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On July 29 2012 20:03 JoeSchmoe wrote:Show nested quote +On July 29 2012 19:40 Toxi78 wrote:
and in what world am i gonig to use litterature, history, geography when i work?
i fucking know how to spell and write, i know my birthdate and who is the president, and i can find my house ezpz with my GPS.
with this kind of reasoning we're not going to go very far.
whoever wrote this article is an idiot. the redundancy of algebra is just an opinion of the author, it could be any subject yet people place so emphasis on this fact. it's hard to argue against the bias of the considerable majority of TLers here that come from a scientific/mathematic background but the more important issue lies with the linearity of our education system. There should be an option that allows you to focus on fields pertaining to your interest at a much younger age. of course there will be students who are unsure about their future in which they are encouraged to dip their hands in various fields much like what we have today. honestly, there's a ton of shit from high school that either I've completely forgotten or never given a second thought to and yet our people will insist that it has helped subconsciously without us realizing. has it? maybe. do i think so? no, i think my time would've been better invested in developing my interests but that's just me.
yeah.
what i liked when i was 3 was drawing.
writing my name was way too hard.
and counting on my fingers? lol counting on my fingers, no way, it was impossible. i didn't even understand the concept of counting : why would i ever need to count ? i have food, a place to sleep, what's all that counting thing useful for?
hell, they should have let me draw all day long, period.
turns out i'm not an engineering school student and i also study financial mathematics in parallel. maybe that counting thing was actually my stuff in the end?
how can you know you're not interested in something if you never try?
highschool courses are EASY and not very deep, they are here to help you understand what you like most and making sure you can develop rational thinking in different fields. turns out it worked perfectly with you, you've developed different interests and you didn't like some other courses.
now about your scientific mathematics thing, what i miss the most in my studies right now is philosophy and literature courses. i also think that at my level some courses i must pass are unnecessary for my career. but hell, highschool courses? everyone needs them, even if you don't like them, reality check : you won't like everything you do, your being able to perform in something you don't really enjoy is something you should also develop.
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On July 29 2012 20:57 ZenithM wrote:Show nested quote +On July 29 2012 20:42 paralleluniverse wrote:On July 29 2012 20:37 ZenithM wrote:I don't even understand what kind of algebra we're talking about. Is that really the miserable equation solving we did in high school? Maybe this: http://en.wikipedia.org/wiki/Elementary_algebra ? Because if that's it, I do think this basic knowledge should be taught in high school, it even seems rather useful. Believe me, way more than what we actually call algebra over here :D. In fact, I didn't know it was "algebra" we were doing all along until we started studying structures and vector spaces and all that shit... If you want to learn about something truly useless in mathematics, check out category theory. And it's 13:37 here. Yes, we're talking about elementary algebra. I think you're talking about groups, rings, and vector spaces which is abstract algebra, and as with most areas of advanced mathematics, usually the only applications are to other areas of mathematics or to physics. I believe group theory has applications in quantum physics, something to do with spins or states or particles? But I'm not a physicist so that example might be wrong. Ok, thanks. I think in France the word "Algèbre" is really not used to talk about the things we do up to high school that are actually algebra, so that's why I was confused :D.
The Bourbaki influence?
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On July 29 2012 17:03 sOda~ wrote:Show nested quote +On July 29 2012 17:01 paralleluniverse wrote: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!
Yo, arguing about this is about as productive as arguing whether people should use injective/surjective over one-to-one/onto - _____________ -;;;
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On July 29 2012 21:04 DoubleReed wrote:Show nested quote +On July 29 2012 21:02 paralleluniverse wrote:On July 29 2012 20:58 DoubleReed wrote:On July 29 2012 20:55 paralleluniverse wrote:On July 29 2012 20:46 DoubleReed wrote:On July 29 2012 20:35 paralleluniverse wrote:On July 29 2012 20:24 DoubleReed wrote:
You can't even start physics and chemistry or advanced biology without algebra. Do you expect young people to be attracted to these things if they don't even finish algebra?
But this is typical idiotic American educational thinking: If our students are failing because of a standard, rather than try to better our educational methods and teaching, let's just make it super easy on the students and pass them anyway. Who cares if they learned anything in school? Our passing rates are up!
