A series of great questions. First, the snotty fast answer:Did you ever encounter students like this? Did they go from being obviously dumb/low IQ to being smart? Or were they always smart and hi IQ - they just have a problem with one particular subject, until the light bulb goes off?
It doesn't take a lot of brilliance to get to a Ph.D. It takes mostly persistence and hard work, and an IQ in the 2+ Sigma range. Maybe for mathy fields, it takes closer to 3 Sigma, but still, that's not impressive. Almost all of us know some one who is substantially smarter than an average professor, but without the Ph.D. Probably that also indicates a lack of academic habits (and thought habits and prejudices), and a lack of a 10K academic articles read in one specialty. This is not entirely off the cuff. But it shouldn't be the whole answer.
The slower, fairer version:
This is every teacher's dream. This is why people go into teaching as a profession. Finding the kid who didn't understand it...who is having a hard time with a subject...and for whom your 7th explanation finally clicks, and the student begins to veritably glow with understanding...that is the God-moment for a teacher. If you've never felt it...you don't understand why people are teachers...and if you have felt it, you don't know how anyone can ever want to do something else. Mild exaggeration? Sure. The point stands.
This happens...sometimes. If a normal teacher teaches Algebra to 6 classes of 30 kids for a (4-month) semester, she may see this once. Maybe twice. It's generally worth all the crap for the whole semester for that once...if it happens. If it doesn't happen for 2 or 3 or 4 semesters, maybe she gets tired of teaching, and quits.
The Aretae explanation:
Interest is huge. Practice is huge. Cognitive readiness is huge. IQ is merely big. A smart enough, but slow-developing student who figures something out, gains an interest, and puts in effort to a Ph.D. 10 (or sometimes 20) years later is a real possibility. I've personally seen it done: Ph.D. in the real sciences by kids who were academically near dropping out of school but for an art teacher who believed in them, or a sports coach. And those weren't the 4+ sigma kids dropping out because school was hatefully slow and stupid...but rather kids who just weren't in the whole academic thing at 14.
Much more often, in subjects...I've seen folks who were more than a bit competent in a subject...but whose motivation and self-efficacy were destroyed by bad teachers. A particular teacher of pre-calculus many years ago did that to a number of people I knew. Her bad teaching broke the math spirit of an awful lot of otherwise math-comfortable students who never pursued the math that they would have been perfectly able to do, given a tolerable teacher and a decent book (they had neither).
With multiple thousand hours spent tutoring, I concluded that half my job was to straighten out the messes made by bad teachers. The other half was to do catch-up that no one else had noticed needed done. I mean, really...how DO you do fractions in a college level teaching-certificate pre-algebra course (or worse, when studying for the teacher-cert test) if your multiplication tables aren't solid? And how the hell do you teach the 6th graders when you personally don't actually understand the material at better than test-cram level? But I digress.
On top of all this, there's also the Pygmalion effect. Learning is massively (It's probably close to a 1 stdv difference) impacted by the teacher's expectations of a class. Futhermore, in school, IQs are not generally well measured, and it's not too hard to get a +1.5 Sigma kid placed in the slow group due to bored behavior problems. Once there, it's also often true that they're tracked in, and then you're really screwed.
As an aside...I'm something of an opinion outlier regarding subject-level intelligence. I think that the whole Howard Gardner multiple intelligences thing is 90% premium grade hokum. There is g, and there is interest and practice. I suppose there are (almost necessarily, given evolutionary understandings of the brain) various modules, and that verbal and spatial intelligence vary separately a little. But basically, g + practice (mostly determined by interest) seems to be far and away the best explanation for the picture we see.
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It doesn't take a lot of brilliance to get to a Ph.D. It takes mostly persistence and hard work
The number one requirement to get a Ph.D. is the ability to "suffer fools gladly". (aka dance like a trained monkey to please your committee.) This is why I have an M.S. instead of a piled higher and deeper.
Thanks for the response.
I agree about the multiple intelligences too. It seems like there is a basic ability talent in manipulating abstract symbols, and that talent can then be applied to math, reading, writing, song writing, painting, oration, mechanical engineering, etc. I would not call this ability "g", though. I would just call the ability "native intelligence" or "raw cognitive power". The definition being: "the ability to learn/perform a novel task involving abstract symbol manipulation." This ability cannot be precisely measured. IQ and g-loaded tests are best understood as proxies that can measure ability to learn under certain circumstances.
It seems like raw intelligence mostly functions as threshold effect. If you have enough for a given profession or task, then after that practice matters more than anything. But if you do not have a sufficient level of native intelligence, no amount of practicing will turn you into a great programmer.
There might be a different type of intelligence that aids in quick response. Drumming, freestyle rapping, and basketball playing may rely on this kind of intelligence.
Devin,
Your analysis is strong, and it pulls out some fuzzinesses not addressed in my orignial post.
1. I mostly agree with your 'g' comments. A few caveats.
A) It's awful hard to measure what they call fluid intelligence, and so they tend to measure crystallized intelligence, which just isn't the same thing, and relies on more homogeneity than really exists. Fluid intelligence is much harder, and though I think I have a model for how to measure it, I haven't seen much in other good models.
B) I'd actually say there's 3 levels. There's what really is going on. There's our mental model (talent/intelligence) of how we think it works. There's what the test measures. I agree that the tests measure something that doesn't match our models.
