Curse Of The Gifted (2000)

We actually ended up separated in our advanced math, and I was bullied heavily because I had to end up eating lunch with 8th graders while only being in 6th and 7th grade. It was socially sub-optimal and it sure wasn't rainbows and unicorns. However, I was already an outcast amongst my own grade level, so being an outcast amongst older kids wasn't much of a difference.

My point is that it was not intellectually hobbling, it did not set me up to feel a Curse of the Gifted in Math, nor did it teach me bad habits as the analogy with the marshmallow test would imply.

The reasons skipping that grade was good: I avoided a poor teacher, whom I would not have gotten along well with. Part of the reason for me skipping a grade was that the disparity in reading levels was actually detrimental to the class, because of the diversion of the teacher's resources. Second reason is that I have an early birthday, so I was never tooo far behind my peers in the next grade, and in fact I felt much more comfortable in that situation and made friends better.

Just for an alternate perspective!

Can't agree more. -- someone who's happily skipped two grades at school (not in the US, mind you) and sometimes wishes he had skipped all twelve.

Why? Because before his teachers, back to his age 7 or so, had carefully walked him through the music note by note and bar by bar and, likely then, the artistic expression. But, still he was darned gifted. So, a few years later, relearning violin, he was fine again for the rest of his life.

Being able to do arithmetic, algebra, and other mathematical operations in your head is fine. E.g., during WWII, John von Neumann, one of the best mathematicians of the 20th or any century, sometimes went to people working on war projects to see if he could help them out. At one stop, a guy was unsure about how to find a solution, so von Neumann suggested, "Let's try a local solution via infinite series and look at a few terms. So, von Neumann did the arithmetic in his head [he could take two eight digit numbers and multiply them together in his head]. When von Neumann left, the guy was near tears. Why? Because he had been up all night using a mechanical desk calculator to get just some of that arithmetic right!

I found in doing research in math (I've published such stuff), once get into the problem well then do most of the thinking for the actual research just between the ears and writing very little. Can even do some of the algebraic derivations just between the ears. The actual research, at least the way I do it, is heavily 'conceptual' where writing isn't very efficient anyway.

From what you wrote, I see nothing wrong with your abilities. If you are not handy with paper and pencil, then it is not too much to expect you to become handy with just some usage. So, try, and soon you will 'get it'. It sounds like your problem with calculus was mostly just a problem with paper and pencil -- so, 'get it' with paper and pencil. Unless are, say, another von Neumann, can't expect to do significant derivations in calculus, say, integration by parts or multiple integrals, without writing down the expressions step by step.

But, of course, for calculus, long ago some software efforts for integration worked out what expressions could be integrated in closed form and what ones could not and wrote software to do the integrations for all the ones that could. The results are in at least one of the old computer algebra packages! So, with that software, "Look, Ma, no pencil or paper!".

About your suspected faults, don't be the least discouraged about them! Some are just your imagination. Some can be easily enough corrected. Essentially all the rest can be circumvented.

In particular, it appears that you are concerned about some skills that were supposed to take you from a few days to at most a few months to get good enough with way back long before you shaved! Doing catch up on that material now should be a few days' walk in the park. E.g., in K-12, I didn't learn English grammar and punctuation very well. In college I was in math and physics where this gap was not very important, and otherwise I just wrote only sentences where I did understand the grammar and punctuation. Now I've long had a 12th grade English grammar book right at hand and look up details when I'm in doubt; long ago I got nearly everything I missed in K-12.

Back to working without writing, in plane geometry I refused to do the homework the way the teacher wanted, write out in full detail proofs of just three problems. Instead I worked all the non-trivial problems and then also the more challenging ones in the back of the book, often writing nothing, sometimes writing in the margin of the book, sometimes on scraps of paper, and only for a few of the most difficult problems in the book, actually writing out a complete proof. Worked fine! When the teacher wanted to see my homework, I showed her nothing, and she was torqued. When I came in second in the class on the state test, she was 'confused' since she thought that I didn't do any of the homework! Heck, I solved every non trivial problem in the book and, thus, likely did the most homework of anyone in the class. Also, I slept in class -- I learned from the book in a quiet room, not when she was making noise in front of the class! Being able to learn math just from a book proved crucial, the main way I got my Ph.D.!

Lesson: You don't always have to do it their way!