It's terrible. It's a disgusting disservice that we're doing to our children. Getting an education is actually supposed to mean something. By lowering the standards you aren't making education easier on students, you are simply reducing what "education" means. I don't know anyone who wants to do physics or chemistry because they love algebra. It goes the other way around. If you're inspired to do science, you will need to learn mathematics and algebra is an important part of that. But if you're not going to do mathematics or science or anything that is mathematical in nature, then why do you need to know how to factorize a quadratic or integrate log(x)? The argument isn't simply remove algebra or math. Not everyone will be a mathematician or will use math in any way, so it shouldn't be required. But the article and Gowers' blog post I linked to suggests teaching optional courses that makes people mathematically literate and appreciate mathematical thinking, as opposed to forcing down some convoluted and unrealistic "application" of mathematics, then requiring students to perform symbolic manipulation to solve the problem. No, you need algebra to even get interested in physics or chemistry in the first place. It's a necessary condition, not a positive correlation. And again, symbolic manipulation is necessary to understand rates of change, which is actually useful for understanding mortgages and blah blah blah. If you're incapable of understanding and learning Algebra, then why should I pretend like you've gotten a basic education? There are plenty of jobs out there that you do not need ANY kind of education for. That's not an argument to lessen the standards of education. That's an argument for letting people fail, so we can differentiate between the two. Education actually is supposed to mean something. A high school diploma is supposed to mean something. By reducing the standards you aren't solving any problem. You're faking it. You're simply passing kids who haven't earned it. How does this solve the problem? You need algebra to learn physics, which is why no one is arguing to abolish math education. But no one is inspired to do physics because they find algebra fun. If you find algebra fun, be a mathematician (on second though, no mathematician will ever be hired to their ability to do symbolic manipulation),. You're point about mortgages to high ironic. [It] is deeply boring, and not even all that relevant to the people who are actually taking the exam, who should be enjoying their last few years of not having to think about mortgages, income tax returns and the like. (Does anyone seriously think that teenagers will be filled with enthusiasm by personal finance, when for adults, who are directly affected by it, it is an awful chore?) A conventional A’level student will do plenty of word problems and more mathematics, and will also solve modelling problems when they do statistics and mechanics. Who will end up better at solving mathematical problems that arise in the real world? http://gowers.wordpress.com/2009/07/11/help-im-stuck-in-my-ivory-tower/How is it lessening the standard of education to not force people who want to do something with their lives to do not math? What is the educational value for them, or for society for force them into doing something they don't like, and won't use? What is the societal value for pretending like they have a basic education? What is the societal value for passing them, when other people passed by learning how to do basic fucking algebra? There are plenty of jobs that do not require any education whatsoever. That doesn't mean we should just hand out diplomas on the street. It might be shocking, but it's possible to be learned and intelligent without being learned and intelligent in math. And this is coming from a mathematician. It's possible to be learned and intelligent without getting a diploma or college degree. What's your point? And I'm a mathematician too! *fistbump*
A high school diploma says "I didn't fail high school", it doesn't imply that "I'm good at math." There are many college degrees. If you learned Art History or Music Theory, then it will say that you majored in that on the piece of paper, so why do they need to know math?
Your argument is, unless algebra or math is required, diplomas and college degrees are worthless for distinguishing the intelligence of graduates?
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On July 29 2012 21:02 paralleluniverse wrote:Show nested quote +On July 29 2012 20:58 DoubleReed wrote:On July 29 2012 20:55 paralleluniverse wrote:On July 29 2012 20:46 DoubleReed wrote:On July 29 2012 20:35 paralleluniverse wrote:On July 29 2012 20:24 DoubleReed wrote:
You can't even start physics and chemistry or advanced biology without algebra. Do you expect young people to be attracted to these things if they don't even finish algebra?
But this is typical idiotic American educational thinking: If our students are failing because of a standard, rather than try to better our educational methods and teaching, let's just make it super easy on the students and pass them anyway. Who cares if they learned anything in school? Our passing rates are up!
