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As far as Tim's point you may very well not need advanced degrees in Math to be a good grammer school or hs math teacher. BUT with that said I would prefer any teacher at my school live a life of constant learning whether in taking math classes or nonmath classes.
Education Reform
#21
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Posted 2010-December-28, 10:38
#22
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Posted 2010-December-28, 10:52
A general understanding of feedback is certainly important, but I don't think most people really need to know the underlying mathematics. I've forgotten all the diff-eq I learned at MIT, because it never comes up. Even calculus, which IS taught in high schools, doesn't come up much.
Anyway, I think the problem has much less to do with specific curriculum than the whole educational process. Not enough resources are devoted to public schools, and recent economic problems have only made things worse. Teachers in America have always been underpaid; as a result, many potentially good teachers choose to work in industry. And class sizes keep growing, making it more and more difficult for teachers to provide individual attention that some students need.
Education reform is almost always mentioned in campaign platforms, but once politicians get into office they just pay lip service, and little really gets done.
As long as the bulk of the US budget keeps going to the Defense Dept., I don't think we'll ever solve domestic problems like this. Education reform costs money, and that money has to come from somewhere.
Anyway, I think the problem has much less to do with specific curriculum than the whole educational process. Not enough resources are devoted to public schools, and recent economic problems have only made things worse. Teachers in America have always been underpaid; as a result, many potentially good teachers choose to work in industry. And class sizes keep growing, making it more and more difficult for teachers to provide individual attention that some students need.
Education reform is almost always mentioned in campaign platforms, but once politicians get into office they just pay lip service, and little really gets done.
As long as the bulk of the US budget keeps going to the Defense Dept., I don't think we'll ever solve domestic problems like this. Education reform costs money, and that money has to come from somewhere.
#23
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Posted 2010-December-28, 11:08
1998-99 spending was 6,500 per student, in 2006 it was 10,000.
Yet posters still say not enough money is spent.
"Not enough resources are devoted to public schools,"
When people say not enough resources are devoted to school, just how much more needs to be devoted. Keep in mind in many urban areas the school spends 10-20K per student per year.
"At the combined elementary and secondary level in 2006, the United States spent $10,267 per student, which was 41 percent higher than the OECD average of $7,283. At the postsecondary level, U.S. expenditures per student were $25,109, more than twice as high as the OECD average of $12,336."
http://nces.ed.gov/p...indicator38.asp
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An average of $6,911 was spent on each student—an increase of 6.2 percent from $6,508 in school year 1998–99 (in unadjusted dollars). Total expenditures for public education, including school construction, debt financing, community services, and adult education programs, came to nearly $382 billion.
----
Yet posters still say not enough money is spent.
"Not enough resources are devoted to public schools,"
When people say not enough resources are devoted to school, just how much more needs to be devoted. Keep in mind in many urban areas the school spends 10-20K per student per year.
"At the combined elementary and secondary level in 2006, the United States spent $10,267 per student, which was 41 percent higher than the OECD average of $7,283. At the postsecondary level, U.S. expenditures per student were $25,109, more than twice as high as the OECD average of $12,336."
http://nces.ed.gov/p...indicator38.asp
-----------
An average of $6,911 was spent on each student—an increase of 6.2 percent from $6,508 in school year 1998–99 (in unadjusted dollars). Total expenditures for public education, including school construction, debt financing, community services, and adult education programs, came to nearly $382 billion.
----
#24
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Posted 2010-December-28, 11:26
I don't think there's really any great mystery about how to "fix" education. The reason it doesn't get done is mostly a political issue. Essentially:
(1) We need ways to evaluate teachers, to reward the most effective with increased pay and to fire the least effective. However, basing this evaluation primarily on student test scores is naive. Student test scores are often heavily effected by things like their family situation, the preparation they received in previous grades, their degree of English proficiency, etc. Basing things on test scores also encourages "teaching to the test" rather than teaching reasoning/life skills. The right way to evaluate teachers is through frequent observation by experienced teachers, through interactions with parents, and so forth. However, this is more labor intensive and doesn't lend itself to easy "patches" like more testing.
