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On July 29 2012 16:49 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:47 Mallard86 wrote:On July 29 2012 16:40 TheRabidDeer wrote:On July 29 2012 16:37 Mallard86 wrote:On July 29 2012 16:31 TheRabidDeer wrote:On July 29 2012 16:28 Mallard86 wrote:On July 29 2012 16:26 TheRabidDeer wrote:On July 29 2012 16:23 paralleluniverse wrote:On July 29 2012 16:16 r.Evo wrote:On July 29 2012 16:08 paralleluniverse wrote:
[quote]
Now you've basically proven the point that we should teach mathematical literacy to the general population instead of just symbolic manipulation.
If the convention was to do addition then multiplication, we could have just written,
position = [.5(acceleration)(time)^2] + [(initial velocity)(time)] + (initial position)
and still have gone to the moon.
There is NO reason why multiplication should be done before addition, other than because people say so. It's a convention, it's notation. It's not a mathematical truth. Actually I think you're wrong. If I can believe one of my better math teachers t he reason for multiplication first is that a multiplication is just short for multiple additions. e.g. 3 x 7 + 4 x 5 has to give the same result as 7+7+7+5+5+5+5 or 3+3+3+3+3+3+3 and 4+4+4+4+4. The result in both of those additions is 41. Getting this result with using multiplicatives instead of multiple additives is ONLY possible if you deal with the multiplications first. PS: FUCK YES I LEARNED SOMETHING IN MATH. My teacher would be proud of me. PPS: The feeling of being a complete math-smartass is fucking awesome. Why did I never think of that during school? Now you're just stacking convention on top of convention. Why should 3 x 7 + 4 x 5 mean 7+7+7+5+5+5+5 instead of [(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]*[(7+4)*(7+4)*(7+4)]? The idea that multiplication is repeated addition is something that is taught in primary school, but it's not generally true, how is pi*e, the sum of pi, repeated e times? Again, you only know it is that order because youve learned it. Somebody new might try to pair it up as 3 x (7 + 4) x 5. They dont know the brackets arent supposed to go there. They just see some numbers and they know they need brackets somewhere. Also, pi * e is the sum of pi repeated e times, it is just strange because you have awkward numbers. Now you are arguing against yourself. If it has to be explained then it is not naturally logical. log·ic [loj-ik] Show IPA noun 1. the science that investigates the principles governing correct or reliable inference. That is to say you follow a known pattern. I dont know if I can think of anything off the top of my head that is "naturally logical". Maybe music... MAYBE... though most music has a learned structure too. Westerners read from left to right and reading is usually something learned well before algebra. PEMBAS is not a naturally logical conclusion from the perspective of the western reader because it does not always follow the previously set standard of left to right. Westerners read left to right top to bottom, but many forms of music have you read 2 bars at the same time. Music is not natural. Also, PEMDAS exists because math generally requires you to use logic, not "natural logic". Whatever that may actually mean. Why dont you actually read your own quote? You are criticizing the population for not being able to follow a simple logical procedure yet it is not a simple logical procedure if it has not been taught or it has been taught and the knowledge was not retained. If you want to criticize the population for ignorance then go ahead but dont claim the population is stupid for not being able to follow a simple set of rules when they dont know the rules. PEMDAS is taught in 4th grade (or earlier) and is used for every single bit of math beyond 4th grade. If you cant retain the knowledge of the foundations in math by the time you are in high school, that is a failure of teaching and learning. If I stopped learning english rules in the 4th grade, that would be a damned shame.
Thanks for finally making a proper complaint!
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Algebra has more uses than just mathematical ones, it teaches problem solving, which is an important life skill to have.
Also every other country, with a well funded school system, teaches algebra maybe it would be more productive to focus on why American students struggle with algebra than to try and find excuses to not have to learn it. There are obviously some deep flaws in the American school system, because students in other western countries better results aren't because they're harder working, because they're not.
