How accurate is this article?
- Donn
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Re: How accurate is this article?
How do you feel about music? So far the way we've been talking about music in this thread, you'd think we all played the bassoon, or violoncello. Now that we've sort of trampled on the idea that a symphony tuba player isn't such an enviable position, it seems to me that opens the door to consideration of other types of music where a tuba might be welcome.
The commercial basis for music has changed a lot from when I was young. I've noticed small bands playing popular music and working certain online media real hard, I think with some success. As it has broken out from under the record companies, it has gotten more vital and less formulaic, sometimes, if less remunerative. I don't know for sure that anyone makes a decent living, but on the other hand I think you can play that game with less invested.
If at some point your ambitions wander off in the direction like that, I suppose you might benefit from theory and practice of composing and arranging, some practical business, and people skills - including of course entertainer skills, but I don't know where you learn those.
The commercial basis for music has changed a lot from when I was young. I've noticed small bands playing popular music and working certain online media real hard, I think with some success. As it has broken out from under the record companies, it has gotten more vital and less formulaic, sometimes, if less remunerative. I don't know for sure that anyone makes a decent living, but on the other hand I think you can play that game with less invested.
If at some point your ambitions wander off in the direction like that, I suppose you might benefit from theory and practice of composing and arranging, some practical business, and people skills - including of course entertainer skills, but I don't know where you learn those.
- bort
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Re: How accurate is this article?
Not sure if it is still true, but it used to be said that if you want the easiest way into an orchestra job, play viola.
Something to think about before you put in your 10,000 hours behind the tuba.
Something to think about before you put in your 10,000 hours behind the tuba.
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vespa50sp
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Re: How accurate is this article?
One regret occurred to me. i got talked out of applying for the Army Reserve band, because I had friends during the Regan era being training to spot airplanes in addition to band. I believe the MN Army Reserve band was sent to the green zone? during the recent war, but if I would have been able to pull one weekend a month at the local army base, pulled my two week duty subbing for other army bands, I could have had a pension after 20 years.
The Former Army Reserve Conductor directs our community band now. I think I might have missed that opportunity.
The Former Army Reserve Conductor directs our community band now. I think I might have missed that opportunity.
- Donn
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Re: How accurate is this article?
Yeah, that's what I'm talking about, and I think it would make more sense as a respectable alternative to a young person today than it would to someone like me who's closer to the striped-shirt pizza-parlor thing. But the tuba-friendly music world also comes from musical traditions of eastern Europe, maybe even Bollywood stuff from India, Mexican banda. Any of that can be stale or even putrid, but for someone with inventive musical talent, a flair for entertainment and the ability to work with people? There's a lot more to music than the instrument you play it on.bloke wrote:...and within the last few years formulated (with him as the "leader") a NOLA-style brass band.
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pineapple-power
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Re: How accurate is this article?
Like, me personally, how I feel about music? I love it a lot, but again, I'm a kid.Donn wrote:How do you feel about music? So far the way we've been talking about music in this thread, you'd think we all played the bassoon, or violoncello. Now that we've sort of trampled on the idea that a symphony tuba player isn't such an enviable position, it seems to me that opens the door to consideration of other types of music where a tuba might be welcome.
The commercial basis for music has changed a lot from when I was young. I've noticed small bands playing popular music and working certain online media real hard, I think with some success. As it has broken out from under the record companies, it has gotten more vital and less formulaic, sometimes, if less remunerative. I don't know for sure that anyone makes a decent living, but on the other hand I think you can play that game with less invested.
If at some point your ambitions wander off in the direction like that, I suppose you might benefit from theory and practice of composing and arranging, some practical business, and people skills - including of course entertainer skills, but I don't know where you learn those.
Well, this is certainly very interesting. I'll have to do some research into it.
- kontrabass
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Re: How accurate is this article?
The article is extremely accurate. With that said I wouldn't tell the subject of that article not to try. Mastering an instrument teaches life skills that are their own reward. So does striving to be the best in a field. I wouldn't trade my experience for anything. And because I kept my eyes open I was able to see opportunities to build on the skills I learned and I'm still going in music.
The problem with young tuba players is not that there's no jobs. It's that nobody is thinking of how to create a job for themselves, everybody wants things to be nice and "easy", as in requiring no constant re-defining and self-examination, just play the same music everyone else plays and slide in to the steady symphony gig. Honestly most people find it less scary to be 1 in 100 at a cattle call every two years than learn how to improvise. It shocks me. If we trained more artists instead of audition-bots there wouldn't be such a glut of unemployed tubists.