(2) We need to consider how our education money is being spent. It turns out that having a safe and well-maintained building helps substantially in student performance. Yet many schools are physically deteriorating. The money certainly isn't going to teacher pay either. I suspect that a lot of the funding goes to things like computer equipment and administrator salaries, which are really less useful to education than good teachers and a good physical environment. Further, the way that education is funded in the US tends to direct more and more resources towards the schools which are doing the best, whereas "failing" schools (often in poor communities) which receive less money from donations (again, poor communities) also seem to receive less local government funding (again, poor communities) and to be punished on the state and federal level (initiatives like "no child left behind" that cut funding for the low performers). Of course, "more money" is always needed/helpful too.. and redirecting funding to "for profit" charter schools (i.e. lining some corporate pockets in the process) is unlikely to substantially improve matters.
(3) We need to encourage our best and most experienced teachers to help in failing schools. In the current system, good teachers are often promoted into administration (i.e. they stop teaching, in part because salaries for principals and superintendents are much better). Even if they continue to teach, their level of experience often gives them the choice of schools, and since salaries are roughly the same they pick the schools with better students, more funding, etc. We should be giving top teachers "hazard pay" to go into some of the worst schools and teach. Instead, these schools usually get the "right out of training" teachers who have a lot of enthusiasm but weak classroom management skills. Many of these enthusiastic young teachers "burn out" because teaching in the worst schools in the country is honestly really hard. They realize they could make better money doing something else (well, at least the bright ones could) and quit. Meanwhile the expert teachers who might actually be able to handle teaching in poor urban communities have no incentive to do it.
(1) We need ways to evaluate teachers, to reward the most effective with increased pay and to fire the least effective. However, basing this evaluation primarily on student test scores is naive. Student test scores are often heavily effected by things like their family situation, the preparation they received in previous grades, their degree of English proficiency, etc. Basing things on test scores also encourages "teaching to the test" rather than teaching reasoning/life skills. The right way to evaluate teachers is through frequent observation by experienced teachers, through interactions with parents, and so forth. However, this is more labor intensive and doesn't lend itself to easy "patches" like more testing.
(2) We need to consider how our education money is being spent. It turns out that having a safe and well-maintained building helps substantially in student performance. Yet many schools are physically deteriorating. The money certainly isn't going to teacher pay either. I suspect that a lot of the funding goes to things like computer equipment and administrator salaries, which are really less useful to education than good teachers and a good physical environment. Further, the way that education is funded in the US tends to direct more and more resources towards the schools which are doing the best, whereas "failing" schools (often in poor communities) which receive less money from donations (again, poor communities) also seem to receive less local government funding (again, poor communities) and to be punished on the state and federal level (initiatives like "no child left behind" that cut funding for the low performers). Of course, "more money" is always needed/helpful too.. and redirecting funding to "for profit" charter schools (i.e. lining some corporate pockets in the process) is unlikely to substantially improve matters.
(3) We need to encourage our best and most experienced teachers to help in failing schools. In the current system, good teachers are often promoted into administration (i.e. they stop teaching, in part because salaries for principals and superintendents are much better). Even if they continue to teach, their level of experience often gives them the choice of schools, and since salaries are roughly the same they pick the schools with better students, more funding, etc. We should be giving top teachers "hazard pay" to go into some of the worst schools and teach. Instead, these schools usually get the "right out of training" teachers who have a lot of enthusiasm but weak classroom management skills. Many of these enthusiastic young teachers "burn out" because teaching in the worst schools in the country is honestly really hard. They realize they could make better money doing something else (well, at least the bright ones could) and quit. Meanwhile the expert teachers who might actually be able to handle teaching in poor urban communities have no incentive to do it.
