[prodigies] are not given a lot of opportunities in schools that are designed for typically developing kids
... nor should they be. I was learning calculus in elementary school and writing the Putnam in high school. No matter how hard they tried, there's no way the schools I was enrolled in could have given me those opportunities. What prodigies need it not opportunities in school, but rather schools which are flexible enough to let them access opportunities outside of school -- in my case, starting my days at Simon Fraser University and packing my high school courses into the afternoon.
Those of us who managed sky-high SAT scores at 13 were 20 times as likely as the average American to get a doctorate; let's say, being charitable, that we're 100 times as likely to make a significant scientific advance. Since we're only 1 in 10,000 of the U.S. population, that still leaves 99% of scientific advances to be made by all those other kids who didn't get an early ticket to the genius club. We geniuses aren't going to solve all the riddles. Most child prodigies are highly successful — but most highly successful people weren't child prodigies.
This is probably the most important paragraph in the article. The numbers are unsupported, but I don't think they're so far off as to invalidate the point.
It isn't exactly wrong to say that Terry Tao and other former prodigies like him are geniuses. But it is more accurate to say that what they accomplished was genius. Genius is a thing that happens, not a kind of person.
Genius is both a noun and an adjective describing some people. It's a shame that Dr. Ellenberg felt it necessary to end an otherwise good article with such a piece of pithy nonsense.
Genius is poorly defined. Take all the different ways someone can qualify and you end up with something far more common than people assume.
EX: Apparently, Einstein was an ok chess player and Oppenheimer sucked. Yet, chess prodigy's are often called geniuses even if that's the only thing there particularity good at.
Businesses, Language, Math, Music, Go, Chess, IQ tests, Poetry, Physics, Early development, and Sculpture don't really have all that much in common. In the end it's much more meaningful to say someone is a _ genius than simply calling them a genius because g is closer to a myth than reality.
Businesses, Math, Music, Go, Chess, IQ tests, Poetry, Physics, Early development, and sculpture don't really have all that much in common.
... except for the people who excel at them. The author of this article is a mathematics professor and an author. I'm a computer scientist and a violinist. And in my time reviewing entrance scholarship applications for my alma mater, I don't think I've ever seen a student who excels in a single academic field and has no other unusual talents or accomplishments.
It takes more to be outstanding as you get older, so a 10 year old can be outstanding in several of them. And a collage student may keep up with 3 or 4.
However, none of the worlds best people in any of those, as in top 5, is also the worlds best any in any of the others. Not to step on anyone toes here. Michael Jordan was an incredible baseball player as in better than 99.99% of everyone that has ever played the game and by the 1:10,000 concept he may have been a dual genius, but that was not enough to be outstanding at the top level. And that is for two vary closely related sports.
So sure you can be outstanding in 2 or 3 of them but good luck finding people that can play at even just the professional level in Go, Physics, Sculpture, AND Poetry.
PS: My point is that collectively they don't share much in common. The Music / Math link while strong is not the same as the Music / Sculpture link.
I agree with your post, however, there are exceptions. While Jordan didn't have the best baseball career, Bo Jackson did excellent in both football and baseball.
Bo Jackson won't make the Hall of Fame in either of those sports, let alone both.
IMO, making the Hall of Fame is one obvious/indisputable mark of someone who is truly distinguished by excellence in the sport. (He did make the All Star & Pro Bowl, but those are far less distinguished honors, with something like 5-10% of players making those teams each year. So, rather than being a "top 5" type of mark, it's a "top 68" (baseball) and "top 110-ish" (football).)
Don't forget "mile-wide inch-deep" generalist geniuses. They aren't particularly gifted in one area, but are able to achieve simultaneous competency in a very large number of discrete disciplines. We used to call these folks "Renaissance Men", but the recognition of excessive achievement in specialties has virtually eliminated recognition for that kind of intellect.
Success in life is more correlated with ambition than with knowledge: an average educated but very ambitious person have more probabilities of being successful than a super smart individual that is ambitious but about knowledge and ideals, not money.
If you link this lack of focus in taking profit from your actions in life with a master in a struggling field, you are on your way to an underachiever life. That's me.
That probably depends if your definition of "success" is centred around "money" or around "happiness". (Or some other factor that I haven't considered).
Not so. Renaissance people (there are a few, even today) tend to end up underemployed. If you want to be a "business multimillionaire", you go the opposite way. You focus, you narrow yourself, but you have to focus on something that can actually make you money (i.e. not medieval history).
Why are most of the true Renaissance people underemployed, obscure, and financially mediocre? It's because the only thing that can tell a polymath from a dabbler is time.
