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#1
Many of you have probably seen this paper before, A Mathematician's Lament by Paul Lockhart. What does math have to do with music? Well this paper is less about math and more about the way math is taught/learned in school. Not only does it provide great (IMO) philosophies about teaching that would be a benefit for those of you who are currently teaching guitar here, but it also opens a window on what learning is really about. Parallels could be drawn here between learning music and learning mathematics. In fact, that's how the paper opens. Keep music in mind as you read this. It's only 25 pages, it's not bad. It's really a 25 page rant.

Remember to keep an open mind as you read.
i don't know why i feel so dry
#2
I've never heard of it before, but I've just read the first page and am intrigued! Thanks for sharing!
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#3
Quote by Eastwinn
Many of you have probably seen this paper before, A Mathematician's Lament by Paul Lockhart. What does math have to do with music? Well this paper is less about math and more about the way math is taught/learned in school. Not only does it provide great (IMO) philosophies about teaching that would be a benefit for those of you who are currently teaching guitar here, but it also opens a window on what learning is really about. Parallels could be drawn here between learning music and learning mathematics. In fact, that's how the paper opens. Keep music in mind as you read this. It's only 25 pages, it's not bad. It's really a 25 page rant.

Remember to keep an open mind as you read.


I'm not much for reading long rants. Any chance you could give a short summary of what the article says (or you're opinion of it)? Like is there a definitive point being made?
shred is gaudy music
Last edited by GuitarMunky at Sep 27, 2010,
#4
Quote by GuitarMunky
I'm not much for reading long rants. Any chance you could give a short summary of what the article says (or you're opinion of it)? Like is there a definitive point being made?


It's really all over the place so I couldn't begin to summarize it, but it's really based a philosophy that I can assure you is not new to you: learning straight academics is no substitute for learning by doing and the ideal is both together.
i don't know why i feel so dry
#5
Quote by Eastwinn
It's really all over the place so I couldn't begin to summarize it, but it's really based a philosophy that I can assure you is not new to you: learning straight academics is no substitute for learning by doing and the ideal is both together.



after browsing further, it seems to me the guy is ranting about an approach to learning that excludes creativity and/or a motivating context for the student. I definitely agree that it's a problem.

Good article.
shred is gaudy music
Last edited by GuitarMunky at Sep 27, 2010,
#6
It's easy to yap about being butthurt for 25 pages and pointing every little problem without proposing any definitive solution or idea to solve it.


I don't see the connection to music either. Music and musicians (as well as mathematicians) have been more abundant than at any other time combined. On top of that, the vast majority of them don't even know anything about music theory or notes, they just use a computer and make musical collages of rhythm and sound.

The notion here in MT about the classical, counterpoint and the general fear of anything theoretical beyond anything from the 1700s is a pretty isolated case of bullcrap. Music today is light years beyond that.

It's not the teaching system that's wrong, it's that people nowadays are lazy and couldn't give a rat's ass about paying their dues on anything.

Instant Gratification, and if it isn't instant there's a new age crap method "so kids don't have to suffer from the evils of system education that robs the creativity from the children."
#7
Quote by Pillo114
It's easy to yap about being butthurt for 25 pages and pointing every little problem without proposing any definitive solution or idea to solve it.


I don't see the connection to music either. Music and musicians (as well as mathematicians) have been more abundant than at any other time combined. On top of that, the vast majority of them don't even know anything about music theory or notes, they just use a computer and make musical collages of rhythm and sound.

The notion here in MT about the classical, counterpoint and the general fear of anything theoretical beyond anything from the 1700s is a pretty isolated case of bullcrap. Music today is light years beyond that.

It's not the teaching system that's wrong, it's that people nowadays are lazy and couldn't give a rat's ass about paying their dues on anything.

Instant Gratification, and if it isn't instant there's a new age crap method "so kids don't have to suffer from the evils of system education that robs the creativity from the children."


So, I take it you didn't read the article..... or you only read enough to trigger a rant of your own. Understandable, but I think you missed the point.
shred is gaudy music
#8
I did read the whole thing, and I still stand by what I posted. Maybe you should be the one reading it instead of skimming it and trying to be the head honcho.
#9
Quote by Pillo114
I did read the whole thing, and I still stand by what I posted. Maybe you should be the one reading it instead of skimming it and trying to be the head honcho.


Ummm I read it. not trying to be a "head honcho".... just disagreeing with your post.
shred is gaudy music
#11
Quote by Pillo114
So what's the disagreement then?

1) you don't see the connection to music
2) you think that.."people nowadays are lazy and couldn't give a rat's ass about paying their dues on anything. "

Quote by Pillo114


Instant Gratification, and if it isn't instant there's a new age crap method "so kids don't have to suffer from the evils of system education that robs the creativity from the children."


and I have to say I've never heard of ^ this method.
shred is gaudy music
Last edited by GuitarMunky at Sep 27, 2010,
#12
Quote by GuitarMunky
1) you don't see the connection to music
2) you think that.."people nowadays are lazy and couldn't give a rat's ass about paying their dues on anything.



