EPTI think the problem is the same here as with general knowlege, we used to call people who didn't know history or weren't interested in politics stupid and ignorant. Now we accept that not eveyrone needs to be interested in certain areas. Same goes with maths. We shouldn't accept that and just keep calling those people stupid.
Is Algebra Necessary? - Page 40
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Soyemia
Finland12 Posts
I think the problem is the same here as with general knowlege, we used to call people who didn't know history or weren't interested in politics stupid and ignorant. Now we accept that not eveyrone needs to be interested in certain areas. Same goes with maths. We shouldn't accept that and just keep calling those people stupid. | ||
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Neo7
United States922 Posts
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]343[
United States10328 Posts
On July 30 2012 14:06 sluggaslamoo wrote: I agree, know they fall under the same umbrella, but you are missing the point of my argument. Hmm, well then, what's your argument? On July 30 2012 12:15 sluggaslamoo wrote: The algebra needed for comp sci can be learned in just a week, This is false; you need to know about things like exponential functions and polynomials and logarithms and their relative growth rates. and you won't see it as "algebra" you will see as something far more interesting as that. Algebra is a tool, much like arithmetic, which is necessary for understanding computer science. You don't study high-school algebra just to "do algebra" later. Indeed, With comp sci you are also not really learning maths, you are learning about logic and patterns. Algebra is among the first steps in gaining the mathematical (or more generally, intellectual) maturity to think abstractly---and abstract thought is essential in any sort of technical subject. There's "logic" and "patterns" to be learned in algebra as well. The rest like lambda calculus and big O notation is stuff that you will never learn in school anyway. That's the problem. Yes, most high schools don't teach it (which suggests that high schools ought to offer more math classes, though that's sort of unrelated to whether algebra should be mandatory or not.) But to learn lambda calculus or big-O notation requires algebraic abstraction. Once you see the relevance the basic stuff that took you years to learn in school will take just a few days to learn. That's why there is no point. Very true for anyone in a technical field, though perhaps not so much for those who are not so inclined. American schools spend far too much time on rote memorization of arithmetic and the like, while Eastern European/Asian schools introduce interesting problems (i.e. not just regurgitating formulae) early on. On your friends who were "bad at math" yet brilliant programmers/computer scientists: high school geometry (a sad excuse for the word "geometry"), trigonometry (more memorization), and calculus (yet more memorization, though often at this level there may be glimpses of actual mathematics) are, indeed, not so relevant to discrete math and problem solving. But the solution here isn't to get rid of them or make them electives; it's to improve the teaching of these subjects so that it does actually teach problem solving. | ||
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Prplppleatr
United States1518 Posts
On July 30 2012 14:31 Soyemia wrote: I think the funny part here is that in Finland people are also very worried about our math standards and they're actually rising be bar again, e.g. in University admissions maths are getting a bigger part aswell as in the ground school. Also the fact that Germany has many types of secondary school is not the key, in Finland everyone, I mean everyone, goes to the same type of school for 9 year, from 7 to 15 years of age. I think the problem is the same here as with general knowlege, we used to call people who didn't know history or weren't interested in politics stupid and ignorant. Now we accept that not eveyrone needs to be interested in certain areas. Same goes with maths. We shouldn't accept that and just keep calling those people stupid. I was just using Germany as an example for what you stated...ie. not everyone needs to have as much general knowledge as is required and some people simply aren't interested in certain things. However, everyone should have a certain amount of general knowledge (just maybe not as much, ie in school until 18 for it) and I believe algebra is something everyone should know...it is extremely useful in life, especially finances. | ||
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GT350
United States270 Posts
On July 29 2012 23:56 Vega62a wrote: I understand the basic problem - looking for ways to make education more accessible - but removing a subject because people don't like it or don't do well at it is the wrong way to go about it. 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. That's why we have experts and statisticians. I never understood the need for math with all the advanced computers around. | ||
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Lightwip
United States5497 Posts
On July 30 2012 14:40 GT350 wrote: That's why we have experts and statisticians. I never understood the need for math with all the advanced computers around. Computers don't solve your problem for you. They just do the calculations to save you time and possibility for error. If you don't understand how it works, you get nowhere. There's a saying involving computers: garbage in, garbage out. If you know nothing, computers are worthless. | ||
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ZackAttack
United States884 Posts
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dreamsmasher
816 Posts