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United States10328 Posts
On July 29 2012 16:35 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:30 paralleluniverse wrote:
What order you solve an equation in is irrelevant.
Consider 2x+1 = 0, under the convention that addition happens before multiplication.
So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go?
On a side note: statements like "foil it out" are good examples of how the American math system teaches formulae and algorithms, not mathematics.
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United States10328 Posts
On July 29 2012 16:53 sOda~ wrote:Show nested quote +On July 29 2012 16:46 paralleluniverse wrote:
For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists. An inner product is bilinear you noob!
Hermitian inner products aren't... you have to take a Hermitian conjugate on one side.
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On July 29 2012 16:48 ]343[ wrote:
But an actual mathematician is concerned about maps between objects and universal properties rather than explicit constructions (that is, how an object behaves, not how it's written; the written convention is merely for communication's sake), so he reasonably would not see a test of "knowledge of convention" as a test of mathematical aptitude.
Knowledge of convention allows you to read and learn from what others have done. Also, its pretty much required for any form of work or publication, where it needs to be checked or certified or whatever.
I would say it's reasonable to accept a "test of knowledge of convention" as a test of mathematical aptitude for any practical purpose.
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On July 29 2012 16:40 UrsusRex wrote:
Not one person has given a compelling reason how making algebra mandatory improves critical thinking skills. All of you supporting and condeming it are missing the basic problem. The entire world teaches algebra to their students but nowhere has it ever been shown to improve the quality of the people who learn it. All of you talking about tools and learning skills and resonating knowledge do not one shred of evidence for your position beyond asserting it as fact repeatedly. Show me any data than doesn't even imply, just correlate thats all I ask, any data that would link studying algebra to improving learning skills, because if it doesn't do that, we are teaching an irrelevant subject to millions of people.
Pragmatism much?
If you have access to databases such as Academic Search Premier, LexisNexis Academic, and so on, you can find dozens of published and peer-reviewed research articles and scientific journals on this.
Besides, why would learning algebra NOT improve your critical thinking skills? As Malgrif said, many of the skills used in logical thinking are used in mathematics. That's pretty much a given...
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On July 29 2012 16:40 UrsusRex wrote:
Not one person has given a compelling reason how making algebra mandatory improves critical thinking skills. All of you supporting and condeming it are missing the basic problem. The entire world teaches algebra to their students but nowhere has it ever been shown to improve the quality of the people who learn it. All of you talking about tools and learning skills and resonating knowledge do not one shred of evidence for your position beyond asserting it as fact repeatedly. Show me any data than doesn't even imply, just correlate thats all I ask, any data that would link studying algebra to improving learning skills, because if it doesn't do that, we are teaching an irrelevant subject to millions of people.
Take your high school subjects and rank them from most useful to least useful to the average student. I can guarantee you that algebra is one of the most useful. You don't need history. Your science classes have even more niche uses than your algebra classes. You don't need literature. What's left of high school education?
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On July 29 2012 16:55 ]343[ wrote:Show nested quote +On July 29 2012 16:53 sOda~ wrote:On July 29 2012 16:46 paralleluniverse wrote:
For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists. An inner product is bilinear you noob! Hermitian inner products aren't... you have to take a Hermitian conjugate on one side.
fine sesquilinear or whatever, they are basically linear
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On July 29 2012 16:50 paralleluniverse wrote:Show nested quote +On July 29 2012 16:36 RageBot wrote:
Algebra isn't neccessary in itself, but as a roadblock for dumb (or "not so smart herp derp") people.
Honestly, if someone can't pass highschool algebra, he just isn't smart.
And also, they talk about lowering the demands for the SAT? This is really fucking stupid.
Some people are bad in things, some people are good in things, we are not equal, life has winners and losers, deal with it. You haven't said why people should be forced to learn algebra when they're not going to use it, and they want to be a mathematician or engineer or whatever.
Why are people forced to learn science or history when they're not going to use it?
