# calculus for a 12 year old...

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do you think it is reasonable for a 12 year old to learn calculus...and if so how would he/she learn it in a way that does not confuse him/her ?

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an approach to calculus is using and trying to measure slopes - this is accessible to a 12 year old. the movement from calculating a slope - via learnign algebra - to calculus might be a little too much; but then kids thrive when pushed. as long as it isn't the only time he/she would learn calculus then why not try and see if it works.

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do you think it is reasonable for a 12 year old to learn calculus...and if so how would he/she learn it in a way that does not confuse him/her ?

Not unless the 12 year old is VERY exceptional (think Gauss or Terry Tao).

It is much more important that younger people get a very solid foundation in geometry, algebra and trigonometry than to get into calculus too quickly. In fact there is a great deal to be said for waiting until one is in a university to study calculus.

Calculus is qualitatively different from high school mathematics. Despite the way that it is often taught in high schools, the objective of calculus is far more sophisticated than the usual "find the solution". Unfortunately calculus at lower levels often becomes just a game of symbol-pushing and finding the number. This misses the real point of the subject, which is to understand what derivatives and integrals really are and how to use the concepts. Calculating specific derivatives and integrals is only secondary. The point of derivatives is not "find the slope" and the point of integrals is only in part "find the area". Moreover the important theorems in calculus -- Rolle's Theorem for instance -- are dependent on properties of the real numbers that are somewhat abstract and usually poorly treated in an ordinary calculus class.

People's thought processes with respect to mathematics actually do change and mature. To learn calculus properly it is a great benefit to have reached an age at which one's thought processes are aligned with a subject like calculus. Age twelve is a bit early, though it depends very strongly on the individual.

IF you have a twelve-year-old who already has completely mastered algebra, geometry and trigonometry, and IF you have a twelve-year-old who has a deep interest in mathematics and a strong drive to pursue that interest, and IF that twelve-year-old is exceptionally mature in an intellectual sense then it might be appropriate to study calculus under the guidance of someone who has a deep knowledge of mathematics. But if those exceptional conditions are not met, then I suggest that the student concentrate on mastering algebra, geometry and trigonometry completely. It will be time well spent.

Edited by DrRocket

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I think I was about 14 when I started learning it and I'm not that good at maths.

As I see it, the problem is that calculus on it's own isn't useful or interesting.

You need to know other things like trig and algebra first otherwise it's not going to mean anything.

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I think you could teach the rules of differentiation of polynomials in one variable quite easily to a 12 year old. I am sceptical as to how much they will appreciate or understand what is going on.

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I think you could teach the rules of differentiation of polynomials in one variable quite easily to a 12 year old. I am sceptical as to how much they will appreciate or understand what is going on.

Yes, as they say, the ends does not justify the means. Calculus is not, for example, knowing the rules of differentiation of polynomials in one variable. It is, for example, knowing the foundations, implications and applications of the rules of differentiation of polynomials in one variable. That is, it's the integration (pun intended) of the algebra, geometry, trigonometry etc that lead to calculus.

Years ago, Kim Ung-yong was a 4-year-old Korean boy who could perform calculus. Even with an alleged IQ of 210, it gave him the mind of a normal 8-year-old, but that's not old enough to understand the calculus in depth. So sure, I grant that he was a child prodigy, but his calculus skills seem like sophisticated parlor tricks to me.

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As I have found by meeting many different people who have exceptional talents and skills at young ages and developed them from childhood, some of whom who even work for my LLC, you can accomplish a lot if you just put the work into it. The biggest problem for a 12 year old would probably just be getting stressed about how much work it actually is. But if they really go for it and try hard with a lot of determination, they will learn it. Besides, younger brains are better at learning anyway; the earlier the better.

I'd recommend they also learn another language, because studies have shown that learning a foreign language actually stimulates the parts of your brain that use math and that also proved true for me, as whenever I studied a foreign language more, thinking in terms of math also seemed easier. But then again, they'd have to be really determined to do that much work at that young of an age.

