countries, and it did not seem to be attributable to the depth of immersion in English upon arriving in Canada, as sometimes the adults immediately found work in Anglophone settings, or immediately began to study for examinations which would qualify them to resume their home-country careers, and so initially held a wide lead over their offspring who during the same interval might be still at home speaking only their native language.

Being There starring Peter Sellers and Shirley MacLaine, Jerzy Kosinski Jerzy Kosinski's Being There
got turned into a movie


But no matter how great the early lead that the adult might enjoy, it would eventually prove to be the case that the youngster would be the one who ended up speaking without an accent, and the adult who would always be stumbling over English subtleties, the one I happen to particularly notice in Slavic adults being use of the articles a, an, the which they either inserted where they didn't belong, or omitted where they were obligatory.

The observation is repeatedly confirmed.  Take the case of Jerzy Kosinski (14-Jun-1933 to 03-May-1991) who earned two MA degrees, one in History and one in Political Science, at the University of Lodz, Poland, and worked as a Professor of Sociology at the Polish Academy of Sciences, emigrating to the US in 1957, and therefore beginning his immersion in English at around age 23.  www.britannica.com/~.

The depth of Kosinski's immersion in English is highlighted by his graduating from Columbia University, publishing 13 books in English, winning several literary awards, lecturing at Yale, Princeton, Davenport, and Wesleyan universities, and appearing 12 times on The Tonight Show Starring Johnny Carson.  His three best-known books were The Painted Bird (1965), Steps (1968) for which he won the US National Book Award for Fiction, and Being There (1971) which was made into the 1979 movie of the same name, and for which Kosinski shared the Writers Guild of America, East Best Screenplay Award.

What immersion in English!  And what accomplishment!

Jerzy Kosinski autographing one of his bestsellers
Jerzy Kosinski autographing his novel, Passion Play.

But there is one accomplishment that forever eluded Jerzy Kosinski and which for him would have been the most important accomplishment of all — fluency in English:

Kosinski did well enough in spoken English, to be sure; his accent and his occasional Slavicisms were charming.  But writing was a different matter.  [...]  In writing English, the omission of articles or the clustering of modifiers did not strike readers as charming; instead, it made the writer appear ignorant, half-educated, even stupid.  [...]  Which might not have been such a handicap had not Kosinski been a writer by profession.

From the beginning of his life as a professional writer, Kosinski had to protect a terrible secret: He could not write competently in the language in which he was published.  Whenever he wrote a simple business letter, his reputation was at risk.  Even a letter he wrote to his British agent, Peter Janson-Smith, required a hasty followup; the solecisms and grammatical errors were explained as the result of failure to proofread.

James Park Sloan, Jerzy Kosinski: A Biography, Dutton, United States, 1996, p. 174

And with reference to a letter Kosinski wrote to The Nation literary editor Betsy Pochoda:

The letter had been riddled with such errors that, in her view, its author could not possibly have been the writer of Kosinski's award-winning novels.  Over the years she had picked up literary gossip about Kosinski's supposed "ghost writers" and had decided that such gossip was altogether plausible.

James Park Sloan, Jerzy Kosinski: A Biography, Dutton, United States, 1996, p. 384

Jerzy Kosinski's deep immersion in the English language during the last 34 years of his life was unable to give him the command of English that a child gains in one-fifth the time.  Kosinski had simply started learning English too late.  He had learned Polish and Yiddish well enough, because he had learned them in childhood, but no matter how long he spent immersed in English, he could never get the hang of it because he didn't start until he was 23.

The unbending rule admits of no exception.  Napoleon Bonaparte, who might be expected to have picked up a little English during his protracted wars against the English, and while playing whist with English officers during his banishment to Saint Helena, finally mounted a concerted campaign to conquer English, but to what avail at the end of the sixth week of his battle, given that he was 46 years old?

Napoleon Bonaparte couldn't learn English

But there were no events on Saint Helena.  He dug in the garden.  He dictated.  He tried to learn to speak and write English, without success, as a scrap in his handwriting, dated 7 March 1816, testifies:  "Count Lascasses.  Since sixt wek, y lern the english and y do not any progres.  Sixt wek do fourty and two day.  If might have learn fivty word, for day, I could knowm it two thousands and two hundred."

