Furthermore, ask any Calc I or Calc II student (even many math majors!) to prove that ln x is the (rather, an) anti-derivative of 1/x and you'll find that just about none of them can. They simply memorized it. They do just fine on tests and no one complains.
The problem is, at the lower levels math education heavily favors the "how" question. The "why" is something the teacher/professor explains, but doesn't test. If "how" is what you're focused on, these CAS's are a major detriment to your class. If, however, you focus on the "why", you find that in many cases, CAS's can help students develop an intuitive understanding of the nature of some problems.
For example, give a student some differential equations, a bifurcation diagram, and a solution plot with sliders for initial conditions and let them play with it. A few minutes, a few examples and they will have a memorable, intuitive idea of what we mean when we say, "Small changes in initial conditions can lead to drastically different solutions." Educators need to harness the power of these systems. They can aid learning, if used correctly.
I think you, and everyone else ragging on the Teachers' unions are missing a key point. If contracts are negotiated on a per-hire basis, then you have essentially handed full control of the curriculum over to the bureaucracy. "Teach to the test" will finally become an explicit order. Pressure to focus and make "adequate yearly gains" on these soul-crushing, curiosity-killing multiple choice tests will overwhelm.
And, sure, that's fine. If I don't like the contract, I don't sign it. But every student at that school will be affected by the wording and mandates of that contract. Who's place is it to protest?
Parents. But, alas, parents are rarely well organized - especially in poor, transient populations. So it falls to teachers. When the politicians and bureaucrats try to push more fill-in-the-bubble-and-be-thusly-measured education down the throats of students, someone has to stand up and protest. Who better than the people who have spent years studying and experiencing the practice of education? This is what the union is for.
That being said, yes, teachers should be fired. Lots of them. And the main impediment in the way is the union. But this is not the *only* thing the union does. And to be honest, I'm also not a big fan of the union. But I don't think that dissolving the union is the first step. I think that comes later, after much more pressing reforms.
Re:If you ever lived in a foreign country
on
Censorship By Glut
·
· Score: 1
I always thought of The Jerry Springer Show as satire. Which is why I liked it (though I couldn't stand to watch it much). His show was all about the emperor's wardrobe. He shoved our culture right back in our face and the fact that we liked it so much only made it that much more poignant.
Or maybe not really. That's the beauty of it. Kaufman reborn?
Ahhh, yes. He must have pushed an officer just so he could get some publicity! Genius! I'm sure the ACLU didn't look into any of the police reports!
But really, how would I respond to your drug-mule issue? First, I would recognize that we will never cut off the supply of drugs. And the more we do, the more rewarded individual suppliers are. Every drug bust only entices more into the trade. It's an issue of demand, not supply. No one would sell if Americans didn't buy.
Illegal immigration? Again, they come to the US because they get jobs here. Find the American companies illegally hiring these immigrants and punish them. Again, it's a demand problem.
Personally, I don't want a fence on the border, but, you're right, I'm probably insane. I just sort of figure that since an integral part of the free market is freedom of movement, then because of NAFTA, we should not only allow the freedom to move Mexican goods across the borders, but also people. It really seems unethical to me to push for a free-marketish system that restricts one of the fundamentals of the free market in such a way to almost unilaterally benefit the United States.
"I love you. I believe you're going to hell. And I won't do everything in my power to convince you to convert."
One of these three must be insincere, no? I'm not arguing that it would be logical to disallow disbelief, I'm arguing that it is illogical to stand by as someone you love makes their way to Hell.
Is it possible to both love someone and believe that s/he will spend an eternity in hell without doing everything in your power to convince them to convert? I'm not saying that the president would abuse his/her power, I'm simply saying that it seems inconsistent to me to say "I love you. And I will encourage you to worship according to your own conscience. And you're going to hell." One of the three has to be insincere.
Of course a question about religious belief is inherently unfair, because it is irrelevant...