The problem with young tuba players is not that there's no jobs. It's that nobody is thinking of how to create a job for themselves, everybody wants things to be nice and "easy", as in requiring no constant re-defining and self-examination, just play the same music everyone else plays and slide in to the steady symphony gig. Honestly most people find it less scary to be 1 in 100 at a cattle call every two years than learn how to improvise. It shocks me. If we trained more artists instead of audition-bots there wouldn't be such a glut of unemployed tubists.
- anonymous4
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Re: How accurate is this article?
You are a kid. Don't take this the wrong way, but the risk center/decision making part of your brain isn't fully developed. Totally not your fault though, so don't feel bad.pineapple-power wrote:Like, me personally, how I feel about music? I love it a lot, but again, I'm a kid.Donn wrote:How do you feel about music? So far the way we've been talking about music in this thread, you'd think we all played the bassoon, or violoncello. Now that we've sort of trampled on the idea that a symphony tuba player isn't such an enviable position, it seems to me that opens the door to consideration of other types of music where a tuba might be welcome.
The commercial basis for music has changed a lot from when I was young. I've noticed small bands playing popular music and working certain online media real hard, I think with some success. As it has broken out from under the record companies, it has gotten more vital and less formulaic, sometimes, if less remunerative. I don't know for sure that anyone makes a decent living, but on the other hand I think you can play that game with less invested.
If at some point your ambitions wander off in the direction like that, I suppose you might benefit from theory and practice of composing and arranging, some practical business, and people skills - including of course entertainer skills, but I don't know where you learn those.
Well, this is certainly very interesting. I'll have to do some research into it.
You might really, really, realllly, love music, and to you RIGHT NOW, it might be more important that anything you have ever known to one day be on stage performing. What is really on the line if you can't get what you want?
I'll be blunt. If you are in high school, someone asks you what you want to do in life, and you say "I'm going to play the tuba in the Chicago Symphony Orchestra", you might as well have said that your life plan is to win the next 1.6 Billion Powerball drawing. Maybe it will work out, but the overwhelming odds are that it won't. Especially if you are not first chair in your all state band and among the best 17 year old's in the country right now. Even if you do meet those criteria, odds aren't so great.
You need to know what is at stake if your plan doesn't work out:
I know people who are really good, like multiple final rounds at audtions good, that never made it through. In their 30's were doing entry level work alongside 21 year kids. That could happen to you if you spend a decade after high school practicing excerpts and nothing else.
I know people who are in their 40's still convinced that sooner or later they will win their symphony job, despite enormous evidence to the contrary. This could also happen to you if you "never give up", but it still doesn't work out for you.
I know a person in his 50's who died because their lifelong freelancing career never provided enough money for them to get adequate medical care or insurance. He was a friend of mine, and he didn't have to go when he did.
I know a person in his 60's who has been divorced three times, and occasionally has to sleep on the floor of his studio at the school where he teaches. Money and time issues of being a musician contributed to the problems he had in his personal life. This could happen to you.
I know I have finally achieved "grumpy old man" status with this post, but you're young and need help. All the things that seem super duper important to you now (like being a bad *** on tuba) will not always be so. One day you will want more out of life. Will the choices you make now be able to get that for you?
I'm not telling you what to do, (even if I were, why would you listen to some random guy from TubeNet?) but what I am telling you is to strongly consider the RISK you are taking.
- Donn
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Re: How accurate is this article?
The tune the author of The Thunderer wrote for president Chester A Arthur, who also didn't enjoy Hail to the Chief: Presidential Polonaise, John Philip Sousa. I've never played it, but I think I would enjoy it quite a bit. He supposedly had in mind to keep people moving in the White House receiving line, hence the sort of danceable feel. [edit - he also composed Semper Fidelis for the White House, for outdoors occasions.]DP wrote:talked out of it by a performance major who ignored my love for "The Thunderer" and insisted I would not enjoy playing "Hail to the Chief"
(Arthur finished Garfield's term after his assassination, and didn't live very long himself - never got to hear the tune.)
Last edited by Donn on Thu Jan 14, 2016 2:04 am, edited 1 time in total.
- Donn
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Re: How accurate is this article?
