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theinvisiblePLER
United States110 Posts
On October 15 2010 15:13 bbq ftw wrote: What is science's purpose? What is language's purpose? To be used to better mankind, no more, no less. To study the world around you. To communicate. | ||
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krndandaman
Mozambique16569 Posts
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Squeegy
Finland1166 Posts
On October 17 2010 21:29 floor exercise wrote: How many socks are you wearing? One on the left foot, one on the right foot? 1 + 1 = 2 Math bro Yeah, but it still doesn't make my socks math. As I said, try consulting your math professor. Dictionary may be helpful too. | ||
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Sky
Jordan812 Posts
On October 18 2010 05:00 Squeegy wrote: Yeah, but it still doesn't make my socks math. As I said, try consulting your math professor. Dictionary may be helpful too. When someone says that everything is math, it usually means everything can be described by math. He's not really stating that the objects you wear are made of an logical language system. He's likely stating that everything existing can be explained using math. Your statement that socks are just clothing can be similar to stating that you wear objects on your feet that have a specific mass, length, width, and depth in a three dimensional space (A mathematician could explain a sock through math better than I). They are both two different languages, you simply chose to use the word sock, specific to a few languages, to define the things you put on your feet. Everything currently can be explained by math, but when people find new objects (quarks, mesons, probability events, chemical and evolutional equilibriums, and compounds) they have to rely on math to define it first, then it's up to all the other languages to describe the event in their own way so that it can be more comprehensible. It's all about definition. Now run along and learn a new language from your math professor. | ||
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category
United States85 Posts
I also agree with some of the posts about how lousy the math education is here in America. Kids learn to hate math, and considering the way they are taught the subject, I completely understand where they are coming from. It's ironic that so many people think math is about memorizing formulas and procedures. The reality is that by approaching math as something to memorize, people manage to spend years in math classes without developing even the slightest bit of mathematical reasoning. Kids graduate high school in this country without knowing how to add fractions. They only know how to divide fractions by "invert and multiply", but sometimes they forget which fraction to invert.. And they can't multiply general polynomials, because if either factor has more than 2 terms, FOIL no longer applies. It's a sad state of affairs. I am hoping to change it =p. | ||
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DragonDefonce
United States790 Posts
Turns out though, you need to have a decent amount of logic and brainpower to do high school math. So it became a sort of a measuring stick for humanities majors also. And because of the way math is taught, many people go to college and think "oh I did awesome in Algebra in high school" or "calculus is so easy" and decide to major in math, only to realize real math is a pain in the ass that only masochists should attempt to do. And they struggle in agony while us physicists laugh at them and play with our lasers and magnets. But then again, we think we are better than everyone else so its not very surprising. Except for engineers. We know we are better than them  | ||
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hochs
United States10 Posts
On October 19 2010 07:25 DragonDefonce wrote: Honestly, aside from basic arithmetic (you know, not real math), not everyone needs math. It only is needed for science. Calculus was invented purely for the purposes of physics, differential equations for bunch of other natural sciences, so on and so forth. It became so important during the cold war era when people realized that in order to beat the commies (or the bourgeoisie bastards depending on which side of the iron curtain you were on), reading up on Shakespeare or trying to find historical evidence that Aristotle had gay sex with boys weren't gonna help. That is when you started seeing a lot of resources being put into math and science. Because pre-university curriculum had to be pretty much the same for everyone, even people who were not going into the sciences had to learn it. Turns out though, you need to have a decent amount of logic and brainpower to do high school math. So it became a sort of a measuring stick for humanities majors also. And because of the way math is taught, many people go to college and think "oh I did awesome in Algebra in high school" or "calculus is so easy" and decide to major in math, only to realize real math is a pain in the ass that only masochists should attempt to do. And they struggle in agony while us physicists laugh at them and play with our lasers and magnets. But then again, we think we are better than everyone else so its not very surprising. Except for engineers. We know we are better than them It's fairly well known in academia that physicists tend to focus on intelligence so much because they secretly know they're second to mathematicians, and hence the insecurity. A little blog linked by Terry's blog: http://blogs.discovermagazine.com/cosmicvariance/2007/02/25/the-cult-of-genius/ "We don’t put mathemeticians on this scale, because we secretly believe they’re smarter than us" ^^ | ||
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Cyber_Cheese
Australia3615 Posts
funnily enough, this just about makes more sense than the OP's version | ||
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Squeegy
Finland1166 Posts
On October 18 2010 06:29 Sky wrote: When someone says that everything is math, it usually means everything can be described by math. He's not really stating that the objects you wear are made of an logical language system. He's likely stating that everything existing can be explained using math. Your statement that socks are just clothing can be similar to stating that you wear objects on your feet that have a specific mass, length, width, and depth in a three dimensional space (A mathematician could explain a sock through math better than I). They are both two different languages, you simply chose to use the word sock, specific to a few languages, to define the things you put on your feet. Everything currently can be explained by math, but when people find new objects (quarks, mesons, probability events, chemical and evolutional equilibriums, and compounds) they have to rely on math to define it first, then it's up to all the other languages to describe the event in their own way so that it can be more comprehensible. It's all about definition. Now run along and learn a new language from your math professor. That's now what it means though. They can mean that by it, but it actually means something else. People should say what they mean, or at the very least mean what they say. And thank you for the encouragement. I do learn math from my professors five days a week. | ||