Honestly, I think this is stupid and disgusting. I read this as people wanting to justify stupidity and ignorance; blaming it on external factors rather than simply accepting that the education system and the societal attitude towards education in the United States is shit and needs fixing. Failure in school is not simply the fault of the school system, parents and families of the students are equally at fault. If your student/child is failing, get him help instead of complaining. Stop buying your 10 year old children fuckin iPhones and invest that money in a tutor instead. Nut up and learn your shit.
When I was a kid in elementary or middle school, my parents (namely my mom) made me do extra academic work on top of school assigned homework. It wasn't much; just 15-20 minutes a day of arithmetic or other stuff. While that's definitely not the entire reason why, all through elementary, middle, and high school I breezed through every fucking class, while the vast majority of my classmates all struggled at some point or another. Yea, some kids are more naturally gifted and smarter than others, but honestly, if you (or your parents) give a shit and made you put effort into it, I don't believe anyone (unless you have some kind of learning disorder) should ever have to even study until you get to college or are taking AP/IB courses in high school. US education standards are shit low.
These opinion writers can whine all they want, but it still doesn't mask the fact that the cutting edge of technological advances are slowly moving out of the United States. While the US is still the leading innovator in many areas, we're already lagging hard in terms of growth in innovation. While our economic policies, it certainly doesn't help that as a society, we hate education.
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On July 29 2012 16:55 ]343[ wrote:Show nested quote +On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:
What order you solve an equation in is irrelevant.
Consider 2x+1 = 0, under the convention that addition happens before multiplication.
So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? On a side note: statements like "foil it out" are good examples of how the American math system teaches formulae and algorithms, not mathematics.
The american math system has far worse problems than that. All throughout learning math, we are told things are impossible. Then a year later, we learn how to solve what was previously thought to be impossible. I am curious though, how would you teach somebody to do (9+3)(9+3) without telling them about foil? I only ever learned it because of that, and would like another perspective.
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On July 29 2012 16:50 paralleluniverse wrote:Show nested quote +On July 29 2012 16:36 RageBot wrote:
Algebra isn't neccessary in itself, but as a roadblock for dumb (or "not so smart herp derp") people.
Honestly, if someone can't pass highschool algebra, he just isn't smart.
And also, they talk about lowering the demands for the SAT? This is really fucking stupid.
Some people are bad in things, some people are good in things, we are not equal, life has winners and losers, deal with it. You haven't said why people should be forced to learn algebra when they're not going to use it, and they want to be a mathematician or engineer or whatever.
I've clearly did say that.
I don't think most people should know algebra, I said that it's easy, and that if you can't finish highschool algebra, you're either an idiot, or should be treated as such by society until you can prove otherwise (by opening a successful business, for example).
A highschool diploma loses it's worth if you make it easier and easier, if everyone can have one, than actually, no one has one, because it stopped meaning anything.
It's the same for Bachelor degrees in america right now, they are so damn easy, and so many people have them, that they are practically worthless, you make people waste years of their lives, getting something that isn't worth anything unless you get a masters degree.
I think, if anything, we should amp the difficulty of everything, that way, people won't waste years of their lives getting something that is worthless, and the capable people would be recognized earlier.
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On July 29 2012 16:35 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:30 paralleluniverse wrote:
What order you solve an equation in is irrelevant.
Consider 2x+1 = 0, under the convention that addition happens before multiplication.
So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go?
You could only come to the conclusion that (9+3)^2 =9^2+3^2 if you don't know how to expand brackets properly, thats not a problem with order its just wrong.
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United States10328 Posts
On July 29 2012 16:56 thesideshow wrote:Show nested quote +On July 29 2012 16:48 ]343[ wrote:
But an actual mathematician is concerned about maps between objects and universal properties rather than explicit constructions (that is, how an object behaves, not how it's written; the written convention is merely for communication's sake), so he reasonably would not see a test of "knowledge of convention" as a test of mathematical aptitude.
