Can you learn to be good at math or are you just born with it ?

[cristo]

Most people out there have the potential to become decent mathematicians but their discipline and effort is lacking.

How are you defining "most"? Do you mean most people who are in university for maths, most people who are in university for any subject, most people who successfully graduate high school, or just most people in the country(/world)? If you mean the latter, then I think you're very wrong!

 

[turbo]

I pile because I care :) Like I said, there are at least a dozen other threads that address this exact topic and I see no reason why any newbie to our forum couldn't just use the search button instead of asking the same question three million times.

I understand your motivation and I don't disagree with the "hard love" approach, but I went through HS in a tiny rural school in the largest graduating class (42) that the district ever fielded. Our math programs were severely deficient, and in my senior year the new math teacher had to cobble together a pre-calculus program to cater to me and a couple of other kids who were headed into Uni. The kids in college that had the hardest times with math were those that appeared to have never gotten any effective training in applied math. Pure maths might be fun (and sufficient) for some, but for any kids wanting to dive into any advanced physics or engineering programs, they not only have to learn how to do computations, they need to learn how to evaluate a problem, decide which computational tools to apply to it, and tackle it and even re-evaluate it and see if the results can be verified or at least bolstered by any other methods. When kids have not been taught how to apply the mathematical tools that they have learned, math can be unhinged from reality.

 

[Wellesley]

The kids in college that hard the hardest times with math were those that appeared to have never gotten any effective training in applied math. Pure maths might be fun (and sufficient) for some, but for any kids wanting to dive into any advanced physics or engineering programs, they not only have to learn how to do computations, they need to learn how to evaluate a problem, decide which computational tools to apply to it, and tackle it and even re-evaluate it and see if the results can be verified or at least bolstered by any other methods. When kids have not been taught how to apply the mathematical tools that they have learned, math can be unhinged from reality.

I'm kind of confused as to what you mean. Maybe I misinterpreted MissSilvy's post (#23), but I thought she was talking about students who use excuses as a reason for not doing well in math. If someone tried hard and made an honest effort, and still struggled, as you described in your post, than they are doing nothing wrong.


As for the original topic, some people may be more mathematically oriented, than others, but,this will only get them so far, if they don't work hard, learn the material, do the homework, etc.

My question is this: can I still try hard and learn all that stuff (I'd have to take some grade 10 prerequisites) even in grade 11? Or are people just born with good math skills?

You can do anything that you put your mind to. Don't ever let people dissuade you from doing something simply because they said you're not good enough.
Definitely the best advice so far:

Man, if anyone ever tells you that you weren't "born" with something and will thus fail, I'm telling you right now they're full of it.
Its true that there is such a thing as natural talent in mathematics, and it might even be true that to achieve the greatest heights you must be such a genius.

But at the level you and me are talking about, its determination and guts that wins the day. The willingness to sit down and not get up till you've solved it- you have that, and you'll be fine all the way to the edge.

 

[turbo]

I'm kind of confused as to what you mean. Maybe I misinterpreted MissSilvy's post (#23), but I thought she was talking about students who use excuses as a reason for not doing well in math. If someone tried hard and made an honest effort, and still struggled, as you described in your post, than they are doing nothing wrong.

Some kids may be helpless and adrift because they have been taught to do calculations, but have not been taught how to break down problems and determine what mathematical tools would be appropriate to use to attack those problems. Pure math might fine for many people, but more people can grasp math then they are taught it in an atmosphere in which the math can be applied. Young kids might not appreciate this, and may (reasonably) ask if some people are "better" at math than others. I'm not trying to give anyone a hard time - just putting out the viewpoint that HS kids coming out of a deficient math program may not have the perspective to ask that OP's question in any better manner.

 

[Wellesley]

Some kids may be helpless and adrift because they have been taught to do calculations, but have not been taught how to break down problems and determine what mathematical tools would be appropriate to use to attack those problems. Pure math might fine for many people, but more people can grasp math then they are taught it in an atmosphere in which the math can be applied. Young kids might not appreciate this, and may (reasonably) ask if some people are "better" at math than others. I'm not trying to give anyone a hard time - just putting out the viewpoint that HS kids coming out of a deficient math program may not have the perspective to ask that OP's question in any better manner.

I get it now...thanks for the explanation.

 

[Raizy]

What about Dyscalculia ?

 

[snipez90]

Um, I'm sure that is not what the OP had in mind and is not the point of this thread. Obviously, if one has a learning disability, one will have difficulties learning math, and we should be helping those who have such disabilities.