Of course I see the connection to music. But just like the main math topic, like I said before, creativity hasn't diminished whatsover since both fields have expanded exponentially in the amount of people who partake in it and in the general advancement of the science. Even like he said, the teaching system has been the same one for centuries and is "wrong" according to him even though dozens and dozens of history's brightest people have spawned from it.

And though I do see your creativity point, it doesn't mean you're going to start taking stuff out because the author thought they were useless or old.

How sad that fifth-graders are
taught to say “quadrilateral” instead of “four-sided shape”


I could put over a dozen examples of this from that essay. Is that not an example of the general laziness of society now? Put it in the context of music, why dont we get rid of all the old and useless terms and names so the kids dont get bored or confused?

What's it going to come down to? whether the kid likes it or not if he wants to be a mathematician, musician or whatever he knows that no matter how bad it tastes it will make him grow. Playing catch in the backyard all day might be fun but it won't make you a professional baseball player unless you put in the hard work.

and I have to say I've never heard of ^ this method.


No? How about all the crappy books, DvDs, youtube videos and random blogs that promise kids "quick mastery of so and so technique" or the crappy new age books to achieve mastery through meditation. Even in this forum you'll see it every day, kids want to pick up whatever and be able to do it instantly. When they realize that music is not like that you'll see them come back here and post about quitting because they've played for 3-4 years and all they have done is learn and play a couple of songs, would rather spend their money on a video game instead of lessons and they don't really want to learn anything in theory because it's too hard.

If you don't see the Instant Gratification in society today you have been living under a rock for a long, long time.


From the essay:
And there you have it. A complete prescription for permanently disabling young minds— a
proven cure for curiosity
. What have they done to mathematics!
There is such breathtaking depth and heartbreaking beauty in this ancient art form. How
ironic that people dismiss mathematics as the antithesis of creativity. They are missing out on an
art form older than any book, more profound than any poem, and more abstract than any abstract.
And it is school that has done this! What a sad endless cycle of innocent teachers inflicting
damage upon innocent students.
#13
^ I think the article had some good points.

seeing the value of knowledge by way of meaningful application can be a strong motivator.

Is this meaningful application (learning music in our case) what you mean by "instant gratification"? If so, I'm all for it.... IMO it's essential.
shred is gaudy music
Last edited by GuitarMunky at Sep 27, 2010,
#14
Pillo, I wasn't specific enough about how I thought this related to music and I believe you have misinterpreted munky and me. Or you've misinterpreted me and I've misinterpreted munky, so I speak for myself.

What I found to parallel music really well was with formulas. Memorizing a bunch of formulas and calling it math is like memorizing a bunch of scales and calling it music!
i don't know why i feel so dry
#15
Quote by Eastwinn

What I found to parallel music really well was with formulas. Memorizing a bunch of formulas and calling it math is like memorizing a bunch of scales and calling it music!


or learning music theory formulas & fancy words from a book (or online) and then trying to write music without having the experience of listening to and playing music on your instrument.

The gist of the article as I understand it is simply that people are often not motivated because they are not shown practical/meaningful application of the information they are being taught.
IMO this very relevant to learning guitar/music.


Quote by Pillo114
Of course I see the connection to music.


Well, earlier you said this.....
Quote by Pillo114


I don't see the connection to music either.
shred is gaudy music
Last edited by GuitarMunky at Sep 27, 2010,
#16
Sure, it's the ideal learning scenario; but it doesn't mean you're going to take the information or terms or lessons out just because they are outdated.

Picasso had to learn all styles of painting before he began his own style and vision of art. He probably hated doing it but he had to and did it. Same with anyone else, I'm sure you faced a hard decision about learning something you knew was going to suck but you did it anyways and it helped you in a myriad of ways even though you'll probably never use the information directly again.

Best example in music? Sightreading with the instrument.

EDIT: The above was meant for Munky before he edited

The first time I said I didnt see the connection was toward Eastwinn and not toward the general sense of the essay.

And I do see that Eastwinn, but you still have to learn all that stuff. Otherwise what are you going to do? Just mess around with the guitar aimlessly and come here 3 years later saying you want to quit because you never learned anything?
Last edited by Pillo114 at Sep 27, 2010,
#17
I agree, the way we approach instrumental technique as a community is terrible. the way we approach improvising music is similarly egredious. We basically don't teach improvisation in school kids get to jazz band, and then expect them to play over complex chord progressions well above anything their used to, instead of having them figure out improvisations over greensleaves and mary had a little lamb and the major scale when their beginning their musical development. we also place notation far above musical intuition (notation is important for playing at a medium-high level of musicianship for the general population or if any professional aspirations are to be pursued, but its probably better for a student to be taught mary had a little lamb by ear, with help from an instructor then for them to read it off the page). We also do the same thing with ear training--we don't expect our musicians to have a basic ability to play by ear (if there being taught music in school/by most instructors) until they get to a fairly advanced level when it's time to do dictation and transcription and if the student did not develop a good ear on their own, they will have little to no chance of going so when they start taking musicianship courses in college.
#18
Quote by Pillo114
Sure, it's the ideal learning scenario; but it doesn't mean you're going to take the information or terms or lessons out just because they are outdated.

Picasso had to learn all styles of painting before he began his own style and vision of art. He probably hated doing it but he had to and did it. Same with anyone else, I'm sure you faced a hard decision about learning something you knew was going to suck but you did it anyways and it helped you in a myriad of ways even though you'll probably never use the information directly again.

