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Mathematics education in schools

by Millennial
Tags: education, mathematics, schools
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Millennial
#1
Dec23-12, 10:49 AM
P: 295
I thought I'd make a topic about this here and see what everybody else thinks about it. Just so you know before reading the entire post, I am fourteen years old and I know math topics up to and including complex analysis. I wrote some of what I have been going through as well, so I thought I might as well mention it.

The thing that has been bugging me is, is compulsory mathematics education necessary? Normally, this is a question I hear from those who aren't good at the subject, but even though I am and I like mathematics very much, I am still incapable of understanding why there exists compulsory mathematics education. I do think the same thing applies to science as well, but I am simply far more proficient in mathematics than in any other field, so I thought I'd make the topic math-oriented. The same idea also applies to people who like math, as they shouldn't have to learn literature, but they do.

Don't get me wrong - math education indeed is necessary up to eigth grade, because it is simply life skills until then. If you buy three chocolate bars from a store, you won't have to ask the price for one when you come back again. This is an use of algebra that's common in daily life. What I'm talking about is abstract and pure mathematics, like precalculus topics. Just because we enjoy it and find it necessary does not mean that everybody else will as well. Indeed, science and mathematics are essential for human life - where would we be without them? However, are they necessary to be known by those who do not want to know them? Without fishers, we wouldn't be able to eat any fish; but we don't learn fishing, we go and buy fish from fishers. Don't you think the same logic applies here as well?

In a TED talk about math education, the speaker, who was a math teacher at a high school, said: "I'm trying to sell a product to a market that doesn't want to buy it but is forced by law to." When you take a moment and think about it, it really does not make sense. The possible counter-arguments to this can be that students (well, most of them anyway) don't want to see any lessons at all, so if we go by this logic, we shouldn't have schools entirely. This logic is flawed in one way: We shouldn't have compulsory schools. People can go to school if and only if they want to, and you can't intervene with that. Sure, universities might require an initial knowledge of the non-compulsory topics, but if you want to get in a university then you might as well take your time learning those topics. If you don't, well, it's your life.

In comparison to other topics, math has a certain vulnerability in arguments made with others: Some other lessons, like history, are perceived as "necessary for intellect" by the public. This may or may not be true depending on your definition of an intellectual, but what I do know is that not everybody has to be an intellectual! (Just for the record, I know history very well too.) This issue in general is complicated even more in the country I live in and a lot of other countries, where you can't attend a university without having a high school degree, making it "even more compulsory" (whatever that means). If I already know everything I'm going to learn up to 12th grade by 7th grade about the subject I want to study, why should I waste five years of my life in school? I would not be so discontent with the situation if it was merely wasting your time. You also have to go there every single day and waste most of your day as well, which strikes generally as being just weird. So basically, if you don't know math you are screwed, but if you do know math you are going to waste your time. How can you benefit from this disfunctional system? I say you can't.

I don't know what to blame here, but I nominate the idea (and maybe the policy) of "liberal education", where everybody has to learn about everything up to an extent. I agree with the idea as a whole, but "the extent" at which general education must be stopped and specialized education should be introduced should be chosen so as to be beneficial instead of harmful. This is nothing else than sheer torment to students, those who can't do well and those who do well alike, and I haven't even mentioned the competitive examination systems existent in some countries; which simply discourage "bad" students even further. As I am not certain about the topic, I would like to ask you: What do you think? Should mathematics education (and in general, education itself) be compulsory? Why?
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Rono
#2
Dec23-12, 11:35 AM
P: 53
I've always considered high school, besides a place to learn and acquire skills useful for life, a place where the students can find what they want to do in university. If you don't teach highschoolers topics like precalculus or introductory chemistry, how can they know if they'd like engineering, math, science... The same for topics like law or political ideologies for lawyers and politicians and so on.

In my case, I always disliked English classes (Latin American here), but I'm sure they could've been useful for classmates who would go to work instead of going to the university or who would study something related like English Translation or Public Relationships.

Also, if some courses wouldn't be compulsory, how can universities assure the quality of their freshmen? They could put requisites like taking precalculus for entering an engineering course, but maybe, due to a lack of demand in the course, the high school would have a horrible math background which would bring students from that school in disadvantage of other schools.

