If politicians understood calculus, then they would understand the relationship of the budget deficit to the national debt (hint: one is the derivative of the other) and not get so excited when the rate of increase of the budget deficit is beginning to slow down.
Re:Great, more calculator dependence
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TI-84 Plus Released
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· Score: 4, Interesting
One says you should be able to do everything by hand (as every good mathematician should) and the calculator is simply a guide for some of the tougher problems.
Really? I know some astounding mathematicians who are not able to do square-root extraction by hand. They forgot the algorithim to compute sqrt(11) to ten decimal places. (It is similar to the long-division algorithm, and used to be taught to every student)
And, technically, you should not be adding or multiplying numbers unless you can derive the concept of "number" from the five Peano axioms using set theory. Yet I know some lazy mathematicians who never took enough set theory to do this "by hand." Yet they get by.
Calculators are not like cliff notes. Mathematics is not all about the arithmetic. Calculators are more like word-processors, that allow us to formulate our thoughts on books without having to stop every five minutes to sharpen our nibs, grind our own ink, and change blotters.
I was the tech-editor on a book about this calculator, so I was playing with a prototype for the past two months.
I thought that Cabri Jr and all were just toys, and would not be worth a damn if I were trying to use the calculator to either learn or actually do work. The resolution was not good enough to gain insight into any sort of complex figure, and it was overall a pain in the ass to use.
They also have another Geometry program on it that fares no better. I would never use a pocket calculator screen to try to do geometry.
Oh college student, the day will come when you have to meet with your Realtor, your Lawyer, your Insurance agent. They will shoot numbers at you fast and furious while the two of you sit (perhaps somewhere like a coffee shop or Perkins - my realtor always bought me lunch).
Yes, you COULD whip out your laptop, clear some space on their desk or the booth, wait for it to boot up, open up Maple9 (click "no" for connecting to the internet when it opens) so you can multiply 25,235 by three-point-nine percent. Or you can quickly do it on a handy pocket calculator.
I don't mean to dis you totally. I can't see EVER using a TI-89 to draw slope-fields in the real world... if you are the type of person who needs a slope field drawn, you are also the type of person who brings your laptop to Big Boy to do it. But when it comes to doing simple arithmetic or quickly computing the arctangent of 24, I think that a small calculator will beat your Laptop hands down.
Similarly, if I'm thinking about some curve, it is easier for me to whip out my calculator and plot a few functions in the time it takes Maple9 to boot up.
On the other hand, do people want AOL to shelter them from the web, from the real world?
Yes. Absolutely. That is why many use it. Look at the ads - it is all about parental controls and filtering. AOL was dragged into allowing users basic things like telnet, usenet and the like kicking and screaming.
I'm not just spouting here - the parental controls and all are the REASON several people I know use it, and they leave the controls on when they, themselves use the internet. "Keep me safe."
a derivative is a derivative, no matter what field you are in
Yes and no.
If you are a pure mathematician, a derivative involves taking the limit of a difference quotient. The shortcuts (x^2 goes to 2x) are not really relevant.
If you are an engineer, you probably have already forgotten how to take the limit of a difference quotient, and you probably don't even care.
If you are a scientist, a "function" is probably not an algebraic rule, but a table of data, and a derivative is the slope between two data points.
If you are an economist or business type, a "function" is given by a graph more often than an equation, and the derivative graph is related to the graph of the function. (concave up functions have increasing derivatives, etc.)
The older calculus books tended to be purely algebraic. A student could go through the course, thinking they know calculus, and be unable to draw the graph of the derivative of a function unless they had the explicit formula. As an engineer, you know that you don't always (often?) have explicit formulas for functions - sometimes you are lucky to even have a graph.
The even older calculus books didn't even go that far - half the book was about rigorous epsilon-delta limit proofs, and then the theoretical derivative. Actually computing the derivative of x^2 was an afterthought.
The even even older calculus books did limits a different way, using differentials and introducing the "surreal" or "hyperreal" numbers, involving the "dx" as a quantity unto itself.