is algebra really this difficult? i did not like algebra when i was a child not because i didnt understand the concepts but because it was taught in a very meaningless manner. it wasn't until liake the later half of pre calc that i started thinking math was interesting (talking about limits and what not) and I was more inclined to learn and memorize what was needed to be successful. hmm there are a lot of really interesting philosphical ideas within math and applications that are never introduced in school (and i went to some pretty good high schools). although i don't really enjoy doing proofs or what not, i can appreciate the beauty behind mathematics, but most of that was self realized, for the greater part of my mathemaical educaiton, school just makes it more boring. | ||
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r.Evo
Germany14080 Posts
On July 30 2012 14:14 Prplppleatr wrote: I think the word you were looking for is incentivize. Also, I agree that the USA has a poor educational system. Germany students, for example, go into one of five different types of secondary school much earlier on (10-12ish, i think). Where as, in USA, we all go to the same secondary school (middle & high school) until we are apprx 18. PS. This is a terrible opinion article that grossly misinterprets Georgetown's research to better serve the authors agenda (refer to page 33). But that is American media for you, as well. And you guys are getting way off-topic, this is about ALGEBRA. Uh. Since someone already quoted the finnish system I might as well try and explain the German one real quick: 1st - 4th grade (6-10) = elementary school. We don't really have some kind of pre-school. Right there (which is probably the most discussed part about our school system) the kids go onto one out of 3 different types of school depending on their performance in 4th grade. While switching between those types of schools IS possible they aim to teach different things and in some subjects (e.g. math) the stuff is so vastly different that switching is really hard later down the road. a) "Hauptschule" (5th to 9th grade, aims to get students into.. let's say classic worker jobs. Their math is e.g. closer to what you'd need as a cashier and they have (or used to, not 100% sure) subjects where they learn cooking and stuff.) b) "Realschule" (5th to 10th grade, it's basically in the middle of the other two. They are above the future "workers" and below the future "academics") c) "Gymnasium" (5th to 12th/13th grade, basically aims to prepare you for university and a future career in academics) Of course it's possible to achieve all of the degrees via education later on in your life but what could cost you 1-2 years earlier will definitly turn into a 3-5 year effort if you didn't do it "right" before you're leaving school. Another major thing is that education here is a matter of the individual countries and not the whole state which leads to rather big differences up to the point that a future employee might reject you if you come from Berlin but will love to take you if you got the "same" education from Bavaria. | ||
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dreamsmasher
816 Posts
On July 30 2012 14:52 Lightwip wrote: Computers don't solve your problem for you. They just do the calculations to save you time and possibility for error. If you don't understand how it works, you get nowhere. There's a saying involving computers: garbage in, garbage out. If you know nothing, computers are worthless. yet we still learn differential equations, they still teach you proofs in linear algebra, and you have to learn several rather useless methods of integration in calculus. dont get me wrong, i loved calculus, i did well in like all of these classes, but practically none of it is useful other than knowing the basis of the ideas. same goes for most of the probability theory i've taken. hell we spent all this time in regression analysis talkint about the matrix constructs, and in the end none of it is really useful. i dont even think linear algebra is really necessary to understand regression or to use it in any practical manner. you're right though computers do not solve things for you, they merely speed up the calculations, you still need to know how to correctly model, or think about a problem, which mathematics education certainly SHOULD be helping, but mostly math classes as i far as i can remember just emphasize rote computation,memorization and most word problems that are given (even if they are given) are poorly written or don't really stress those analytical methods well. | ||
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ZackAttack
United States884 Posts
its a problem in the US if most of middle/high school teachers are incompetent. this is because you don't have to be academically excellent to become a middle/high school teacher. then it rolls on. anyone can confirm with personal experience and stories? I was on the college track to become a highschool physics teacher for a while, and I can assure you that to be a middle/high school teacher you just have to know how to be a good baby sitter, not good at the area you teach. The vast majority of secondary math teachers are terrible. A lot of them don't even know what they are teaching. | ||
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-_-Quails
Australia796 Posts
On July 30 2012 14:40 GT350 wrote: That's why we have experts and statisticians. I never understood the need for math with all the advanced computers around. If you do not understand the mathematics underlying the problem, you will not know what questions you can try to ask the computer. | ||
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dreamsmasher
816 Posts
On July 30 2012 14:57 ZackAttack wrote: I was on the college track to become a highschool physics teacher for a while, and I can assure you that to be a middle/high school teacher you just have to know how to be a good baby sitter, not good at the area you teach. The vast majority of secondary math teachers are terrible. A lot of them don't even know what they are teaching. hmm really? some math education majors i know for high school have to take a 2nd semster of proof based linear algebra, its almost the same as a full blow math major. although i dont realyl undrstand it, because i've definitely had hs teachers who were imcompetet. i dont really understand why you're allowed to get a degree in education and be hired as a teacher, the primary degree should be the subject that you're to teach...there's like plenty of research that's been done on this mattter. its fucking disingenuous as hell. | ||