Math is compulsory not just because, but because it's really needed. Maybe not for all students, but that would be the same for all classes.
Sankaku
#3
Dec23-12, 04:03 PM
P: 717
Quote Quote by Millennial View Post
The thing that has been bugging me is, is compulsory mathematics education necessary?
I have great sympathy for this question, and I frequently take this position (as Devil's Advocate) in discussions around compulsory courses. Lockhart's Lament and Dudley's "What is Mathematics For?" both argue that Mathematics should be taught more like Art or Music.

However, in the real world, things are a bit different. Most students will never have the chance to experience good mathematics teaching, so that they become inspired enough to want to take mathematics voluntarily. Forcing everyone to fulfil basic requirements means there is some kind of base-level that high-school graduates achieve. Not the best solution, but probably not the worst, either.

Are there other possibilities? Certainly. There are many alternative schools that have good success, but changing the whole school system of a country is a different matter. This is a great question to ask, and it is good to have blue-sky ideas, just don't be disappointed if the world doesn't change very quickly!

johnqwertyful
#4
Dec23-12, 05:26 PM
P: 362
Mathematics education in schools

Quote Quote by Sankaku View Post
Lockhart's Lament
God I hate this essay. "yeah man, don't give them like problems you know, but like PROBLEMS you know? there's too many problems, but there's not any PROBLEMS. the reason why kids hate math is cause it's useful, it's like ART, you know?"

Just mindless bitching about nothing.

The best quote about math education was from a friend's math teacher "if the way we teach math was bad, it would have been bad since the beginning of time. The reason why people don't like math is because they don't like to be wrong. In math you're wrong a LOT"

That's the truth. People hate being wrong. In math and science there's a DEFINITE right and wrong. Your proof makes sense or it doesn't. Your answer is right or wrong. When learning, you're going to be wrong a LOT. People have egos.
MarneMath
#5
Dec23-12, 10:35 PM
P: 439
What do you think? Should mathematics education (and in general, education itself) be compulsory? Why?
I'll just focus on this little bit here. Of course I do. You may have the benefit of knowing a lot of mathematics and you probably have a clear vision of what you want to do and if not clear, then at the very least a good idea of what kind of career you want to have.

For the rest of us, life wasn't so straight and narrow. When I was a 14 yr old kid (and I do put emphasis on the word kid here), I had no idea what I wanted to do in life. I was a straight A student, but I did a lot of illegal activities and really only cared about playing baseball.

I was accepted into a top 20 university for my freshman year, where I quickly gained a reputation as the king of the keg. I promptly failed and was thrown out with my awesome GPA of 1.

So what does this have to do with anything? After being kicked out, I ended up in the Army, and visited nice places like Iraq and Afghanistan. During my tour of duties, I spent a lot of time interacting with the Iraqi's and Afghani's. Due to taking world history, I had a good idea of why sects of Islam hated each other. Due to US History, I knew about the US role in Afghanistan prior to 9/11. Classes in chemistry helped me identify a bomb maker's house (I got a ARCOM for this :D ).

The point is that, you're a kid and everyone in high school is a kid. You have no earthly idea what you'll need in life and what can be useful to you. Heck, even if it won't be useful to you, I've learn the reason why Democracy won't succeed in a place like Afghanistan is not because the people don't want it, but because the general population is ignorant. When I was there, some people thought we were still Soviets! If you like in a country with a democracy, it heavily depends on the general education of the population to make informed decisions. School is not there to teach you how to do a job, it's there, in my opinion, to make you a good citizen.
Sankaku
#6
Dec24-12, 12:19 AM
P: 717
Quote Quote by johnqwertyful View Post
The reason why people don't like math is because they don't like to be wrong.
I would disagree very strongly with this. People don't like math because there is often unnecessary/arbitrary punishment for being wrong. When students have no idea what is going on and are also being told they are stupid, they give up.

Yes, in real upper-level mathematics, you have to work continually with your intuition leading you astray. Yes, when learning new mathematics we are often (if not usually) wrong. That is not the point. The point is making it interesting and enjoyable to work through this process. We eventually have to answer questions correctly, but there is more than one way to get there and the current way doesn't work for a lot of people.