Best example in music? Sightreading with the instrument.



I'm pretty sure that we didn't get the same thing out of that article. Here you're arguing that you should be open to learning other styles as a means of development, yet nobody has implied that you shouldn't do this in the 1st place. Personally I consider it crucial... so you're preachin to the choir on this issue.
shred is gaudy music
Last edited by GuitarMunky at Sep 27, 2010,
#19
Picasso had to learn all styles of painting before he began his own style and vision of art. He probably hated doing it but he had to and did it. Same with anyone else, I'm sure you faced a hard decision about learning something you knew was going to suck but you did it anyways and it helped you in a myriad of ways even though you'll probably never use the information directly again.


Yes, but if you squelch his creative drive in the beginning by making him learn tons of technique, he'll quit before he learns all the styles of art (which I'm not sure he has) then cubism never happens. And the arguement that if he can't thrive in a broken educational system, he doesn't have what it takes to pursue a subject is just a justification for a shitty educational system. The article actually discusses that there's a time for technique, but it has to serve a purpose. When a student reaches a point where they need a technique they are taught it and practice it and learn it, but are not expected to be technically masterful before they have any means or context of using technique. This is exactly how, when music is taught correctly it is taught. A student finds (or is at sometimes given) a piece, and a qualified teacher looks over it and helps the student get an understanding of it and what they will need to practice to play it well and the student is given additional etudes or studies or excersizes to get the deficient aspect of their technique together so that they can play the piece. the way we teach math (and oftentimes music) is to expect technical mastery before musical understanding (or mastery of the written forms of mathmatics without any actual application) which often leads to a student getting frusterated or quitting before they can actually put anything to use, and if it does not the student will have more technique then they know what to do with, and be nothing more then a glorified ipod as an instrumentalist.
#20
Quote by Pillo114
How sad that fifth-graders are
taught to say “quadrilateral” instead of “four-sided shape,”:
Is that not an example of the general laziness of society now?:


How sad that fifth-graders are taught to say “quadrilateral” instead of “four-sided shape,” but are never given a reason to use words like “conjecture,” and “counterexample.”


Way to take it completely out of context.

EDIT: The post above me says it all.
Last edited by canvasDude at Sep 27, 2010,
#21
Perspective: I am a teacher and teach math (among other things) to grade five students.

Great read! And really, I agree with it very much.

The good news: The way math is being taught is changing. Pedagogues across North America are taking a more "problem solving" approach to math instruction and sharing these ideas with teachers. The focus becomes the journey towards the solution, and encouraging the kids to come up with their own solutions - not being spoon-fed a bunch of rules and then having them demonstrate that they can follow them accurately. The math curriculum in Ontario embodies language that affirms, and indeed necessitates this style of instruction. Students are required to come up with their own rules, theories, explanations, etc. Students are required to use numbers, pictures, words, and make models or use other concrete representations.

The bad news: ... is also the curriculum. The Ontario Curriculum requires that students do SO many things in a year that it really is unwieldy. Compound that with the fact that we have to teach math in compartmentalized strands - or at least report on compartmentalized strands - a certain number of times throughout the year. The end result finds us, say, in term two, having to teach four math strands in 9 weeks. There is no time to allow kids to muck about and find solutions and methods. You find the most efficient way of getting your kids to demonstrate what they need to do, and you pedal-to-the-metal it through for a couple of weeks and change channels to the next one.

Back to the good news: The reporting periods in Ontario have changed. We now have a fall progress report that is decidedly brief, a mid-term report in January and another final report in June. The pressure to railroad through 5 math expectations in a given strand in two short weeks is gone. Thank goodness. The kids feel that stress too. You can sense it in the room. The current government has also promised to revisit the expectations, how they are organized, and the sheer number of expectations. We're still waiting, but hopeful that it will be a step in the right direction.

As far as the connections to music... I thought they were both obvious and equally valid.

CT
Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.
#22
Geez Captain paragraphs please.

So what if the student just brings simple songs all the time? When is he going to learn the rest?

Technical mastery is the easiest thing to teach. Improvisation on the other hand is the hardest, because the more you know and learn the better you will be on top of individuality being a factor. Nothing in math can be compared to that, and thats where music goes beyond math. But you still have to learn everything in order to be a good improviser. Technical mastery, sight reading and theory knowledge will affect improvisation directly and thats why they are all taught right away.

If you really love doing something, nothing will ever squelch your drive. And like I said before, there are more musician's than ever and the diversity of styles is wider than ever. So because a few kids can't do it the whole system is wrong?

If no one pushes people to learn and just let them learn by leisure or by whatever they feel like learning, we would never get anywhere as a society.

I'm pretty sure that we didn't get the same thing out of that article. Here you're arguing that you should be open to learning other styles as a means of development, yet nobody has implied that you shouldn't do this in the 1st place. Personally I consider it crucial... so you're preachin to the choir on this issue.


uhh the author is the one implying it by wanting to remove the old and the outdated, just because the current system bores the kids. The ironic part of it is that he doesn't propose a system to teach so it makes it just another yap of people angry with the current system. It's easy to make a list of every math subject in school and knock it down without having something to replace all the stuff you knocked down in the first place.