... nor should they be. I was learning calculus in elementary school and writing the Putnam in high school. No matter how hard they tried, there's no way the schools I was enrolled in could have given me those opportunities. What prodigies need it not opportunities in school, but rather schools which are flexible enough to let them access opportunities outside of school -- in my case, starting my days at Simon Fraser University and packing my high school courses into the afternoon.
Not to derail from the article's point too much, but there are schools / programs specifically for talented youth - although they are not everywhere (sounds like there were none wherever you grew up). I know of one high school where a large number of students write the Putnam. I think it is important to have these schools / programs because pursuing opportunities outside of school is not always possible / easy for disadvantaged youth.
there are schools / programs specifically for talented youth
Yes and no. There are schools and programs specifically for kids in the 99th percentile, sure. In a large city, there will be enough kids for that to be feasible (as long as the kids have parents who will drive them across town).
But I'm pretty sure there are no schools dedicated to students in the 99.99th percentile. Even in New York City there are only 10 students per year at that level.
True, the top 0.01% is not going to work, but Los Angeles has a public school program that explicitly focuses on the top 0.1% (although recently they have rounded out their admissions with those in the top 0.5%):
I attended this program in elementary school and it seems to have spoiled me socially, since the students in the program were so much more interesting to me than other kids.
I suspect the reason the school district chose to create the program is because of the notoriety of the Mirman School, a lauded K-8 private school which also has top-0.1% admissions requirements.
So at least in some areas, education tailored to the 99.9th percentile has a long track record. But sadly, I have no idea if the practices and knowledge of that experience are available to inform highly-gifted education in other parts of the world.
Yes, I think aiming for the 99.9th percentile is a good target -- for reasonable-sized cities, that gives you a large enough segment to ensure that students have age peers, while being selective enough that the kids in the 99.99th percentile are likely to have at least some intellectual challenge.
I don't consider that to be part of the school system, though -- rather, that's a scheme to allow students to escape from the school system, just like the one I used.
Well, you're right that it's not part of any school that is designed to handle the general population. But I was making the point that prodigies don't need to look outside of their schools if they attend schools designed for them.
But apart from a short transition program, they're not attending an institution designed for them -- they're being mixed in with the general UW population.
If you think about the needs of gifted youth, there's basically two broad categories - academic and social. From an academic perspective, they're fine and probably better off in college, where they can take undergraduate and graduate level courses, do research with professors, etc. From a social perspective, the program actually does fulfill that need too, by providing resources and social opportunities to Transition School alumni (it's on campus, so it's sort of just a place for them all to hang out with each other). By and large, I don't think the students feel like they are just abandoned after they graduate from the Transition School. Also, Transition School is a year long, so it's a decent chunk of time.
Could you elaborate on the level for programs like these? I am familiar with a kid who was writing proofs regarding tensors (this is how it was described to me, my own math skills are extremely minimal in comparison) in the 5th grade. His father is worried about his social life going forward while wanting to nurture his talent. The kid was sent to the Johns Hopkins Center for Talented Youth for a summer which he apparently found really boring. I think he is actually being tutored by a professor at a local university now, but I wonder if he'd find peers of his own age group and ability level at these programs?
It sounds like his math skills might be slightly more advanced than the kids in these programs, but I would say that these programs are probably still worth a look for two reasons: (1) the kid may not similarly advanced in other subjects (it's not uncommon for kids to come in advanced in math but at the same level or lower for, say, English), and (2) even though the other kids are not as good at math, the kid you're familiar with may nevertheless get along with them better than they would with kids at a normal school.
What about democratic free schools like Sudbury Valley School? Where all the children, ages 4-19, are free to do what they want, whether playing video games or studying abstract algebra.
9 min video: https://www.youtube.com/watch?v=awOAmTaZ4XI
>Genius is both a noun and an adjective describing some people. It's a shame that Dr. Ellenberg felt it necessary to end an otherwise good article with such a piece of pithy nonsense.
It's a shame that you felt it necessary to end an otherwise good comment on Dr. Ellenberg's essay with such a literal reading of his last sentence. It reeks of unearned arrogance.
What prodigies need it not opportunities in school, but rather schools which are flexible enough to let them access opportunities outside of school
Interesting point, it reminds me of the 60 Minutes story of this kid [1] who showed signs of autism and was starting to become very inward-focused and withdrawn until his parents decided to trash the therapy and encourage his own exploration... Seems to have really changed his disposition to be far more communicative and most certainly affected the direction of his life. (Whole video is decent, but ~7:00 on is his parents)
Regarding that last bit, I think you discard it too quickly. What I read him as saying is that putting people in the category "genius" is a shallow understanding, and that he's arguing for a deeper one.
I do think that paragraph should have been substantially longer, and I suspect it got trimmed for print. But what he's trying to do with it is to summarize the rest of the article.