Be very careful about patting yourself on the back and calling everyone else lazy.
johnqwertyful
#7
Dec24-12, 01:39 AM
P: 362
Quote Quote by Sankaku View Post
I would disagree very strongly with this. People don't like math because there is often unnecessary/arbitrary punishment for being wrong. When students have no idea what is going on and are also being told they are stupid, they give up.

Yes, in real upper-level mathematics, you have to work continually with your intuition leading you astray. Yes, when learning new mathematics we are often (if not usually) wrong. That is not the point. The point is making it interesting and enjoyable to work through this process. We eventually have to answer questions correctly, but there is more than one way to get there and the current way doesn't work for a lot of people.

Be very careful about patting yourself on the back and calling everyone else lazy.
I never patted myself on the back, and I never called anyone lazy.

I have never once been in a classroom where someone was called stupid for not knowing something. Ever. I don't get where people get these ideas. I have never once been in a class where someone was "punished" for not knowing something. Yeah, if you don't know it and you fail the test you're going to fail the class. I see nothing wrong with that. What are these unnecessary "punishments" you speak of? Bad grades if you don't know the material? How is that unnecessary or arbitrary?
johnqwertyful
#8
Dec24-12, 01:48 AM
P: 362
Quote Quote by Sankaku View Post
The point is making it interesting and enjoyable to work through this process.
Why?

Why do we have some obligation to make it "fun" or "interesting"? Why not just teach the material? Either you find math interesting or you don't. Don't try to make it cute or interesting or relevant or anything. Just teach math how it is. In the real world, we don't have any obligation to make work interesting and enjoyable. Do you think your boss in the real world gives a damn if you're interested or enjoying your work? No, he just needs it done. That's not to say that you can't enjoy your work. That doesn't mean you can't enjoy doing math. But there is absolutely no obligation to make it interesting or enjoyable at ALL.
Hurkyl
#9
Dec24-12, 02:18 AM
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Quote Quote by johnqwertyful View Post
Bad grades if you don't know the material? How is that unnecessary or arbitrary?
If one don't understand why something is right or why something is wrong, then one cannot distinguish between the distinction having cause or being arbitrary.
symbolipoint
#10
Dec24-12, 02:47 AM
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Quote Quote by johnqwertyful View Post
God I hate this essay. "yeah man, don't give them like problems you know, but like PROBLEMS you know? there's too many problems, but there's not any PROBLEMS. the reason why kids hate math is cause it's useful, it's like ART, you know?"

Just mindless bitching about nothing.

The best quote about math education was from a friend's math teacher "if the way we teach math was bad, it would have been bad since the beginning of time. The reason why people don't like math is because they don't like to be wrong. In math you're wrong a LOT"

That's the truth. People hate being wrong. In math and science there's a DEFINITE right and wrong. Your proof makes sense or it doesn't. Your answer is right or wrong. When learning, you're going to be wrong a LOT. People have egos.
People's wanting to not be wrong is only part of the trouble. Learning Mathematics requires a hard mental effort. People often tend not to want to think hard.
chiro
#11
Dec24-12, 03:41 AM
P: 4,578
Quote Quote by symbolipoint View Post
People's wanting to not be wrong is only part of the trouble. Learning Mathematics requires a hard mental effort. People often tend not to want to think hard.
It's interesting you brought this up because a while ago I read a biography about Gauss and apparently his father didn't consider mathematics "real work" because it wasn't hard physical labor like the type his father had to endure.

According to the book, his father harbored resentment against Gauss throughout a lot of his life towards the idea that "mental work" wasn't as hard or as demanding as the "hard labor" kind of work.

I get a feeling that this kind of thinking still exists today in some circles and probably the opposite type as well (in other words, mental workers think that physical work is easy).
Stephen Tashi
#12
Dec24-12, 03:43 AM
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P: 3,313
Designating a course as not required doesn't give it a well defined status. One thing to consider about making a course voluntary is who gets to make the decision to take it - the kids or the parents? (Perhaps it will vary according to the culture of various famiilies, but for most kids the parents will have to "sign off" on the decision.) Also, if a course if voluntary, there could be parents that prohibit their kids from taking it.
johnqwertyful
#13
Dec24-12, 11:29 AM
P: 362
Quote Quote by chiro View Post
It's interesting you brought this up because a while ago I read a biography about Gauss and apparently his father didn't consider mathematics "real work" because it wasn't hard physical labor like the type his father had to endure.

