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paralleluniverse
4065 Posts
On July 29 2012 23:47 S_SienZ wrote: That is quite an eye opener for me. Thanks for explaining. Back when I was in secondary school (high school equivalent) calculators were only there for values with lots of decimals, logs and trig. Same here in Australia. | ||
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farvacola
United States18866 Posts
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paralleluniverse
4065 Posts
On July 29 2012 23:51 farvacola wrote: I'm not exactly sure why the article makes the connection between flawed primary/secondary school math education and a need to remove certain educational requirements; it would make sense, at least to me, to instead focus on better teaching methodologies, as algebra and many of the "hard" areas of study have been taught in relatively the same manner for many, many years now. As posters above are explaining, I certainly think that Algebra ought to be requisite, as it lends itself to so many endeavors in life, and perhaps the key in improving its teaching is a more vocational or everyday focus in application, and a change from the standard drudgery of problem sets and timed tests. I'm thinking on my own honors math education, where in 8th grade we learned the quadratic formula via song and were required to sing it at the door one day in order to get into class. Simple little changes in teaching technique can do wonders for making subjects such as math more palatable. As I see it, there are simply too many inherent problems in putting forth entire populations of people who are unable to the basic algebraic underpinnings of the economy and their own personal finances. Are you saying that's good or bad? | ||
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-_-Quails
Australia796 Posts
When I moved to Australia, my high school required students to have a graphing calculator, except for higher level maths students in their last 2 years. I had just come from a school where there was no calculator use at all, and it was a little jarring to see students using a calculator for fairly simple multiplication. That was in NSW, I'm not sure how other states deal with the issue. | ||
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Vega62a
946 Posts
People don't HAVE to be bad at math. Not everybody is going to ace their college calc courses, but basic algebra doesn't really require mental pushups. We are bad at math because we don't care about it, and because we spend most of our lives talking about why we don't care about it. Think about it. How many times have you asked yourself, or been asked, where you're going to use a math course in the future? We lack a fundamental appreciation for the basic goal of basic math courses: To make ourselves comfortable with numbers, and to gain an appreciation, at a really personal level, for how much they impact our lives. Maybe you'll never need to use precisely what you learn in high school algebra. But then, you'll probably never need to know why the war of 1812 was fought, either. You can get by without both. But ask anyone why they're learning history, and you've got a decent chance of hearing, "because those who don't remember the past are destined to repeat it." I've heard no such similar slogan for mathematics, and that's not math's fault. It's ours. Those who don't understand numbers in a world that's run by them are destined to flounder. Imagine if all those people getting tricked into subprime loans had been mathematically literate enough to whip out a pencil and paper when they were presented with the terms of the loan, and figure out that they probably couldn't afford it. Wouldn't have helped everyone (some of them were just too desperate) but I assert that it would have been a good start. | ||
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iGrok
United States5142 Posts
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Roachu
Sweden692 Posts
I'm in my third year of physics in university right now and I've been struggling a lot simply because the mathematical process has been uninteresting to me (this has been a serious problem for me and goes deeper than "math is hard/boring"). Of course there have been outside influences affecting this a a lot but my brain simply started to say no to the basic process of solving mathematical problems. If I got to see a solution I understood it immediately which says to me I personally have a problem with my study technique. This might have been slightly off topic but I kinda needed myself as an example of its not the subject itself which is particularly difficult, the problem lies in motivation and self-discipline. | ||
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Cutlery
Norway565 Posts
But I don't agree with everything. Certain aspects of math CAN reach further than you suggest. Not everyone will connect the dots (as evident by the article), but they are there for those who use mathematics as a tool. Take "But there is no reason to force them to grasp vectorial angles and discontinuous functions". Vectorial angles are the basis for physics in 2 or 3 dimensions. Meaning you will essentially lose out on everything that today is calculus. Without knowing what type of functions calculus applies to, you may aswell write: "But there is no reason to force them to grasp physics and calculus". This must be your statement. If you're ok with this, then that statement made sense. You are not required to grasp the rigorous details of proving a continuous function (in order to apply calculus); but it is essential to realize wether you're looking at a continuous function or not. Trigonometry is essential for any physics or engineering class, as is calculus. But if you do not pass these subjects, then this line of work probably isn't for you anyway. Ofcourse there could/should be an "alternative" form of schooling, one which puts less emphasis on math. But there's no point in beating around. Quantitative reasoning cannot be done without the actual equations and knowing their dependence. i.e consumer price index. (Hence the word "quantitative") Any form of quantitative reasoning without the application of the mathematics behind will result in completely random outcomes. I fail to see that if general algebra and calculus isn't "as widely applicable in jobs as we