I believe that all non-believers should be put to death. Irrelevant? I believe creationism is true and should be taught in schools. Irrelevant?
..and any response will offend some group of bigots...who believe differently.
Do you mind breaking that down into what you actually worked on? My mom is a teacher in her 2nd year and has a similar work load, but to be honest, I could do a lot of the after-school stuff in half the time. (I've helped her before, so I'm not pulling that out of my ass.)
Well, that I never fully kept stats on. But I can tell you that most people underestimate the amount of work teachers have thrown at them. If you want to make good curriculum, something that works with your students' interests, something that helps reach out to those disinterested, failing students, I would be looking at about a 1:1 ratio for planning time. One hour of thinking, planning, preparing for a one-hour class. If you've got two subjects, you're looking at two-hours of planning just to get through the day. That, obviously, doesn't happen. So you cut your losses. One class subject gets book led, uninspiring classes that cost you 15 minutes in copier time and the other subject gets your real attention.
Don't forget the 5 hours of after school meetings to go to each week.
Then you've got the kids that come in after school for tutoring help. This always ate up a lot of my time, but I felt that this was something that the school should have been providing. I provided it instead. I would often have kids in my classroom being tutored until 4:30 or 5pm each day I didn't have meetings.
I would often try to grade papers during class, but that process will eat up 15% of your class time every day. And, since you're doing it as quickly as possible, you don't get to know students mathematically. You don't know who struggles with negatives, who is great at solving equations and who mostly understands it but keeps getting that one little thing wrong. This is what grading on the weekends is for. To get to know your students. Even then, I was a quick grader. Check for completion, maybe check one specific problem, write it down and move on. But do that 130 times then deal with late-work, make up tests and special cases and you've burned more than an hour or two.
And what about planning curriculum with your colleagues? What about discussing specific student issues with multiple adults? What about meeting with parents, counselors and others involved?
As to your comments on job-searching woes, I think many of the things you are pointing out are, in fact, good things. I think that job searchers *should* be biases towards people with education degrees. Teaching is a difficult thing. *Good* teaching requires study, thought and experience. A degree points out that, at least, you have two of the three.
And, yes, I think it's a good thing that a problem school would not want to hire a new teacher, no matter what his/her potential. Problem schools are the schools that need the most experienced teachers. You need to have your act together from day 0 to even have a chance of getting through to students in a problem school.
Finally, I certainly didn't say that the biggest problem in our schools is lack of teacher pay. There are much bigger problems.
I guess I can speak to that, being a teacher who, after three years, has decided to leave teaching.
According to my contract, I worked 37.5 hours a week. According to my personal records I worked 55. That includes one day per weekend as well. That's a pretty significant discrepancy, and when I calculated my hourly wage based on actual hours worked, I was making about the same as a fellow math major working an internship at a financial institution. I had a master's degree. She did not.
And then there were working conditions. No air conditioning, minimal heating. Kids throwing things, yelling at each other, coming in drunk, and constantly disrespecting me. (For the record, these weren't all students. Many students are fairly well-behaved and respectful.) And don't forget angry phone calls from parents: "WHY DID YOU FAIL MY DAUGHTER?!" Constant cut-backs means teachers end up with ever-more responsibilities: "We used to have a full-time test coordinator, but we had to let her go. Now you'll have to cover those responsibilities during your planning-period." "Please don't send anymore students to the office with referrals. We can't handle the number we receive. Please deal with issues in your class".
Oh yeah, and if you've never done lunch duty, then you really don't understand what I'm talking about...
So, look. I got a living wage, sure. And I got all federal holidays and a nice 7-week break during summer. But every day left me absolutely exhausted and depressed. There's really two fixes: fewer students/classes/responsibilities or more money.