2. Wonderful selection of examples.
A) Programming may be the best example I know that violates my outline, because it seems as if practice is insufficient to good programming. The research says that there are at least 10x ability differences between equally experienced programmers.
B) Drumming is the only musical task that does not appear to be correlated with IQ at all, while everything else is.
C) Quick Response: I know a lot of folks who vary substantially on the dimension of quick smart vs. slow depth. In particular, I know several people who are quite witty, but unable to follow a conversation at much of a deep level. I also know a few academics who are quite slow on their feet, but eventually come to much stronger arguments, some self-generated, than the witty ones.
I think it's especially tricky in that most folks who are one type of intelligence or the other don't recognize that there are multiple response speeds for intelligence.
D) Steve Sailer wrote some really good stuff a while back reminding us that IQ != everything cognitive. Charisma, for instance, seems to be semi-unrelated...more akin to courage than to IQ. Just like there are different physiques for long distance running (Kenyans) than for Sprinting (West Africans), or upper body strength (Caucasians), so too are different cognitive tasks appropriate to different cognitive makeups as well. Also, verbal IQ seems to vary at least a bit off spatial IQ.
I never liked the way researchers distinguished between "fluid intelligence" and "crystallized intelligence". Let me define two terms: "cognitive skills" refer to specific skills in cognitive manipulation - algebra, writing, programming, etc. "Cognitive dexterity" refers to the ability solve novel cognitive problems and acquire new cognitive skills.
One might think that testing vocabulary may be a test of just memory or "cognitive skills" or "crystalized intelligence". However, if you give a vocab test to two students of the same age and same environmental exposure, that vocab test will actually to a large degree test "cognitive quickness" - the ability to learn new cognitive skills. To repeat, if you control for environment, any test of a cognitive skill is also a test of how quickly students acquire cognitive skills. Conversely, a supposed test of "fluid intelligence" may really be a test of how time a person spent learning something, rather than how quick they are. If you give a Raven's test to someone who has practiced taking the Raven's 3 hours a day for a year, they'll do much better than someone who has never seen it before.
The reason why IQ tests work is that have a built in environmental control. Because no one actually does sit down and study the Raven's matrices just for fun, most students will have had similar environmental exposure to the types of problems on the test. With similar environmental exposure, differences in test scores will be a result of "cognitive quickness"/raw ability to learn. But IQ tests break down as measures of cognitive quickness if environmental exposure greatly differs.
I think that threshold effects matter for a lot more than just programming. For instance, I don't think someone with 90 IQ could ever become a great corporate contracts lawyer, no matter how hard they studied. I also highly doubt they could become a great orchestra composer.
Devin,
It seems like we're pretty close on almost everything now. Only major difference:
You agree with the "smart person consensus" that threshold effects matter a lot for IQ. I think they only matter a little as compared to interest. Since you are on the side of the consensus, we should believe you.
However, I have 20 years of teaching experience as well...and my experience suggests (loosely) that IQ threshold effects are not as strong as the consensus says. Given that I know the consensus, and am (mostly) properly Bayesian, and still disagree, one might have to back off the consensus view a bit.
On the other hand, being a teacher biases one towards the practice view, because it's much easier to observe than the IQ threshold view. So I am probably unconsciously biased in my observations.
I could play princess bride all day, I think, on this topic.
Summary: I accept that there is a consensus view (and corresponding bias) of "smart people", and that there is a different consensus (and corresponding bias) for teachers. Clearly the answer is somewhere in the middle...and I don't think that the "smart people" have corrected enough.
I might agree that thresholds are lower than commonly believed. For instance, I totally buy that the threshold for becoming a Nobel winning economist might be 1std or 2std rather than the 3std or 4std as conventional wisdom would hold.
But let's say you were teaching a student who seemed pretty slow, tested at 90IQ and <1200 on his SAT's. With the proper coaching, teaching, motivation, and effort, do you think there is any chance that student could become a top corporate lawyer?
Devin,
Now we're in difficult territory, where the phrasing of the question matters a lot.
Your question regarding "top corporate lawyer" is similar to the question can a short half-hispanic kid (5'5") with birth defects regarding the correct numbers of fingers and toes get into the NBA?
Specifically you're asking whether he can hit the top ten-thousandth of a percent skill-wise. Almost certainly not. But Larry Bird could. And that kid could still beat all my friends 1-on-1, and was probably in the top 10% of kids his age on that skill-set when I was growing up.
Your question is all around competition with folks who are nearly equally interested, but much more naturally talented.
If you switch the question to "can he do X", where X is not a competitive thing...but rather an impressiveness thing...then you get a whole different picture.
Can person X, IQ 90, be better than person Y, IQ 150, at arbitrary task Z, given that X likes it a lot, Y doesn't, and they can both spend time as they please? Heck yeah.
If you say the word "TOP", then you've turned it into a competition, and natural skill eventually dominates, because interest and effort and coaching are all close enough to equal. If you're not talking "TOP", or you're in a narrow enough market, then effort dominates talent and interest dominates discipline.
Your example again. I believe that a 90 IQ/1000 SAT kid can, with sufficient interest/effort/coaching, do every single thing a top corporate lawyer does, at an excellent level. But he would never be a top corporate lawyer, because someone else has as much interest/effort/coaching, but more skill, so they're mostly better than excellent.
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