According to the book, his father harbored resentment against Gauss throughout a lot of his life towards the idea that "mental work" wasn't as hard or as demanding as the "hard labor" kind of work.

I get a feeling that this kind of thinking still exists today in some circles and probably the opposite type as well (in other words, mental workers think that physical work is easy).
Interesting story.

I object to the whole premise, though. Who gives a damn how "hard" something is? Do we need ditch diggers because it's "hard"? No. We need them because ditches need to get dug. We don't need mathematicians because it's "hard", we need them because math needs to get done. We admire talent, certainly. People that solve problems no one else could, do things that are difficult. But it's not doing things that are difficult for the sake of difficulty. It's doing things that people need/want, things that are useful. When I listen to Valentina Lisitsa play La Campanella, I'm in awe. Yes, it is difficult. But that's not why I listen to it. I listen to it because it's AWESOME. It's an amazing piece of music.

The reason why Gauss was great wasn't because he did things that were hard. It's because he made substantial contributions to math. Developed things that are beautiful, useful, cool, etc.
Choppy
#14
Dec24-12, 01:43 PM
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P: 2,744
I asked a lot of similar questions when I was fourteen.

There are a lot of hoops that you have to jump through in life to get where you want to be. If you're lucky, you can figure out how to circumvent some of those that are just hoops and nothing more, and you will eventually see the value in those that seem like excessive wastes of time in the beginning.

Should math be compulsory? I was pretty happy with the system I went through. In it, students were required to complete 10th grade mathematics in order to achieve a high school diploma. At the time high school classes were streamed, so this meant those that weren't strong could get by with a "basic" class that aimed at giving the students some very practical mathematical skills. Those interested in going on to university could take the "advanced" classes which often required a little more intellectual horsepower. I think they've since de-streamed the system and lumped everyone together, which in my opinion penalizes the students on both the high and low end of the performance spectrum.
Millennial
#15
Dec24-12, 01:57 PM
P: 295
Quote Quote by MarneMath View Post
I'll just focus on this little bit here. Of course I do. You may have the benefit of knowing a lot of mathematics and you probably have a clear vision of what you want to do and if not clear, then at the very least a good idea of what kind of career you want to have.

For the rest of us, life wasn't so straight and narrow. When I was a 14 yr old kid (and I do put emphasis on the word kid here), I had no idea what I wanted to do in life. I was a straight A student, but I did a lot of illegal activities and really only cared about playing baseball.

I was accepted into a top 20 university for my freshman year, where I quickly gained a reputation as the king of the keg. I promptly failed and was thrown out with my awesome GPA of 1.

So what does this have to do with anything? After being kicked out, I ended up in the Army, and visited nice places like Iraq and Afghanistan. During my tour of duties, I spent a lot of time interacting with the Iraqi's and Afghani's. Due to taking world history, I had a good idea of why sects of Islam hated each other. Due to US History, I knew about the US role in Afghanistan prior to 9/11. Classes in chemistry helped me identify a bomb maker's house (I got a ARCOM for this :D ).

The point is that, you're a kid and everyone in high school is a kid. You have no earthly idea what you'll need in life and what can be useful to you. Heck, even if it won't be useful to you, I've learn the reason why Democracy won't succeed in a place like Afghanistan is not because the people don't want it, but because the general population is ignorant. When I was there, some people thought we were still Soviets! If you like in a country with a democracy, it heavily depends on the general education of the population to make informed decisions. School is not there to teach you how to do a job, it's there, in my opinion, to make you a good citizen.
Quote Quote by Rono View Post
I've always considered high school, besides a place to learn and acquire skills useful for life, a place where the students can find what they want to do in university. If you don't teach highschoolers topics like precalculus or introductory chemistry, how can they know if they'd like engineering, math, science... The same for topics like law or political ideologies for lawyers and politicians and so on.