The article built the point that worshiping individual genius was counterproductive for the majority (non-genius) practitioners of math and science. The last sentence was would not pass as a dictionary entry on "genius" for sure, but that was not the point either. It was a rethorical device. Too bad i chose to start this post with such a piece of pithy nonsense.
These kids also need schools with staff who are capable of interceding, and are able to provide the means to do so when parents aren't educated well enough to recognize an especially gifted child or financially capable of nurturing the talent, so that the opportunities you note are less likely to be passed by.
As a kid, I was always in the 99th percentile of any standardized test. People complimented me on being smart, but smart isn't something you can control, so I learned tricks to maximize how smart I appeared. That included jumping in to anything that came naturally to me and avoiding anything else. I basically never learned to work at anything, to endure frustration, to sit with failure and get past it.
People meant well, I agree with the author: the common notion of genius as something innate and magical is toxic. By all means, make sure kids are properly challenged. But we should do it for every kid.
> People complimented me on being smart, but smart isn't something you can control, so I learned tricks to maximize how smart I appeared. That included jumping in to anything that came naturally to me and avoiding anything else. I basically never learned to work at anything, to endure frustration, to sit with failure and get past it.
This is a pretty common mistake made by parents and teachers during child development:
Great article. This bit is especially interesting: “The key is intermittent reinforcement,” says Cloninger. The brain has to learn that frustrating spells can be worked through. “A person who grows up getting too frequent rewards will not have persistence, because they’ll quit when the rewards disappear.”
Like quite a few on this site, I'm one of those kids.
I have a kid now, he's not going to be sent to a regular school. I wasted about 30 years trying to work out what/how other people were thinking. School wasn't a challenge, everyone in it was - so I initially focused on that.
They'll spend time trying not to offend people. (I really like people, and want them to like me). It's really tiring and difficult to maintain a persona that's compatible with the crowd. Is it even right to do that?
The smarter you are, the less people listen to the 'true' you (boring, being annoying etc). My guess is being around 30% smarter than average is the sweet spot.
They need a framework to cope with the entire inefficiency of everything in society, and the apparent willingness of everyone around them to perpetuate it.
They need to learn to let people they love be, even if it appears they are walking off a cliff. That sucks.
Being smart is wonderful but it's not everything. It means things are easily understandable to you. It doesn't mean you know everything, but it means you can learn almost anything quickly.
If you want a PHD you can get one easily, it's like when you're really rich - things have a different meaning. Many smart people I know don't care about things like 'PHDs' - infact, quite the opposite. Friends and family matter, not PHDs.
TL;DR; IQ is one over-sold metric; teach your kids to be happy first.
I read this and thought: spot on. Smart enough to do well in life but not be isolated through rarefied levels of intelligence, or excessively burdened by awareness of the world's troubles, probably makes for a happy individual.
My issue is with the phrasing. There's no such concept as "30% smarter than average", because there are no (known) intelligence units that could increase by 30%. Intelligence is measured relative to other people; we don't have any cardinal numbers for it. As such, saying "30% smarter than average" makes exactly as much sense as saying "fg wnthmsz ijwklwe uagp whajqlx".
My apologies. I conveyed the meaning as best as I could, those who 'felt' the concept where able to forgive the obvious inaccuracies inherent in any statement such as that.
Also there is an average IQ (though a poor metric). The average is 100, a 30% increase would be approximately 133 points.
"Intelligence tests are one of the most popular types of psychological tests in use today. On the majority of modern IQ tests, the average (or mean) score is set at 100 with a standard deviation of 15 so that scores conform to a normal distribution curve. This means that 68 percent of scores fall within one standard deviation of the mean (that is, between 85 and 115), and 95 percent of scores fall within two standard deviations (between 70 and 130)."
Therefore, roughly speaking - what I proposed is that being in the top 5% can be either a blessing or (more easily) a serious impediment to a happy life.
And to this point, the parents must learn to be happy themselves. This is a great challenge for most people, who are often torn between social norms and their own internal forces, and never fully resolve these tensions. A parent with a clear understanding of their own nature can do a lot for a kid.
The great barrier to happiness for a parent of a gifted child is ego and vanity. Some parents become afflicted with inordinate pride in their progeny. "Look at how smart my son is!" they exclaim. The parents' peers, friends, teachers, family, tire of hearing about it. This can alienate the kid from these adults, and even worse the kid's ego can also become inflated. In the end, the parents' pride amplifies what is already a terrible alienating, lonely, and depressing existence when no-one really seems to "get" you.
