Calculus textbooks are difficult but rewarding.

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.

Calculus has a myth built up around it on how hard it is. A kindly professor once showed me how it worked in about a half hour, and I was like "is that all"? Of course that wasn't all, but that bit of help served me very well for years of more advanced math.

Would you have a reference to similar material I could spend a couple hours on?

The video series "The Mechanical Universe" has a very similar and simple explanation.

I tried to learn calculus a couple of times but always get stuck on integrals. I'm pretty sure when I was 10 I would also have gotten stuck there.

Forget the algebraic mechanics of symbolically evaluating an integral -- let a CAS do that for you -- and just focus on the relationship to the shape of the function being integrated.

> must have some gift

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.

Agreed. How many comments have we had on HN about particular subjects saying things like, "I just didn't enjoy learning the math, I never got a mathematical concept at an intuitive level, etc, until particular use case X came up for me, and now I really understand it. Why didn't my teachers teach it like that in the first place??"

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.

It just means the rest of us have to work harder. It doesn't mean you have to be content with less intellectual pursuits.

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.

I think that's exactly backwards.

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.

Indeed, I love https://betterexplained.com/ which is all about intuitive understanding of calculus and other stuff. A post on the constant 'e' - nobody ever told me what that number really means. More such material, and a willingness to learn is all thats needed for a majority of folks, in my opinion

Edit: typo

I was self-taught. It was actually very frustrating asking my mother for an explanation because what she told me was technically correct, but not useful in explaining why the textbook said what it did. What we both missed is that the textbook said it was a UNIT circle which meant that the radius was one.

After this I didn't really rely on her help anymore.

Some people just can't be taught certain things. That article about programming aptitude matches a lot of my obssrvations and I'm reliving it again with one member of a chemistry class group activity.

Calculus class simply provides a method for testing how good your algebra is. It's an elaborate algebra test. The stuff where you use calculus is the calculus test, etc. etc.

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."

Those weren't my studies. Those were my hobbies. Give me homework and I'll run away screaming.

I used to HATE the language subjects. Now that I'm not being forced to do it, I enjoy linguistics.

When you disagreed in your first comment you disagreed to this:

> 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.

You're just describing one of the most well-established facts about learning: the dominant factor is intrinsic motivation.

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.

> Those weren't my studies. Those were my hobbies.

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 didn't have lazer focus, in fact I spread myself over many different subjects. I studied zoogeography, physics, chemistry, history, etc. because I thought those things were interesting. This didn't stop me from finding calculus to be approachable and easy.