Adam W. Meyerson
a.k.a. Appeal Without Merit
a.k.a. Appeal Without Merit
#25
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Posted 2010-December-28, 12:09
I was also surprised by those figures, and wondering where all the money is going. I suspect a big chunk of it is health insurance (for both teachers and other staff), not teacher salaries or school equipment (textbooks and computers). So education reform is probably intimately tied with health care reform.
All I know is that every year my town newspaper reports on further cuts in our school budget. You hear about art and sports programs being cut back or dropped entirely. In my town, families have to pay extra for each sport their kids participate in (ranging from $408 to $720/season, but they recently compromised by adding a per-family cap and multi-sport discounts).
All I know is that every year my town newspaper reports on further cuts in our school budget. You hear about art and sports programs being cut back or dropped entirely. In my town, families have to pay extra for each sport their kids participate in (ranging from $408 to $720/season, but they recently compromised by adding a per-family cap and multi-sport discounts).
#26
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Posted 2010-December-28, 12:55
As far as math goes, I think a lot of the problem is rooted in failure to build foundation skills in the middle grades, something like 5th through 8th.
Like KenBerg pointed out, kids get to high school without being able to handle things like determining the measure of an angle in a triangle given the measure of the other two angles. High school teachers spend time reviewing (and teaching) material that kids should have down pat. This time drain prevents them from presenting the material they are supposed to and students fall further behind.
It is not a matter of throwing better educated and more skilled teachers at high school students. Their talents will be wasted on kids lacking a solid foundation.
Like KenBerg pointed out, kids get to high school without being able to handle things like determining the measure of an angle in a triangle given the measure of the other two angles. High school teachers spend time reviewing (and teaching) material that kids should have down pat. This time drain prevents them from presenting the material they are supposed to and students fall further behind.
It is not a matter of throwing better educated and more skilled teachers at high school students. Their talents will be wasted on kids lacking a solid foundation.
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Posted 2010-December-28, 13:18
barmar, on 2010-December-28, 12:09, said:
I was also surprised by those figures, and wondering where all the money is going. I suspect a big chunk of it is health insurance (for both teachers and other staff), not teacher salaries or school equipment (textbooks and computers). So education reform is probably intimately tied with health care reform.
All I know is that every year my town newspaper reports on further cuts in our school budget. You hear about art and sports programs being cut back or dropped entirely. In my town, families have to pay extra for each sport their kids participate in (ranging from $408 to $720/season, but they recently compromised by adding a per-family cap and multi-sport discounts).
All I know is that every year my town newspaper reports on further cuts in our school budget. You hear about art and sports programs being cut back or dropped entirely. In my town, families have to pay extra for each sport their kids participate in (ranging from $408 to $720/season, but they recently compromised by adding a per-family cap and multi-sport discounts).
My understanding is that the US spends enormously more on "special needs" education than is typical in the rest of the world.
Alderaan delenda est
#28
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Posted 2010-December-28, 13:57
People who are good at maths can find jobs that pay better than high school teaching. Schools don't have the budget to pay enough to retain a full complement of knowledgable math teachers. I think there are three things that can reasonably be done:
1. Set salaries based on supply and demand so math teachers earn much more than others.
2. Accept that most students can graduate from high school without ever learning calculus, advanced algebra or maybe even trigonometry. Then you can spread the most capable teachers among the 10-20% of students who will benefit from learning this stuff.
3. Have larger class sizes for advanced maths or other subjects where teacher supply is low.
I suspect the reasons why these three things don't happen are, respectively: unions, some distorted notion of equality, and unions.
Of course, none of this will help the students who can't subtract a number from 180. For that, I think parents have to take at least half the blame. Partly for not making sure their kids know this stuff even if they have to teach it themselves, and also for failing to hound the responsible teacher until they either get better or give up teaching altogether.
1. Set salaries based on supply and demand so math teachers earn much more than others.
2. Accept that most students can graduate from high school without ever learning calculus, advanced algebra or maybe even trigonometry. Then you can spread the most capable teachers among the 10-20% of students who will benefit from learning this stuff.