A corollary to this sin of pride is focusing too much on academic performance and ignoring entirely the importance of social learning. Parents in general, and smart kids in particular, might make the mistake of believing that kids are in school to absorb academic knowledge alone. Yes, it is good to encourage native curiosity and satisfy the demands of a budding intellect. But even more important, I think, is for the child to understand his relationship to his peers. He must discover, essentially, what he wants from other kids and what they want from him, and (importantly) what they want from each other. This process of discovery, I think, should be done quietly, deliberately, and consciously. There is nothing more harmful than telling a kid, "You shouldn't care what other people think." Humans are born caring what other people think, and to deny that is just crazy. A smart kid starting with the right premise will be able to accomplish quite a lot - a smart kid given the wrong initial conditions will end up dejected, miserable, and a failure, all because he got bum information from parents who were just plain wrong.
It may seem counter-intuitive, but I believe that a critical element for happiness in intelligent kids is silence. Silence serves (at least) two purposes - first, and most importantly, it can better connect them to what they really enjoy. Sports, for example, can be enjoyed without words. So can music, and art, and even just the simple act of being around other kids. It frees up the kid to just be, and not to think, to not have to try and justify their value, often agonizingly, to a social group. In a similar way, it shows them that even without a brain, they are an intrinsically important, valuable human being - which not only takes a lot of pressure off, but helps them empathize with those that aren't as smart.
Anyway, just some random thoughts. Thanks for the post. :)
A lot of parents are intimidated by their 'smart' kids, there's absolutely no reason for that. Even the smartest child can learn a wealth of wisdom from the most 'ordinary' (obviously I'm just relating that to IQ) parents. Genius child means high IQ - fast learning ability, not knowledge or wisdom - so school is much less important than loving family values or the wisdom of elders.
"I believe that a critical element for happiness in intelligent kids is silence"
That's just perfect. I never thought of it that way, I'll take this and apply it to the mix! That blew me away, it had never occurred to me and is completely accurate in both an intellectual and emotional context.
A very good Saturday essay that two of my Facebook friends told me about, and I'm glad to see that it was already submitted here, as it deserves a read from all of us who have ever commented in threads about "genius" or "geniuses." And the first two comments here, by kenjackson and j2kun, are very good too. What Jordan Ellenberg, a member of the Study of Mathematically Precocious Youth, writes about here is based on the extensive modern research on the development of advanced young learners of mathematics and other subjects. I recently heard a talk about this line of research by David Lubinski[1] (mentioned in the article) and I have been following this research[2] for years.
Summing up the research, yes, it's good to be supportive rather than oppositional to children developing their special talents in their youth. But the most talented young people will not save the world. We will save the world together through lots of incremental improvements, the kind of incremental improvements we discuss here on Hacker News. Personality traits (one could also say qualities of character) like curiosity and persistence matter quite as much as raw brain power in allowing young people to gain the best development from having good learning opportunities, and good learning opportunities are important for all learners.
I'd like one message to come across to all child-prodigies and precocious geniuses: You're not a "rare natural resource", "human capital" or any other such demeaning term. You're not responsible for solving ANY of the world's problems: you don't have to cure cancer or AIDS, you don't have to extinguish poverty, you don't have to solve the energy crisis. It's jut not your problem if you don't WANT it to be. Do what YOU ENJOY and LIKE, forget about other people's problems, forget even about the problems of your future selves! And do take advantage of you "special" or "celebrity" status, use it to get money and any unfair benefits you can get and waste them having fun. You're human beings and you are only supposed to live for your own enjoyment! If you enjoy helping others or solving the world's problems, do so. If not, fuck it all and just have fun!
Just to play devil's advocate here, most people actually do enjoy helping others. If you're the rare person that doesn't like helping other people at all, then it's probably a waste of my effort to try to make you. So "do what you like to do" != "be selfish" in all cases.
That's basically what it is, and maybe also a mindset of believing you matter as your own person, rather than just a means to and ends. Having at least some selfishness of that sort (at least when living in a culture designed for it - maybe things are different in more group-oriented cultures) is really important for things like being confident, being able to say no to others' requests, and not getting depressed.
Why wouldn't you advocate pure selfishness? Selfishness is a Good Thing. Why do we do anything? Because it satisfies some internal desire or drive. Selfishness is the epitome of living.
This is a really good article. And the author is right that it is so easy to feel like you should quit doing math or physics or CS, because you see that person who is your age, that just seems better at it than you are.
What I have found really humbling in life is how many people have accomplished so much more than I have, without my background. And if you look at the resumes of folks like David Cutler, Linus Torvalds, Ed Witten, etc... these folks didn't rise up through Olympiad events with the genius label their whole life.
I know this is cliché, but it really does seem like building determination and excitement is at least as important than simply pouring skills in child geniuses.
I don't have the citations on hand, but someone looked into the breakthroughs scientists discovered in their 20's and those in later stages of their career.
The types of papers published from younger scientists (Einstein, Newton) were more abstract, while those published from the older generation were those that could only be realized from decades of hard work.