These changes are based on who is taking calculus, which has changed. The purpose of the course has changed as well. And there were political pressures - engineering departments were so disgusted with the "we are teaching mostly to benefit math majors" calc course that they started threatening to teach their own calc course for their own majors.
There is a lot of variation. Right behind me is a bookshelf filled with current calc books. Some are similar, and some are very different. The subject "calculus" is broad enough that there is a great deal of variety in what should be included, what should be emphasized, etc.
One more thing, if you are teaching a course in Calculus, and let people solve certain problems using a graphing calculator, you aren't really teaching them calculus, are you?
Depends on who you ask. Hence the need for a variety of books, depending on the instructor's answer to that very question.
I certainly take your point. The counter-point is "Would you teach a class in carpentry without allowing your students ever to pick up an actual hammer and do what real carpenters do with their tools?"
I'm not telling you my take on it, but I'm trying to illustrate why there are so many calculus books, with so many editions. (a teacher who is heavy into the use of technology isn't going to want a textbook that ignores the existence of calculators like the TI-92, for example)
The one thing I don't get about courses teaching basic calculus is that the material hasn't really changed much in some 10's to 100's of years
There is more "material" then would ever be covered in a first year calculus course. What has changed in the past hundred years (actually even in the past FIVE years) is the relative importance of various topics to various populations.
If, for example, applications involving slope fields started to grow in importance, it would start being emphasized more in first year calculus.
In addition, available technology does affect things. I don't want to open that whole can of worms now, but I'm sure you will agree that, for example, extracting square roots by hand is less important now than it used to be. Similary, there are things in calculus that are still important, but less so now that a graphing-calculator is less than $80.
Furthermore, student populations and majors are different. It used to be that only engineers and mathematicians took calculus, so all books were written towards that audience. (actually, earlier than that, everyone took calculus. The first elective in History was at Harvard, where students were allowed to "elect" out of calculus to take... Hebrew) So now there are calc books aimed at people in the chemistry and biology fields, etc.
If your introductory calculus course allowed you to use such technology, you probably didn't learn anything Studies and my own experiments have shown the complete opposite.
But I will give you the benefit of the doubt. Perhaps you know what you are talking about. Cite a source. What classes have you taught with technology? Have you looked at Jerry Uhl's Calculus and Mathematica course at the University of Illinois? What do you think about the Maple Labs that come with the adoptor's package? What examples of multivariate functions where the limit does not exist, yet equals zero on any parabolic path do you have the students investigate without technology?
You are on the money. I hate it when someone does something creative, and the TV watchers he works with tell him "you must have a lot of time on your hands" or "get a life" or whatever.
Issac Asimov has the right to tell me to "get a life." But someone whose seen every episode of Law and Order does not.
I've always pictured him sounding exactly like Simon Jones (I think that's his name) and when I saw the show I started picturing him as looking exactly like him - it will be hard for me to change
It is that way for every Ph.D. thesis in the United States. It has to do with copyright issues that were at the time, frankly, are over my head. I don't know if I would understand them better now.
Here is a slashdot story on the issue - it isn't the one I remember reading; there may be more than one.
How about educating kids to write and think while they're still in gradeschool instead of training them to pass standardized tests? Then maybe they wouldn't be afraid to write their own papers. Never happen. GWB got his way on No Child Left Behind - and Rush Limbaugh and Ann Coulter like it. The libertarians, who should be outraged, are in hypocritcal silence, and the Democratic Presidential candidates are doing their standard strategy of pulling down their pants and bending over.
No Child Left Behind is law, and things are going to get worse.
I remember being asked to submit a paper electronically once. I happily compiled by printing the paper, and then scanning it at low DPI into a PDF file without using OCR. They couldn't say anything because they asked for it in 'electronic format' without specifying further.
How proud you are! You were able to deliberately make someone's life more difficult, and I'm sure you bragged about it to your friends, and they smiled and told you how "cool" you were that you made things tougher on a grown-up.
