>I was reading calculus textbooks when I was 10 years old.
I suggest that you, indeed, spent effort on your studies.
A 10 year old child who can enjoy them must have some gift that makes it easier for them to understand the difficult parts quickly and get straight to the rewarding part.
Or what?
The rest of us are dumb?
It could have been a good teacher, who found a way to make it make sense, or some other series of positive reinforcement that shaped them and prepared them, to be thinking about mathematics clearly. It doesn't have to be the luck of the draw.
I don't want anyone to give up, thinking they just didn't get the gift, so they should be content with playing with the ball. If you don't get mathematics, you might just haven't had the right circumstances to get it yet.
Whether or not it would have worked to teach it that way in the original circumstances (perhaps there were other things that needed to fall into place first), it's very clear that the right motivation and the right context have a huge impact on people's eagerness to learn and their ability to grok a concept.
Just because most people will never be Olympic medalists doesn't mean they shouldn't play sports and exercise. Lots of people do those things even when they don't have a particular gift.
If you want to be an olympic medalist, you need to work as hard as an olympic medalist.
If you do not want to be an olympic medalist, you do not work more hard than an olympic medalist.
And indeed, if you actually did work as hard as an olympic medalist, you could possibly receive an olympic medal.
Edit: typo
After this I didn't really rely on her help anymore.
I know of a specific technique for teaching algebra - write down the principle used to justify each step in a derivation/solution - that will teach algebra cold but it "costs" too much so we don't do that.
I've heard at least one "officer" ( like dean ) level academic say "We use calculus class to keep the stupid people outta med school."
I used to HATE the language subjects. Now that I'm not being forced to do it, I enjoy linguistics.
> But it boils down to the hours that kids put into their interests.
While you then go on to say that that is exactly what you yourself did. That you don't like being forced to learn is besides the point, but also sort of confirms it. You spend time (learning) on things you enjoy. That's how you become "gifted". The trick is having kids be engaged with something productive and not spending time on [insert subjective detrimental activity here]. Whether parents can influence that or it's down to luck is debatable, but I definitely lean towards the former.
Whether you call them hobbies or studies, the fact that you were intrinsically motivated to pour effort into them is why you got so good at them.
Then your case does not contradict the OC's view that "Gifted children are "gifted" with a laser focus on the unusual things that they find fun - math, music, what-have-you."
I would sit in class and play games (which I'd programmed) on my TI-83, or read books. I would drift my attention to the teacher's lecture occasionally, just enough to convince myself I understood what was being taught, then back to my game.
I never took notes, nor did I study for tests, even through my undergrad in computer science. I got an A+ in multivariable calculus just by listening to the prof talk, and piecing together my comprehension on the fly.
As far as focus goes, often my focus is laser guided but I'm not in control of the laser. When something catches my interest, it becomes all I can think about for weeks. I'll obsess over it and learn everything I can about it, until my interest wanes.
I'm left with really deep knowledge of really obscure topics, and shallow-to-nonexistent knowledge of many common topics, which makes me a surprising conversation partner.
And yet you also told us:
I was reading calculus textbooks when I was 10 years old.
I scored in the 99th percentile in math on the California high school exit exam.
I transferred to a university as a junior at 17.
Regardless of the nature/nurture debate, if you can achieve those things at those ages with any amount of work then you are clearly far smarter than most people, at least when it comes to mathematics.
Not being a genius means that he is merely 2 standard deviations smarter than the mean (think "there's a few of those in every high school class") rather than 4 standard deviations smarter like the kids in the SMPY.
Rather a few of those in every high school. 2 standard deviations means 2.5% per side. This is one in 40 people, so probably on average 2-3 people per year in an average high school.
Of course, pre selection can lead to higher values, but having several children outside of 2std dev in a class won't be average in the vast majority of schools.
It's probably more fun or compulsive than laser focus. One savant was described as a calendar addict. He'd ask when you were born first thing when he met you. He developed an ability to calculate the day of the week for any given date in seconds.
according to who? The best I can find is that a particular IQ test (the Stanford-Binet test) used that definition from 1916 to 1937[1]. Might be time to update your sources :P
As compared to other people trying things for the first time I'm usually a very quick learner. I think being a quick learner is innate. I've had the ability to learn things quickly since early childhood.
> Reading is not understanding - maybe you just enjoyed the attention that you got from it.
I didn't get any attention from this, I tried to hide it from other kids so I don't stand out too much. When I placed first in the math Olympiad they kind of resented me and said "oh, he studies like a grade ahead of the rest of us". I was actually much further ahead. Calculus is NOT that hard. It's not a super power to be able to understand calculus. It's just a little bit more abstract (limits and so forth are not intuitive for some people).
> This contextually implies you consider yourself talented
I think I'm talented. I just don't actually do anything useful with my life. The last course I had to complete to finish college was a technical writing course. It was 100% busywork and presentations and posters and BSing. It was the worst.
mmh ... what a calm and measured response. and now I feel a bit bad for having responded so harsh - though honestly more tongue in cheek.
actually I can relate to what you said. also read calculus and algebra books as a teenager, wrote a book about JavaScript when I was fifteen, later studied math, most of my teachers in high school told me on a regular basis that I'm a genius and our gifted.
now, I wouldn't say that I didn't do anything useful with my life ... though nothing useful of the academic or technological kind. I rather lost respect for intelligence, the focus on IQ, status symbols and success in general. instead i try to become a happier and inspired person which brings something good to the world and into the life of the people surrounding me.
It took me longer to graduate at that point, but it was mostly because I was expected to do work and I never did before. I hated learning in a structured manner and being forced to do things. In fact, my lack of focus is what led me to learn about things on my own. I was reading calculus textbooks when I was 10 years old. I struggled with it, but it was fun. Then I'd read some physics instead because I felt like it.
Maybe successful people have lazer focus. But not all talented people are focused.