Edited by questionposter

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.... as whenever I studied a foreign language more, thinking in terms of math also seemed easier.

Damning with faint praise ?

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Damning with faint praise ?

No, I did a research paper for an English class before on ways to increase cognitive thinking abilities. Tetris is bull, at least from what I could gather. But I had checked with me, Spanish professors and a math teacher that they agreed with the survey of Spanish helping with math.

Edited by questionposter

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No, I did a research paper for an English class before on ways to increase cognitive thinking abilities. Tetris is bull, at least from what I could gather. But I had checked with me, Spanish professors and a math teacher that they agreed with the survey of Spanish helping with math.

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I fail to see how this relates to 12-year-olds being able to learn calculus.

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Not unless the 12 year old is VERY exceptional (think Gauss or Terry Tao).

It is much more important that younger people get a very solid foundation in geometry, algebra and trigonometry than to get into calculus too quickly. In fact there is a great deal to be said for waiting until one is in a university to study calculus.

Calculus is qualitatively different from high school mathematics. Despite the way that it is often taught in high schools, the objective of calculus is far more sophisticated than the usual "find the solution". Unfortunately calculus at lower levels often becomes just a game of symbol-pushing and finding the number. This misses the real point of the subject, which is to understand what derivatives and integrals really are and how to use the concepts. Calculating specific derivatives and integrals is only secondary. The point of derivatives is not "find the slope" and the point of integrals is only in part "find the area". Moreover the important theorems in calculus -- Rolle's Theorem for instance -- are dependent on properties of the real numbers that are somewhat abstract and usually poorly treated in an ordinary calculus class.

People's thought processes with respect to mathematics actually do change and mature. To learn calculus properly it is a great benefit to have reached an age at which one's thought processes are aligned with a subject like calculus. Age twelve is a bit early, though it depends very strongly on the individual.

IF you have a twelve-year-old who already has completely mastered algebra, geometry and trigonometry, and IF you have a twelve-year-old who has a deep interest in mathematics and a strong drive to pursue that interest, and IF that twelve-year-old is exceptionally mature in an intellectual sense then it might be appropriate to study calculus under the guidance of someone who has a deep knowledge of mathematics. But if those exceptional conditions are not met, then I suggest that the student concentrate on mastering algebra, geometry and trigonometry completely. It will be time well spent.

i know a 12 year old that has mastered algebra,geometry...and about halfway through trig.

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i know a 12 year old that has mastered algebra,geometry...and about halfway through trig.

Well there you go. You don't have to actually be an exceptionally smart person to learn calculus which *seems* like what DR is saying (even though that might not be the case), but you do have to be mature and motivated in certain ways in order to handle the work load. But, some people do develop that maturity at a young age.

Edited by questionposter

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I fail to see how this relates to 12-year-olds being able to learn calculus.

You fail to see a lot of things.

That is certainly among them.

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You fail to see a lot of things.

That is certainly among them.

Well 12 year olds can learn calculus if they try very hard to learn all the pre-requisite math and are very determined, and that's about it.

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Well 12 year olds can learn calculus if they try very hard to learn all the pre-requisite math and are very determined, and that's about it.

yay....because i know somebody that has accomplished that...

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yay....because i know somebody that has accomplished that...
Yes many can. Also some can't.

true...true

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You fail to see a lot of things.

That is certainly among them.

!

Moderator Note

Personal attacks are still against the rules. See Maturity.

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do you think it is reasonable for a 12 year old to learn calculus...and if so how would he/she learn it in a way that does not confuse him/her ?

Would this be confusing?

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Would this be confusing?

hmmm... it would take paying attention but no...if you really catch on to it...then no

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hmmm... it would take paying attention but no...if you really catch on to it...then no

"If you really catch on to it" then nothing is confusing.

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hmmm... it would take paying attention but no...if you really catch on to it...then no

Watch a few videos in the calculus section of this website and see if you can follow them. There are other areas such as biology and physics on that site as well.

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