Sorry for the rant. Back to your original question, competitive with what? Well, I couldn't say off-hand. But I'm sure that as someone with a degree in math, there are options with better pay and working conditions out there. I think that the national shortage of math and science teachers will attest to that. We will know that the education wages are competitive with other industries when finding a position as a math/science teacher is difficult. I got my last job after one over-the-phone "interview". This is not how you get hired for a job with a competitive wage.
All Americans suck because their TV's are 20 years behind.
Re:What do you mean by unknown?
on
Happy Pi Day
·
· Score: 1
I think that I chose the wrong bit to quote in my response. The OP said "Pi's value is known totally precisely" which is what I'm taking issue with. Sure, you can do all sorts of fun stuff to calculate pi. But does that give you its value? Sure, in a sense. Sometimes in a useful sense, but not in the way we traditionally use the word value.
For example, what's the value of sqrt(9)?
It's the number such that when you square it you get 9. Oh, it's also what you get when you take 81 to the 0.25 power. It's the number such that when you cube root it and then take it to the sixth power you get 9.
Is the value of sqrt(9) known totally precisely in this example? Sure, in a way... but also not, in a way.
Using the traditional usage of the word value, we cannot place pi on a number line. We do not know the 1.4 sextillionth digit. We do not know how to represent pi using our decimal system. This representation is (almost always) what we mean when we say value.
Re:What do you mean by unknown?
on
Happy Pi Day
·
· Score: 1
It doesn't make pi any less definite though.
I think it does in a sense. Pi is precisely defined: it's the number that you get when you divide the circumference of a circle by its diameter. But that's not its value, that's its definition. And then we say, "Oh and look at all the other places it pops up and all of the other things we can do with it." We can say, it's the number that does this. It's the one you get when you do that. But we can't precisely place it on a number line. There is something unknown about its value.
Slashdot Mirror
Furthermore, ask any Calc I or Calc II student (even many math majors!) to prove that ln x is the (rather, an) anti-derivative of 1/x and you'll find that just about none of them can. They simply memorized it. They do just fine on tests and no one complains.
The problem is, at the lower levels math education heavily favors the "how" question. The "why" is something the teacher/professor explains, but doesn't test. If "how" is what you're focused on, these CAS's are a major detriment to your class. If, however, you focus on the "why", you find that in many cases, CAS's can help students develop an intuitive understanding of the nature of some problems.
For example, give a student some differential equations, a bifurcation diagram, and a solution plot with sliders for initial conditions and let them play with it. A few minutes, a few examples and they will have a memorable, intuitive idea of what we mean when we say, "Small changes in initial conditions can lead to drastically different solutions." Educators need to harness the power of these systems. They can aid learning, if used correctly.
I think you, and everyone else ragging on the Teachers' unions are missing a key point. If contracts are negotiated on a per-hire basis, then you have essentially handed full control of the curriculum over to the bureaucracy. "Teach to the test" will finally become an explicit order. Pressure to focus and make "adequate yearly gains" on these soul-crushing, curiosity-killing multiple choice tests will overwhelm.
And, sure, that's fine. If I don't like the contract, I don't sign it. But every student at that school will be affected by the wording and mandates of that contract. Who's place is it to protest?
Parents. But, alas, parents are rarely well organized - especially in poor, transient populations. So it falls to teachers. When the politicians and bureaucrats try to push more fill-in-the-bubble-and-be-thusly-measured education down the throats of students, someone has to stand up and protest. Who better than the people who have spent years studying and experiencing the practice of education? This is what the union is for.
That being said, yes, teachers should be fired. Lots of them. And the main impediment in the way is the union. But this is not the *only* thing the union does. And to be honest, I'm also not a big fan of the union. But I don't think that dissolving the union is the first step. I think that comes later, after much more pressing reforms.
I believe the correct phrase is: "Be excellent to each other" -Bill S. Preston Esq.
Luckily, as you grow older, you soon won't be able to hear the difference!
FFS, all you need to do is click the colored words.
Dan, is that you?