It's terrible. It's a disgusting disservice that we're doing to our children. Getting an education is actually supposed to mean something. By lowering the standards you aren't making education easier on students, you are simply reducing what "education" means. I don't know anyone who wants to do physics or chemistry because they love algebra. It goes the other way around. If you're inspired to do science, you will need to learn mathematics and algebra is an important part of that. But if you're not going to do mathematics or science or anything that is mathematical in nature, then why do you need to know how to factorize a quadratic or integrate log(x)? The argument isn't simply remove algebra or math. Not everyone will be a mathematician or will use math in any way, so it shouldn't be required. But the article and Gowers' blog post I linked to suggests teaching optional courses that makes people mathematically literate and appreciate mathematical thinking, as opposed to forcing down some convoluted and unrealistic "application" of mathematics, then requiring students to perform symbolic manipulation to solve the problem. No, you need algebra to even get interested in physics or chemistry in the first place. It's a necessary condition, not a positive correlation. And again, symbolic manipulation is necessary to understand rates of change, which is actually useful for understanding mortgages and blah blah blah. If you're incapable of understanding and learning Algebra, then why should I pretend like you've gotten a basic education? There are plenty of jobs out there that you do not need ANY kind of education for. That's not an argument to lessen the standards of education. That's an argument for letting people fail, so we can differentiate between the two. Education actually is supposed to mean something. A high school diploma is supposed to mean something. By reducing the standards you aren't solving any problem. You're faking it. You're simply passing kids who haven't earned it. How does this solve the problem? You need algebra to learn physics, which is why no one is arguing to abolish math education. But no one is inspired to do physics because they find algebra fun. If you find algebra fun, be a mathematician (on second though, no mathematician will ever be hired to their ability to do symbolic manipulation),. You're point about mortgages to high ironic. [It] is deeply boring, and not even all that relevant to the people who are actually taking the exam, who should be enjoying their last few years of not having to think about mortgages, income tax returns and the like. (Does anyone seriously think that teenagers will be filled with enthusiasm by personal finance, when for adults, who are directly affected by it, it is an awful chore?) A conventional A’level student will do plenty of word problems and more mathematics, and will also solve modelling problems when they do statistics and mechanics. Who will end up better at solving mathematical problems that arise in the real world? http://gowers.wordpress.com/2009/07/11/help-im-stuck-in-my-ivory-tower/How is it lessening the standard of education to not force people who want to do something with their lives to do not math? What is the educational value for them, or for society for force them into doing something they don't like, and won't use? What is the societal value for pretending like they have a basic education? What is the societal value for passing them, when other people passed by learning how to do basic fucking algebra? There are plenty of jobs that do not require any education whatsoever. That doesn't mean we should just hand out diplomas on the street. It might be shocking, but it's possible to be learned and intelligent without being learned and intelligent in math. And this is coming from a mathematician.
As I understand it, we're not talking about "being intelligent in math", we're talking about this : http://en.wikipedia.org/wiki/Elementary_algebra, which is basically replacing a quantity by a variable and having some rules to manipulate such expressions...
That little of an abstraction level should be accessible to everyone pretending to be "learned and intelligent".
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Russian Federation748 Posts
On July 29 2012 16:28 nicknack wrote:
My memory of high school maths below
Teacher:
x + 5 = 7
Get X on its own, minus 5 from one side of the equation, what you do to one side you do to the other.
x = 7- 5
x = 2
2 + 5 = 7
This proves x = 2
Next question
x + 8 =11
Get X on its own, minus 8 from one side of the equation, what you do to one side you do to the other.
x = 11- 8
x = 3
3 +8 =11
This proves x = 3
Half the kids in class "but sir X = 2 in the first problem now X = 3, it cant be both!" *face palm*
Hey, you reminded me of high school. The teacher tells us that a function is called monotonic if it's either increasing or decreasing, and then he draws a sinus-like curve and exclaims: " See that one is not monotonic! " And our reaction :
" Yes, it is. It's either increasing, or decreasing." " No, it must be always one or always the other".
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On July 29 2012 21:08 Kyrillion wrote:Show nested quote +On July 29 2012 16:28 nicknack wrote:
My memory of high school maths below
Teacher:
x + 5 = 7
Get X on its own, minus 5 from one side of the equation, what you do to one side you do to the other.
x = 7- 5
x = 2
2 + 5 = 7
This proves x = 2
Next question
x + 8 =11
Get X on its own, minus 8 from one side of the equation, what you do to one side you do to the other.
x = 11- 8
x = 3
3 +8 =11
This proves x = 3
Half the kids in class "but sir X = 2 in the first problem now X = 3, it cant be both!" *face palm*
Hey, you reminded me of high school. The teacher tells us that a function is called monotonic if it's either increasing or decreasing, and then he draws a sinus-like curve and exclaims: " See that one is not monotonic! " And our reaction : " Yes, it is. It's either increasing, or decreasing." " No, it must be always one or always the other".