 

[neslte]

It can be tempting to "pile on" the OP and similar posters, but please throw them a bone. Too often, kids are taught math by a "cookbook" method that emphasizes how to make calculations, and they are not taught how to dissect a problem to figure out which mathematical tools to apply to it. This process implies a deeper degree of understanding (and it is absolutely essential for applied mathematics in engineering and similar fields) and it may be something that young students do not appreciate. It's too easy for kids to look at their performance and the performances of peers in HS, and wonder if they might be lacking in "talent" when in fact they have not been adequately educated in how to evaluate problems and apply the mathematical tools at their disposal to solve them.

Lol you guys understood me wrong somewhat. I never even tried advanced courses of math so I'm not complaining that the reason I did bad is because of genetics, because I never even tried them in the first place, I just wanted to confirm that there would be no inherent problem if I do take the advanced courses before I take em.

 

[Jack21222]

Could it be the "im smart so I don't need to study" syndrome?

I'm starting to run into this problem for myself. All throughout high school, and up until now in college, I never needed to study. I just aced every test I took. Even in Calc 1 in college I blew through it (because I already took the material in high school).

But, now that I'm in Calc 2, I find myself struggling. Well, by my standards, anyway. I've got a middle B in the course, and I find myself having to learn effective study habits. Since it's an online-only course, it's even more important to learn self-study.

My General Physics 1 class is like that too. Without study, I wouldn't be doing so well. But, I'm doing extra problems out of the book, even aside from homework, and reading ahead on material before we get to it in class. I've got the only A in the class at about a 95%. Second in the class only has about an 85%.

Intelligence PLUS hard work is a potent combination, it seems. I can easily see how somebody that has the "natural ability" could fall into a horrible trap in some of the harder courses. It's been a big shift in my personal outlook on school.

 

[Werg22]

I'm starting to run into this problem for myself. All throughout high school, and up until now in college, I never needed to study. I just aced every test I took. Even in Calc 1 in college I blew through it (because I already took the material in high school).

But, now that I'm in Calc 2, I find myself struggling. Well, by my standards, anyway. I've got a middle B in the course, and I find myself having to learn effective study habits. Since it's an online-only course, it's even more important to learn self-study.

My General Physics 1 class is like that too. Without study, I wouldn't be doing so well. But, I'm doing extra problems out of the book, even aside from homework, and reading ahead on material before we get to it in class. I've got the only A in the class at about a 95%. Second in the class only has about an 85%.

Intelligence PLUS hard work is a potent combination, it seems. I can easily see how somebody that has the "natural ability" could fall into a horrible trap in some of the harder courses. It's been a big shift in my personal outlook on school.

I beg of you, find a more transparent way to boast in the future. You blew through your math classes up to Calculus 1. So what. You come a dime a dozen.

 

[ice109]

I'm starting to run into this problem for myself. All throughout high school, and up until now in college, I never needed to study. I just aced every test I took. Even in Calc 1 in college I blew through it (because I already took the material in high school).

But, now that I'm in Calc 2, I find myself struggling. Well, by my standards, anyway. I've got a middle B in the course, and I find myself having to learn effective study habits. Since it's an online-only course, it's even more important to learn self-study.

My General Physics 1 class is like that too. Without study, I wouldn't be doing so well. But, I'm doing extra problems out of the book, even aside from homework, and reading ahead on material before we get to it in class. I've got the only A in the class at about a 95%. Second in the class only has about an 85%.

Intelligence PLUS hard work is a potent combination, it seems. I can easily see how somebody that has the "natural ability" could fall into a horrible trap in some of the harder courses. It's been a big shift in my personal outlook on school.

I beg of you, find a more transparent way to boast in the future. You blew through your math classes up to Calculus 1. So what. You come a dime a dozen.

hahahahaha werg22 you took the words right out of my mouth.

tip for Jack21222. we can tell you're a show off because 3/4 of your post is about you and then the last 1/4 addressing op is thrown in like an afterthought.

 

[Tobias Funke]

Does it really matter? If you care about the subject, then you'll continue to study and improve regardless of what your highest level may be. It's the same reason I still play basketball even though I'll never make the NBA.

But if I had to answer, I'd say yes, you can learn to be pretty damn good at math if you're willing.

 

[chiro]

I think its actually a curse to be too smart because you end up learning habits of coasting through courses become bored, then depressed, and then when things get rough you pick something else to blame.

If you aren't as smart (but smart enough to do well if you work hard), then its a lot better because you are constantly putting in consistent work to get down what you need to and this is a better paradigm of behaviour over say the smart genius' way of learning through pure intuition.