Paul Johnson, Napoleaon: A Life, Penguin, New York, 2002, p. 176.     Arithmetic error seems to be Napoleon's: 42 times 50 equals 2,100 and not 2,200.


And so I and my many immigrant friends showed ourselves capable of acquiring fluency in two languages in our earliest years, mastering each of them without the least sense of exertion, certainly without anything approaching strain, which raises the question of whether we were all maxed out.  Was it exactly two languages that nature had endowed us with the power to acquire, and not more than two?  I have never had close acquaintance with anybody who had grown up in three different linguistic environments and who had become fluent in three languages, but I have heard that this happens.  Noam Chomsky thinks that five languages is no problem:

Noam Chomsky talks about critical periods for learning

Noam Chomsky On Why Kids Learn Languages Easily
10.24.05, 9:00 AM ET    Excerpted from an interview with David M. Ewalt on Oct. 3, 2005     www.forbes.com/~

Noam Chomsky is a professor of linguistics at the Massachusetts Institute of Technology.  His work in linguistics has earned him the Kyoto Prize and the Helmholtz Medal.  He writes and lectures widely on philosophy, international affairs and U.S. foreign policy.

[...]  But most of what's known about animals shows that everything does have a critical period.  And it could be that there is a critical period for language acquisition, roughly from birth to around puberty, and that if you don't learn language at that time, you'll never learn it.  If you have learned a language by that time, you will be able to learn more languages later, but probably in a different way, and maybe by connecting it to the languages that you do know.

In many parts of the world, young children pick up four or five different languages with no awareness that they're talking different languages.  It's just: This is the way you talk to your aunt, this is the way you talk to your father, and so on and so forth. In fact, it's been recently shown that children who live in bimodal environments — that is, where one parent speaks, and the other parent uses sign language — pick up both languages with apparently no preference.  It's just like learning both English and Japanese.

How broad this capacity is, we don't know, because we don't experiment on humans.  If we treated humans the way we treated cats and monkeys, these questions would get fairly quick answers, but we don't allow ourselves those experiments, rightly.

Until better information becomes available, let us adopt as a working hypothesis Noam Chomsky's generalization that a child is able to master five languages, so long as he is immersed in them before puberty, which hypothesis we can render more explicit by supposing that "before puberty" means while still in the pre-teen years 1 to 12.  Let us further suppose that the teen years, 13 to 19, witness a progressive decline in learning ability such that by the age of 23 at which Jerzy Kosinski begins learning English, the voracious childhood learning has long vanished.

This is not at all to say that all learning vanishes at 13 or at 19 or at 23.  Jerzy Kosinski did learn English starting at 23, which was no small feat — but he never became fluent.


  Junior's first million "Oh look, honey.  Junior just made his first million..."

Bruce Willis: How do you know all this stuff? VIDEO: How do you know all this stuff?


And it is not only language that the prepubescents pick up quickly and profoundly, it is every skill, as is reflected in the joke that the chief benefit of having children is that they will be able to explain the family's electronic equipment, and as is echoed by John McClane (played by Bruce Willis) in Live Free Or Die Hard.  "How do you know all this stuff?" will be the adult's awestruck question whenever he watches an immersed-since-childhood graduate perform.  And, of course, the seeming prodigy does not have the answer to that question — he cannot point to any course of study that he pursued, or any lectures that he attended, or any examinations that he wrote, he just picked it up spontaneously.  Nature had hard-wired him to absorb it.

But there must be some limit.  Perhaps if a child were totally immersed in a different language each day of the week, then his average mastery of the seven languages would be lower than his average mastery if he had only three languages to contend with.  Perhaps as the number of languages escalates, interference encroaches, such that where a purely Anglophone child would know to say "I have been living in Toronto for five years," his simultaneously learning French might lead him to say "I have been living in Toronto since five years."

In imagining just how broad and deep learning might be during the pre-teen years, three principles might be kept in mind, in which the capitalized "Mastery" is taken to mean achieving first-class-honors standing in a rigorous first-year-university course.