There is a reason why all that old and outdated information is still taught, same with music theory.


EDIT:

Way to take it completely out of context.

EDIT: The post above me says it all.


It's not out of context, because there are dozen more examples expressing the same thing. He wants to remove the old, the "meaningless", and the outdated to bring in new stuff. But he doesn't provide anything to fill in for what he takes out, which brings it back to my first post. Pointing at problems does not equal finding solutions.
Last edited by Pillo114 at Sep 27, 2010,
#23
Great post Chris -- I actually had a 6th grade math teacher who's proper teaching really inspired me!

Quote by Pillo114
uhh the author is the one implying it by wanting to remove the old and the outdated, just because the current system bores the kids. The ironic part of it is that he doesn't propose a system to teach so it makes it just another yap of people angry with the current system. It's easy to make a list of every math subject in school and knock it down without having something to replace all the stuff you knocked down in the first place.

There is a reason why all that old and outdated information is still taught, same with music theory.


By relating this to music I was not implying that music theory was old and outdated and should be removed. I think you misunderstood me.
i don't know why i feel so dry
#24
Quote by Eastwinn



By relating this to music I was not implying that music theory was old and outdated and should be removed. I think you misunderstood me.


I already answered how I understood you on my last post of the first page. I'm not going to keep repeating myself just because people dont read the posts.
#25
^^ His main argument isn't that it just bores the kids, it's that what is being taught isn't even true mathematics (in the sense of mathematics as an artform). Rather, kids are being forced into rote memorization of useless formulae that they haven't had the time or motivation to properly understand or appreciate. And the teachers don't even understand the material. It's a horribley depressing cycle of tedium and neglect of creativity and interest. Take it from someone in High School; my trigonometry teacher last year (and all before her) was/were utterly pathetic when it came to understanding and appreciating even the tedius formulae that she was "teaching" us. I was constantly finding simpler, more efficient, and (quite frankly) much more elegant and beautiful ways of getting to the same answer. I don't know where you're from, but in my school I'm the only person who actually likes math (as far as I know). And that's out of nearly 3500 students. And the teachers.
#26
Quote by canvasDude
^^ His main argument isn't that it just bores the kids, it's that what is being taught isn't even true mathematics (in the sense of mathematics as an artform). Rather, kids are being forced into rote memorization of useless formulae that they haven't had the time or motivation to properly understand or appreciate. And the teachers don't even understand the material. It's a horribley depressing cycle of tedium and neglect of creativity and interest. Take it from someone in High School; my trigonometry teacher last year (and all before her) was/were utterly pathetic when it came to understanding and appreciating even the tedius formulae that she was "teaching" us. I was constantly finding simpler, more efficient, and (quite frankly) much more elegant and beautiful ways of getting to the same answer. I don't know where you're from, but in my school I'm the only person who actually likes math (as far as I know). And that's out of nearly 3500 students. And the teachers.


I know that, I was in high school as well not that long ago and I did feel the same way. But the further I move on and get older the more I understand why I had to go through all that school shit. I know the teacher thing is a big problem too, as soon as people caught on that the teacher didnt know the stuff either people would jump on him.

I still think the material has to be learned regardless of the pain or tedium it might cause. Especially in the US, this "lets take it soft on the kids" is causing big problems. People from all over the world come to the US to study and succeed beyond what the Americans are doing. A good number of the over achievers in high school are immigrants and once they are done they leave and go back to their own country. The big brain drain is caused, because there's no one left.

What you're going to tell me the system is bad with all these people excelling?

Like I said on my first post, the field of math has grown incredibly in the last few decades the same with music. If it was as bad as the author put it, we'd be stagnant.
Last edited by Pillo114 at Sep 27, 2010,
#27
The biggest problem is that the foundation of mathematics is propositional and predicate logic, but it is not taught. Instead, math is taught as a hodge podge of tricks and techniques in computation, without regard where the arithmetic came from or how to develop ideas deductively in systematic manner from simpler components. Even educated engineers I worked with in many places don't understand the foundations, and in fact one popular phrase they overuse is "it is what it is." I bet if I told them butter tastes buttery or water is wet, they would look at me like I have three heads - oh the irony.
Last edited by KingStill at Sep 27, 2010,
#28
I still think the material has to be learned regardless of the pain or tedium it might cause. Especially in the US, this "lets take it soft on the kids" is causing big problems. People from all over the world come to the US to study and succeed beyond what the Americans are doing. A good number of the over achievers in high school are immigrants and once they are done they leave and go back to their own country. The big brain drain is caused, because there's no one left.


Specifically, what big problems? And the US has some brain drain (being a multinational center for post-secondary education), but it is by no means an epidemic and many leading companies are still headquartered in the US.
#29
Quote by tehREALcaptain
Specifically, what big problems? And the US has some brain drain (being a multinational center for post-secondary education), but it is by no means an epidemic and many leading companies are still headquartered in the US.