3. Have larger class sizes for advanced maths or other subjects where teacher supply is low.
I suspect the reasons why these three things don't happen are, respectively: unions, some distorted notion of equality, and unions.
Of course, none of this will help the students who can't subtract a number from 180. For that, I think parents have to take at least half the blame. Partly for not making sure their kids know this stuff even if they have to teach it themselves, and also for failing to hound the responsible teacher until they either get better or give up teaching altogether.
#29
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Posted 2010-December-28, 14:04
"Total spending ratio. Based on 1999-2000 school year data, the total expenditure
to educate the average student with disabilities is an estimated 1.90 times that
expended to educate the typical regular education student with no special needs.
This ratio has actually declined since 1985, when it was estimated by Moore et al.
(1988) to be 2.28.
• Total current spending ratio. Excluding expenditures on school facilities, the
ratio of current operating expenditures on the typical special education student is
2.08 times that expended on the typical regular education student with no special
needs."
•
http://csef.air.org/...nal/AdvRpt1.pdf
to educate the average student with disabilities is an estimated 1.90 times that
expended to educate the typical regular education student with no special needs.
This ratio has actually declined since 1985, when it was estimated by Moore et al.
(1988) to be 2.28.
• Total current spending ratio. Excluding expenditures on school facilities, the
ratio of current operating expenditures on the typical special education student is
2.08 times that expended on the typical regular education student with no special
needs."
•
http://csef.air.org/...nal/AdvRpt1.pdf
#30
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Posted 2010-December-28, 14:09
mike777, on 2010-December-28, 14:04, said:
"Total spending ratio. Based on 1999-2000 school year data, the total expenditure
to educate the average student with disabilities is an estimated 1.90 times that
expended to educate the typical regular education student with no special needs.
This ratio has actually declined since 1985, when it was estimated by Moore et al.
(1988) to be 2.28.
Total current spending ratio. Excluding expenditures on school facilities, the
ratio of current operating expenditures on the typical special education student is
2.08 times that expended on the typical regular education student with no special
needs."
to educate the average student with disabilities is an estimated 1.90 times that
expended to educate the typical regular education student with no special needs.
This ratio has actually declined since 1985, when it was estimated by Moore et al.
(1988) to be 2.28.
Total current spending ratio. Excluding expenditures on school facilities, the
ratio of current operating expenditures on the typical special education student is
2.08 times that expended on the typical regular education student with no special
needs."
Any figures about what percentage of students are classified as special needs compared to other parts of the world?
Alderaan delenda est
#31
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Posted 2010-December-28, 14:12
According to the Department of Education, approximately 6 million children (roughly 10 percent of all school-aged children) currently receive some type of special education services.[38]
http://en.wikipedia....ecial_education
http://en.wikipedia....ecial_education
#32
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Posted 2010-December-28, 14:33
mike777, on 2010-December-28, 14:12, said:
According to the Department of Education, approximately 6 million children (roughly 10 percent of all school-aged children) currently receive some type of special education services.[38]
http://en.wikipedia....ecial_education
http://en.wikipedia....ecial_education
I suspect that this percentage explains a lot
Alderaan delenda est
#33
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Posted 2010-December-28, 15:25
A few things.
I very much enjoyed reading the essay linked through here.
I would actually back up further. I think when it comes to math and reasoning skills the system fails before the school even starts, or around kindergarten time. Ability to think about problems, whether algebraic, arithmetic, or geometric in nature does not require complicated expressions, just a touch of imagination an interested parent/guardian/teacher. I feel like too many parents think it is the schools' responsibility to teach their kids math, science, or languages. Some of this might stem from the parents' own math phobia, but come on... it's not like we expect 5 year olds to be doing calculus, but simple logical reasoning, why not?
There is too much meddling of politics in education (I think some touched on this already). Saw this article recently, and it nearly made me throw up. WTF?
No, a democratic society needs scientists who can leave their politics behind.
Frankly, we need more of this.
I very much enjoyed reading the essay linked through here.