Knowledge of convention allows you to read and learn from what others have done. Also, its pretty much required for any form of work or publication, where it needs to be checked or certified or whatever. I would say it's reasonable to accept a "test of knowledge of convention" as a test of mathematical aptitude for any practical purpose.
Hmm, let me try to reword that then. Testing knowledge of convention is a test of memory, not a test of mathematical reasoning ability (which is what mathematicians value).
Anyway, more on topic: this (admittedly over-referenced) article by Lockhart has much to say on this issue. The problem isn't that algebra is unnecessary, but that the way it (and everything up to intro undergraduate math) is taught in the US turns people off.
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On July 29 2012 16:40 UrsusRex wrote:
Not one person has given a compelling reason how making algebra mandatory improves critical thinking skills. All of you supporting and condeming it are missing the basic problem. The entire world teaches algebra to their students but nowhere has it ever been shown to improve the quality of the people who learn it. All of you talking about tools and learning skills and resonating knowledge do not one shred of evidence for your position beyond asserting it as fact repeatedly. Show me any data than doesn't even imply, just correlate thats all I ask, any data that would link studying algebra to improving learning skills, because if it doesn't do that, we are teaching an irrelevant subject to millions of people.
The foundations of mathematical word problems are in algebra and these problems do improve critical thinking skills. Without algebra, the only math possible would be pure memorization and does nothing to improve critical thinking.
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On July 29 2012 16:59 Eufouria wrote:Show nested quote +On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:
What order you solve an equation in is irrelevant.
Consider 2x+1 = 0, under the convention that addition happens before multiplication.
So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? You could only come to the conclusion that (9+3)^2 =9^2+3^2 if you don't know how to expand brackets properly, thats not a problem with order its just wrong.
How did you learn to expand brackets properly? Is that a "natural logic"? No, its something you learned.
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On July 29 2012 16:53 sOda~ wrote:Show nested quote +On July 29 2012 16:46 paralleluniverse wrote:
For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists. An inner product is bilinear you noob!
No, that's only true of the real inner product. In general the inner product has conjugate symmetry.
If you define linearity in the second slot instead of the first, then the first becomes conjugate linear, not linear.
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On July 29 2012 17:01 paralleluniverse wrote:Show nested quote +On July 29 2012 16:53 sOda~ wrote:On July 29 2012 16:46 paralleluniverse wrote:
For example, the inner product <.,.> is linear in the first slot for mathematicians, but linear in the second slot for physicists. An inner product is bilinear you noob! No, that's only true of the real inner product. In general the inner product has conjugate symmetry. If you define linearity in the second slot instead of the first, then the first becomes conjugate linear, not linear.
ye ur right D:, my bad!
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society likes to remember each and every aspect of their favorite celeb or sports team. doesn't surprise me much.
On July 29 2012 17:01 TheRabidDeer wrote:Show nested quote +On July 29 2012 16:59 Eufouria wrote:On July 29 2012 16:35 TheRabidDeer wrote:On July 29 2012 16:30 paralleluniverse wrote:
What order you solve an equation in is irrelevant.
Consider 2x+1 = 0, under the convention that addition happens before multiplication.
So we want to solve 2(x+1)=0, you can divide by 2 and subtract 1 from both sides to get x=-1. Or you can expand to get 2x+2=0, subtract 2 and divide by 2 to get x=-1. (9 + 3)^2 If you dont use pemdas you could come to the conclusion of 9^2 + 3^2, which is entirely different than 12^2. You could foil it out, but foil uses the same principles of pemdas in that you must know it to use it. Also, if you actually plug a number into your equation you could arrive at the conclusion of: let x = 1 2(1 + 1) = 4 or 2(1) + 1 = 3 How do you know where the brackets go? You could only come to the conclusion that (9+3)^2 =9^2+3^2 if you don't know how to expand brackets properly, thats not a problem with order its just wrong. How did you learn to expand brackets properly? Is that a "natural logic"? No, its something you learned.
everything was thought of at one point, not learned
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On July 29 2012 15:15 paralleluniverse wrote:Show nested quote +On July 29 2012 14:58 RodrigoX wrote:
Well, I mean I use algebra on a daily basis, and the argument "Let's just not teach it, because stupid people exist" really is not good logic.