I feel the biggest thing differentiating child geniuses is that they get things done on their own without being told to. They'll explore the world, they'll naturally have a thirst for learning, etc. The worst thing you can do to a kid like that is to give them the kind of "guidance" you give normal children. They're fine on their own; it's pushing them into a structure that screws them. But often the programs designed to coach genius children think of coaching as the kind of help you'd give normal children.
I find it interesting that society thinks it's important to "guide" genius children. A question I'd like to ask is: what exactly do these children lack that we need to compensate with guidance? Children who get things done on their own just need space.
I don't agree with this at all. Having a high level of intellect doesn't mean one has the worldly experience to navigate life's obstacles. These children, intelligent as they are, are still children, and impressionable by adults especially when they are young. All it takes is a few years in the early period of development for a budding genius' potential to be clamped. There are many reasons so many end up not doing well. I don't mean by merely the financial measure as noted elsewhere in this thread, but across the board, in that they end up not fulfilling their potential to achieve great things. For some the biggest contributing factor is having one of many different kinds of negative parental and adult influences at an early age.
> One of the most painful aspects of teaching mathematics is seeing my students damaged by the cult of the genius. That cult tells students that it's not worth doing math unless you're the best at math—because those special few are the only ones whose contributions really count. We don't treat any other subject that way. I've never heard a student say, "I like 'Hamlet,' but I don't really belong in AP English—that child who sits in the front row knows half the plays by heart, and he started reading Shakespeare when he was 7!" Basketball players don't quit just because one of their teammates outshines them. But I see promising young mathematicians quit every year because someone in their range of vision is "ahead" of them.
Being identified as a child genius puts you into the unfortunate default circumstance of always competing with everybody, instead of just competing with yourself like you are supposed to do when learning and growing. You are supposed to be uniquely smart, and when other kids do something better than you you start to question yourself.
Importantly, well meaning educators try to foster the areas you test as exceptionally gifted in, when what they should be doing is teaching you how to work through and overcome areas you are weaker in -- to achieve a better cognitive balance. This can help the child break the "curse of being gifted", where effortless achievement in one area becomes a kind of short-loop positive feedback drug they focus all of their attention on and harder/less obvious areas are ignored much to later detriment.
But it's almost never done, because it's assumed that since you're gifted in one area you're gifted in them all and they'll just focus on the ones you test the highest in. You've been given a magical spark, and they want to capture that spark. The cruel irony is that quite often, the harder they work to grab it, the faster it goes away.
I think one of the problems is that many of the educators responsible for guiding exceptionally gifted children through all this were not themselves exceptionally gifted and have a poor understanding and empathy for what it's like to walk around with all this, often very uneven, nascent intelligence.
I see from many of the comments here that other really bright kids were put in competitive environments where scores and placements became a big focus of their lives: SAT scores, Putnam, IQ scores...I'm sure most of us also did state or regional competitions of some sort or another. The most important thing I learned from all that when I was going through it was that "there's always somebody better than you so don't get all emotional when you have the bad fortune to cross paths with them in the same competition."
Actually, the better lesson I learned was to not bother competing at all and just focus one challenging myself. I'm already in the top 1-2% in whatever narrow subject area according to some test, without any effort, why don't I achieve competency in something I outright suck at? If I'm so smart, I should be able to figure out how to attack and surmount any weakness I have.
I think that little philosophy has gotten me much farther than any of the areas I was identified as being gifted in as a child.
50th percentile outcome is mediocrity, depression, booze.
This isn't gloating at their expense, because I was one. This is a fucked-up society and the "tallest nail" phenomenon ensures that most people like them eventually reach a stage of life where they don't do well, and it's harder to recover once that "golden child" image (untarnished success, monotonic progress) is lost and the world would rather invest in someone else.
Is it? I'd love to see some real data on this. For sure, some have succeeded. But there have been a lot who've not done much (especially in academia, which seems to tolerate laziness if you're smart).
Outside of academia, one who I know pretty well (he actually went to IMO, not just MOP) was no-offered at two different hedge funds because of the "tallest nail" phenomenon. When people found out that he'd attended IMO, there was a certain glee with which his co-workers (at least, in one of those two firms) made sure that he failed. After that, he was pretty much unhireable.
Has anyone here who is gifted with this level of ability looked into or experienced a Montessori-style education? Perhaps for your children?
My two young children are currently enrolled in a Montessori school and I can draw a lot of parallels between what the many gifted commenters here suggest as a better way to teach and my understanding of the Montessori philosophy.
Emphasis on engendering self-directed learning, freedom to explore their interests, avoidance of intelligence labels/praise such as "you're so smart", etc.
What's the point on focusing on children with high test scores? If that's what makes genius, the geniuses could -- and should -- be replaced by computers.
What makes a real genius is absolute honesty, willingness to re-evaluate their core assumptions over and over again, not get deluded by ruling dogma etc. Being able to multiply five digit numbers doesn't help with that.