In my case, I always disliked English classes (Latin American here), but I'm sure they could've been useful for classmates who would go to work instead of going to the university or who would study something related like English Translation or Public Relationships.

Also, if some courses wouldn't be compulsory, how can universities assure the quality of their freshmen? They could put requisites like taking precalculus for entering an engineering course, but maybe, due to a lack of demand in the course, the high school would have a horrible math background which would bring students from that school in disadvantage of other schools.

Math is compulsory not just because, but because it's really needed. Maybe not for all students, but that would be the same for all classes.
The truth here is that you are right about an arbitrary person not knowing what they'll need. That's natural, we can't see the future! However, if you had an aim of learning everything that could possibly be of use to you, then you'd have to learn every single bit of information!

An attempt of a justification here can be "Yes, we can't do that, so we focus on the rather common topics." This attempt is solid, but as I mentioned in the OP; I am not against the policy of liberal education, I am against the extent at which it is applied. Of course everybody needs to know a bit of maths, a bit of literature, a bit of history and et cetera. Someone I can't remember had a nice quote: "Learn something about everything, and learn everything about something." The problem isn't that you have to do this, the problem is that the "something" here is consistently being enlarged in terms of capacity.

Quote Quote by Sankaku View Post
I would disagree very strongly with this. People don't like math because there is often unnecessary/arbitrary punishment for being wrong. When students have no idea what is going on and are also being told they are stupid, they give up.

Yes, in real upper-level mathematics, you have to work continually with your intuition leading you astray. Yes, when learning new mathematics we are often (if not usually) wrong. That is not the point. The point is making it interesting and enjoyable to work through this process. We eventually have to answer questions correctly, but there is more than one way to get there and the current way doesn't work for a lot of people.

Be very careful about patting yourself on the back and calling everyone else lazy.
I agree. Again a quote: "In modern society, being wrong is perceived as somewhat 'bad', while it should be celebrated; for it elevates someone to a new level of understanding." If you aren't prepared to be wrong, then you shouldn't deal with science at all, for it is a fundamental property of science that it is falsifiable. Meanwhile, at schools, students always learn that being wrong is a bad thing. It is not. In fact, it is inevitable in science. As Einstein said, "If you haven't been wrong so far, then you didn't do anything at all." Being wrong isn't something to be afraid of. Well, maybe in schools, but that's the whole point of the topic, isn't it?

Quote Quote by Hurkyl View Post
If one don't understand why something is right or why something is wrong, then one cannot distinguish between the distinction having cause or being arbitrary.
Certainly true, and I have nothing to say.

Quote Quote by Stephen Tashi View Post
Designating a course as not required doesn't give it a well defined status. One thing to consider about making a course voluntary is who gets to make the decision to take it - the kids or the parents? (Perhaps it will vary according to the culture of various famiilies, but for most kids the parents will have to "sign off" on the decision.) Also, if a course if voluntary, there could be parents that prohibit their kids from taking it.
This is certainly of import here. To what extent can children be free to make their own decisions? I don't know of any system or society which lets children take control of their lives, and this possibly would prevent this system from functioning. Normally, of course, the kids should get to make the decision - but often there's some difference between theory and practice. I disagree how the parents get to make every choice about the life of a kid. They could potentially ruin the life of the kid by simply not letting him/her to do what he/she wants. Freedom in this case might be dangerous, as children are often judged as not being able of making decisions of import properly. For most children however, the legal age of being an adult is way past the actual age at which a child can make his/her own decisions. I end the paragraph by saying that this is somewhat a complicated topic that belongs to social and educational science and not mathematics. (this does not mean the topic is irrelevant, it means that it would require some extensive thinking to find an actual functioning solution.)

Quote Quote by Choppy View Post
I asked a lot of similar questions when I was fourteen.

There are a lot of hoops that you have to jump through in life to get where you want to be. If you're lucky, you can figure out how to circumvent some of those that are just hoops and nothing more, and you will eventually see the value in those that seem like excessive wastes of time in the beginning.