Life is math, if you wanted educated people, math at the algebraic level is always going to be needed. I mean, granted you are never going to need to use integral calculus or even F.O.I.L things but that is not exactly the point of education at that level. You need to give children a sampling of everything to know what they like or are good at, and you need to at least give them basic knowledge of life in general. I mean chemistry is probably the most useless subject for the masses to take, because you really won't use it unless you become a doctor or chemist etc, but to know how the world actually works is very useful, not because you'll use it but for the sake of knowledge itself. I use algebra daily too, but seriously, how many people do you think need to know algebra? The article cites some source which places it at 5%. I'm not saying to stop teaching algebra and I don't think that's what the article says. In fact, the article agrees that society would collapse without math, but 5% of people need to use algebra means that 95% of people don't. And I have no wish to force it upon them.
Everyone needs to know basic algebra. Because in order to develop a budget you have to use basic algebra to solve for any unknown expenditures to see how much spare money you have to work with. Any time you solve for an unknown quantity you are going to use algebra. Now does everyone need to know Algebra 2 and other advanced math like trig and calc? Probably not.
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Very good quality OP. My background is currently studying a Masters in Chemistry, Math Minor.
"If I'm never gonna use it, why should I be forced to learn it and be tested on it?"
Ah, such a familiar gripe of high-school students kids. A lot of the time (in my experience) the people who don't do well in math don't enjoy it, its a mysterious drudgery - they fear it. This is partly a cultural thing where its generally condoned and even slightly encouraged to dislike math, because 'everyone does', '~the cool kids~ don't like it'. Does that sound like a subject you'd excel in?
That's because we've got a really screwed up system where the voice of teenagers and their leisure is valued and heard more than -doing well in school-. How many Korean students would foster an attitude 'oh I don't like it, and no one does, so why do I have to do it waaaaa'. They'll be left behind in an instant. [there are problems when you go too hardcore with a system so hard you need 4 hours of extra study-academy a day to keep up, but the point is, its generally uncool and ill-valued in US culture, go figure its not a priority but a stumbling block].
You can't just memorize trivia or themes and details from some books, you have to internalize the skills and ideas (rather than just the material) and apply it to whatever's thrown at you. Ok when your entire system is geared around big exams its a bit different (you learn for the sake of the exams), but my point is Mathematics is valuable because it gives you a developed way to think about the world, on an equal level that English does for thoughts emotions and ideas. i.e. IT'S VALUABLE
Again (sorry, I didn't have the misfortune of doing US high-school math) no wonder students (a large majority) have no drive for doing math, the type of math they're forced to do sucks! It's boring as hell, when people give you mysterious equations, that you have no idea where they come from, and no idea 'what it is about them that makes them work'. But you need to know the basic building blocks to be able to make a cool structure or creation. So people are stuck on doing algebra? Well one reason is probably the greatest use and extent of algebra on a high-school level is to do shitty un-inspiring problems like those PEMDAS or F.O.I.L. ones. Those suck, really, because they're like two kids with a measly grasp of school-level-Spanish trying to 'find more words that rhyme' in that language. You can get somewhere, maybe it'd be a bit fun, but there's so much more you can do with it, so much further and deeper you can go with it!
College maths is where stuff gets fun! Until you can handle triple integrals and differential equations, you won't be able to actually use Maxwell's Equations of electromagnetism. Until you do linear and vector algebra, dot product, cross product, determinant and even just matrices will have no geometrical meaning and just be some mystery ritual.
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EPT