The problem is that the teacher is using the definition of "or" in logic, whereas the student is using the definition of "or" in plain English which confusingly is sometimes the logical "and".
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Incredibly that this was published, and in the NYTimes.
Well, I guess it makes things easier for those of us fotunately enough to already know maths.
PS: I giggled when I read "I say this as a writer and social scientist whose work relies heavily on the use of numbers". Explains a lot.
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On July 29 2012 21:08 Kyrillion wrote:Show nested quote +On July 29 2012 16:28 nicknack wrote:
My memory of high school maths below
Teacher:
x + 5 = 7
Get X on its own, minus 5 from one side of the equation, what you do to one side you do to the other.
x = 7- 5
x = 2
2 + 5 = 7
This proves x = 2
Next question
x + 8 =11
Get X on its own, minus 8 from one side of the equation, what you do to one side you do to the other.
x = 11- 8
x = 3
3 +8 =11
This proves x = 3
Half the kids in class "but sir X = 2 in the first problem now X = 3, it cant be both!" *face palm*
Hey, you reminded me of high school. The teacher tells us that a function is called monotonic if it's either increasing or decreasing, and then he draws a sinus-like curve and exclaims: " See that one is not monotonic! " And our reaction : " Yes, it is. It's either increasing, or decreasing." " No, it must be always one or always the other".
haha pretty true...well, eventually I guess they work their way around to it. I could have sworn that they come up with the same problem every year and would have learned to address it before the kids are confused. Maybe they just think that it's better to let the kids be confused and then figure it out in terms of learning.
But sometimes....there are just some serious facepalm moments... the kind of level of algebra he was mentioning probably shouldn't be confusing to those kids for too long, otherwise I have some serious reservations about the education system :x
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On July 29 2012 20:55 DoubleReed wrote:Show nested quote +On July 29 2012 20:52 Deadlyhazard wrote:On July 29 2012 20:48 DoubleReed wrote:On July 29 2012 20:46 Deadlyhazard wrote:On July 29 2012 20:24 DoubleReed wrote:
You can't even start physics and chemistry or advanced biology without algebra. Do you expect young people to be attracted to these things if they don't even finish algebra?
But this is typical idiotic American educational thinking: If our students are failing because of a standard, rather than try to better our educational methods and teaching, let's just make it super easy on the students and pass them anyway. Who cares if they learned anything in school? Our passing rates are up!
It's terrible. It's a disgusting disservice that we're doing to our children. Getting an education is actually supposed to mean something. By lowering the standards you aren't making education easier on students, you are simply reducing what "education" means.
The real thing that's important to day-to-day life is understanding rates of change. That's Calculus. Everything about our math education is a stepping stone to get average people to learn Calculus, as it is one of the most powerful tools we have in almost everything we do. So yes, we need Algebra because we want as many people to understand Calculus as possible. Nobody is saying Algebra should be taken out of education. Most people are saying it shouldn't be a requirement to people not wanting to go into math/sci related fields. It's pointless to make someone like me, who is learning to graphically design images, to learn anything beyond basic math because I simply don't need it or have an interest in it. Why do you need an education at all to graphically design images? Why is it necessary for you to have a high school diploma when you have not earned it? Why should everyone's diploma be worth less because you don't want to take basic education course? Because education is very, very necessary to illustrate. Whether it be self-taught or through school, every artist/designer/whateveryouwanttocallthem is educated on the past 600 years of advancements in graphical imagery -- otherwise you can't produce anything interesting because you won't know how to (since art is based on observational science, really). I think basic education is fine -- I don't feel advanced algebra (in other words -- college level or beyond) is necessary to everyone. I was fine passing algebra in high school, but I felt it was a huge waste of time and really unnecessary in college. I feel that past basic high school level algebra, math should not be required to receive higher level education in non-math/sci related fields. I think I'm getting confused on what everyone means by 'algebra.' There are several different basic algebras with the same name taught in middleschool, highschool, and college -- the one I'm referring to is college algebra. I don't think it's necessary for everyone. We're talking about high school algebra. Generally it means symbolic manipulation. I fail to see how education is necessary to illustrate. Maybe artistic education. I'll agree with that. But you can get that at Art Schools. But English, History, Science, these are all unnecessary to you. You don't need a high school diploma to illustrate.