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57 Corvette
Canada5941 Posts
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jjun212
Canada2208 Posts
i guess from what i can remember; people i knew back in highschool including myself always questioned when would i ever need to know say.. quadratics in order to become like a police officer or an english teacher or a journalist or camera operator, etc. well maybe you dont need to know it.. but a lot of jobs require aptitude tests and whether the job itself requires math or not, those tests do (mostly simple but you never know) people these days dont just want one certain type of person. they want a well rounded person. so even if you're in the arts, it couldn't hurt to be adequate with math | ||
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Zortch
Canada635 Posts
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hochs
United States10 Posts
On October 21 2010 07:09 Zortch wrote: In my opinion the reason math is required as part of a general education its not so much about being able to do the math, but about being about to think is a certain way. This "mathematical" way of thinking about situations is very useful to have. What are some "mathematical" modes of thinking that you have in mind and are referring to? Unfortunately in USA, most people come out thinking math is about executing/applying series of rules/algorithms to compute something (integrals, derivatives, coefficients of fourier series, multiplying two integers, etc.). Rarely do they learn to think through things logically, creatively, and be able to give precise argument/proof for why certain facts/propositions/theorems are true using definitions, quoting previous theorems. The latter set of skills is what most idealists would have in mind, but it's so poorly executed by teachers / curriculum now. Sure the idea is great, but it's like D- noobs trying to copy Flash by turtling in base all day long (and getting raped in couple minutes), i.e. execution (how to) for teaching is terrible. USA had this "new math" thing in the 50's where people actually learned the language of set theory and learned to really prove things from the basic principles. Where did that go? The reasons for including math in general education is great, but I really think teachers (in k-12 in USA, say) ought to stick to those ideas. | ||
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Zortch
Canada635 Posts
Its not necessarially "mathematical" thinking - maybe that was a poor word choice on my part - so much as ways of thinking that arise naturally and commonly in mathematics and thus can be learned through the study of math. However, as you pointed out these nice ideas are not always taught very well in practice. | ||
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hochs
United States10 Posts
On October 21 2010 07:38 Zortch wrote: Just simply thinking logically and deductively is one example that mathematics and help to teach. Later on, being able to think abstractly becomes essential. A lot of people have trouble with ideas like "Let f be a function." or "Let x be a real number." and through math they can learn to deal with this sort of abstract notion. Then this sort of thinking can be applied to some other situations (maybe haha). Its not necessarially "mathematical" thinking - maybe that was a poor word choice on my part - so much as ways of thinking that arise naturally and commonly in mathematics and thus can be learned through the study of math. However, as you pointed out these nice ideas are not always taught very well in practice. I see. I find that also quite important. There's something I've always had a qualm with in K-12 mathematics in this country (USA). When people teach arithmetic, why do they only teach rules and algorithms for computing addition, multiplication, or division of natural numbers? For example, most people learn how to compute 56*13, say, by the rule 6*3 = 18, then 1 goes above 5, etc. etc. I think it's very rare to find a class where they actually prove that this rule works by using distribute law (which is another rule/law that ought to be discussed more and proved I think) by decomposing 56 = 50 + 6 and 13 = 10 + 3, after having memorized the basic multiplication results for digits of base 10. There some other things in the current math education where math is reduced to a series of rules/algorithms to follow. I think the problem may be that tests / assessments in mathematics put too much emphasis on these rules/computations aspects of math, which leads most students to feel that that's what math is all about. I find important what you find important (the kind of thinking you mentioned) but way too many teachers in this country just put easy-to-grade computational problems in their tests. Result: Students learn to think of math as a set of unmotivated rules/algorithms. Here's a suggestion, tell me what would be wrong with this: * Teach how to really prove results, and put them on tests as well as the computational kind of math * In fact when we teach arithmetic just do (elementary) number theory. Prove euclidean algorithm in class and in tests, show representations of integers with different bases, how to add/multiply/divide and prove they work, show unique factorization into primes, etc. for example what you may find in niven & zuckermann's book. * Instead of the calculus we have now, where students just memorize derivatives and integrals without any motivation, just do real analysis - follow rudin or something. We already have enough of those "calculus for other science majors" running amok, we don't need to do this for an actual math class. I'm not saying throw out computational math. Computational math is very much part of mathematics, but doing only computation doesn't help students to think "mathematically" at all. If we're to really teach students how to think "mathematically," then I find the above suggestions quite reasonable. Do exercises in constructing rational numbers from the integers (that are constructed from Peano Axioms) properly, learn that there's something to do to go from rationals to reals (either by dedekind cuts or cauchy-sequences) to have it satisfy nice properties (existence of inf, sup, etc.), and do the god-damn epsilon-delta proof instead of hand-waving "oh limit of x^2 as x goes to 3 is 9 because it looks like it." It will genuinely teach students how to handle abstract data!! One of the merits of doing math is (and should be!) that you learn to write things with precision with solid, valid logical arguments from the definitions and givens. | ||
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blankspace
United States292 Posts
Yes addition and division rules should be explained and justified but just imagine trying to get a group of third graders focused enough to pay attention to you...they'd rather have an efficient way of being "right." Personally, although I dislike the heavy emphasis on computation and algorithm, I think if students in general were smart enough (I'm obviously talking math smart, not other types of intelligence) to find it trivial there would have been less of it. Although I really do think that math education in the us could be improved greatly at least in calculus. As it is now, ap calculus is not much different than 6th grade word problems and arithmetic. | ||
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