Well, yeah, you! Can you improvise a bass line? Do you like getting up in front of people and showing your act? Would you be up for playing in a polka band for barn dances once a month? Stuff like that. At some point, if this is for real, you're going to be ready to be a musician, not just someone who's going along for the ride in band or whatever. It isn't too early for that, at all - there's no better time.pineapple-power wrote:Like, me personally, how I feel about music? I love it a lot, but again, I'm a kid.
Regarding comments from anonymous grumpy old man above - I'm not saying "professional musician" is a good life goal. That's for people who can't do anything else. But musicians can be pretty serious and still have other options, and it's just as satisfying to be able to keep up with the big kids when you don't have to.
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timothy42b
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Re: How accurate is this article?
The OP is a 15 year old kid.
I don't know how well he plays tuba but I'm impressed with his contribution to the thread.
He writes clearly and coherently and manages to do spelling, grammar, capitalization and punctuation correctly. He responds to the points made, seems to actually consider the input logically, and doesn't get in a snit if somebody has a contrary opinion. He writes with an individual style and demonstrates a sense of humor.
In my experience on various forums this is somewhat of an anomaly for high school kids.
I don't know how well he plays tuba but I'm impressed with his contribution to the thread.
He writes clearly and coherently and manages to do spelling, grammar, capitalization and punctuation correctly. He responds to the points made, seems to actually consider the input logically, and doesn't get in a snit if somebody has a contrary opinion. He writes with an individual style and demonstrates a sense of humor.
In my experience on various forums this is somewhat of an anomaly for high school kids.
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Three Valves
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Re: How accurate is this article?
pineapple-power wrote:<teen angst about wanting to marry for LOVE and live out a HAPPY FAIRYTALE SOMETHING SOMETHING>Three Valves wrote:
I was a band nerd, all my friends were band nerds.
My band nerd friends that majored in engineering make more money than I do.
My advice to young people??
Go to work every day on time.
Sober.
Live within your means.
Never underestimate the value of marrying well.
(Not necessarily in that order)
You said you wanted to marry a doctor.
Marrying well means marrying the RIGHT doctor!!
Marrying poorly (not necessarily money poor, but ending in divorce) can set you back in ways that can take YEARS to recover from.
So be careful.
I am committed to the advancement of civil rights, minus the Marxist intimidation and thuggery of BLM.
- Rick Denney
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Re: How accurate is this article?
Everything is hard if done to a standard of excellence. All of it takes single-minded commitment. Talent? We've had that argument before. Certainly some people have an aptitude for a topic, but perhaps that aptitude manifests as the drive to pursue it with single-minded commitment. But in every field, there are those who did so and did not succeed. Even engineering!
University education used to be about becoming a well-rounded person, a person who could be given a range of duties and would do them well. But in our increasingly specialized, technical world, a general college education of that traditional type has less value. But most people now believe college to be about learning how to make money, and that is not what it's for. It's for equipping a person to make their way in life, but what they need to learn to make money may come after college, even though it depends on what they learned in college. Education is not training.
The problem is the distinction between, well, distinction and mere competence. In many fields, it's possible to make quite a decent living by being merely competent. In some fields, only excellence will do. And in a few fields, even excellence is necessary but not sufficient. The guys who spend six hours a day shooting hoops throughout their childhood may dream of being an NBA star, and they are certainly demonstrating the commitment, but, of course, the chance of making it to the NBA is vanishingly small. And that doesn't even consider that many of those kids will not grow up to the the required minimum 6-1/2 feet tall.
I know many merely competent engineers who put together a decent enough living. These were not the guys for whom integral calculus came easily, though they managed to survive it, let alone vector mechanics in n-space. At some point, math moves from determination to intuition, and not everyone has the intuition.
But, generally, the things that pay the best for mere competence are the things that nobody particularly wants to do because they are hard. Even in highly technical fields, that is true. Astrophysicists and cosmologists, like basic researchers in most fields, struggle to find the work that interests them even with many degrees, simply because too many of them are trying for too few paying gigs. The more people want to do something for fun, the less likely it is that someone will pay them to do it. There are many, many, many musicians who are motivated to practice hours a day for no pay at all. It's very difficult for those who want to be paid to compete with all that desire. Some amateur astronomers dream of becoming astrophysicists, but vanishingly few make it, or even realize that most of it is doing math and not looking at the sky.