It's not just art that doesn't require high school education. You can drop out and get a GED and still become a doctor/engineer/actor/painter/younameit. Basic education isn't required from schooling -- you can pick and choose what you want to do and pursue it at a university level or higher if you feel it's necessary. You can self-educate yourself on algebra or any other topic if you're really interested in it.
I don't feel algebra is necessary to all students, I think middleschool math (pre-algebra) is fine for most people and I really do feel that you don't need algebra from that point forward. A topic like English, however, most people have to use throughout their entire lives and so I see it fit for something like that to stick (at least in an English speaking country) through high school.
I just think algebra begins to get into more advanced mathematical concepts that aren't necessary or even helpful for people that aren't going into math related fields. I have not used anything algebraic in my day to day tasks because it's highly unnecessary know-how for the way I want to live my life.
So if you want to pursue a career from university onwards, you should be able to do just that. If you have a sudden change of heart, and say, I want to study academic mathematics! but you lack basic algebraic education -- you can still self-teach yourself that and get into a university program, which should help that skill grow. It's not like removing something like algebra from basic education is a big deal. Anyone can teach themselves it if they want to pursue it or there can even be classes set up as an elective to learn it. I think high school should be elective based to get students to figure out what they might want to do, with a few necessary classes like English. College should be a time of specificity and a more narrow, challenging program that has set requirements for these skills.
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Algebra is the most practical and commonly used back that there is, correct? Aside from basic addition, multiplication, division, etc.
If there's math taught at all (And it shouldn't even be a question as to whether math should be taught), shouldn't algebra be it?
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Subjects are often taught stupid. There's gotta be a greater motivation for learning material than "it's on the syllabus" or "it's on the test." However, the problem does not lie in the difficulty of introducing basic abstraction to arithmetic.
http://www.maa.org/devlin/LockhartsLament.pdf
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On July 29 2012 21:11 paralleluniverse wrote:Show nested quote +On July 29 2012 21:08 Kyrillion wrote:On July 29 2012 16:28 nicknack wrote:
My memory of high school maths below
Teacher:
x + 5 = 7
Get X on its own, minus 5 from one side of the equation, what you do to one side you do to the other.
x = 7- 5
x = 2
2 + 5 = 7
This proves x = 2
Next question
x + 8 =11
Get X on its own, minus 8 from one side of the equation, what you do to one side you do to the other.
x = 11- 8
x = 3
3 +8 =11
This proves x = 3
Half the kids in class "but sir X = 2 in the first problem now X = 3, it cant be both!" *face palm*
Hey, you reminded me of high school. The teacher tells us that a function is called monotonic if it's either increasing or decreasing, and then he draws a sinus-like curve and exclaims: " See that one is not monotonic! " And our reaction : " Yes, it is. It's either increasing, or decreasing." " No, it must be always one or always the other". The problem is that the teacher is using the definition of "or" in logic, whereas the student is using the definition of "or" in plain English which confusingly is sometimes the logical "and".
Isn't the teacher using XOR whereas the pupils are using OR in this sense (and are therefore correct)? I mean XOR = 'false' for both arguments 'true', so in this case, 'increasing' OR 'decreasing' = 'true', but 'increasing' XOR 'decreasing' = 'false'
if 'increasing' = 'true' = 'decreasing'.
But this is waaaay offtopic ^.-
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Learning how to think with maths is the best way to learn how to think logically. That's a skill worth having for everyone in every aspect of life.
