<p>I think the recall is natural. Many “natural mathematicians” can remember and use everything they learn. For some, it’s really easy to remember and apply because it all makes sense and fits into one giant, consistent framework.</p>
<p>Math most certainly is artificial. How many people would have discovered multiplication without being taught it??</p>
<p>Being really good at math is a natural trait resulting from the way some people’s brains work–I think it is comparable to being a talented musician. Good teachers can enhance this talent.</p>
<p>But most reasonably intelligent people can learn math skills and problem-solving techniques–Slorg is right, though, for some people remembering and using these skills does not come easily–my D has always had to work very hard to keep up in math, while reading-verbal skills have always come easily and she has an excellent memory for non-math information.</p>
<p>i was about to mention the music analogy…</p>
<p>Math skills are both acquired and natural. Everyone can learn up to a certain degree of math. Everyones brain is hardwired into being able to understand a certain level of it. Just as anyone can learn to play the piano. For the math that 99% of us learn (basicly through calculus 1 or 2), everyone who doesn’t have like a learning disability can get through. Probably most of us if we studied our asses off could get through all of calculus and some other mid level undergrad math classes. After that it gets significantly harder to advance I would assume. I know i had enough trouble in calc 2… But anyway, some people will be able to understand the concepts (and apply them!) quicker than others. But the same point holds that if you’re not “gifted” you’ll hit a barrier, just like a musician. So, at a higher level, natural ability comes into play.</p>
<p>Interestingly enough, I read that there are only 3 things a child can legitimately be a prodigy in; music, chess, and math - with music and chess drawing on a math foundation. Other then that, everything else has to be acquired.</p>
<p>I think math skills are a lot like writing skills. Math and writing both have strong foundations in acquired skills – number operations and processes (from division to derivatives) versus grammar and structure (paragraphing to participials!). So “skills” are all acquired. But “skillz” as in “mad math skillz” come from number-analyzing ability and imagination, just like writing ability comes from word-analysis and imagination in a different way.</p>
<p>I agree with the threshold idea, but it’s not exponentially harder after that. I think I reached the end of my status as pretty much a math genius in middle school. It got a bit harder but I still always got the A+. Now it’s even a bit harder but it still hasn’t gotten me down yet.</p>
<p>The majority of math classes until you get into upper level college courses(Dynamics, numerical analysis, etc) are a joke. The problem is that you have to learn to think math not just do it. The problem is that most students don’t know how to learn math. You don’t just do problems in the book. You apply it. Apply it to everything. There is also a distinct difference between competition math(AMC, AIME, USAMO, IMO) and just taking advanced math(linear algebra, differential equations, etc).</p>
<p>I think calling upper level high school math courses a joke is idiocy.</p>
<p>I’m a junior at the moment, taking Calculus. To me, Algebra 1 and below is like counting from 1 to 10, it’s more than a joke. I’m sure it’s a bit harder than that for even the smartest of middle school kids.</p>
<p>If you’re a college math major and you get way past Calculus, I bet it’s a joke.</p>
<p>To call something a joke is subjective based on how much experience you’ve had in it. So it is lame to generalize high school mathematics as “a joke,” for it is only a joke to college math majors.</p>
<p>Um, </p>
<p>A) I’m not a college math major, and neither are a vast majority of my friends.</p>
<p>B) The concepts you learn in these classes are not that difficult.</p>
<p>Sagar, I think that’s really unfair? By what standard are those concepts “not difficult”? Maybe for you Calculus is easy as pie, but don’t tell us we’re stupid if we consider them “difficult.” What we’re saying is, by a college math major standard they are “not difficult.” And that’s the standard you’re using.</p>
<p>I’m saying that these concepts aren’t that difficult. Of course you can say that chemistry isn’t difficult, as I have a lot of trouble with that. Just because everyone has a hard time in a topic doesn’t mean the topic is difficult, just that everyone is not at the top of their game.</p>
<p>Besides, we are on CC, so I reserve all rights to hold ludicrously high standards :p</p>
<p>i think for high school math, and SAT Math, etc., its mostly acquired because you can sort of study for that</p>
<p>but math contest math- there’s a lot more natural ability needed IMO… there’s only so much you can study</p>
<p>There’s a book that discusses this topic in great depth, for anyone interested.</p>
<p><a href=“http://www.amazon.com/gp/product/0618251413/qid=1135972342/sr=2-1/ref=pd_bbs_b_2_1/103-1108894-5358213?s=books&v=glance&n=283155[/url]”>http://www.amazon.com/gp/product/0618251413/qid=1135972342/sr=2-1/ref=pd_bbs_b_2_1/103-1108894-5358213?s=books&v=glance&n=283155</a></p>
<p>if you need help with math i suggest wel… to get tutors from anywhere and theyll give you advice and even tell you how to prepare for math if youre having trouble</p>
<p>I think these skills are acquired. I took calculus at the state school when I was 14 with other 8th and 9th graders and none of us had problems with it. None of the students in this large sample was exposed to more math or math at an accerlated pace relative to other students; we just started high school math in middle school while holding our math education in elementry school consistent with other students. When I was a teacher assistant at the time for seniors I realized most of the seniors couldn’t understand concepts such as integrals and convergence/divergence. From this I beleive math skills at purly natural. As if it matters.</p>
<p>its skill not natural… maybe a bit but people that have no idea of math at first can come out to be a genius and getting 4.0s in math</p>
<p>The ability to get an A in math class is acquired- it’s memorization.</p>
<p>The ability to understand what’s ACTUALLY going on in math class is natural- I don’t think logic is a learned trait. You’re either logical or you’re not…</p>
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<p>You’re dead wrong. When it comes to math competitions, “natural” ability, whatever that is, is absolutely meaningless. You need to do practice. Lots and lots of practice. By many estimations, to reach the highest level of math competitions one needs a similar amount of work as an undergrad math major.</p>
<p>Most people in this thread who are trying to defend the “natural” position point to either people struggling in various math classes or people who seem to “get” them easier. Neither is proof of anything. For example, if my parents taught me calculus in 8th grade, I might seem to “naturally” get the concepts faster. That doesn’t change the fact that it isn’t natural, it was acquired. (Of course, I wouldn’t be telling my friends that - I’d go for “I’m a genius, yeah.” :)). Struggling in a math class? OK, that happens. Some who struggle eventually end up focusing on it, loving the subject, and end up majoring in it in college. There’s no real evidence of any kind of threshold.</p>
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<p>So why do we even bother to have logic classes? Logic is a learned discipline.</p>
<p>I don’t buy this “natural” stuff. There are kids who easily understand the concepts–they do well. On the other hand, there are kids who study very hard to understand only the formulas and numbers–they tend to poorly. If you ever get behind in math, you’ll have difficulty learning new material that builds on the previous material and you’ll end up getting confused and just studying the formulas and numbers and problems in the book. It’s paramount to never fall behind or do the bare minimum to get an A.</p>
<p>I also disagree with the poster who claimed children can be prodigies in chess, music, and math. There is no such thing as a chess prodigy. No one is ever good at chess right away. It takes thousands of games until your brain can build up the proper pattern recognition skills to even understand chess well. The 15 year old grandmasters are prodigious because they’ve managed to cram more games into their lives, and happen to be exceptional at pattern recall.</p>
<p>rather “acquired” is the answer that you should be looking fore</p>
<p>math is completely acquired through one word: PRACTICE.</p>
<p>i doubt anyone is born knowing how to do derivatives, antiderivatives and logs</p>