I think that the best way to test the genius out is to put them somewhere where they are slightly out of their league as soon as possible so that it can coach them to not only realize that they have limits but to also get the idea that even they have to work at something. Personally I think that hard working geniuses are very rare as to the proportion of very smart people who are just lazy. Someone like Nikola Tesla stands out but he is the exception rather than the rule.

 

[quasar987]

I'm 16 and in grade 11. I've taken only the minimum amount of math required and only college level math at that. But computer science requires a lot of math, mainly calculus, advanced functions and physics. My question is this: can I still try hard and learn all that stuff (I'd have to take some grade 10 prerequisites) even in grade 11? Or are people just born with good math skills?

I've come to believe that everyone's brain has its limit when it comes to math: it could be that your limit is set at high school math, or undergrad math or grad math or math research or field medal level math.

But if you don't work your best, you'll never know where that limit is.

There's a stunning example at my school of a guy I met in a few of my undergrad classes. I met him in differential geometry and it was his second time taking the class. A session later, I also had probability with him and it was also his second time taking that class. The session after that, I met him in the hallway and it turned out he had flunked probability again and was now taking it for the third time.
I admired his tenacity but at the same time felt sorry for him because I had categorized him as someone very much attracted to math but whose brain limit was sadly set below undergrad math. But the year after that, he aced all his classes, became a TA, became responsible for the math undergrad weekly conferences, applied and got accepted to grad school.
I haven't asked him what happened because it's a touchy subject but I guess he just started to give it his best!

 

[Bourbaki1123]

I find it difficult to claim natural ability does not exist when I hear of people like this:
http://en.wikipedia.org/wiki/Kim_Ung-yong

My conclusion would be that the vast majority of people all fall within a rage of do-ability with a few outliers. Some people are like http://en.wikipedia.org/wiki/William_James_Sidis" , some can't function above the level of a ten year old, but the vast majority(which certainly nearly everyone if not absolutely everyone on this forum falls into) can achieve similar results with varying degrees of effort.

I have found college math to be often fairly easy, I have a very good memory and understand things quickly, but I still have had to put in a lot of work in the background. I can breeze through algebra or number theory because I muscle through math texts, undergraduate and graduate in my spare time and during the summer. I might find a class easy but its because I struggled with similar material in self study before.

Some people in a couple of my classes have told me that they think I have a natural ability beyond theirs, but I'm not so sure that its really that big and I tell them why to set them straight. I put in a lot of time outside of what is necessary with the faith that it will make me a stronger mathematician, and that reciprocates when I need it to.

 

[maze]

I've had the advantage of hanging around a few reputed "math geniuses" over years, as friends and roommates. I've watched how they work, and there is no magic to what they do. When a they figure something out, it is because they are doing very specific things that have a high probability of leading to an insight - taking special cases, thinking about what theorems are related, making diagrams, trying to reason by analogy to other concepts, etc. I found that if you work just as hard and apply the same techniques, you will get insights at approximately the same rate.

 

[hollyrenee]

Yeah I sucked horribly at math throughout high school (mainly because I was never interested). I finally buckled down my junior year and decided to pay attention and attempt to learn it. It was just a precalc/trig class, but I did really well. I too always figured that some people were just better at math than others (which may actually be true), but I realized that if you just really study the material it's not so bad.

Oddly, math is now my favorite subject in college and I'm finding it really easy to understand, despite my hatred for it in high school.

 

[snipez90]

Yeah I also started seriously studying mathematics my junior year, when I took precalculus. I was fortunate to have a very good precalculus course taught by a teacher who emphasized a good intuitive feel for the topics while presenting sound derivations of the theorems. I think a strong precalc course is very important and in my case, much more important than the AP Calculus course I took the year after. Despite the fact that I learned just about everything about derivatives with proofs in my precalc class, my AP Calc teacher insisted on drilling us on the applications of differentiation. He never covered proofs and his intuitive explanations were fairly bad.

Somewhere along the way in AP Calc, I wanted better explanations, even when I spent so little time on math due to the emphasis on computational aspects of calculus. If I didn't realize that there was such a huge difference between the way that topics were presented in my precalculus course and the way they were covered in AP Calc, I probably would have been content with just being able to get a 5 on the AP exam. There are many ways to be spurred on to pursue mathematics. One of them is to have just one good teacher throughout middle school and high school, but sometimes even this is considered very fortunate.

 

[deferro]

The thing about math is, you have to stop "trying to" in order that the understanding you had already is realized.