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On July 29 2012 21:31 KuKri wrote:Show nested quote +On July 29 2012 21:11 paralleluniverse wrote:On July 29 2012 21:08 Kyrillion wrote:On July 29 2012 16:28 nicknack wrote:
My memory of high school maths below
Teacher:
x + 5 = 7
Get X on its own, minus 5 from one side of the equation, what you do to one side you do to the other.
x = 7- 5
x = 2
2 + 5 = 7
This proves x = 2
Next question
x + 8 =11
Get X on its own, minus 8 from one side of the equation, what you do to one side you do to the other.
x = 11- 8
x = 3
3 +8 =11
This proves x = 3
Half the kids in class "but sir X = 2 in the first problem now X = 3, it cant be both!" *face palm*
Hey, you reminded me of high school. The teacher tells us that a function is called monotonic if it's either increasing or decreasing, and then he draws a sinus-like curve and exclaims: " See that one is not monotonic! " And our reaction : " Yes, it is. It's either increasing, or decreasing." " No, it must be always one or always the other". The problem is that the teacher is using the definition of "or" in logic, whereas the student is using the definition of "or" in plain English which confusingly is sometimes the logical "and". Isn't the teacher using XOR whereas the pupils are using OR in this sense (and are therefore correct)? I mean XOR = 'false' for both arguments 'true', so in this case, 'increasing' OR 'decreasing' = 'true', but 'increasing' XOR 'decreasing' = 'false' if 'increasing' = 'true' = 'decreasing'. But this is waaaay offtopic ^.-
Ahh, yes you're right.
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On July 29 2012 20:16 JoeSchmoe wrote:Show nested quote +On July 29 2012 20:00 Groog wrote:On July 29 2012 19:27 JoeSchmoe wrote:On July 29 2012 19:10 Groog wrote:
Using the part of the brain where logic comes from trains that part of the brain. There is no other way to train logical thinking besides mathematics and philosophy. No other mental activity accesses the parts of the brain where that kind of abstract thinking is required. point me to credible studies where learning elementary algebra has lead to measurable increases in a person's logic and reasoning abilities that helped contribute to their success later on in their life regardless of career path. also we're talking about algebra. do not generalize this into mathematics in general. I'm not going to spend my free time looking for an article that might or might not exist. It is common knowledge and if you had any basic knowledge of neurology you would know that continuously stimulating a certain part of the brain leads to an increase of neural pathways in that area of the brain (while it's still in developement, ofc. i.e. <21years). Not sure if a person who can't distinguish between neurology and neuropsychology/neurophysiology should be educating anyone on what is common knowledge.
I can't counter his arguement, I'll attack his choice of wording. Grats, you have great rethorics.
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On July 29 2012 21:28 Severedevil wrote:Subjects are often taught stupid. There's gotta be a greater motivation for learning material than "it's on the syllabus" or "it's on the test." However, the problem does not lie in the difficulty of introducing basic abstraction to arithmetic. http://www.maa.org/devlin/LockhartsLament.pdf
That was a really fantastic read and I agree with the points it made. Thanks for that.
Although they made painters look dumber than musicians, it would be more like students being forced to paint in greyscale from 1-100 and blend seamlessly so as to make a perfect gradation of values. OR FORCED INTO FULLY RENDERED 30 HOUR STILL LIFE STUDIES with IMPECCABLE perspective and edge qualities. Okay, no high school student can do that, BUT STILL.
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On July 29 2012 15:04 zezamer wrote:
Isn't the whole purpose of math to teach rational thinking,problem solving etc ?
Yes, and especially for the people who struggle the most learning it.
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While I agree there are some basic fundamental concepts in the early maths that need to be understood, call it "pre-algebra", I do not agree that algebra needs to be understood by everyone. At least it doesn't need to be taught on such an abstract level. If it is going to be taught, it should be as part of the course load for another class. For instance, if you're teaching psychology, you're inevitably going to need to address "correlation versus causation" in discussions of studies. You can teach students how to better understand what a study's results implies - something that is very practical. Or if you're teaching programming, you can relate to students what the modulus function does by talking about converting from 12-hour times to 24-hour times, or with discussion on how to go about creating a Calendar like program.
If someone is genuinely interested in the more abstract side of math, they can pursue that on their own. I agree with the author that it doesn't need to be mandatory at the high-school level. The more applicable and practical portions of math can be taught as part of other classes.
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On July 29 2012 21:07 paralleluniverse wrote:Show nested quote +On July 29 2012 21:04 DoubleReed wrote:On July 29 2012 21:02 paralleluniverse wrote:On July 29 2012 20:58 DoubleReed wrote:On July 29 2012 20:55 paralleluniverse wrote:On July 29 2012 20:46 DoubleReed wrote:On July 29 2012 20:35 paralleluniverse wrote:On July 29 2012 20:24 DoubleReed wrote:
You can't even start physics and chemistry or advanced biology without algebra. Do you expect young people to be attracted to these things if they don't even finish algebra?