A professor has a certain amount of time, and many professional duties. Scholarship, teaching, and service. By asking you to submit things electronically, the professor was hoping to spend more time doing what you are paying him for, reading your work carefully. But yes, by finding a loophole, you were able to take his time away from grading the smart kids' papers so he could read your smartass paper.
And now you brag about it in slashdot. Someday you may be an adult in a position where you are asking for results from somebody, and I hope you don't have to deal with "You didn't say they couldn't be in base 8" "You didn't say they had to be in English" "You didn't say I couldn't smear excrement on them first"
It annoys me when people deliberately make other people's jobs harder.
I think the biggest problem here is probably your lack of respect for undergrads. If the university was ordering PHD students to turn over their dissertations free of charge to an external, for profit cpmpany, I'm sure you could easily see what's wrong with that.
I hate to break this to you, but this is exactly the case. My dissertation, and everybody else's, is currently available for purchase by a for-profit company, and there is not a damn thing I can do about it. Check slashdot archives for more details - this was a story a while ago. Now it is just accepted.
Students are subject to peer pressure. Everyone is subject to it. But if your classmate cheats, that doesn't mean that you will too. Granted, where one's view differs on this is dependant on one's belief/trust/faith in other humans.
I agree with this statement. But you should be aware it isn't just peer pressure here - if the professor grades "on the curve" (I don't) then it isn't just social pressure - your grade will suffer if everyone is downloading professionally written essays and you are blathering on with your freshman-level writing skills.
If the professor is basing your grade, in whole or in part, on the work of your classmates, then s/he has the responsibility to do something to enforce cheating rules.
While that may be true, why deny students access to the tools they'll be using in their day-to-day lives in future? Never before have our lives, personal and professional, been so dominated by a particular implement as the computer.
I agree with you. I was responding to the previous poster, who made the ridiculous exaggeration "Unless other parents get vocal and oppose this luddite activity, they'll further the progress of their children towards a future job at Burger King." It stuck out particularly because the rest of the post was intelligent.
Why can't people discuss complex things, such as educational policy, without having to make wildass claims about the role of technology?
You say: "Socialization isn't vital to a child's ability to learn fractions or write prose. It is, however, vital for their survival in the Real World." Obviously this is true. And children have been learning socialization just fine on the playground, playing with toys and other children, for centuries. You cannot conclude "wireless technology is now important, but soon crucial to their overall education." from this. CRUCIAL? Come on, give me a break. I will grant you "NICE", I will grant you "USEFUL", I will grant you "HELPFUL" but why do you have to go and go for "CRUCIAL"? If the computers are in a computer lab, then the fifth graders will suddenly no longer be able to learn using computers and the internet? Spare me.
Think about this seriously - something can be Good without being Crucial. Banning wireless for fifth graders can be Stupid without causing them all to grow up having to work at Burger King.
I'll go further. Ideally a fifth grader should have a classroom with a small class size, a well-trained, excellent teacher, access to computers, and a wireless connection. If funding dictates that the child can only have three of the four, which do you think is the least "crucial"?
Their students will lack the access to information that other students might have. Unless other parents get vocal and oppose this luddite activity, they'll further the progress of their children towards a future job at Burger King.
Why did you have to go and sully such an intelligent, thoughtful post with silly hyperbole?
You know, I have a hunch that it is possible, possible, if a teacher is sufficiently brilliant, to get an elementary school education without a wireless connection. A good enough education that it actually is a step AWAY from Burger King.
Slashdot Mirror
Calculus is more than solving derivatives.
If politicians understood calculus, then they would understand the relationship of the budget deficit to the national debt (hint: one is the derivative of the other) and not get so excited when the rate of increase of the budget deficit is beginning to slow down.
One says you should be able to do everything by hand (as every good mathematician should) and the calculator is simply a guide for some of the tougher problems.