That is, learning math is (a lot) like realizing you knew it already. It's really a shame to realize that all that effort some teacher put into explaining all those ideas, is because of quite a simple and straightforward thing after all.

 

[Metaleer]

I think it tends to be a case of 99% perspiration, 1% inspiration. In a nutshell, natural ability may help somewhat, but there's nothing like sitting down with a book, reading it carefully and doing the end of chapter problems.

 

[lagwagon555]

I'm going to post from the negative point of view, obviously because I'm not getting As at the moment :)

I think that some people are incredibly good at learning. My friend is one of the top scholars in the country. He never studies except before exams, and just somehow understands everything instantly, and memorizes it forever. I'm the complete opposite, lectures go in through one ear and out the other, and I don't learn anything until I actually do questions.

I don't get As, but that's because I don't study a lot. Most people aren't the natural genius that my friend is. All (most) of the other smart kids I know all study, heaps. I know the top scholar for calculus in my country, she does nothing but study. Literally. She could be someone with my amount of natural talent, but just works bloody hard. Or she could be a combo of genius/hard worker.

Anyway, I'm sure that it's possible to get As, no matter what your ability, if you just study hard. I don't mean make studying your life. Just make sure you go over everything, understand everything, and do it constantly throughout the semester to make sure you don't have to re-learn anything just before your exams.

I haven't done this yet, so my grades show for it. But I'm getting into the routine now (as well as having to relearn all the thermo from the first quart... argh).

 

[cristo]

Anyway, I'm sure that it's possible to get As, no matter what your ability, if you just study hard.

If your ability is over a certain threshold, then yes. But there are lots of people who will never be able to get top marks, regardless of how hard they work.

 

[lagwagon555]

If your ability is over a certain threshold, then yes. But there are lots of people who will never be able to get top marks, regardless of how hard they work.

For sure, not everyone can make it to the 99th percentile, A+ marks. But I think most, if not all people can make it to A- or A.

 

[deferro]

How's this math assignment:

"deduce from the symmetries of space and time the existence of a subgroup of SU(2)xSU(3), Pauli's sigma-closed algebra over fermions with mass"

 

[cristo]

For sure, not everyone can make it to the 99th percentile, A+ marks. But I think most, if not all people can make it to A- or A.

I made this point earlier on in the thread in response to someone else, but what do you mean here by "most"? If you mean that most people in high school could make it to an A in maths, then you must either go to an incredibly good high school, or maths education in high school must be very easy where you're from! If you mean that most people enrolled in a maths degree at university could be able to obtain A's, then this is perhaps more of a believable statement, though I still disagree with it!

 

[Wellesley]

I made this point earlier on in the thread in response to someone else, but what do you mean here by "most"? If you mean that most people in high school could make it to an A in maths, then you must either go to an incredibly good high school, or maths education in high school must be very easy where you're from! If you mean that most people enrolled in a maths degree at university could be able to obtain A's, then this is perhaps more of a believable statement, though I still disagree with it!

Would you agree that the average student has the ability to either improve their grades, or possibly get an A, depending on how hard they work?

 

[maze]

If your ability is over a certain threshold, then yes. But there are lots of people who will never be able to get top marks, regardless of how hard they work.

I think you mistook lack of ability for lack of motivation, low perserverence, and poor foundations.

 

[cristo]

Would you agree that the average student has the ability to either improve their grades, or possibly get an A, depending on how hard they work?

Clearly if a student studies more, then they are more likely to get a higher grade. All I'm saying is that it is not possible for all students to obtain A grades in mathematics, even on leaving high school, say.

I think you mistook lack of ability for lack of motivation, low perserverence, and poor foundations.

I disagree. It's very easy for people who are good at mathematics to look at this through rose-tinted glasses and say 'well anyone can do it if they work hard enough.. students who fail are just lazy', but in reality things are not so simple: there is a large proportion of the population who simply have no natural ability.

 

[thrill3rnit3]

Ever heard of tabula rasa??

 

[maze]

I disagree. It's very easy for people who are good at mathematics to look at this through rose-tinted glasses and say 'well anyone can do it if they work hard enough.. students who fail are just lazy', but in reality things are not so simple: there is a large proportion of the population who simply have no natural ability.

See, this whole notion that there is this magical thing called "ability" that let's you solve problems - it's a false notion. It's too vague to be useful and obscures the truth, which is that problem solving "ability" is a simple machinery of specific strategies, tricks, tactics, and heuristics.

Let put it this way,
1) With enough effort, one could write a program to solve any high school or university maths problem
2) The human mind is Turing-complete
3) Therefore, any student can learn to do high school or university mathematics.