I think this is a horrible article. His central argument is that the kids who demonstrate exceptional intelligence have too much attention heaped upon them, and discards the argument that in fact out school system fails these kids. While I agree in part that it is easy to put too much pressure on these kids by talking about their "potential" too much and pressuring them in directions they may not actually want to go, the answer is not to simply treat them as average.
He was part of the Vanderbilt University study of kids who score at least 700 on the verbal part of the SAT, or 630 in math, by age 13. I was part of the Johns Hopkins program, which is now the Center for Talented Youth which has similar requirements. he scored 800 on the math portion, 680 on verbal at age 12. I scored 800 on the verbal and 530 on the math at 12. He's a tenured math professor and published author. I'm an IT consultant of 20 years and a published author. I think I'm just as qualified to speak on behalf of this group as he is.
Those kids are under-served by the school system to the point of failure or near failure.He's completely right, talent isn't a number, but that number is indicative on an innate skill for knowledge assimilation and synthesis that is greater than average. Given the proper scholastic environment, these kids ARE capable of more than most, and should be allowed to find their niche just as much as the majority.
The problem, in my opinion, isn't that the school system is too rigidly skewed towards the majority, or that there are bad teachers. On the contrary, throughout my school career I've had a number of exceptional teachers that I still admire, respect, and cherish my time with, even the ones with whom I didn't necessarily get along with well (I was a jackass at times).
The school system had always seemed to me to be too cookie-cutter oriented, and was very difficult for anyone who didn't fit the mold. I didn't fully understand why until about 10 years ago when I read an article and then a book by John Taylor Gotto. The article is "The Six Lesson Schoolhouse". http://www.cantrip.org/gatto.html is the article. The book is "Dumbing Us Down" for sale here: http://www.amazon.com/Dumbing-Down-Curriculum-Compulsory-Ann... or at any good library.
The problem is the way the school system itself is structured. In the US, we're utilizing a school system that was designed 150 years ago and hasn't changed much since. We created this "modern" system during the industrial revolution's sweep across America. As machines made farming orders of magnitude more efficient, cities grew at an astounding rate, and industrial jobs became the dominant employment sector. The need for rigorous schedules became the norm with time zones and train schedules, and later with the whistles and bells of assembly line manufacturing. Strict scheduling in schools helped acclimate kids to the forthcoming work environment. It was a great thing, and helped build a strong and well educated workforce.
As times changed, however, schools didn't. We acclimated to special needs kids with attention or learning disorders, which is fantastic because we're able to take these kids, and get then up to the level of their average counterparts, and make them into productive members of society rather than ignoring and shunning them. But we don't do nearly enough for the small fraction who are highly gifted. We simply put them into "harder" or "higher level" classes than their peers. This isn't an acceptable solution. We need to stimulate them, to find out where their passions lie then feed them accordingly. Do they react better to lectures, or readings? Do they react better to more solitary studies, or in group environments? Do they need a standard amount of repetition to help boost retention, or does that simply bore them and artificially stunt their natural abilities?
Mr. Ellenberg is right that pressure is not the proper tool to make the most of these young minds, but neither is pretending they're not exceptional, and not giving them the opportunity to see exactly how far they can go.
But we don't do nearly enough for the small fraction who are highly gifted. We simply put them into "harder" or "higher level" classes than their peers. This isn't an acceptable solution. We need to stimulate them, to find out where their passions lie then feed them accordingly. Do they react better to lectures, or readings? Do they react better to more solitary studies, or in group environments? Do they need a standard amount of repetition to help boost retention, or does that simply bore them and artificially stunt their natural abilities?
We should do this for everyone. It's unclear to me why we should not find the passion and best way to teach "average" students too.
The only difference between "gifted" and "average" students is really how quickly they can learn certain material -- and maybe an increase in their ceiling for learning certain material. But I don't think there is a fundamental qualitative difference in how they should be taught.
Why don't we hand-tailor a bespoke educational curriculum and methods for each student? Primarily, it's a cost issue; secondarily, it's an aptitude issue for the educators. (My parents were both in public education, and some of what I saw as a user and what they reported as members was utterly appalling.)
But, it's the cost issue that makes it a total non-starter. Very few school districts will, across the board, be able to afford the teacher:student ratios required by individualized, customized instruction processes for each student.
If they could not afford to do custom-tailored program for average student, why should they do it for gifted? Results of the survey shows that gifted kids do alright in life, make more than average, get Ph.Ds, etc. Should schools (and average Joe who pays for it) provide them with even more advantages?
Why should we tailor our educational processes for the non-gifted end of the spectrum or those with behavioral difficulties?