I always thought of The Jerry Springer Show as satire. Which is why I liked it (though I couldn't stand to watch it much). His show was all about the emperor's wardrobe. He shoved our culture right back in our face and the fact that we liked it so much only made it that much more poignant.
Or maybe not really. That's the beauty of it. Kaufman reborn?
I think the current events confirm my belief that, for all our song and dance about the free market, we only implement it insofar as it benefits us.
Ahhh, yes. He must have pushed an officer just so he could get some publicity! Genius! I'm sure the ACLU didn't look into any of the police reports!
But really, how would I respond to your drug-mule issue? First, I would recognize that we will never cut off the supply of drugs. And the more we do, the more rewarded individual suppliers are. Every drug bust only entices more into the trade. It's an issue of demand, not supply. No one would sell if Americans didn't buy.
Illegal immigration? Again, they come to the US because they get jobs here. Find the American companies illegally hiring these immigrants and punish them. Again, it's a demand problem.
Personally, I don't want a fence on the border, but, you're right, I'm probably insane. I just sort of figure that since an integral part of the free market is freedom of movement, then because of NAFTA, we should not only allow the freedom to move Mexican goods across the borders, but also people. It really seems unethical to me to push for a free-marketish system that restricts one of the fundamentals of the free market in such a way to almost unilaterally benefit the United States.
Fair enough:
"I love you. I believe you're going to hell. And I won't do everything in my power to convince you to convert."
One of these three must be insincere, no? I'm not arguing that it would be logical to disallow disbelief, I'm arguing that it is illogical to stand by as someone you love makes their way to Hell.
Of course a question about religious belief is inherently unfair, because it is irrelevant...
I believe that all non-believers should be put to death. Irrelevant? I believe creationism is true and should be taught in schools. Irrelevant?
..and any response will offend some group of bigots...who believe differently.
Don't confuse "offended" with "in disagreement".
Granted it's not the *most* important question to ask them, but boy would it be fun to watch them squirm!
Naah, easy-out question ("God bless America!"). I think you need to pin 'em down a bit:
Do you prescribe to the belief that non-Christians will spend eternity in Hell?
If yes, what influence does this have on your dealings with non-believers?
If no, how do you reconcile this belief with the bible?
You also won't get that impression by listening to his running mate.
I would not recommend the crackpot option. That gets you hiiiiiiiiiiiiiiiiigh as a motherfucker.
Do you mind breaking that down into what you actually worked on? My mom is a teacher in her 2nd year and has a similar work load, but to be honest, I could do a lot of the after-school stuff in half the time. (I've helped her before, so I'm not pulling that out of my ass.)
Well, that I never fully kept stats on. But I can tell you that most people underestimate the amount of work teachers have thrown at them. If you want to make good curriculum, something that works with your students' interests, something that helps reach out to those disinterested, failing students, I would be looking at about a 1:1 ratio for planning time. One hour of thinking, planning, preparing for a one-hour class. If you've got two subjects, you're looking at two-hours of planning just to get through the day. That, obviously, doesn't happen. So you cut your losses. One class subject gets book led, uninspiring classes that cost you 15 minutes in copier time and the other subject gets your real attention.
Don't forget the 5 hours of after school meetings to go to each week.
Then you've got the kids that come in after school for tutoring help. This always ate up a lot of my time, but I felt that this was something that the school should have been providing. I provided it instead. I would often have kids in my classroom being tutored until 4:30 or 5pm each day I didn't have meetings.
I would often try to grade papers during class, but that process will eat up 15% of your class time every day. And, since you're doing it as quickly as possible, you don't get to know students mathematically. You don't know who struggles with negatives, who is great at solving equations and who mostly understands it but keeps getting that one little thing wrong. This is what grading on the weekends is for. To get to know your students. Even then, I was a quick grader. Check for completion, maybe check one specific problem, write it down and move on. But do that 130 times then deal with late-work, make up tests and special cases and you've burned more than an hour or two.