The U.S is way behind in technological innovation and the sorts, like way behind. It's not a big issue at the moment because the U.S. buys the technologies and patent designs but it wasnt like it was say 40-50 years ago when pretty much all innovations came from the U.S. Before, people generally tended to stay and live in the U.S. but now they would rather go elsewhere to do their research or

It's not really related to the topic but to me I think it somewhat ties to the whole thing. I think the shift of college being the new "requisite" education has a lot to do as well. It ties with most of you guys's point of the stuff being force fed for no reason because of college preparation but how else are you going to teach all that new information streaming in? You couldn't explain the reasoning behind all the formulas because you'd fall behind.

In music it's easier to deal with since art music (i.e. "classical") took it to such an extreme in the 20th century that most people said **** it lets go back; so there hasn't been any pile up of information streaming in and people trying to catch up like in math and the sciences.

You do have good points on the music education thing you were talking about earlier but there's no way to get past a certain point in music without diving into the swamp. You have to swallow it all and eventually all the things will start to fall together. Once you finally hit solid ground you can slowly expand and focus on what you want to do.

How well can you sightread? I don't think anyone liked learning to read music and it's the most annoying thing ever until you can do it and all of a sudden you're standing on a new plane with access to all this music you normally couldnt access before. The same goes for all the other things in music theory, it might seem ridiculously hard but one day you wake up and you can do it. But you have to buck up and do it whether you like it or understand where it came from and once you have it down you'll know right where it came from and how it applies to everything.

Some things in music and everything else aren't practical and there's no way around to explain or learn them the boring tedious way.
#30
pillio, im not going to quote your entire post
I can sightread quite well, but did not focus on it when I was beginning (in fact, I did not learn to read until I was 17) and only became proficient when I realized it was required for a musical career/to get into college for music. Theres a difference between learning to read music (as in, learning what numbers are for math) and becoming dependant on written notation do to a lack of musical understanding. The math education we have today would be like a musical education without aural training or any kind intuitive process.

also, if you've ever taken a course on species counterpoint, you realize how terrible it is to write in a convention that is outdated and a mere pedagocial excersize which has no bearing the types of music your going to be playing/writing.
#31
Since you learned to sightread, how much have you used it to study and look at scores and other music from other people? I hate playing from it because it makes me sound like a midi robot with no feel but I think I've improved musically just to be able to look and read a score or transcription without having to go "ok this is D, ok thats E, wait is that B or Bb?" It might be dwindling fast as an on stage tool because of computer music but as a personal asset I think is was worth the mind numbing pain and hate I went through.

Same with the baroque and counterpoint stuff. I have to play those crap baroque pieces for my private lessons every week. It's old and meaningless information to modern day, but music is built from it the same way you have to go through all the math topics.

Even jazz though, I know youre interested in that. You're going to spend so much time studying an artform that has no place today. You need a ridiculous amount of theory and practice for something you cant make a living out of.

Why do you go through all that pain? When all you need to know is couple of chords here and there and pentatonic scales with a little major scale flavoring for literally 90% of music today.

Sure it could crush your dreams and creativity, but Im sure you would rather risk and suffer through it to see whats on the other side because you like music that much. You'll thank yourself or your teacher later for putting you through it.


Now for a system like math education where you know that not everyone is going to love it or make a career out of it, you do need to make it interesting but you can't start taking stuff out nor wasting time explaining why the greeks decided to conceive each and every postulate and formula. We'd be studying forever, because the material learned in school is already a diluted summary. Look at history class in high school, I'd say thats worse than math in terms of the system. But what are you going to do? Teach every single viewpoint of every single event in history to keep it objective and practical? You'd never end.

The SATs get harder and harder every year and people are getting smarter by the second and this guy is talking about math education being stagnant because it's the same as the 19th century and how it's not practical?

EDIT:

On a practical note, I have a friend that goes to MIT and studies math logic and freshman year he told me he hadn't seen a single number yet because it was all letters and variables. If the author told the professors at MIT to make math more practical and applicable, they would laugh in his face.
Last edited by Pillo114 at Sep 28, 2010,
#32
Quote by Pillo114
Now for a system like math education where you know that not everyone is going to love it or make a career out of it, you do need to make it interesting but you can't start taking stuff out nor wasting time explaining why the greeks decided to conceive each and every postulate and formula. We'd be studying forever, because the material learned in school is already a diluted summary. Look at history class in high school, I'd say thats worse than math in terms of the system. But what are you going to do? Teach every single viewpoint of every single event in history to keep it objective and practical? You'd never end.

The SATs get harder and harder every year and people are getting smarter by the second and this guy is talking about math education being stagnant because it's the same as the 19th century and how it's not practical?

EDIT:

On a practical note, I have a friend that goes to MIT and studies math logic and freshman year he told me he hadn't seen a single number yet because it was all letters and variables. If the author told the professors at MIT to make math more practical and applicable, they would laugh in his face.
After reading your posts I get the feeling you either didn't read fully, or didn't comprehend the article.

The author never said that mathematics should be made more practical. Quite the contrary, he goes to lengths to explain that real mathematics IS NOT practical and applicable but an art of the imagination. It is very clear he is of the opinion that mathematics should be taught simply for the sake of studying something that is beautiful and wonderful and not for practical real world application.

He also NEVER said anything about any quick mastery of mathematics or "instant gratification" as you call it. What he said is that mathematics can be taught in a more engaging and interesting way. He makes no claims that what he proposes is a quick and easy method that requires no work.