TimG, on 2010-December-28, 12:55, said:
As far as math goes, I think a lot of the problem is rooted in failure to build foundation skills in the middle grades, something like 5th through 8th.
I would actually back up further. I think when it comes to math and reasoning skills the system fails before the school even starts, or around kindergarten time. Ability to think about problems, whether algebraic, arithmetic, or geometric in nature does not require complicated expressions, just a touch of imagination an interested parent/guardian/teacher. I feel like too many parents think it is the schools' responsibility to teach their kids math, science, or languages. Some of this might stem from the parents' own math phobia, but come on... it's not like we expect 5 year olds to be doing calculus, but simple logical reasoning, why not?
There is too much meddling of politics in education (I think some touched on this already). Saw this article recently, and it nearly made me throw up.
Quote
A democratic society needs Republican scientists.
No, a democratic society needs scientists who can leave their politics behind.
Frankly, we need more of this.
#34
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Posted 2010-December-28, 17:55
matmat, on 2010-December-28, 15:25, said:
It is stated humorously, but this is fundamental. I can't think of any mathematician I have ever met who would say that he chose his line of work to be of service to humanity. I explain to people that I became a mathematician because I enjoy mathematics and I can make a decent living at it. People pay us because it is useful, and the fact they pay us is important, but we didn't really think much about social utility when we signed on. There may be some exceptions, but I haven't met them.
Ken
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Posted 2010-December-28, 18:20
matmat, on 2010-December-28, 15:25, said:
I found it quite amusing that an article that professed to complain about the under-representation of Republicans amongst scientists could be so confused regarding cause and effect.
Alderaan delenda est
#36
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Posted 2010-December-28, 18:45
hrothgar, on 2010-December-28, 18:20, said:
I found it quite amusing that an article that professed to complain about the under-representation of Republicans amongst scientists could be so confused regarding cause and effect.
That was one of my reactions as well. It reminded me a little bit of an article from a few years back when a journalist argued that mathematics was not important, since he managed to get through life without knowing it. Citing his lack of understanding of percentages as a badge of honour. let's see if i can dig that old piece out...
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Posted 2010-December-29, 07:08
TimG, on 2010-December-27, 22:36, said:
It is my opinion that any post graduate degree is an excess when it comes to teaching high school students. In math, for instance, things like Abstract Algebra, let alone Differential Equations, will be of little or no use when teaching Pre-Calculus.
Several people in this thread have complained that their math classes were lacking, mostly because they focused too much on memorization and that their teachers failed to enthuse them.
But how can a math teacher inspire you for mathematics if they have never seen the true beauty of mathematics themselves? And isn't abstract algebra for most math students a first glance at what mathematics is about? If a math teacher has never gone as far as abstract algebra, what then does that say about his or her love for the subject?
And how can a high school teacher be enthousiastic about calculus if they don't know the importance of differential equations? If they haven't seen how Newton derived Keplers laws using differential equations? If they can't understand why current day's scientists, engineers and bankers to a great extend depend on differential equations? I'd say that a mathematics teacher that doesn't know about differential equations is completely out of touch with modern science.
hrothgar said:
If we don't motivate math with practical, real world problems we're never going to convince kids to care.
Please note: I am interested in boring, bog standard, 2/1.
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Posted 2010-December-29, 07:24
matmat, on 2010-December-28, 15:25, said:
I read the essay last night and left it with mixed feelings:
I very much agree with the pedagogic approach that the author recommends.
I think that I would have loved to have him as a math teacher.
At the same time, he seemed to think that math could be treated as an elective.
Not everyone needs to take art or music.
In a similar vein, not everyone needs to take math.
I'm not sure that I agree with this. Most high paying jobs in the modern "knowledge" economy require strong math skills. I'm not sure whether kids are in a good position to make an informed decision about whether or not they need to take math. In a similar vein, I doubt that their parents are necessarily any better placed (especially if "math" is being taught in the manner described in this article).
The methods that the author is describing are very far removed from the standardized testing approach currently in vogue...