Really? I know some astounding mathematicians who are not able to do square-root extraction by hand. They forgot the algorithim to compute sqrt(11) to ten decimal places. (It is similar to the long-division algorithm, and used to be taught to every student)
And, technically, you should not be adding or multiplying numbers unless you can derive the concept of "number" from the five Peano axioms using set theory. Yet I know some lazy mathematicians who never took enough set theory to do this "by hand." Yet they get by.
Calculators are not like cliff notes. Mathematics is not all about the arithmetic. Calculators are more like word-processors, that allow us to formulate our thoughts on books without having to stop every five minutes to sharpen our nibs, grind our own ink, and change blotters.
I was the tech-editor on a book about this calculator, so I was playing with a prototype for the past two months.
I thought that Cabri Jr and all were just toys, and would not be worth a damn if I were trying to use the calculator to either learn or actually do work. The resolution was not good enough to gain insight into any sort of complex figure, and it was overall a pain in the ass to use.
They also have another Geometry program on it that fares no better. I would never use a pocket calculator screen to try to do geometry.
Quick and dirty portability.
Oh college student, the day will come when you have to meet with your Realtor, your Lawyer, your Insurance agent. They will shoot numbers at you fast and furious while the two of you sit (perhaps somewhere like a coffee shop or Perkins - my realtor always bought me lunch).
Yes, you COULD whip out your laptop, clear some space on their desk or the booth, wait for it to boot up, open up Maple9 (click "no" for connecting to the internet when it opens) so you can multiply 25,235 by three-point-nine percent. Or you can quickly do it on a handy pocket calculator.
I don't mean to dis you totally. I can't see EVER using a TI-89 to draw slope-fields in the real world... if you are the type of person who needs a slope field drawn, you are also the type of person who brings your laptop to Big Boy to do it. But when it comes to doing simple arithmetic or quickly computing the arctangent of 24, I think that a small calculator will beat your Laptop hands down.
Similarly, if I'm thinking about some curve, it is easier for me to whip out my calculator and plot a few functions in the time it takes Maple9 to boot up.
He was reading Atlas Shrugged and saying "why should I?" when asked to pass the salt.
On the other hand, do people want AOL to shelter them from the web, from the real world?
Yes. Absolutely. That is why many use it. Look at the ads - it is all about parental controls and filtering. AOL was dragged into allowing users basic things like telnet, usenet and the like kicking and screaming.
I'm not just spouting here - the parental controls and all are the REASON several people I know use it, and they leave the controls on when they, themselves use the internet. "Keep me safe."
a derivative is a derivative, no matter what field you are in
Yes and no.
If you are a pure mathematician, a derivative involves taking the limit of a difference quotient. The shortcuts (x^2 goes to 2x) are not really relevant.
If you are an engineer, you probably have already forgotten how to take the limit of a difference quotient, and you probably don't even care.
If you are a scientist, a "function" is probably not an algebraic rule, but a table of data, and a derivative is the slope between two data points.
If you are an economist or business type, a "function" is given by a graph more often than an equation, and the derivative graph is related to the graph of the function. (concave up functions have increasing derivatives, etc.)
The older calculus books tended to be purely algebraic. A student could go through the course, thinking they know calculus, and be unable to draw the graph of the derivative of a function unless they had the explicit formula. As an engineer, you know that you don't always (often?) have explicit formulas for functions - sometimes you are lucky to even have a graph.
The even older calculus books didn't even go that far - half the book was about rigorous epsilon-delta limit proofs, and then the theoretical derivative. Actually computing the derivative of x^2 was an afterthought.
The even even older calculus books did limits a different way, using differentials and introducing the "surreal" or "hyperreal" numbers, involving the "dx" as a quantity unto itself.
These changes are based on who is taking calculus, which has changed. The purpose of the course has changed as well. And there were political pressures - engineering departments were so disgusted with the "we are teaching mostly to benefit math majors" calc course that they started threatening to teach their own calc course for their own majors.