If anything he is denouncing the current system for becoming a "quick and easy" approach. He is upset that people are given a solution to a certain set of problems before really giving them a chance to consider the problem and come up with solutions on their own.

He would prefer to pose a problem (or better yet have the students pose a problem and allow students the opportunity to solve it themselves, then after the students have engaged and attempted their own solutions (sometimes for a number of days) he would explain to them not just the solution but how the solution came about and why the solution works - in plain english so that the students can understand. He simply wants students to be involved and partake in the process of discovery rather than simply regurgitating a bunch of formulas when they see a certain type of equation. He's not proposing a short cut, or any kind of "instant gratification".

This quote I feel best sums up his feelings
Quote by Paul Lockhart
If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself.


You say the current system works. He's saying there are flaws in that system and that it could work much better. He points out where he thinks it's gone wrong but it seems to me he also explains how he thinks it should be.

I have difficulty seeing how any of your criticisms thus far show an understanding of the article's content, let alone any real counter arguments to what the guy has to say.

I understand my words may not be well received but I'm just being honest; it's not my intention to offend you in anyway.
Si
#33


Since you learned to sightread, how much have you used it to study and look at scores and other music from other people? I hate playing from it because it makes me sound like a midi robot with no feel but I think I've improved musically just to be able to look and read a score or transcription without having to go "ok this is D, ok thats E, wait is that B or Bb?" It might be dwindling fast as an on stage tool because of computer music but as a personal asset I think is was worth the mind numbing pain and hate I went through.

Same with the baroque and counterpoint stuff. I have to play those crap baroque pieces for my private lessons every week. It's old and meaningless information to modern day, but music is built from it the same way you have to go through all the math topics.

Even jazz though, I know youre interested in that. You're going to spend so much time studying an artform that has no place today. You need a ridiculous amount of theory and practice for something you cant make a living out of.

Why do you go through all that pain? When all you need to know is couple of chords here and there and pentatonic scales with a little major scale flavoring for literally 90% of music today.

Sure it could crush your dreams and creativity, but Im sure you would rather risk and suffer through it to see whats on the other side because you like music that much. You'll thank yourself or your teacher later for putting you through it.


Now for a system like math education where you know that not everyone is going to love it or make a career out of it, you do need to make it interesting but you can't start taking stuff out nor wasting time explaining why the greeks decided to conceive each and every postulate and formula. We'd be studying forever, because the material learned in school is already a diluted summary. Look at history class in high school, I'd say thats worse than math in terms of the system. But what are you going to do? Teach every single viewpoint of every single event in history to keep it objective and practical? You'd never end.

The SATs get harder and harder every year and people are getting smarter by the second and this guy is talking about math education being stagnant because it's the same as the 19th century and how it's not practical?

EDIT:

On a practical note, I have a friend that goes to MIT and studies math logic and freshman year he told me he hadn't seen a single number yet because it was all letters and variables. If the author told the professors at MIT to make math more practical and applicable, they would laugh in his fac


To begin with that jazz comment you made. Sytlistically correct bebop has no place today, but I transfered colleges specifically to avoid falling into the trap of bebop obsession and not learning any applicable skills. Moreover, I'm intersted in jazz because I enjoy playing it. If I just wanted to play pop music with a jazz informed education I would be doing something else entirely. I learned enough of that style both because I had to and because I very much enjoy playing it. Jazz is alive and well today and while it is not as big as it was in the late 30's and 40's there are still a handful of great musicians (as there always were) playing music that is extremely current. parouse this website if you doubt me: http://www.nextbop.com/

As far as baroque being unapplicable, the fact that your studying baroque pieces instead of finger excersizes like the steve vai 12 hour workout makes what your doing superior to the way we teach math (and the way some teach music). Not liking baroque music is like not liking trigonometry, but if what your studying is actually trigonometry, not the shallow written imitation were taught in school then you are already several steps ahead of the current pedagogical method. Likining the study of baroque music to what you are taught in school in a math course (or really, a lot of public school courses) would be learning the fingerings to and analyzing a two part invention, but never actually playing it.
Secondly, sightreading only sounds like a soulless midi robot if you sound like one. Sightreading isn't about hitting all the notes, its about making the music come alive. Follow dynamics, make each phrase have a logical arch. Move the time to your advantage. Use different time feels. Use articulations to re-enforce these things and, if none of this is written (like for example, in William Leavitt's Sightreading for guitar) then make it up as you go. If your sightreading an ensemble piece without dynamics, follow your conducter/the other musicians.

And your example of your friend at MIT is sort of moot. He's at MIT because he obviously intuitively found the self-discovery, artistry aspect of math and is now ready for the technique. Just like many people don't start with theory until they get to college (or at least late high school).