But this is typical idiotic American educational thinking: If our students are failing because of a standard, rather than try to better our educational methods and teaching, let's just make it super easy on the students and pass them anyway. Who cares if they learned anything in school? Our passing rates are up!
It's terrible. It's a disgusting disservice that we're doing to our children. Getting an education is actually supposed to mean something. By lowering the standards you aren't making education easier on students, you are simply reducing what "education" means. I don't know anyone who wants to do physics or chemistry because they love algebra. It goes the other way around. If you're inspired to do science, you will need to learn mathematics and algebra is an important part of that. But if you're not going to do mathematics or science or anything that is mathematical in nature, then why do you need to know how to factorize a quadratic or integrate log(x)? The argument isn't simply remove algebra or math. Not everyone will be a mathematician or will use math in any way, so it shouldn't be required. But the article and Gowers' blog post I linked to suggests teaching optional courses that makes people mathematically literate and appreciate mathematical thinking, as opposed to forcing down some convoluted and unrealistic "application" of mathematics, then requiring students to perform symbolic manipulation to solve the problem. No, you need algebra to even get interested in physics or chemistry in the first place. It's a necessary condition, not a positive correlation. And again, symbolic manipulation is necessary to understand rates of change, which is actually useful for understanding mortgages and blah blah blah. If you're incapable of understanding and learning Algebra, then why should I pretend like you've gotten a basic education? There are plenty of jobs out there that you do not need ANY kind of education for. That's not an argument to lessen the standards of education. That's an argument for letting people fail, so we can differentiate between the two. Education actually is supposed to mean something. A high school diploma is supposed to mean something. By reducing the standards you aren't solving any problem. You're faking it. You're simply passing kids who haven't earned it. How does this solve the problem? You need algebra to learn physics, which is why no one is arguing to abolish math education. But no one is inspired to do physics because they find algebra fun. If you find algebra fun, be a mathematician (on second though, no mathematician will ever be hired to their ability to do symbolic manipulation),. You're point about mortgages to high ironic. [It] is deeply boring, and not even all that relevant to the people who are actually taking the exam, who should be enjoying their last few years of not having to think about mortgages, income tax returns and the like. (Does anyone seriously think that teenagers will be filled with enthusiasm by personal finance, when for adults, who are directly affected by it, it is an awful chore?) A conventional A’level student will do plenty of word problems and more mathematics, and will also solve modelling problems when they do statistics and mechanics. Who will end up better at solving mathematical problems that arise in the real world? http://gowers.wordpress.com/2009/07/11/help-im-stuck-in-my-ivory-tower/How is it lessening the standard of education to not force people who want to do something with their lives to do not math? What is the educational value for them, or for society for force them into doing something they don't like, and won't use? What is the societal value for pretending like they have a basic education? What is the societal value for passing them, when other people passed by learning how to do basic fucking algebra? There are plenty of jobs that do not require any education whatsoever. That doesn't mean we should just hand out diplomas on the street. It might be shocking, but it's possible to be learned and intelligent without being learned and intelligent in math. And this is coming from a mathematician. It's possible to be learned and intelligent without getting a diploma or college degree. What's your point? And I'm a mathematician too! *fistbump* A high school diploma says "I didn't fail high school", it doesn't imply that "I'm good at math." There are many college degrees. If you learned Art History or Music Theory, then it will say that you majored in that on the piece of paper, so why do they need to know math? Your argument is, unless algebra or math is required, diplomas and college degrees are worthless for distinguishing the intelligence of graduates?
A high school diploma says "I didn't fail high school." Well, no, actually it means "I passed high school." What exactly do you think that means? Is high school just a period of time for people now? Is it another word of adolescence? No, it means you passed courses in basic education. And that's what algebra is. Basic education.
No, I'm saying by allowing people to get a diploma without passing algebra lessens the worth of all degrees. By definition it does this. It no longer means "I have basic math skills." The goal of education is not to pass everyone. The goal of education is to educate.
Furthermore, it's also about work, not just intelligence. What you're saying is that neither should be required for a high school diploma. And that, to me, is horrible.
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EPT