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ZackAttack
United States884 Posts
hmm really? some math education majors i know for high school have to take a 2nd semster of proof based linear algebra, its almost the same as a full blow math major. Yeah. It was really sad to me because I wanted to be a teacher for a long time, but my eyes were opened to the fact that to be a physics teacher, my passion should be teaching, not physics. | ||
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r.Evo
Germany14080 Posts
On July 30 2012 15:01 dreamsmasher wrote: hmm really? some math education majors i know for high school have to take a 2nd semster of proof based linear algebra, its almost the same as a full blow math major. although i dont realyl undrstand it, because i've definitely had hs teachers who were imcompetet. i dont really understand why you're allowed to get a degree in education and be hired as a teacher, the primary degree should be the subject that you're to teach...there's like plenty of research that's been done on this mattter. its fucking disingenuous as hell. Waitwaitwaitwhat. Hold on. Now I have to ask. Is it normal in the USA to get a degree in education and have your subject as some kind of secondary thing? Over here for the higher schools (Gymnasium) teachers have the exact same subjects as a BA student (and some pedagogics on top of that) for the others it's a seperate subject at university - but also with the primary focus on the subject and a - sometimes too small - focus on pedagogics and methodical stuff. People here actually have a tendency to complain about our teachers knowing too much about their subjects and too little about as to how they should deal with kids. | ||
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sluggaslamoo
Australia4494 Posts
On July 30 2012 14:37 ]343[ wrote: Hmm, well then, what's your argument? This is false; you need to know about things like exponential functions and polynomials and logarithms and their relative growth rates. Algebra is a tool, much like arithmetic, which is necessary for understanding computer science. You don't study high-school algebra just to "do algebra" later. Indeed, Algebra is among the first steps in gaining the mathematical (or more generally, intellectual) maturity to think abstractly---and abstract thought is essential in any sort of technical subject. There's "logic" and "patterns" to be learned in algebra as well. Yes, most high schools don't teach it (which suggests that high schools ought to offer more math classes, though that's sort of unrelated to whether algebra should be mandatory or not.) But to learn lambda calculus or big-O notation requires algebraic abstraction. Very true for anyone in a technical field, though perhaps not so much for those who are not so inclined. American schools spend far too much time on rote memorization of arithmetic and the like, while Eastern European/Asian schools introduce interesting problems (i.e. not just regurgitating formulae) early on. On your friends who were "bad at math" yet brilliant programmers/computer scientists: high school geometry (a sad excuse for the word "geometry"), trigonometry (more memorization), and calculus (yet more memorization, though often at this level there may be glimpses of actual mathematics) are, indeed, not so relevant to discrete math and problem solving. But the solution here isn't to get rid of them or make them electives; it's to improve the teaching of these subjects so that it does actually teach problem solving. Exponential functions and polynomials can be learned in just a few days, I don't see why it would take any longer than that. I learned polynomial functions when I was 12 years old in just a few days, and I learned how to do it by balancing experience point calculations in excel for a game I was making. My point is that learning things before it has relevance is pointless. There is only point to learning something when there is relevance. It doesn't matter how good you are at teaching, if you can't see e.g algebra, having any benefit to your future career its gonna take months instead of days to learn, and your ability to recall it will diminish significantly within the next few weeks. That time could have been much more efficiently spent learning material relevant to your future career. If I'm gonna become a panel beater when I grow up, it doesn't matter how good the teacher is, I'm not gonna give a shit about maths. It makes no sense to put future panel beaters with future maths professors in the same class. There's nothing wrong with education, if this panel beater ends up leaving school without knowledge of algebra, because regardless of whether algebra is taught or not, this person is going to leave school without knowledge of algebra. The only difference is that in one case, he can leave college more adequately equipped for his career, or he leaves college with low self esteem thinking he's really dumb when he's not. Communication and organisational psychology is hardly taught in schools, yet even as a programmer, I believe it is the single most important thing that needs to be taught. Even for professors and academics, communication is a problem, garnering support for global warming is frustrating for a lot of scientists, but they don't understand its because their ability to share their information to the rest of the world is lacking. What defines my income is not my programming skill, it is my ability to carry myself, talk to other people, do good presentations, not say stupid things, etc. My skills as a programmer comes secondary to that. Communication is taught very little if at all in schools, yet if you look at all the successful people in the world, their primary asset is communication. Look at Steve Jobs, he's a great presenter/communicator, Microsoft's success was initiated by Bill Gates ability to receive help from other people at his university and even convincing IBM to use the worst product on the market. Mark Zuckerberg, Facebook, pretty self explanatory there. Creator of Minecraft, wrote terrible code. There are plenty of genius code monkeys, taxi drivers, who can't land a job because they don't know how to talk to people. | ||
