A simple example that I've encountered in real life: some students are VERY good at math, and can get 100% on a calculus exam, and be experts in manipulating trigonometric functions - far better than I ever have been. Trigonometry and calculus are weird parts of math that are helped very much by memorizing very specific formulas and methodologies: it isn't obvious that one expression is the same as the other, or that if you substitute things "just so", a complicated integral becomes a simple integral. BUT ...
I can take those students who are used to using "m*g*sin(theta)" to get the force on an inclined plane, and instead of measuring the angle from the horizontal, I mark it as being measured from the vertical. And I can point out that this is not the normal angle theta, but its complement, so I'm being fair and letting them know that something is up, and not being sneaky/tricky about it. It doesn't matter. They'll still use "m*g*sin(theta)" and not "m*g*cos(theta)". Why? Because the "right answer" is "m*g*sin(theta)". That's what they've memorized. They know it's reliable and correct. They can do all this complicated and abstract math, integrating and differentiating trig functions and so on, but a simple problem that involves nothing complex, just an understanding
of what sin means and what cos means, is beyond them.
That isn't to say that they can't learn that, too, but only in the sense of it's being a variation of the original problem
. I.e., they memorize the new solution as applicable to the new case. They're weak at figuring out how to figure out things from first principles if I changed yet again something else in the problem. (Same physics principles, almost the same math, slightly different set-up.)
I also see this in an ISTJ coworker of mine, who is an excellent software developer. If it's a pattern he's followed before
, everything is tic-toc-logical-beautiful. But if there is something new, or it's a new technology, he tries to apply the old patterns in the new paradigm, and wonders why he's having so much trouble. I can explain and teach to him the new patterns, and he eventually figures it out with practice, but he doesn't "just see" those patterns which are obvious to me
. He sees the form and works with the form, but he doesn't see the function except as a side effect of the form
. I see the function (all of those patterns that I can "just see" without having to think hard), but I don't see the forms he sees except as a side effect of the function.