Note that my "drive to pursue it with single-minded commitment" is NOT the same thing as "loving to do it". There are many aspects of the work that I do that I do not love, and some of it I despise (at least until I'm doing it), but I'm still driven to pursue it to excellence. This is the conflict between feelings and intellect. The work I do is intellectually satisfying at a deep level, despite how I feel about it at times. Would something else be as intellectually stimulating? Of course! I became good at something, and that feeds the satisfaction of doing it. That becomes a self-reinforcing cycle. My point in describing it this way is that we sometimes have to set aside how we feel and pursue something for which we have an aptitude that will drive us to the level of excellence needed in that field. Music is easy to love, but I can love it without being paid to do it. I can choose to be satisfied by what I'm good at, and that's good enough to sustain a lifelong career--I would not do the work that I do as a hobby. But I have to renew the choice to be driven by that satisfaction from time to time. That is an act of a will.
Rick "sorry for the ramble--too busy to give it the needed editing" Denney
University education used to be about becoming a well-rounded person, a person who could be given a range of duties and would do them well. But in our increasingly specialized, technical world, a general college education of that traditional type has less value. But most people now believe college to be about learning how to make money, and that is not what it's for. It's for equipping a person to make their way in life, but what they need to learn to make money may come after college, even though it depends on what they learned in college. Education is not training.
The problem is the distinction between, well, distinction and mere competence. In many fields, it's possible to make quite a decent living by being merely competent. In some fields, only excellence will do. And in a few fields, even excellence is necessary but not sufficient. The guys who spend six hours a day shooting hoops throughout their childhood may dream of being an NBA star, and they are certainly demonstrating the commitment, but, of course, the chance of making it to the NBA is vanishingly small. And that doesn't even consider that many of those kids will not grow up to the the required minimum 6-1/2 feet tall.
I know many merely competent engineers who put together a decent enough living. These were not the guys for whom integral calculus came easily, though they managed to survive it, let alone vector mechanics in n-space. At some point, math moves from determination to intuition, and not everyone has the intuition.
But, generally, the things that pay the best for mere competence are the things that nobody particularly wants to do because they are hard. Even in highly technical fields, that is true. Astrophysicists and cosmologists, like basic researchers in most fields, struggle to find the work that interests them even with many degrees, simply because too many of them are trying for too few paying gigs. The more people want to do something for fun, the less likely it is that someone will pay them to do it. There are many, many, many musicians who are motivated to practice hours a day for no pay at all. It's very difficult for those who want to be paid to compete with all that desire. Some amateur astronomers dream of becoming astrophysicists, but vanishingly few make it, or even realize that most of it is doing math and not looking at the sky.
Note that my "drive to pursue it with single-minded commitment" is NOT the same thing as "loving to do it". There are many aspects of the work that I do that I do not love, and some of it I despise (at least until I'm doing it), but I'm still driven to pursue it to excellence. This is the conflict between feelings and intellect. The work I do is intellectually satisfying at a deep level, despite how I feel about it at times. Would something else be as intellectually stimulating? Of course! I became good at something, and that feeds the satisfaction of doing it. That becomes a self-reinforcing cycle. My point in describing it this way is that we sometimes have to set aside how we feel and pursue something for which we have an aptitude that will drive us to the level of excellence needed in that field. Music is easy to love, but I can love it without being paid to do it. I can choose to be satisfied by what I'm good at, and that's good enough to sustain a lifelong career--I would not do the work that I do as a hobby. But I have to renew the choice to be driven by that satisfaction from time to time. That is an act of a will.
Rick "sorry for the ramble--too busy to give it the needed editing" Denney
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tbn.al
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Re: How accurate is this article?
Rick, Too well written from the heart to require editing.
I am fortunate to have a great job that feeds my family well, but music feeds my soul.
- proam
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Re: How accurate is this article?
Huh. I didn't encounter algebraic topology until graduate school at Northwestern. That's been quite a few years ago, too.Mark wrote:My absolute favorite was algebraic topology. The class was two students and the professor and we met in the professor's office and in addition to the course matter talked a lot about rock climbing.
As a math major who worked as a software engineer, who tried teaching high school math and failed miserably and then returned to software and was recently laid off .... most of whose children are engineers -- I am not super-de-duper convinced that math is the gateway to the happy life that everyone seems to think it is.
I do think that the current method of teaching math in the US is pretty terrible and serves mostly to make students hate math.
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Re: How accurate is this article?