There is a lot of variation. Right behind me is a bookshelf filled with current calc books. Some are similar, and some are very different. The subject "calculus" is broad enough that there is a great deal of variety in what should be included, what should be emphasized, etc.
One more thing, if you are teaching a course in Calculus, and let people solve certain problems using a graphing calculator, you aren't really teaching them calculus, are you?
Depends on who you ask. Hence the need for a variety of books, depending on the instructor's answer to that very question.
I certainly take your point. The counter-point is "Would you teach a class in carpentry without allowing your students ever to pick up an actual hammer and do what real carpenters do with their tools?"
I'm not telling you my take on it, but I'm trying to illustrate why there are so many calculus books, with so many editions. (a teacher who is heavy into the use of technology isn't going to want a textbook that ignores the existence of calculators like the TI-92, for example)
The one thing I don't get about courses teaching basic calculus is that the material hasn't really changed much in some 10's to 100's of years
There is more "material" then would ever be covered in a first year calculus course. What has changed in the past hundred years (actually even in the past FIVE years) is the relative importance of various topics to various populations.
If, for example, applications involving slope fields started to grow in importance, it would start being emphasized more in first year calculus.
In addition, available technology does affect things. I don't want to open that whole can of worms now, but I'm sure you will agree that, for example, extracting square roots by hand is less important now than it used to be. Similary, there are things in calculus that are still important, but less so now that a graphing-calculator is less than $80.
Furthermore, student populations and majors are different. It used to be that only engineers and mathematicians took calculus, so all books were written towards that audience. (actually, earlier than that, everyone took calculus. The first elective in History was at Harvard, where students were allowed to "elect" out of calculus to take... Hebrew) So now there are calc books aimed at people in the chemistry and biology fields, etc.
My highly excellent physics teacher (Leonid Minkin) reads the problem from the book, writes it on the board, and then solves it
He sounds like a good teacher. A great teacher would write it on the board, and get YOU to solve it.
If your introductory calculus course allowed you to use such technology, you probably didn't learn anything Studies and my own experiments have shown the complete opposite.
But I will give you the benefit of the doubt. Perhaps you know what you are talking about. Cite a source. What classes have you taught with technology? Have you looked at Jerry Uhl's Calculus and Mathematica course at the University of Illinois? What do you think about the Maple Labs that come with the adoptor's package? What examples of multivariate functions where the limit does not exist, yet equals zero on any parabolic path do you have the students investigate without technology?
Quality textbooks are well worth keeping, such as James Stewart's Calculus texts.
And they now come with a CD with my voice on it!
Which book?
You are on the money. I hate it when someone does something creative, and the TV watchers he works with tell him "you must have a lot of time on your hands" or "get a life" or whatever.
Issac Asimov has the right to tell me to "get a life." But someone whose seen every episode of Law and Order does not.
I've always pictured him sounding exactly like Simon Jones (I think that's his name) and when I saw the show I started picturing him as looking exactly like him - it will be hard for me to change
I saw it recently, too - having seen it before, decades ago, when it was shown on PBS.
How did the actors get so young? Younger than me, even?
It is that way for every Ph.D. thesis in the United States. It has to do with copyright issues that were at the time, frankly, are over my head. I don't know if I would understand them better now.
/ 20 19202&mode=nested&tid=98
Here is a slashdot story on the issue - it isn't the one I remember reading; there may be more than one.
http://yro.slashdot.org/article.pl?sid=00/08/14
DJS
How about educating kids to write and think while they're still in gradeschool instead of training them to pass standardized tests? Then maybe they wouldn't be afraid to write their own papers. Never happen. GWB got his way on No Child Left Behind - and Rush Limbaugh and Ann Coulter like it. The libertarians, who should be outraged, are in hypocritcal silence, and the Democratic Presidential candidates are doing their standard strategy of pulling down their pants and bending over.
No Child Left Behind is law, and things are going to get worse.
I remember being asked to submit a paper electronically once. I happily compiled by printing the paper, and then scanning it at low DPI into a PDF file without using OCR. They couldn't say anything because they asked for it in 'electronic format' without specifying further.