Id also argue the SATS (and APs) are terrible. I did quite well on my AP's (5 in language, 4 in literature 4 in american history) and did not get a grade higher then 80 in any of those courses in high school, nor did I retain anything I learned. How does that test score (especially when you consider the grade is by how you do in relation to the general population, not your actual score) make me in any way qualified? SATS (which I didn't do great on, with an 1850/2400 and a 1150/1600) did not really get in my way with college applications, because my grades/extracurriculars were solid and I auditioned pretty well. But, they do get in the way of intelligent, motivated kids who have good GPAS and want to persue higher level academic studies. Moreover, there are people who test well who blow off classes (as I did with APs) who look more impressive because of these shallow tests yet have little to no actual, lasting study of the material. I'd imagine Collegeboard and the SATS are one of the biggest things in the way of a quality national education system.
Last edited by tehREALcaptain at Sep 28, 2010,
#34
I read it and I think it was brilliant...absolutely agreed with it on every level.

Anyone who said that it doesn't propose solutions ...didn't read it.

The sad part of the essay is that it will never come true. Anything that threatens the control that bureaucracies, and establishments will always be seen as the enemy.

People fear what they themselves do not understand.

Great article, but sad. And all true.

Sean
#35
Quote by zee789
Well first you have a scale, and that's great but there's one problem. You don't know how to use it in a song, or how all these great guitarists use that very same scale you have, to make such great music.



Get out of here you shill. The post you made was made for one purpose and that is to backlink your payday loan site. Chances are you got hired at some BS seo company to work for peanuts pissing everyone off.

Sean
#36
Moreover, I'm intersted in jazz because I enjoy playing it. If I just wanted to play pop music with a jazz informed education I would be doing something else entirely.


You proved my point. You went through the hassle of a faulty(I already told you about the chordscales and their uselessness last week) jazz education because you loved it and you knew it would make you better.

Captain, you were telling me how counterpoint wasn't relevant on your last post, I give you the example of baroque and how I have to do it regardless of liking it or not and you turn it around. I know it's a new day but I cant be going back and forth over the same thing. that same logic you posted I could have posted on when you talked about the counterpoint, it's the same thing. You still have to learn that era's musical style whether you like it or not, the same way you have to learn trigonometry.

I can read, I hate reading on stage but I can read as well as anyone here. I hate it because I play fretless bass and reading usually gives me a plain jane sound, I have more feeling when I know something by heart and can improvise embellishments on it. I've learned more from reading scores than from anywhere else so I don't see the reason why you posted all that stuff about ensemble playing when I already had cleared that out.

Jazz might be on its deathbed , but good luck making a living out of it, most of those musicians also starve and have to do work and teaching and other things to stay afloat until they eventually (if they ever do) break through. And if anything, you'd probably would have to play bebop and 50s jazz at gigs to make it because no audience is interested in listening to the more on the edge stuff. You think chordscales are going to take you to the edge? Besides, most of the current stuff is a rehash from the old. Where are the people playing Ornette tunes other than Pat Metheny? Where are the people playing even Wayne Shorter tunes and that stuff is old. Where's the thirst for innovation?

And about the SATs, there are always people that do well in them compared to high school grades, but it has no effect on the general percentile. The average score is rising rapidly and the amount of people that apply to colleges each year is multiplied. you're telling me people arent getting smarter?

I read it and I think it was brilliant...absolutely agreed with it on every level.

Anyone who said that it doesn't propose solutions ...didn't read it.

The sad part of the essay is that it will never come true. Anything that threatens the control that bureaucracies, and establishments will always be seen as the enemy.

People fear what they themselves do not understand.

Great article, but sad. And all true.

Sean


Where are the solutions? He shoots down all the grade subjects but doesn't put anything in for them. He has ideas but nothing solid, he couldn't show up at the department of education with this essay and expect change. Like I said before, you'd be wasting too much time trying to explain the background of the formula

This is all like American Politics, of course its faulty but it's easy to point at the mistakes and blame it on everyone instead of trying to fix it.

To 20Tigers, the instant gratification was an extrapolation off of the new age trend of the fear of making the kids feel bad or the fear of having the kids suffer at school. Everyone went through the same system here and I don't see anyone suffering.

That quote you posted, it's easy to say, but do you think kids really give a damn? No one ever wants to learn what they aren't interested in, thats why teachers are there to push you through.

I know where you are all coming from, but one thing is the ideal the other thing is the realistic. Do you know the pressures teachers are in? The trouble the kids cause because think they can do anything they want without fear of reprisal because parents will sue at the drop of a dime? Look at private music lessons, I think you teach (right?) and at least Sean and Munky do. What do you do when the student reaches a point in learning that he's absolutely not interested in doing even though it is a requirement?

The worst classes I've ever had in both high school in college where the ones with this overtone that the author proposes. It sounds great when you're in it but it's the biggest waste of time learning wise. Thats where I'm coming from.

Show me proof where the disengagement or whatever you want to call it of the current system has affected the curiosity, creativity or intelligence of the kids. Show me proof of kids coming out not knowing anything? Show me how you would fit all this engaging stuff over a 12 year curriculum that is already crammed to the max. You'd rather make it more engaging and artistic over quantitave? If you do, whats going to happen with the rest of the information left over on top of the one piling in? A quota of information has to be filled because no one is going to wait.