  1. Although the simultaneous study of similar subjects might lead to interference, the simultaneous study of dissimilar subjects might occasion none.  To consider an extreme case, the acquisition of Japanese might be slowed by the simultaneous study of Mandarin and Tibetan, but not by the simultaneous study of mathematics and piano.

  2. Sometimes studying two subjects at the same time results in facilitation, as for example when studying both Mathematics and Physics.  More specifically, if Mastering Mathematics without any study of Physics takes X hours, and Mastering Physics without any study of Mathematics also takes X hours, then Mastering the two together does not take 2X hours, but perhaps something closer to 1.3X hours.  The facilitation results from overlap, as the study of Physics necessarily requires knowledge of Mathematics, and the study of Mathematics typically includes problems in Physics.

  3. Achieving Mastery of some subjects takes longer immersion than of others.  For example, where Mastery of Finnish takes X hours of immersion, Mastery of Mathematics might take 0.3X hours.

Although actually permitting a child to master five languages may seem to ill-prepare him for any career, the world might find a place for him, as perhaps at the University of London's Warburg Institute, where adding English to the list does happen to sum to five:

It had been founded, however, by refugee scholars from Central Europe, and it was 'taken for granted' that students could read Latin, French, Italian and German.

Rosemary Hill, Looking for a Way Up, Review of Roy Strong, Self-Portrait as a Young Man, London Review of Books, 25 April 2013, p. 33.

Edging toward the more likely of success, though, might be to allow the child, capable of Mastering five languages effortlessly, to Master four languages plus Mathematics-Physics-Chemistry (MPC) effortlessly.  And as four languages still seems excessive, then another equivalent to be considered might be Three Languages plus MPC plus Piano and Drawing and Judo.  And with only two languages, the field opens up to a still broader curriculum.

Reassuring us that such speculation is not mere fantasy is the occasional glimpse we are able to catch of accomplishments pretty much in line with what we have been imagining, as for example in the case of Anastasia Rizikov who can be seen being interviewed both

Eight-year-old Anastasia Risikov on Ukrainian TV
in Ukrainian
  Seven-year-old Anastasia Rizikov interviewed on Russian TV
and in Russian.

From the occasional English that pops up in these two videos, and from her living in Canada, we infer also that she speaks English.  If in consequence of living in bilingual Canada, she also studies French, that would give her four languages.  And what performance do we expect in school generally from a girl so bright and spirited?  My bet is high marks.  And on top of that, we see prodigious achievement in Piano, as can be seen in the two above videos, and in many other videos, as for example her playing, at age 7, primo in a duet at the Vladimir Horowitz competition in Kiev 2006.  What she becomes able to do with a piano by age 12 surpasses not only what I would have thought was possible for a 12-year-old, but what I would have thought possible for anyone to do with a piano.

Twelve-year-old Anastasia Rizikov plays Liszt

Although exactly what achievement might be expected given any particular curriculum is highly speculative, a broad generalization that we might venture to rely on is that early immersion takes advantage of a voracious capacity for learning, and produces stunning results over a broad curriculum of study, as begins to be illustrated in the comparison on the one hand of large swaths of American ten-year-olds deprived of early immersion baffled by multiplication and division, and on the other hand a ten-year-old who is permitted early immersion finding himself completing first-year-university Calculus, and Chemistry, and Ukrainian, among other things.


Example 1: The Killer Asteroid

Barringer Crater, Killer Asteroid, Language of Science

  The Arc de Triomphe is 50 meters tall, Killer Asteroid, Language of Science Arc de Triomphe

Mankind's future is beset by many threats, among them having earth hit by a large object, of which Arizona's Barringer Crater is a reminder.  Although the 50,000-year-old crater is 1.2 km (0.76 mi) wide, the incoming meteorite had been only 50 meters (164 feet) in diameter, which is the height of the Arc de Triomphe, and it looks like the width as well, and such that it would take 22 Arcs de Triomphe standing side by side to span from one edge of the crater to the other.  The damage, then, is caused not by the size of the meteorite alone, but by its size combined with its extremely high speed at impact.

And what would happen if the meteorite were bigger?