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ZackAttack
United States884 Posts
Waitwaitwaitwhat. Hold on. Now I have to ask. Is it normal in the USA to get a degree in education and have your subject as some kind of secondary thing? Yes. It is how it works almost all of the time. | ||
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Soyemia
Finland12 Posts
On July 30 2012 15:05 ZackAttack wrote: Yeah. It was really sad to me because I wanted to be a teacher for a long time, but my eyes were opened to the fact that to be a physics teacher, my passion should be teaching, not physics. Well I supose that for lower classes (like in Finland teachers from 1st to 6th grade) the teacher really need to be teachers, rather than experts in any certain subject. In here it works like that, and the same "class teacher" teaches majority of the subjects, except for specialized ones like music and languages. After sixth grade the teachers have actually studied the subjects themselves, and then taken a short course in teaching to become teachers. I also think that the ability to teach is also very important even up to high school and university. One thing I really don't understand here is about how Americans in general think about education - it's all about what is needed and less so about just being educated. In Finland education itself has a value, so individual subjects and their relevance in every day life has less importance. So we study here stuff that might not be all that useful, like music and art - and high level maths. It has been shown to make you think better and has done pretty good for our international competitiveness. I mean even here at Aalto Uni where I study economics we have math that is totally unrelated to economics and other similar subjects. We're a triple accredited school and the entire uni's really high level, even though we don't make it high in the rankins because we have so homogenic student body (it's ridicolous they give you points if you have more ethnic diversity), and the uni doesn't publish many papers, although if they'd only take account the studies that have been published in high level scientific journals, we'd be pretty much very close to the top of the world. | ||
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ZackAttack
United States884 Posts
One thing I really don't understand here is about how Americans in general think about education - it's all about what is needed and less so about just being educated. I agree. Education has such a high value, and math is one of the most enlightening things to understand. I have never met anyone but my professors that values education as much as I do. Even the students that I have met that do well just want the grade, and would just straigh up pay for it if they could. I think it is very rare that education is truly valued in American schools, even in college, and the reason that American math scores continue to fall is because math isn't something you can bullshit even if you dont care. Edit: And this thread has done nothing but confirm my fear. I suppose math is something that people don't really understand how great it is until they can do it already. | ||
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Garoodah
United States56 Posts
Another problem is that there is little appreciation for math in this day and age. Who would think that math is the reason our entire world is how it is? Little things like your stove heating a pot of water to boil hotdogs, or your cell phone using imaginary numbers to transport your voice over long distances. Any example you can think of comes down to math at its core, and most people ignore that fact, and even less want to understand why. There is a reason there are so few engineers, mathematicians, and scientists coming out of the US today, and its simply because its taken for granted. I only reference the US because this article comes from the US, I am also from the US, and honestly this problem is only a widespread "epidemic" here. The root of the problem is when we are young. Kids in the US need to learn how to solve a problem, not just memorize and repeat something only to forget it after the test in a few weeks. The school system would be greatly sped up if kids were taught true problem solving techniques, and then we would have fewer kids who are just "bad at math" (because they dont know where to repeat what they were told). Im not saying kids need to be an infinite source of knowledge, but they should know where to find that knowledge. I often reference my books when doing homework, infact it would be very hard for me to not do so and still solve the problem fully. I'm an undergrad mechanical engineer in my 3rd year of studies and I can honestly say that the applied science classes I've taken like physics, thermodynamics, statics/dynamics, fluids, etc, all really taught me how to solve a problem. My best examples come from thermodynamics, where my teacher would literally give us a problem, and say go solve it. We had no book and limited lecture information (it always turned out to be enough but it never seemed like it was at the beginning). We could ask all the questions we wanted to. Once a person learns what questions to ask, they can truly start to learn about something. The students who learned this when they were younger excelled in the class, while everyone else struggled to make the grade for the first 2 exams. What was great was this method of asking questions could be applied to ourselves. I had no problem taking fluids because I knew the questions to ask myself and started looking for answers very early on. We can all ask the right questions, and we have the resources to go out and solve the problems on our own, its only a matter of learning how to do it early on. | ||
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