Alderaan delenda est
#39
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Posted 2010-December-29, 08:02
The think the article the OP mentioned misses a main point if not the main point.
Some countries have a "competition" attitude about school, they are interested in the best and don't care much about those who fail.
They don't even care much about the fact that a lot of children with a high potential, don't make it to the top or even finish school.
Company's will hire top people from other countries if there are not enough.
My understanding is that Finland has a different attitude more like the armed forces "We don't leave our people behind" mantra.
Pupils that already understood what the teacher has explained, are immediately involved into teaching those who did not get it the first time.
To do this the teacher creates small groups who teach each other. This way the teacher can focus his efforts to those who need "special education".
The "Nerds" gain social competence and are better integrated into the class. With a little luck every child can be a tutor to his/her classmates somewhere between math and sports.
Some countries have a "competition" attitude about school, they are interested in the best and don't care much about those who fail.
They don't even care much about the fact that a lot of children with a high potential, don't make it to the top or even finish school.
Company's will hire top people from other countries if there are not enough.
My understanding is that Finland has a different attitude more like the armed forces "We don't leave our people behind" mantra.
Pupils that already understood what the teacher has explained, are immediately involved into teaching those who did not get it the first time.
To do this the teacher creates small groups who teach each other. This way the teacher can focus his efforts to those who need "special education".
The "Nerds" gain social competence and are better integrated into the class. With a little luck every child can be a tutor to his/her classmates somewhere between math and sports.
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Posted 2010-December-29, 08:26
A few random comments:
When I was in high school I took algebra and I took metal shop. I helped Lug Larson with his algebra, he helped me with the lathe.
Colman McCarthy was an entertaining and sometimes aggravating columnist some years back. He wrote a column about how kids really didn't need algebra and argued that in the unlikely event that anyone actually did need it he could learn it then. Smart people often make this very wrong argument. Yes, Colman McCarthy could learn it if he needed it. He is smart, he knows how to learn new things, he has the resources to hire a tutor if needed, he has a job with flexible working hours, etc. A twenty-five year old bagging groceries who decides he would like to, say, study chemistry or economics or business or whatever at the community college and maybe get a better job will not find this "just learn it" so easily done.
Mrs. Swan, the woman who taught me math in my first two years of high school, probably knew nothing about differential equations. But we did geometric proofs and constructions, she knew these, and she was excellent. For the next two years I had Mr. Berger, who I am sure knew differential equations but probably was vague (very vague) on how to derive Kepler's Laws from the inverse square law of gravitation. He was also excellent. And he took an interest in me and got me a scholarship. Thanks, Dude, wherever you now are. If all teachers were like these two, we would not be fretting about our children's education. The gap, from there to where we are in some systems, is a chasm.
When I was in high school I took algebra and I took metal shop. I helped Lug Larson with his algebra, he helped me with the lathe.
Colman McCarthy was an entertaining and sometimes aggravating columnist some years back. He wrote a column about how kids really didn't need algebra and argued that in the unlikely event that anyone actually did need it he could learn it then. Smart people often make this very wrong argument. Yes, Colman McCarthy could learn it if he needed it. He is smart, he knows how to learn new things, he has the resources to hire a tutor if needed, he has a job with flexible working hours, etc. A twenty-five year old bagging groceries who decides he would like to, say, study chemistry or economics or business or whatever at the community college and maybe get a better job will not find this "just learn it" so easily done.
Mrs. Swan, the woman who taught me math in my first two years of high school, probably knew nothing about differential equations. But we did geometric proofs and constructions, she knew these, and she was excellent. For the next two years I had Mr. Berger, who I am sure knew differential equations but probably was vague (very vague) on how to derive Kepler's Laws from the inverse square law of gravitation. He was also excellent. And he took an interest in me and got me a scholarship. Thanks, Dude, wherever you now are. If all teachers were like these two, we would not be fretting about our children's education. The gap, from there to where we are in some systems, is a chasm.
Ken