like to think", then how are cases of looking at special cases quantitively of greater value? First ignoring qualitative 'reasoning', AND only looking at special cases (mind you, statistics is harder than algebra and calculus, because statistics need these as a foundation, so you either must learn these, or you limit yourself to the type of statistics you view in the classroom without knowing why this works, so you cannot apply it elsewhere in confidence) does NOT, in any way, give you more tools to do different jobs. It gives you less tools. The reason I say this is because the entire 'reason' for learning algebra and calculus is that you can much more easily apply this knowledge when training for a new job, and more quickly arrive at an understand of the tasks at hand, IF they are related to maths. If you only have quantitative training in special cases, then you have infact trained for very specific things, and might not have gathered enough general knowledge to throw yourself into a field that requires slightly different mathematics: Your training period would take more time. It's a comprimise for sure. But anything should be done to help students pass highschool. For college level I'd be more restrictive. Where math is of issue, it is of issue, and must be included. When it isn't it isn't, and can be omitted. Any math that avoids algebra and calculus at college and university level should not be called math, but should instead be part of a specialized training or even practice. For instance an "electrician" requiring Ohm's law could potentially learn this and only this law; but he would not understand any details about his job; he'd only be able to screw things together in the simplest of circuits, or hope for the best. If you ask him to apply kirkhoffs rules to make sure his circuits are sustainable, or solve differential equations or even just look at the "phases" of the circuits, he'd just scratch his head if he did not know algebra and calculus. And there'd be no way he could train for any of this without this mathematical knowledge. But he could gain enough practical experience to fix typical housing electronics. He'd have to verify that he was familiar with this type of circutry, and then he could begin setting them up, or doing required tasks. But such training would take much longer, as they would look like different recipes for each and every circuit, while someone with a calculus background would see that they are all the same, but with different quantitative and qualitative outcomes. The same goes for areas such as economics and insurance, any form of engineering, programming, and obviously teaching positions, natural sciences, medical staff (anything from nurses to surgeons) and the list goes on. Conclusion, I guess, is that algebra isn't neccesarily neccesary, but you limit yourself when it comes to future careers and how much you can excell in these career choices. But that might not be a bad thing as you probably want to steer clear of these fields of work anyway. But there's ALOT to miss out on. It's not the fact that x^2+y ... is the set of equations you have to solve for the rest of your life, it is that any training for any new position that uses some math, is completed alot faster and with more independence and with greater possibility for excelling, than only having specific training that you have to do from "ground up" for every new position; severely limiting the potential that can be realized within your job or career choice. There shouldn't be any dillusion that "one thing can be just as good as the other". It simply isn't. It can be done, but the cost is greater and possibilities fewer (not that there can't be exceptions). | ||
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farvacola
United States18866 Posts
I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. | ||
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Foolishness
United States3044 Posts
This also reminded me of A Mathematician's Lament (links in a previous post). Everyone should read that as I feel it addresses the heart of the problem and also lays out the groundwork for how to fix it and how curriculum should change. | ||
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paralleluniverse
4065 Posts
On July 29 2012 23:59 farvacola wrote: I am suggesting that such an alternative strategy is a good start when thinking on how math might be taught differently than it is now. My school district happened to have one of the best honors programs in the state of Ohio, but from 4th grade through graduating high school, it was readily apparent to all of the honors kids that we were getting the cream of the districts educational crop while the kids in normal classes fell by the wayside as a result of a less successful and less interesting curriculum standard. Singing math is one of the stupidest ideas I've ever heard. | ||
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Lightwip
United States5497 Posts
Also, for those who mentioned that this is why the US imports workers: completely different issue. Trained professionals in the US are among the best (but most expensive). Our universities are the best in the world. It's the students that fail to reach that level that don't finish high school. Not to say that those students aren't a problem, just that it's a different one altogether. | ||
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paralleluniverse
4065 Posts
On July 29 2012 23:59 Foolishness wrote: Good article, but I feel that it focused too much on the problem and not on what should be done about it. Is it news to everyone that the USA is far behind in math skills compared to a lot of other countries in the world? I feel as if people have known about this issue for a while but nobody has the answers to why or how to fix it (or the guts to do something about it really). This also reminded me of A Mathematician's Lament (links in a previous post). Everyone should read that as I feel it addresses the heart of the problem and also lays out the groundwork for how to fix it and how curriculum should change. I don't think the US has a shortage of mathematical talent: http://www.topuniversities.com/university-rankings/world-university-rankings/2012/subject-rankings/natural-sciences/mathematics/ But this is an issue that has been discussed in one of my old posts: http://www.teamliquid.net/forum/viewmessage.php?topic_id=268603 | ||