Should math be compulsory? I was pretty happy with the system I went through. In it, students were required to complete 10th grade mathematics in order to achieve a high school diploma. At the time high school classes were streamed, so this meant those that weren't strong could get by with a "basic" class that aimed at giving the students some very practical mathematical skills. Those interested in going on to university could take the "advanced" classes which often required a little more intellectual horsepower. I think they've since de-streamed the system and lumped everyone together, which in my opinion penalizes the students on both the high and low end of the performance spectrum.
Your last sentence quite resembles one of my paragraphs in the OP. Everybody gets punished in the system, perhaps not by grades but by the loss of time. Boredom is sometimes the worst punishment you can give to someone.

"...and you will eventually see the value in those that seem like excessive wastes of time in the beginning." This sentence makes no sense to me, as I'm pretty sure a historian won't need knowledge of sigma bonds or inverse functions while doing his job. This topic sort of is followed by my first paragraph in this post (not the OP).

I'll be happy to reply to other posts, there are some interesting ideas here.
johnqwertyful
#16
Dec24-12, 04:47 PM
P: 362
Quote Quote by MarneMath View Post
I'll just focus on this little bit here. Of course I do. You may have the benefit of knowing a lot of mathematics and you probably have a clear vision of what you want to do and if not clear, then at the very least a good idea of what kind of career you want to have.

For the rest of us, life wasn't so straight and narrow. When I was a 14 yr old kid (and I do put emphasis on the word kid here), I had no idea what I wanted to do in life. I was a straight A student, but I did a lot of illegal activities and really only cared about playing baseball.

I was accepted into a top 20 university for my freshman year, where I quickly gained a reputation as the king of the keg. I promptly failed and was thrown out with my awesome GPA of 1.

So what does this have to do with anything? After being kicked out, I ended up in the Army, and visited nice places like Iraq and Afghanistan. During my tour of duties, I spent a lot of time interacting with the Iraqi's and Afghani's. Due to taking world history, I had a good idea of why sects of Islam hated each other. Due to US History, I knew about the US role in Afghanistan prior to 9/11. Classes in chemistry helped me identify a bomb maker's house (I got a ARCOM for this :D ).

The point is that, you're a kid and everyone in high school is a kid. You have no earthly idea what you'll need in life and what can be useful to you. Heck, even if it won't be useful to you, I've learn the reason why Democracy won't succeed in a place like Afghanistan is not because the people don't want it, but because the general population is ignorant. When I was there, some people thought we were still Soviets! If you like in a country with a democracy, it heavily depends on the general education of the population to make informed decisions. School is not there to teach you how to do a job, it's there, in my opinion, to make you a good citizen.
Awesome story. I definitely agree with you too.
Redbelly98
#17
Dec24-12, 05:36 PM
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P: 12,074
Quote Quote by Millennial View Post
The truth here is that you are right about an arbitrary person not knowing what they'll need. That's natural, we can't see the future! However, if you had an aim of learning everything that could possibly be of use to you, then you'd have to learn every single bit of information!
True, and most teachers are aware of this. But one purpose of school is to prove to the world that you are capable of learning a variety of topics. People who must decide to accept or reject your application for whatever you try to do after graduating -- whether its a job or a college application -- look at how well you did in your classes to decide if you'll be able to learn whatever it is that they'll want you to learn -- even if it's not exactly the same as what your learning in your high school classes.

Sure, there are some jobs you might apply for that won't care much about your grades, but they won't be paying you as much as the jobs that do.
Rono
#18
Dec24-12, 05:47 PM
P: 53
Quote Quote by Redbelly98 View Post
True, and most teachers are aware of this. But one purpose of school is to prove to the world that you are capable of learning a variety of topics. People who must decide to accept or reject your application for whatever you try to do after graduating -- whether its a job or a college application -- look at how well you did in your classes to decide if you'll be able to learn whatever it is that they'll want you to learn -- even if it's not exactly the same as what your learning in your high school classes.

Sure, there are some jobs you might apply for that won't care much about your grades, but they won't be paying you as much as the jobs that do.
Actually, here some jobs for just-graduated people look for your grades, also the high school grades are heavily considered during the admission to the good universities of this country. This is really criticized here, because people get difficulties, especially in math.

The problem, at least here with math is the fact that the whole society, even the media talks about how difficult it is. Of course, if people see that everybody says that math is the hardest thing to do (which is not), they will find it stressful and fail.


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