I think this is also true more generally than just for students. I've given a keynote presentation about it at a conference this year if anyone finds that interesting: https://www.youtube.com/watch?v=Lckris5U5iw
I have a friend who's a metalworker. He'd never beat me in an algebra test, but he's damn smart when it comes to manipulating the physical world. He also happens to be very thoughtful and insightful about film and photography. But I'm not sure he considers himself "smart", even though he does original and careful analysis in the areas that he cares about.
Another friend is -- as far as I'm concerned -- an absolute genius at understanding people psychologically, their decisions and motivations. I'll never be as smart in my own preferred areas as she is in this. But I don't think that most people would give her a "smart" badge for it.
Often this comes up in written fiction: authors will describe the characters and their thoughts and motivations in a mode natural to how they perceive things: some authors spin up plots and intrigues at every turn, others focus on raw emoting.
So I tend to view smarts as a personality trait, when we're dealing with healthy folks with no other issues(and realistically, most people are battling something else most of the time without necessarily being aware of it). There's a limited degree of smarter-is-smarter that shows up in testing, and then after that it starts being about personality-driven specializations, the ways in which they overcome problems. The archetypes are easy to spot in school: the student who seems to ignore any lecture or materials and rushes to get help from the teacher or study buddies, versus the student who quietly reads the text and never asks a single question. Both types can get perfect scores in some subjects, but usually not across the board, effortlessly. And as projects grow in scope and cover more skills, awareness of personality-driven limitations becomes more essential to success.
That said, passion can drive you super far.
See Yerkes and Dodson law[1] and I think Hebbs[2] also touched on this topic.
The mice were given 5 levels of (uncalibrated!) electric shocks, which has since been taken to be the "arousal" axis; their task was to learn not to go down a dark hallway, and the number times they attempted this before learning that dark hallway = shock has since been taken to be "performance". This resulted in a jagged 5-point line in which the fastest learning did not occur at the highest or lowest shock levels.
That's it. That's the experiment. Needless to say, even if the result were perfectly trustworthy, extrapolating this out to a neat bell curve that describes the performance of humans studying for a calculus test is unscientific. But like all pseudoscience, it has a sort of intuitive appeal. It should be noted that Yerkes and Dodson themselves never made any claims about "arousal" and so on - they were just trying to measure the effect of electric shocks on the speed of animal habit-formation.
Here's a fairly comprehensive review of the methodological flaws with Yerkes-Dodson, too numerous to go into detail on here: https://docs.lib.purdue.edu/jhpee/vol7/iss1/3/
My understanding tis that the studies were replicated in rats, cats and humans.
From https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2657838/
> Despite the limitations of their study, the findings of Yerkes and Dodson were subsequently replicated in cats (Dodson, 1915), rats (Broadhurst, 1957; Telegdy and Cohen 1971) and people (Dickman, 2002; Bregman and McAllister 1982; Anderson, 1994), and became part of the lexicon of the field of psychology as the “Yerkes-Dodson Law” (Young, 1936; Eysenk, 1955).
But the weird thing is that if you take two adults and compare their IQs the difference there has a negligible weighting for environmental factors. Modern studies put the heritability of adult IQ upwards of 80%. This also has the extremely counter intuitive implication that our privileged child's academic advantage in youth doesn't necessarily carry over into adulthood. And similarly an adult who came from a less fortunate background will not often suffer (at least in terms of intellectual ability in so much as IQ can measure) for it, as an adult.
The reason I mention this is because the person coming from a privileged background would ostensibly have a much higher degree of belief in themselves and presumably a wider array of well supported interests. Our '8 year old solves nuclear fusion in spare time' clickbait articles invariably, coincidentally, happen to have a parent or two who is a nuclear physicist. Yet in the end that self confidence and supported interests don't amount to anywhere near as much as we'd expect.
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One other major argument against this is the sharp rise of parenting where parents genuinely belief, and work to prove, that their child is the next Einstein. And this happening at the same time that the Flynn effect has entirely disappeared, and in some cases substantially reversed, in much of the developed world. The Flynn Effect was the observation that IQs were increasing over time. IQ is a relative value with 100 always set as the mean with a standard deviation of 15 points. But a '100' in 1900 was scoring, in absolute terms, worse than a 100 in e.g. 1920. And this kept happening. But then sometime around the 1990s this trend began reversing. [1]
Flynn observed an average increase of about 3 points per decade. In many places in the world today we are seeing a decline of about 2 points per decade. Think about what that means in absolute values. That's a net change of -5 points per decade. That is one third of a standard deviation decline, per decade! Getting into hypotheses here is counter productive and outside the point I'm making which is simply that we've, in most parts of the developed world, decided to begin pretending that every child is special. If IQ were connected to self confidence and belief in oneself - we'd expect to see something at least vaguely looking like a positive correlation here. Instead we've seen a completely unprecedented and sharp reversal in IQ.
[1] - https://en.wikipedia.org/wiki/Flynn_effect#Possible_end_of_p...
20% isn't negligible.
As a not directly related aside this also leads to another really interesting aspect of heritability. It changes as the average environmental situation changes. As we get closer and closer to environmentally equal, any given trait's heritability approaches 100% as the only differences left between individuals become genetic. As an obvious example consider height. Malnourishment tends to stunt an individual's growth. So in an area where some significant chunks of the population were malnourished and others were not, you'd see a much lower heritability for height than in places like the US where that environmental factor has been mostly eliminated.