The Chicxulub meteorite is estimated to have been 10 km (6 mi) in diameter.  It struck the earth just off the Yucatan Peninsula 65 million years ago with a force of a billion Hiroshima bombs, and left a crater 180 km (112 mi) in diameter, which is reason enough to be concerned about the same thing happening in the future.  If, on top of that, the Chicxulub impact is responsible for extinguishing 75% of all species on earth, including all non-avian dinosaurs, then one might fear that if a similar impact were to happen today, it could wipe out all mankind.  It is not just the blast that would kill.  Among other possibilities is that a thermal wave would cause the release of large volumes of carbon dioxide from sea water, which carbon dioxide, being heavier than air, would quickly blanket the globe at ground level, killing all air-breathing fauna by anoxia, which is to say, by suffocation.

If an asteroid could conceivably wipe out all mankind, then there is reason to worry, because large space rocks are not rare.  The asteroid Ceres is 1,000 km (621 miles) across, and fortunately not scheduled for collision with the earth.  Scientists are already charting all the rocks that could collide with earth, recording how big each one is, estimating what it is composed of, and noting where it's going.  And if any of them are going to hit the earth, predicting exactly when.  When the day arrives that a big one is discovered to be on a collision course with earth, with enough advance notice we will be able change its course.  If it's really big, then we'll need years of advance warning, as big objects are hard to deflect.

NASA Near-Earth Asteroid Census

Russia meteor blast
Photo credit: Alex Alishevskikh    www.space.com/~

Chelyabinsk meteor

On 15 February 2013, a small asteroid entered Earth's atmosphere over Russia [...] with an estimated speed of 18.6 km/s (over 41,000 mph) — approximately 50 times the speed of sound [...].  The dazzling light of the meteor was brighter than the sun [...].

The explosion generated a bright flash, producing many small fragmentary meteorites and a powerful shock wave.  The atmosphere absorbed most of the object's energy, with a total kinetic energy before atmospheric impact equivalent to approximately 440 kilotons of TNT [...], 20–30 times more energy than was released from the atomic bomb detonated at Hiroshima.

The object was undetected before its atmospheric entry [...].  About 1,500 people were injured seriously enough to seek medical treatment.  All of the injuries were due to indirect effects rather than the meteor itself, mainly from broken glass from windows that were blown in when the shock wave arrived [...].  Some 7,200 buildings in six cities across the region were damaged by the explosion's shock wave [...].

[M]easuring between 17 to 20 metres in size, it is the largest known natural object to have entered Earth's atmosphere since the 1908 Tunguska event that destroyed a wide, remote forest area of Siberia.  The Chelyabinsk meteor is also the only meteor confirmed to have resulted in a large number of injuries.  The predicted close approach of a second asteroid, the roughly 30-metre 2012 DA14 occurred about 16 hours later [...].

And what kind of people is it that are able to do such things as detect objects at vast distances from the earth, and determine whether or not these objects are going to impact the earth, and if so exactly when?  Do not overlook the complexity of the problem — the earth isn't just sitting still while the asteroid approaches, it is spinning around the sun in an elliptical orbit at the speed of 108,000 km/h (67,108 mi/h).  Between first sighting of the asteroid and its arrival, the earth may have whipped around the sun ten times, and may be located at any position on its vast ellipse.  And to repeat — what kind of people are able to answer the question of whether the approaching asteroid will hit the earth as it goes tearing around the sun?

Why they are people like the ones who are able to tell us what the tide levels will be at any location on earth on a particular day, even ten years from now, in other words people who can calculate exactly where the sun and the earth and the moon will be on that future date, and who can also calculate what the gravitational forces will be of those three bodies when they are in those positions, and because it is these gravitational forces that determine the tides, they can predict the tides.  Well, this is very much like predicting where our earth and the approaching killer asteroid will be at any time in the future.

And what is relevant here is that these people who are the only ones with the ability to save the earth from the killer asteroid speak a language that most people do not understand.  Below is an example of that language.  Some of it seems to be English, though largely incomprehensible, and much of it looks like mathematics, and we understand that it is not the English but the mathematics that will spit out the numbers mankind needs to know — at exactly what time will that asteroid be closest to earth, and how close is that going to be?