How proud you are! You were able to deliberately make someone's life more difficult, and I'm sure you bragged about it to your friends, and they smiled and told you how "cool" you were that you made things tougher on a grown-up.
A professor has a certain amount of time, and many professional duties. Scholarship, teaching, and service. By asking you to submit things electronically, the professor was hoping to spend more time doing what you are paying him for, reading your work carefully. But yes, by finding a loophole, you were able to take his time away from grading the smart kids' papers so he could read your smartass paper.
And now you brag about it in slashdot. Someday you may be an adult in a position where you are asking for results from somebody, and I hope you don't have to deal with "You didn't say they couldn't be in base 8" "You didn't say they had to be in English" "You didn't say I couldn't smear excrement on them first"
It annoys me when people deliberately make other people's jobs harder.
I think the biggest problem here is probably your lack of respect for undergrads. If the university was ordering PHD students to turn over their dissertations free of charge to an external, for profit cpmpany, I'm sure you could easily see what's wrong with that.
I hate to break this to you, but this is exactly the case. My dissertation, and everybody else's, is currently available for purchase by a for-profit company, and there is not a damn thing I can do about it. Check slashdot archives for more details - this was a story a while ago. Now it is just accepted.
Students are subject to peer pressure. Everyone is subject to it. But if your classmate cheats, that doesn't mean that you will too. Granted, where one's view differs on this is dependant on one's belief/trust/faith in other humans.
I agree with this statement. But you should be aware it isn't just peer pressure here - if the professor grades "on the curve" (I don't) then it isn't just social pressure - your grade will suffer if everyone is downloading professionally written essays and you are blathering on with your freshman-level writing skills.
If the professor is basing your grade, in whole or in part, on the work of your classmates, then s/he has the responsibility to do something to enforce cheating rules.
A good student response would be to collect older papers [like the professor's school papers!] and submit them to services as well.
You meant this as a joke, but this would actually be a fun thing to do to ones professors.
I just had to stand up and be counted along with the others. Gator is spyware.
you.
are.
brilliant.
While that may be true, why deny students access to the tools they'll be using in their day-to-day lives in future? Never before have our lives, personal and professional, been so dominated by a particular implement as the computer.
I agree with you. I was responding to the previous poster, who made the ridiculous exaggeration "Unless other parents get vocal and oppose this luddite activity, they'll further the progress of their children towards a future job at Burger King." It stuck out particularly because the rest of the post was intelligent.
Why can't people discuss complex things, such as educational policy, without having to make wildass claims about the role of technology?
You say: "Socialization isn't vital to a child's ability to learn fractions or write prose. It is, however, vital for their survival in the Real World." Obviously this is true. And children have been learning socialization just fine on the playground, playing with toys and other children, for centuries. You cannot conclude "wireless technology is now important, but soon crucial to their overall education." from this. CRUCIAL? Come on, give me a break. I will grant you "NICE", I will grant you "USEFUL", I will grant you "HELPFUL" but why do you have to go and go for "CRUCIAL"? If the computers are in a computer lab, then the fifth graders will suddenly no longer be able to learn using computers and the internet? Spare me.
Think about this seriously - something can be Good without being Crucial. Banning wireless for fifth graders can be Stupid without causing them all to grow up having to work at Burger King.
I'll go further. Ideally a fifth grader should have a classroom with a small class size, a well-trained, excellent teacher, access to computers, and a wireless connection. If funding dictates that the child can only have three of the four, which do you think is the least "crucial"?
Their students will lack the access to information that other students might have. Unless other parents get vocal and oppose this luddite activity, they'll further the progress of their children towards a future job at Burger King.
Why did you have to go and sully such an intelligent, thoughtful post with silly hyperbole?
You know, I have a hunch that it is possible, possible, if a teacher is sufficiently brilliant, to get an elementary school education without a wireless connection. A good enough education that it actually is a step AWAY from Burger King.