I never suggested STEM was a gateway to a happy life, but I strongly suggest it is a gateway to more marketable skills than a Women's Studies or Fine Arts/Performance major.proam wrote:
As a math major who worked as a software engineer, who tried teaching high school math and failed miserably and then returned to software and was recently laid off .... most of whose children are engineers -- I am not super-de-duper convinced that math is the gateway to the happy life that everyone seems to think it is.
I am committed to the advancement of civil rights, minus the Marxist intimidation and thuggery of BLM.
- opus37
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Re: How accurate is this article?
The options you have to get a good job in many different fields is greatly improved when you have a degree in math or one of the sciences. Biology seems to be the most limiting. As with any profession, you have to have some aptitude for it. Teaching is a special skill set no matter what your degree. Software development is a very fast changing field. You have to really keep up to be successful. Music majors tend to work in music stores, hospitality, or something else to make ends meet. Few make it as a performer. A lot of English, women's studies, etc. majors work at Starbucks.
Brian
1892 Courtiere (J.W. Pepper Import) Helicon Eb
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1892 Courtiere (J.W. Pepper Import) Helicon Eb
1980's Yamaha 321 euphonium
2007 Miraphone 383 Starlight
2010 Kanstul 66T
2016 Bubbie Mark 5
- proam
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Re: How accurate is this article?
I am no expert and, as I already said, I failed at teaching high-school math.
Common core is not the problem per se just like "new math" wasn't really the problem when I was young. They both just tried to look at the teaching methods in a different way, thinking that this other way is an improvement.
And it just might be a better way to teach the concepts -- I don't know. But the main problem is, you are teaching students a way of doing math that their parents did not learn. Too many of the parents do not understand and cannot help. In fact, too many of the teachers do not really understand what they are trying to teach.
So the big problem with all these teaching innovations is that they effectively take the parents out of the loop which greatly increases the chance of failure for the students. If Mom or Pop can't understand this, how can you expect me to?
I have found that most students will learn despite the obstacles we place in their way. The "old" ways of teaching math may not be the "best" (whatever that means) but they are what everyone knows. And it is certainly good enough for everyone to learn the basics.
I used to tell the students that math is like music or sports --- you gotta practice! You want to play a certain lick -- you practice it 100 times or whatever it takes. You want to sink your free throws --- you shoot thousands of them. You want to solve polynomials? You do hundreds of them.
No one does homework anymore. What about your all's music students? It seems to me that fewer students take the time to practice on their own these days.
Math is unlike other subjects. You SHOULD teach to the test. What on earth would you learn in a math class that wouldn't be on a test?? You don't have to memorize dates and details. It is almost all about learning a skill.
AGAIN --- this is all just my opinion. And as someone who never really had too much trouble with math ... (but it did take me a while to adjust from calculus to upper-level courses, where you transition from solving equations to writing proofs.)
Common core is not the problem per se just like "new math" wasn't really the problem when I was young. They both just tried to look at the teaching methods in a different way, thinking that this other way is an improvement.
And it just might be a better way to teach the concepts -- I don't know. But the main problem is, you are teaching students a way of doing math that their parents did not learn. Too many of the parents do not understand and cannot help. In fact, too many of the teachers do not really understand what they are trying to teach.
So the big problem with all these teaching innovations is that they effectively take the parents out of the loop which greatly increases the chance of failure for the students. If Mom or Pop can't understand this, how can you expect me to?
I have found that most students will learn despite the obstacles we place in their way. The "old" ways of teaching math may not be the "best" (whatever that means) but they are what everyone knows. And it is certainly good enough for everyone to learn the basics.
I used to tell the students that math is like music or sports --- you gotta practice! You want to play a certain lick -- you practice it 100 times or whatever it takes. You want to sink your free throws --- you shoot thousands of them. You want to solve polynomials? You do hundreds of them.
No one does homework anymore. What about your all's music students? It seems to me that fewer students take the time to practice on their own these days.
Math is unlike other subjects. You SHOULD teach to the test. What on earth would you learn in a math class that wouldn't be on a test?? You don't have to memorize dates and details. It is almost all about learning a skill.
AGAIN --- this is all just my opinion. And as someone who never really had too much trouble with math ... (but it did take me a while to adjust from calculus to upper-level courses, where you transition from solving equations to writing proofs.)
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Re: How accurate is this article?
This varies greatly.proam wrote:
No one does homework anymore.
Here in MoCo, MD (Just North of DC) the public schools are well regarded.
The homework level is silly huge.