Language of Astronomy, Killer Asteroid, Language of Science

The above, then, is not a disclosure of all the math that is needed to predict collision with the killer asteroid, it is rather only the tiniest snippet from the kind of math that scientists who deal with the locations of celestial bodies are trained to read and to write and to understand.  And it is an example of the oft-heard statement that mathematics is the language of science.  The killer asteroid example tells us that mankind will someday be saved by people who speak the language of science.

Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written.  This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth. — Galileo Galilei

And the most important point for our purposes is that the ones who will be enabled to help most in mankind's hour of need will be the ones who have learned to speak the language of science most fluently.  Fluency in mathematics is necessary to reading math as fluency in English is important to reading English.  A reader who has to pause to ask "Is that a p or a q? — I can never remember which is which!" or "Am I looking at a b or a d? — If they didn't make letters so similar, I'd find reading a lot easier!" is not going to get much out of trying to read War and Peace or Pride and Prejudice.  To understand a book requires that all the low-level skills be so thoroughly practiced that they are reflexive and instantaneous, so that attention can be focussed on such higher-level questions as what conclusions is this book recommending, are these conclusions supported by the evidence adduced, and what immediate application do these conclusions have to our lives?

In the same way, a reader of mathematics cannot be pausing to ask himself "Is cosine opposite-over-hypotenuse or adjacent-over-hypotenuse? — It's unfair to expect anyone to remember such details!" or "What's the difference between sine-squared-delta and sine-delta-squared again? — I used to know but it's slipped my mind!"  To read the math shown above, all such low-level principles need to be so thoroughly practiced that they are reflexive and instantaneous, so that attention can be focussed on such higher-level issues as how will this set of equations need to be modified and elaborated so that it will tell us with the highest possible precision when the time of nearest approach will be?

And just as a Jerzy Kosinski who didn't start learning English until age 23 is likely to bungle when reading or writing English, so anyone who doesn't encounter higher math until age 23 is going to be likely to bungle when reading or writing higher math.  Mastery of English requires immersion to begin at the toddler age, and for fundamental skills to be locked solidly in place by the age of 12, and mastery of Mathematics requires the same.

In the realm of mathematics, "fundamental skills locked solidly in place" means, at the very least, earning a grade of 95% on a university calculus course like that which Marko earned 95% on while still twelve.  If we do not raise an army of scientists with this fluency in the language of science, then we won't be able to detect the killer asteroid in time, we won't be able to calculate if it's aiming to hit us or not, and we won't know what to do about it.

Example 2: The Killer Epidemic

Sooner or later a plague greater than any mankind has ever known is sure to break out, and then who will be able to stop it if not someone deeply versed in molecular biology?

Killer Epidemic, Language of Molecular Biology

The same arguments that applied to our consideration of the killer asteroid apply here.  The student who went into Biology instead of Physics in order to get away from math finds cos creeping into even his biology studies.  There is no avoiding math in biology because biology is science, and mathematics is the language of science.  It will be people who speak mathematics who will save mankind from the killer epidemic.  They will be the ones who first detect the plague, and who track it, and who analyze and unravel it, and who come up with the remedy.  And they will be the ones who began speaking mathematics while still in diapers, and who mastered the fundamental vocabulary of mathematics, and the fundamental grammar of mathematics, before they hit their teens.  They will be ones able to read the above lines of mathematics with the same facility that the average homemaker reads a cookie recipe.

Example 3: Moving beyond fossil fuels

Very soon consensus will be reached concerning how much longer it will be before continuing to burn fossil fuels turns our planet into a cinder, and what alternative and non-polluting source of energy will save our planet.  Perhaps that source will be nuclear fusion, and the people who will be able to implement the nuclear fusion solution will be ones who speak that same strange language — composed in part of words strung together so as to look almost like English, though largely incomprehensible, and the rest looking a lot like math:

Language of Nuclear Energy, Language of Science is Mathematics

The three above are examples from among hundreds that can be cited.  They each illustrate that mastery of a certain language, the language of science — mathematics — is essential to the welfare of the human race, and even to its survival.  From conclusions concerning learning that we arrived at higher above, we expect that fluency in mathematics arises from early immersion and mastery of fundamentals by the age of 12, which happily conforms with what nature has programmed children to be able to do, and to be happy doing.