micronesia
United States24799 Posts
On July 30 2012 00:03 paralleluniverse wrote: Singing math is one of the stupidest ideas I've ever heard. Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. | ||
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paralleluniverse
4065 Posts
On July 30 2012 00:06 micronesia wrote: Suppose your students were to learn the quadratic formula. Would you give it to them or make them somehow come up with it? There are arguments for both, depending on things like at what stage in their math career they are at. However, let's suppose you needed to give them the formula and teach them how to use it. They need to memorize the formula (barring a cheat sheet). How are you going to get them to memorize the formula? This is the same as asking how you will get students to memorize anything else (it isn't math specific). You may not like your core subject teachers requiring you to sing a song to learn something, but don't think that this has anything to do with math. I would not gets students to memorize the quadratic formula. I would teach them how to solve quadratic equations. I would also derive the formula. Once you've solved several quadratic equations you'll naturally remember it without any effort specifically on trying to memorize it. Memorizing formulas has zero educational value. If you think math is about memorizing formulas, then I would direct you to Lockhart's Lament, which has been linked a few times already: http://www.maa.org/devlin/LockhartsLament.pdf | ||
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farvacola
United States18866 Posts
On July 30 2012 00:03 paralleluniverse wrote: Singing math is one of the stupidest ideas I've ever heard. Haha I agree with you in a certain sense, but that this approach to teaching Algebra included singing is more a reflection of my old teacher than the sort of changes in math education I'm talking about. Funnily enough, that same class of individuals turned out some very brilliant math minds, and not a single person I've talked to who has taken Mrs. Flahie's honors algebra class has ever forgotten the quadratic formula  The point is that this article is basically supporting a pedagogical signal of defeat, as though the very nature of Algebra somehow makes it incommunicable to some people. And while this may be the case in an extremely remote sense, the teaching of math is something that can still be improved on dramatically enough to improve the classroom experience by leaps and bounds. | ||
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deth2munkies
United States4051 Posts
If we keep cutting the curriculum like this, it will teach people that the world is wrong, not them: It was the Algebra making me fail, not my own deficiencies. If everyone has that attitude, our nation is truly going to shit. That said, I'm not opposed to educational reform, Extra Credits did a thing on Gamification of education a while back that seems like a good place to start, but perhaps isn't the full solution. I won't offer a full solution because I don't have one, what I do know,though, is that eliminating parts of the curriculum to get people through school is working at it from the wrong angle. | ||
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iSTime
1579 Posts
FWIW, even in fields like philosophy, nearly all of the titans were very good at math. | ||
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Zocat
Germany2229 Posts
On July 29 2012 23:38 Deadlyhazard wrote: + Show Spoiler + 1) Nobody is saying it should be removed -- most are saying it should be something that's more optional or taught in a different way so students struggling can understand it or get something useful out of it. 2) Chemistry displaying work ethic and priority making is too black and white of thinking. I failed college algebra three times -- I have a great mathematical learning disability. I can't even do basic math. I miss 7+6 half the time. I had several private tutors and I studied much harder than those that were lazy and smoothly sailed by -- yet I still failed. I was literally making grades below those that were barely trying, yet many were making A's and B's. I don't think it's that I'm completely stupid -- I simply have a learning disability when it comes to using numbers. So what happens to people like me? It's not because I didn't have priorities set. It's not because I displayed a poor work ethic. It's because of an innate problem with mathematics that I will always have (and have had since I started school as a wee child). For me, it's impossible to have any career related to math because I simply can not understand the type of abstract reasoning it presents. So what use is a mathematics course being mandatory for me? I do fine in almost every single subject. My report cards in college literally read A A B F, and you can guess what I was failing every semester (and having to repeat). I took statistics three times too. It's not that I can't be taught and learn from schooling, it's that I'm absolutely terrible in one department of reasoning -- mathematics. I feel that some courses should be optional for this very reason, so people like me stand a chance at becoming educated without having to suffer through the ordeals of major learning issues like I have. So what am I to do -- not be able to pass regular schooling to get to something more specific (and unrelated) to math just because I can't pass one subject? Attend a special school? Apparently you're not able to complete a regular school - but there are other options. Why should the normal (as in for the majority / masses) education system be changed for the need of a few people with a disability? Should we change every subject so even people with a disability in that subject are able to complete every course? So why do you want to force the issue and bang your head against math courses instead of pursuing another degree in a special school? It's not like people who attend special schools are stupid, so you have the option (or would at least have the option in Germany - dont know the US^^) to get a good degree but for whatever reason you dont want to switch, but rather complain. | ||
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Brutland
United States92 Posts
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