My answer is that we've decided to make larger per capita investments in "outlier" individuals and the vast middle of the distribution population is accommodated with a standardized curriculum. I'm OK with that, though I'm concerned that we concentrate disproportionate resources on the left side of the distribution without investing enough on the right side.
I don't view the problem as "How should we use our limited resources to most effectively level the playing field?" but rather "How should we use our limited resources to most effectively foster the development of our future society?" It's no surprise that those two fitness functions result in different choices.
Best and brightest at 8-15 usually do not end up best and brightest in later career. You can see it even in the fact that average salary of that cohort is only 80k/year - only slightly better than average for ALL college graduates. None of those geniuses are particularly impressive and most ended up doing the same work with the same quality as the rest of us.
There was research that showed that IQ after 120 stops being correlated with success - other factors start being more important.
Yeah, my supervisor for my undergrad thesis is a brilliant researcher who's still publishing good work 20+ years into his career. He was just a normal dude in undergrad who started in engineering but switched to math because he disliked project management, and he certainly wasn't in any sort of "young genius" program through grade school. But his PhD thesis was runner-up for best in the country, he consistently presents at all the major conferences in his field, and he has even won a few teaching awards.
It's not about what those individuals deserve, it's about the societal return on the investment of their education. The potential return is simply greater.
This is the point of the article, really: that educational innovation needs to include all kids, because those are who are going to, collectively, have the most impact on society.
Even if the school system could be perfectly tuned for the top genius kids, there's just not enough of them to outweigh everyone else, in terms of long-term social impact.
I agree that this should be done for the majority of students. Like Gatto, I advocate a complete overhaul of the educational system in the US, and I think it's entirely possible even with the meager resources we currently allocate. Clearly education should be a bigger priority, as well.
Perhaps the best policy is to make a note that these children are gifted, stand by while they do their own thing, and when and only when they start getting bored, give them access to the kinds of challenges they need.
In my case, that would have been great. I had a few teachers along the way who allowed me to shed some of the shackles, and by the end of the year, my grades were always over 100%. Those are the teachers I really admired and felt I learned the most from. In my high school freshman year, by the end of the year I'd done all the work from my Honors Bio 1 class and the Honors Bio 2 class, and had loved every minute of it.
he scored 800 on the math portion, 680 on verbal at age 12. I scored 800 on the verbal and 530 on the math at 12. He's a tenured math professor and published author. I'm an IT consultant of 20 years and a published author. I think I'm just as qualified to speak on behalf of this group as he is.
I was one of "those kids" as well. I attended MO(S)P in 1999, won national writing awards, wrote a card game at 20 (Ambition) that is not just playable but actually played by a lot of people I've never met.
The problem is the way the school system itself is structured. In the US, we're utilizing a school system that was designed 150 years ago and hasn't changed much since. [...] The need for rigorous schedules became the norm with time zones and train schedules, and later with the whistles and bells of assembly line manufacturing. Strict scheduling in schools helped acclimate kids to the forthcoming work environment. It was a great thing, and helped build a strong and well educated workforce.
As times changed, however, schools didn't. [... W]e don't do nearly enough for the small fraction who are highly gifted. We simply put them into "harder" or "higher level" classes than their peers. We simply put them into "harder" or "higher level" classes than their peers. This isn't an acceptable solution. We need to stimulate them, to find out where their passions lie then feed them accordingly.
From first principles, I agree with you.
However, what has changed even less than the school system is corporate employment. If you're a cognitive 0.01-percenter, being a corporate drone is going to be way more painful than a decent public high school. Trust me, I know both.
Now, one might argue that 0.01-percenters are just unlikely to end up in corporate drone jobs, all being tapped to become proteges of the Gordon Gekkos and Peter Gregories (RIP) of the world. The data don't bear that out. The OP stated (a surprising fact) that the median income, at age 40, of these top-0.01% students was only $80,000. (I knew that the average income of prodigies was mediocre, but I was expecting $150-200k.) The number of 0.01-percenters who end up in corporate mediocrity is shockingly high.
The corporate "real world" is indifferent to the cognitive 1% (unless it comes with pedigree) and outright hostile to the correlates and eccentricities that come with being in the top 0.01%. The school system is doing its job. All that awful closed-campus stuff, the bells and no-backpacks-in-classroom rules, the hall passes and rules surrounding them, are inculcating a deference to authority that the corporate world still demands. And high school makes more exceptions for smart kids than any corporation. (Corporations might exempt political favorites from their bullshit rules, but that's a different set.)
If we want to make a world where the cognitive 0.01% actually get to use their talents (and I fully support such change) and have some autonomy/power, we should make haste to fix the work world. A real fix, not this chickenhawking VC-funded bullshit that seems just as willing to fund turds like Evan Spiegel and Lucas Duplan. We should abolish the current corporate system and reinvent capitalism with the right people in charge. That is the best thing we can do for the cognitive 0.01% (and society as a whole, which benefit sfrom their work). Improving the education system is also valuable, but cognitive 0.01-percenters are able to teach themselves so long as they receive a basically reasonable education (and the average U.S. public school qualifies).