And to Fran Liebowitz recommending "Stand firm in your refusal to remain conscious during algebra.  In real life, I assure you, there is not such thing as algebra," those who speak the language of mathematics might propose opposite points of view, such as "Removing algebra from life is throwing away the most powerful all-purpose tool that man has discovered".

And whether it is in language or in mathematics or in athletics, the promoter of talent never forgets that those who start earliest have the best chance of attaining total mastery:

Three year old gymnasts.

Three-year-old twins are among the youngest students at the Changfa Acrobatic School in Wuqiao County.  Their program includes tumbling, juggling, and a basic education; tuition, room, and board is $150 a year.    Photo and caption are from National Geographic, May 2013, p. 139.


Airport Grizzly Bear, Student heterogeneity Airport terminal grizzly bear


I was standing in the Smithers BC airport terminal inspecting the grizzly-bear display opposite when a toddler detached himself from the group of adults he was standing with and walked toward the bear, happily pointing and repeating something that sounded close to "bear".  I expected that one of the adults from his group would immediately join him and crouch down beside him, and take advantage of the opportunity to supply the insights that the toddler longed to receive, perhaps starting with a confirmation of his identification, along with a clarification of the pronunciation: "Yes, a bear!"  Then, perhaps, adding qualifiers: "A big bear.  A very big bear.  This kind of bear is called a grizzly bear.  Yes, that's a grizzly bear.  And look at how big his claws are!  A bear's claws are like our fingers", the adult would say, making claws out of his own fingers, and soon proceed to count his own fingers, then to count the child's fingers, and to express surprise that the number was the same.  And then "I wonder how many claws the grizzly bear has?" would be followed by a count, and would end with the surprising discovery that a bear has five claws just as people have five fingers.

Repeated comparisons, I expected, would lead to the discovery of further similarities and differences between ourselves and bears.  We walk on our feet, and the bear walks on its feet and on its hands at the same time.  We too can move about on all fours if we want, but we prefer not to.  Physical demonstrations might follow which would be sure to be imitated and to kindle delight.  And our hair is similar to the bear's fur.  If the hair on our heads grew also on our faces, and on our hands, then we would begin to look like bears.  Wouldn't that be funny?  But when it is cold, we put on clothes to keep warm, whereas the bear does not wear any clothes.  He doesn't even have any clothes.  His closet is empty of clothes.  Come to think of it, he doesn't even have a closet!  But, you know, even without clothes, he doesn't get cold — he has his fur to keep him warm.  We would compare ears, nose, eyes, teeth.  Each topic would be introduced gradually, and would be delivered with whatever degree of repetition and elaboration and enactment seemed fitting, and the discussion would move ahead only after each insight had been grasped and assimilated.  And the entire introduction-to-bears mini-project would be suspended at the first sign of the toddler's curiosity shifting in some new direction.

That is the sort of thing that I expected to see happening, that I assumed to be the fulfilment of an obligation on the part of every adult to contribute toward the development of any child under his care.  However, that is not at all what happened.  What happened was that a man did separate himself from the group and did walk up behind the toddler — but he neither bent over nor crouched down, and uttered not a single word, only stood staring mutely at the bear.

My expectation together with its disappointment invites the hypothesis that some children do receive the sort of pre-school, or out-of-school, learning experience that I had expected, perhaps averaging even a dozen times a day, while other children receive it rarely, lucky if they average even one per day, such that some children's voracious appetite is fed while that of others is starved.  And while it may be generally the case that children learn more out of school than in, this is particularly true of the fed children — the amount they learn out of school is vastly greater than the amount they learn in, something which is often overlooked, as for example in discussions of why Finland's students score so high on international comparisons of achievement.  The media notice that the Finnish school day is shorter than ours, and so advocate the shortening of our own school day, or they notice that Finnish teachers have more autonomy than ours, and so recommend giving our own teachers greater autonomy.  What they overlook, though, is that Finnish culture values and practices teaching within the family to such a degree that it would by itself produce high performance even if Finnish schools were inferior, even if they were doing everything wrong, even if they needed to be held up as examples of what not to do.