I don't see any of those new age schools with the experimental and creative teaching methods pumping out more geniuses than the regular school system. If anything they are the worst students off, because once they get to college they dont know anything and have the be placed in the lowest levels. Then whats next, the college system is wrong? It would never end.
Last edited by Pillo114 at Sep 28, 2010,
#38
WARNING, VERY LONG POST, but please read

I find this topic very interesting. Here is my opinion:

First of all, my history. I am dutch, so my opinion will be about the dutch education system. I am currently in my 3th year of my bachelor's study Advanced Technology, wich will train me to become an engineer. I always felt frustrated at what we call the middelbare school (between age 13 and age 18, lets call it high school), I wasn't really learning anything, wasn't challenged, it all felt like a waste of time. I thought the school system could do a lot better, and even wrote some concepts on how I would organise the school system.

Before describing the system, let me talk about university first. I think the University's system is brilliant. It prepares you for your job while leaving plenty of room for personal development. I'm in the 3th year now, we get about 1/2 year to do whatever we want, im currently following courses in cosmology, evolution and consciosness. Im feeling like a kid in a candy store!

My 2nd year of education had a course called 'Engineering of Complex Systems'. I think it is a perfect example of what the author of the paper meant. The course description says it best:

The course is set up in the format of Problem Based Learning (PBL), which aims at a way of learning in which optimal use is made of knowledge students already have, to motivate their study, to integrate new with old knowledge and to get a good idea of all the coherence of theories and their relation to the real world. Starting point is the presentation of so-called ill structured problems. Learning is a creative activity. Understanding must happen in the heads of the students, teachers cannot understand anything for students. Students have to work actively with the subjects they have to master. Theories are learned by reconstruction. [Example: students do have to learn F=ma by rote, but they have to understand what this equation says and reconstruct the mathematical expression from this understanding.] Students are participants in a learning process, while teachers are coaches.

The topics where mainly electrostatics, electrodynamics and vibrating strings. I can explain the course further if anyone wants.

So lets to conclude, the University is fine as it is today. Lets return to my system of high school. Following is a direct translation of the concepts ive written 2 years ago, when I just left highschool, translated really fast, so it might be a little sketchy.

-----------------------------------------------------------
The present school system sets the a priority on preparing the student for a future education or job. Because students don't know yet what they will do after highschool, the education is wide, so that all options are still open. When the future education is started, only a small percentage of the knowledge gained in highschool will be actually used. A lot of knowledge is wasted. One could argue that wide education is good foor the general development of people. If general development is a goal, the current system is very inefficient in it. For example, for general development, it is not important to know how to set up a balance equation for an acid-base balance, or to calculate the reaction-enthalpy of solving a certain salt. What -is- important, is the concept of molecules, how stuff looks like on a very small scale, that there is some thing like reaction mechanics, etc.
If one only teaches the things that are important for general education, there is a lot of time left for other things. I think this time is best used in learning social and practical skills, like how to bandage a wound, how to repair your car, how to play bridge, why art is beautifull, how to play an instrument.
Characteristics of my school system:
- Focus will be on general development in stead of preparing for future education
- To avoid having to make radical changes to following educations, the last year of high school can be used to prepare the student for a future study.
- Some examples of what will be taught:
Technical knowledge
Maths: What are variables? What is a function? What are complex numbers? How does the sine work?
Physics: What is an atom? What are the implications of quantum mechanics? What is general relativity? What is the shape of the universe?
Chemistry:How does a battery work? Why do acids attack metal? What can you do with the description of molecules?
Biology: How does evolution work? What are the functions of different organs? How do cells look like and function?
Geography/History: Present way of teaching is fine

Practical knowledge
Cooking, Taxes, Insurance, First Aid, Car Repair, Symptoms of deseases

Personal development
Development of taste in literature, music, movies, theater. Thinking about future profession. Filosofy. Development of personality (public speaking, meeting people)

Physical development
Sports (having played a lot of different sports + self defense training). Knowing the rules of Chess, Bridge, Poker, Blackjack, Pool, etc etc
Lessons in salsa, classical dances.
-----------------------------------------------------------

This seems like an awefull lot to learn. But remember, cutting all the 'technical education', will create a lot of spare time. I think its possible to learn all the above and more. we have six (!) years in high school. What can't be done in six years!
Well, since those two years after highschool, my opinion is a bit more nuanced:
- This system would be perfect for -me-, but that doesnt mean its perfect for everyone. Who sais everyone will be as willing to learn as I am?
- I dont know if this system is practically feasable, because the time spent/cost per student will be a lot higher I guess.
- People who are motivated will find a way to learn all those things by themself
- Maybe it is a good thing that highschool is boring work, this will prepare you for most of the rest of your life (can I get any more depressive? :P). But really, maybe this prepares students to the hard fact that alot of life is done by hard (boring) work.

Well, im done typing. Will think further about this.

Love to see youre opinions!

Sincerly
#39
The dutch may be overly technical, but they are at least effective in their overly technical education, as opposed to americans who are overly technical and widely innefective.
Also, the american university system is pretty eh. Either you dilute your education with a HUGE amount of general education, much of which is predetermined or useless, or you go to a very technical school (BM, BFA, BS type programs) and its almost entirely your major courses with a small amount of liberal arts, and most of the liberal arts are extremely un-intellectually stimulating (aside from a few high level electives). THe choice is basically a more well rounded (meaning mediocre at a LOT of things, ok to good at your major and still not enjoying most of your core classes) or very intensly focusing on your major, with less shitty liberal arts, but also less good ones.
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