Interesting article... but what really makes a prodigy? What's the difference between a prodigy and a normal kid? Is it just a keener sense of curiosity, or a greater interest in reading? Is it neurological? Is it environmental or genetic or something else?
Neurologists who study the brain's wiring are just as fascinated by the missile guidance system that top table tennis players have behind their eyes just as much as world class chess players.
The author laments the rate at which lesser math students leave mathematics, because they are behind the very best.
One of the most painful aspects of teaching mathematics is
seeing my students damaged by the cult of the genius. That
cult tells students that it's not worth doing math unless
you're the best at math—because those special few are the
only ones whose contributions really count. We don't treat
any other subject that way. ... But I see promising young
mathematicians quit every year because someone in their
range of vision is "ahead" of them.
But this is a rational calculation, precisely because mathematics is institutionalized as a highly competitive discipline. If those who score high on the SAT at 13 are 100 times as likely to make a scientific advance as those in the remaining 99% of the population, then there should to be roughly 100 times the opportunity for lower scoring individuals to make those advances than they currently have. But the jobs in academia aren't there. Students see this and they make the rational decision to jump ship. (I was irrational and did not.) The cult tells students that there are no jobs for you unless you are the very best. And with fewer tenure track jobs in a dwindling, pedigree conscious market, the cult is correct.
Grothendieck couldn't solve a Putnam problem, incidentally. Not a contest winner. You might be interested to know what some Fields Medalists say about some prominent prodigies. That they are extremely smart, but haven't done truly major work. The facts and the gossip are no consolation: academic opportunities are overwhelmingly and increasingly weighted in favor of the prodigy.
Likewise, elite employers want to hire the math and programming contest winners. Well, if you're not one of them, it is rational to select yourself out. I've gotten calls from recruiters saying that I'd be working such winning individuals. "Will I be doing the work they're doing?" "Uh, no, you'll be doing system administration." "In that case, maybe you should hire a Nobel Laureate. I am unworthy." Cleaning the digital bedpans of the superstars is not my idea of success. "Better to reign in Hell than serve in Heaven," as one famous antagonist put it.
As long as the STEM subjects remain a zero-sum game, with the overwhelming spoils going to the early bloomers, the winners, like the author, should be satisfied with what they have already won in an unnecessarily and destructively competitive field. The rest of us are doomed to provide them support as members of the economic precariat at slave wages, if we are foolhardy enough to remain in academia. There is no honor in adding to someone else's power law distribution, and I urge the contest winners to hire Nobel Laureates and other members of their own rank to do their support work, and not add to their winnings by exploiting the unworthy persons they elbowed out.
(I did earn a Ph.D. in mathematics, incidentally. This was wasted effort. When I was a toddler, apparently I impressed a child psychologist with my logic; my mother told the woman that she was an idiot for thinking that I was advanced. My experience in academia was not good--I was mostly exploited. I have decided to abandon mathematics and computer science for art.)
Is that compared to the general population overall, or a subset? It might be more informative to look at the subset that actually starts down the road of making discoveries in mathematics - maybe just people who attempt bachelors' degrees in math?
call me cynical but the only thing I expected when going to the comment section was lament of people perceiving themselves as prodiges, and people talking about smart people they know which focus on family.
[prodigies] are not given a lot of opportunities in schools that are designed for typically developing kids
... nor should they be. I was learning calculus in elementary school and writing the Putnam in high school. No matter how hard they tried, there's no way the schools I was enrolled in could have given me those opportunities. What prodigies need it not opportunities in school, but rather schools which are flexible enough to let them access opportunities outside of school -- in my case, starting my days at Simon Fraser University and packing my high school courses into the afternoon.
Those of us who managed sky-high SAT scores at 13 were 20 times as likely as the average American to get a doctorate; let's say, being charitable, that we're 100 times as likely to make a significant scientific advance. Since we're only 1 in 10,000 of the U.S. population, that still leaves 99% of scientific advances to be made by all those other kids who didn't get an early ticket to the genius club. We geniuses aren't going to solve all the riddles. Most child prodigies are highly successful — but most highly successful people weren't child prodigies.
This is probably the most important paragraph in the article. The numbers are unsupported, but I don't think they're so far off as to invalidate the point.
It isn't exactly wrong to say that Terry Tao and other former prodigies like him are geniuses. But it is more accurate to say that what they accomplished was genius. Genius is a thing that happens, not a kind of person.
Genius is both a noun and an adjective describing some people. It's a shame that Dr. Ellenberg felt it necessary to end an otherwise good article with such a piece of pithy nonsense.