Most relevant to our discussion of the Fundamentals of Education is that unequal out-of-school learning contributes to producing children who arrive at school unequal in achievement, and that such inequality of achievement increases over time.  The following recollection exemplifies just such an initial inequality growing over time:

When my first-grade teacher discovered that I could understand fifth-grade math, Umma bought workbooks from a store in Koreatown so that I could practice my decimals.  On weekends, she took me to Flushing to attend hagwan, a Korean academic cram camp.  [...]  As I grew older, Umma complained whenever I didn't finish my hagwan exercises or neglected piano practice.

Victor Zapana, Shaken: A mother's conviction. A son's doubts, The New Yorker, 26 November 2012, p. 32-39, p. 33.

To recapitulate the narrative above, a first-grader doing grade 5 math starts out with a lead of four years, but after that works through math workbooks, and on weekends also attends an "academic cram camp", and also does hagwan homework, and also takes piano lessons — such that a year later when he begins Grade 2 that four-year lead could well have expanded to five years and likely more.

Achievement discrepancies such as the above are not merely occasional observations, they are recognized as among the most pervasive problems bedevilling education:

By the time children complete the fourth grade, the range in readiness to learn (as suggested by the M.A. [Mental Age]) and in most areas of achievement is approximately the same as the number designating the grade level.  In other words, pupils in the fourth grade differ by as much as four years in mental age and achievement; in the fifth, by five years; in the sixth, by six years.  In reality, then, the grade level designation means little.  A fourth-grade teacher who troubles to look back of the grade-level label realizes that, to be honest with himself and his pupils, he really must teach grades one through six or higher.

Goodlad, John I., & Anderson, Robert H.  The non-graded elementary school (revised edition), Teachers College Press, New York, 1987, pp. 13-14.  Italics are in the original.

But what can be the solution?  The call has gone out for some sort of individually-paced learning, otherwise known as multi-tracking:

Classes must be divided according to ability.  The gifted and energetic student must not be condemned to a scholastic prison of tedium because of the background deficiencies of the disadvantaged and less talented.  Nor should the disadvantaged and disturbed be condemned to a scholastic prison of unspeakable tortures of constant discouragement, frustration, and final alienation from school and society.

Lucius F. Cervantes, The Dropout: Causes and Cures, University of Michigan Press, Ann Arbor, 1965, p. 208.

Cervantes, above, has certainly identified the problem, and commendably recognized the need for individual pacing, but if his reference to "classes" has in mind classrooms composed of students of equal ability — that brings small benefit.  Goodlad and Anderson report that after fifth-graders in one school had their high-IQ students removed to a "gifted" class, and their low-IQ students removed to a "retarded" class, the remaining, one-would-imagine-homogeneous, fifth graders still remained heterogeneous enough to exhibit, for example, more than an eight-grade difference in "paragraph meaning and language" (p. 18).  Goodlad and Anderson's review of the literature leads them to conclude that sorting students by performance on any particular measure does not produce groups homogeneous enough to be taught all subjects as if they were at the same level:

The troublesome and yet very significant point, however, is that pupils advanced or retarded in one learning area are not necessarily similarly advanced or retarded in other areas.  Pupils at twelfth-grade standards for reading might well be at tenth-, ninth-, and seventh-grade levels for other subjects. 

Goodlad, John I., & Anderson, Robert H.  The non-graded elementary school (revised edition), Teachers College Press, New York, 1987, p. 25.  Italics are in the original.


In view of what has been said above, let us now visualize the first day of Grade 1.  There sits a classroom of children looking up at their teacher, and there stands the teacher in front of the class looking down at them.  What is the essence of this situation?  What is the gist from which all else will follow?

The essence and the gist is simply that perhaps half the children already know everything that is going to be taught that year, and a few may already know everything that is going to be taught the year after that, and the year after that as well.  And the more advanced the student, the more he will tend to regard with disdain the childish materials being offered him, and the more he will tend to gaze around for something more interesting to do.  And the more he squirms and fidgets, the more he distracts the other students.

