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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 diff

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.

geocar 10y ago
> 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.
- magicalist 10y ago
  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.
- iopq 10y ago
  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.
- neeleshs 10y ago
  Indeed, I love https://betterexplained.com/ 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
- saint_fiasco 10y ago
  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.
  - geocar 10y ago
    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.
- th0waway 10y ago
  why does exceptional ability in one translate to sub-par in another? And why does it matter? We would all agree that a Cheetah is much better at running fast than a house-cat, but that does not take away from either animal. People so often want equal outcomes, and regardless of what the US Constitution says, all men (and women) are not created equal. It does not mean one is better than the other, just that we are different.
- jimmaswell 10y ago
  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.
WalterBright 10y ago
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.
- corysama 10y ago
  Would you have a reference to similar material I could spend a couple hours on?
  - WalterBright 10y ago
    The video series "The Mechanical Universe" has a very similar and simple explanation.
- saint_fiasco 10y ago
  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.
  - nitrogen 10y ago
    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.
ArkyBeagle 10y ago
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."

geocar 10y ago

> 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.

magicalist 10y ago
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.
iopq 10y ago
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.
neeleshs 10y ago
Indeed, I love https://betterexplained.com/ 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
saint_fiasco 10y ago
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.
- geocar 10y ago
  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.
th0waway 10y ago
why does exceptional ability in one translate to sub-par in another? And why does it matter? We would all agree that a Cheetah is much better at running fast than a house-cat, but that does not take away from either animal. People so often want equal outcomes, and regardless of what the US Constitution says, all men (and women) are not created equal. It does not mean one is better than the other, just that we are different.
jimmaswell 10y ago
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.

WalterBright 10y ago

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.

corysama 10y ago
Would you have a reference to similar material I could spend a couple hours on?
- WalterBright 10y ago
  The video series "The Mechanical Universe" has a very similar and simple explanation.
saint_fiasco 10y ago
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.
- nitrogen 10y ago
  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.

ArkyBeagle 10y ago

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."