(That doesn't mean it gets done)
But a lot more is given than I ever remember in the 70s.
I stayed after school for band practice and basketball.
I am committed to the advancement of civil rights, minus the Marxist intimidation and thuggery of BLM.
- ghmerrill
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Re: How accurate is this article?
Not highly germane to the specific discussion, but ... A couple of years before I walked away from the university, I taught an upper-level undergraduate course in recursive function theory. It was offered in my own department (Philosophy) under the rubric of "advanced logic" and attracted, on the first day, six students drawn form philosophy, mathematics, and physics. On the second day, there were three students.Mark wrote: My absolute favorite was algebraic topology. The class was two students and the professor and we met in the professor's office and in addition to the course matter talked a lot about rock climbing.
The physics major went on to medical school. The philosophy major ended up going on to the same graduate school from which I had received my degree -- and got a Ph.D. with a concentration in ethics and political philosophy. She then married a chemist and went to work for Hewlett-Packard as an engineer in their printers/copiers area, where she has had a lengthy career. I don't know what happened to the math major.
For my entire professional career (or careers) I thought I was a philosopher pretending to be a software engineer, a computer scientist, a data scientist, a cognitive scientist ... A couple of years after I retired, I realized that I'd been basically an algebraist pretending to be a philosopher. A close friend of mine (senior chaired professor in philosophy at Notre Dame whom I've known for 45 years) essentially told me this 35 years ago, and I refused to believe it. One thing he said was "You never liked philosophers much."
But there's a kind of moral here: If you learn the good basic stuff -- including math, science, and how to read and write with excellence -- you can (with effort) move in pretty much any direction you want to and have the courage to. What I see as one of the major failures of the contemporary university is that it fails in teaching its students how to learn and in giving them enough of a reliable objective base to work from. So a student has to take it upon himself or herself to get a degree that will reflect that sort of knowledge and skill set. And that's a lot to expect from almost any teenager.
Gary Merrill
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Mack Brass euph (DE LN106J9)
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- Rick Denney
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Re: How accurate is this article?
It's amazing to me, but the greatest mathematicians of the last century learned math the old way. "New Math" is not much different than Old Math, compared to the difference between either of those and the Common Core approach. The old way wasn't just good enough to learn the basics, but it was good enough to support great advances beyond the basics.proam wrote:...I have found that most students will learn despite the obstacles we place in their way. The "old" ways of teaching math may not be the "best" (whatever that means) but they are what everyone knows. And it is certainly good enough for everyone to learn the basics.
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No one does homework anymore. What about your all's music students? It seems to me that fewer students take the time to practice on their own these days.
You are correct that a major problem with Common Core is that it marginalizes or even negates any value the parents might have.
But then we have to ask the question: What is the purpose? It is driven by math performance being low. Is that because of teaching methods? I rather doubt it (see above about the greatest mathematicians of the last century). I suspect there are other influences at play. One of them is the expectation that people who have no aptitude for math (and math is one subject that can only be learned in spite of poor aptitude to a point) become skilled in it. At one time, being skilled in math (versus plain arithmetic) was not needed by a large sector of the population, but now that is perceived to be the case.
I think we can recognize that Asian cultures value math skills more than most these days. Do they use the common core methods? No. But they use math and arithmetic skills in their culture from the time they can speak.
The issue is that too many math teachers don't understand math, and too many parents don't care about it enough to work with their kids to learn it quite outside of whatever is being taught in school. They have focused their education on education, and not on their subject material. I suspect the same is true for English teachers, and history teachers, and geography teachers. Why can I draw, freehand, a reasonably accurate map of the USA and most kids these days aren't sure which end of the country they might find about half the states? Is that teaching methods, or is it a loss of regard for the importance of what is being taught? And I suspect that educational policy is looking for something other than creating the next great mathematician. They are focused on the floor rather than the ceiling.
There is a way to grade math tests that emphasizes the method use rather than the results attained. One home-school teacher I know finds that her kids are questioned on learning method as much as on their ability to actually solve math problems, prove theorems, and so on. The method has become the master, and that's the problem with the Common Core, and with education in general.
Engineers do not have to be great mathematicians, by the way, but they do have to be competent in a range of mathematical methods and tools well beyond what is taught through high school. The first course in advanced calculus with tricky integration is a real eye-opener. And then there are differential equations. But all of those are just building blocks for real mathematicians, who learned math...the old way.
Rick "not a real mathematician" Denney