But worse than that, all the children will be eager to continue learning during that school year at their favorite rate, the only rate they know, the rate at which they have already learned English and sometimes also their home language, which is the voracious rate, and which is to say that they are prepared — or rather that nature has prepared them — to learn far more than the teacher will be able to teach, and even far more than the teacher would herself be able to learn if she joined the class as a mature student alongside the youngsters given free rein.  The children are ready and able during their first year, and the teacher is not, to make substantial gains in, say, Japanese and Mathematics and Physics and Chemistry and Computer Science and Piano and Chess.

In other words, from the teacher's point of view, the situation is not only impracticable, it is intimidating and it is humiliating.

And just what is the teacher to do?  Classroom teaching is predicated on the assumption that all students need to know every day exactly what the teacher has come prepared to teach that day, which is rarely the case, and there seem to be two ways, not mutually exclusive, of coming closer to making it the case: speed up the lagging students and slow down the breakaway ones.  Speeding up the lagging students is acceptable only if it means speeding them up to the snail's pace dictated by the Ministry of Education.  Any greater speeding is unacceptable because it threatens to release the children's voracious capacity for learning, with which release the teacher cannot cope.  Therefore, any serious gains toward the desired homogeneity-at-a-snail's-pace can be realized only by slowing down the breakaway students.

That's the theory, anyway — the theory that among the teacher's foremost preoccupations is to, essentially, destroy excellence.  But is the theory supported by evidence?  Most assuredly so!  The evidence is copious and unmistakable, and will be presented in detail.  Take the following incident as an introductory example.

Early in Grade 1, Marko and a fellow classmate, Jake I will call him, begin racing each other through their math workbooks.  They did so spontaneously, without external prompting, much as they might spontaneously race each other across the schoolyard.  After a week or two of this, it was beginning to look like they would finish off the entire workbook before Christmas.  The benefit to the two rivals promised to be enormous, not only the laying of a solid foundation for further study, but also the perception of themselves as prodigious achievers.  Just such seemingly-small boosts to morale and ambition as these are able to shunt a youngster onto the path of high achievement.

However, the teacher noticed and intervened.  She forbade the race.  She commanded Marko and Jake to submit to the pace that had been decreed.  Years later, rumor circulated that Jake was doing poorly in school.

Let us allow ourselves to speculate freely: Might Jake have arrived at a fork in his road, and have spontaneously chosen the branch leading upward, toward a Nobel Prize perhaps, but which so alarmed his teacher that she forcibly dragged him onto the other branch, the one that led downward, and so sealed his fate?

And why should this incident not be regarded as a teacher suppressing an outbreak of excellence as reflexively and as inevitably as a policeman suppresses an outbreak of violence or a physician suppresses an outbreak of disease?

It may strike the reader as incredible that the high achievement claimed by TwelveByTwelve should be attributed to a removal of obstacles, and yet here is an instance of high achievement that would have occurred had the teacher not interposed herself as the sole obstacle.

This was the suppressive teacher's first year of teaching, and I hypothesize that her teacher's college had not prepared her for an outbreak of excellence, and that the outbreak perplexed her, and that she took the problem to the Headmaster.  Yes, it was a private school.

And I hypothesize further that the Headmaster told her what anyone charged with the welfare of any school would have told her — those boys have to be stopped!  Those boys are flaunting in everybody's face the information that students can learn at a much faster pace than we hold them to, that they can maintain this pace happily and even enthusiastically, and without the help of any teacher, and without the help of any school.  Theirs is an accusation destructive of the prestige of our school, and destructive of the repute of our profession.  Theirs is an accusation that we are warehousing our students, that we are depriving them of the achievement which could be theirs were their talents unshackled.  They threaten to awaken in other students the voracious appetite that children have for learning, and no school can survive intact once that primitive passion is let loose.  How will teachers be able to maintain their self-respect, and their jobs, when waves of students surpass them in their own fields of study?  I repeat — those boys must be stopped!

Such, I hypothesize, was the underlying sentiment which prompted the shutting off of one of the channels of intellectual development of Marko and Jake, though the sentiment was unlikely to have been so candidly expressed.

Without an understanding of the obstacles which educators place in the path of learning, all attempts at education reform are doomed.

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