And what about planning curriculum with your colleagues? What about discussing specific student issues with multiple adults? What about meeting with parents, counselors and others involved?
As to your comments on job-searching woes, I think many of the things you are pointing out are, in fact, good things. I think that job searchers *should* be biases towards people with education degrees. Teaching is a difficult thing. *Good* teaching requires study, thought and experience. A degree points out that, at least, you have two of the three.
And, yes, I think it's a good thing that a problem school would not want to hire a new teacher, no matter what his/her potential. Problem schools are the schools that need the most experienced teachers. You need to have your act together from day 0 to even have a chance of getting through to students in a problem school.
Finally, I certainly didn't say that the biggest problem in our schools is lack of teacher pay. There are much bigger problems.
Competitive with what exactly?
I guess I can speak to that, being a teacher who, after three years, has decided to leave teaching.
According to my contract, I worked 37.5 hours a week. According to my personal records I worked 55. That includes one day per weekend as well. That's a pretty significant discrepancy, and when I calculated my hourly wage based on actual hours worked, I was making about the same as a fellow math major working an internship at a financial institution. I had a master's degree. She did not.
And then there were working conditions. No air conditioning, minimal heating. Kids throwing things, yelling at each other, coming in drunk, and constantly disrespecting me. (For the record, these weren't all students. Many students are fairly well-behaved and respectful.) And don't forget angry phone calls from parents: "WHY DID YOU FAIL MY DAUGHTER?!" Constant cut-backs means teachers end up with ever-more responsibilities: "We used to have a full-time test coordinator, but we had to let her go. Now you'll have to cover those responsibilities during your planning-period." "Please don't send anymore students to the office with referrals. We can't handle the number we receive. Please deal with issues in your class".
Oh yeah, and if you've never done lunch duty, then you really don't understand what I'm talking about...
So, look. I got a living wage, sure. And I got all federal holidays and a nice 7-week break during summer. But every day left me absolutely exhausted and depressed. There's really two fixes: fewer students/classes/responsibilities or more money.
Sorry for the rant. Back to your original question, competitive with what? Well, I couldn't say off-hand. But I'm sure that as someone with a degree in math, there are options with better pay and working conditions out there. I think that the national shortage of math and science teachers will attest to that. We will know that the education wages are competitive with other industries when finding a position as a math/science teacher is difficult. I got my last job after one over-the-phone "interview". This is not how you get hired for a job with a competitive wage.
I have a new strategy: let the Jobs win.
I enjoyed it, fwiw.
Go on.
Every nerd knows that if you can't win, go GOD mode.
All Americans suck because their TV's are 20 years behind.
I think that I chose the wrong bit to quote in my response. The OP said "Pi's value is known totally precisely" which is what I'm taking issue with. Sure, you can do all sorts of fun stuff to calculate pi. But does that give you its value? Sure, in a sense. Sometimes in a useful sense, but not in the way we traditionally use the word value.
For example, what's the value of sqrt(9)?
It's the number such that when you square it you get 9. Oh, it's also what you get when you take 81 to the 0.25 power. It's the number such that when you cube root it and then take it to the sixth power you get 9.
Is the value of sqrt(9) known totally precisely in this example? Sure, in a way... but also not, in a way.
Using the traditional usage of the word value, we cannot place pi on a number line. We do not know the 1.4 sextillionth digit. We do not know how to represent pi using our decimal system. This representation is (almost always) what we mean when we say value.
It doesn't make pi any less definite though.
I think it does in a sense. Pi is precisely defined: it's the number that you get when you divide the circumference of a circle by its diameter. But that's not its value, that's its definition. And then we say, "Oh and look at all the other places it pops up and all of the other things we can do with it." We can say, it's the number that does this. It's the one you get when you do that. But we can't precisely place it on a number line. There is something unknown about its value.
But I will, of course, defer to you, Mr. Nash.
The fun part is that now Slashdot itself can be sued.
For linking to itself? (check your link)