[math-fun] Is algebra necessary?
For what it is worth, I think it would be absolutely absurd to allow getting a CS college degree without knowing calculus. I also have a hard time accepting the idea that general people do not need to know and should not be taught algebra. But the best argument for that stance might be (which is not mentioned at all in the newspaper of course) the advent of software like mathematica. I think that technology like that PERHAPS could be used to completely change traditional math education and both speed it up and make it better. Optimally, you'd learn the principles and ideas while skipping the drudgery and errors. I'm not sure if that goal is feasible, but I am fairly sure that the educators and software writers haven't yet put in a high quality attempt to accomplish it. There have been low-quality attempts which I never saw convincing evidence worked better than 1950s style teaching and may work worse. One thing I'd like to see in education is controlled experiments, like educate class #K with method #K. This would be easy to do in large universities. But I've never seen any ever do it.
I also have a hard time accepting the idea that general people do not need to know and should not be taught algebra. But the best argument for that stance might be (which is not mentioned at all in the newspaper of course) the advent of software like mathematica.
The intersection of people who struggle with basic algebra and the people who use Mathematica has a cardinality equal to the infimum of positive reals. :P Sincerely, Adam P. Goucher
I disagree. Very few of the people who work in computer related fields really need calculus. If there were one essential course I would vote, strongly, for linear algebra. I doubt, seriously, that 98% (or more) of people doing computer programming need to use anything from Calculus. They certainly need to understand the idea of a function, but really only on a discrete set. Maybe they need a qualitative understand of continuity, and really know what exponential means (as opposed to its use in the press -- where it just means "a lot"). One of the big failings in Calculus courses is that they don't do enough to build up their student's intuition about the qualitative behavior of functions. And as far as linear algebra, I was shocked (many years ago) when one of my colleagues at IBM, who had a B.S. in math from NYU and a Ph.D. from Berkeley in CS (and is today on the National Academy of Engineering, an IEEE Fellow, etc. etc.) had really deficient knowledge in linear algebra. Knowing it better would have helped him a lot. Victor On Mon, Jul 30, 2012 at 1:03 PM, Warren Smith <warren.wds@gmail.com> wrote:
For what it is worth, I think it would be absolutely absurd to allow getting a CS college degree without knowing calculus.
I also have a hard time accepting the idea that general people do not need to know and should not be taught algebra. But the best argument for that stance might be (which is not mentioned at all in the newspaper of course) the advent of software like mathematica. I think that technology like that PERHAPS could be used to completely change traditional math education and both speed it up and make it better. Optimally, you'd learn the principles and ideas while skipping the drudgery and errors. I'm not sure if that goal is feasible, but I am fairly sure that the educators and software writers haven't yet put in a high quality attempt to accomplish it. There have been low-quality attempts which I never saw convincing evidence worked better than 1950s style teaching and may work worse. One thing I'd like to see in education is controlled experiments, like educate class #K with method #K. This would be easy to do in large universities. But I've never seen any ever do it.
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On Mon, Jul 30, 2012 at 4:41 PM, Victor Miller <victorsmiller@gmail.com> wrote:
I disagree. Very few of the people who work in computer related fields really need calculus. If there were one essential course I would vote, strongly, for linear algebra.
That's a pretty good one; I'd say statistics and graph theory are pretty fundamental to the practice, too. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Personally I consider education a completely different way to most - to me it's about training the brain to think and not about learning "facts" As far as training the brain to think is concerned logic and mathematics are IMO the most fundamental - and beyond those philosophy. So as far as I'm concerned every effort should be made to take every child's education as far as possible in the fields of logic, math and philosophy in particular. Not to do this, and reducing this will (obviously) lead to a rise in Creationism and new-age superstitious nonsense - this is already happening !! To me the most important change in thought process required is an appreciation of the idea of limits, and algebra and calculus are great for verifying the idea of limits - specifically of course the basic analytical proof of differentiation. On 31 Jul 2012, at 00:52, Mike Stay wrote:
On Mon, Jul 30, 2012 at 4:41 PM, Victor Miller <victorsmiller@gmail.com> wrote:
I disagree. Very few of the people who work in computer related fields really need calculus. If there were one essential course I would vote, strongly, for linear algebra.
That's a pretty good one; I'd say statistics and graph theory are pretty fundamental to the practice, too. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
Many of you might find this article interesting: http://www.dailykos.com/story/2012/08/03/1109331/-In-Laymen-s-Terms-a-segue-...
I keep hoping that someone will do a better job rebutting the Times editorial. But I haven't even been able to come up with a good elementary example for the use of the quadratic formula. (Perhaps the best uses of the quadratic formula come with trig; but somehow, I can't see convincing the general population about trigonometry.) Maybe he's right, after all... ;-) At 05:42 AM 8/4/2012, Robert Baillie wrote:
Many of you might find this article interesting: http://www.dailykos.com/story/2012/08/03/1109331/-In-Laymen-s-Terms-a-segue-...
Why concentrate on the quadratic. Everyone deals with loans and interest rates and investments. I'd say exponentials and logarithms are more widely useful than polynomials. Brent Meeker On 8/5/2012 4:52 PM, Henry Baker wrote:
I keep hoping that someone will do a better job rebutting the Times editorial. But I haven't even been able to come up with a good elementary example for the use of the quadratic formula. (Perhaps the best uses of the quadratic formula come with trig; but somehow, I can't see convincing the general population about trigonometry.)
Maybe he's right, after all... ;-)
At 05:42 AM 8/4/2012, Robert Baillie wrote:
Many of you might find this article interesting: http://www.dailykos.com/story/2012/08/03/1109331/-In-Laymen-s-Terms-a-segue-...
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I think of the primary justification for polynomials is their simplicity (Horner scheme: evaluate using only addition and multiplication) and their ability to interpolate any smooth function (the Weierstrass theorem). No disagreement on the value of logarithms in basic finance, though. Charles Greathouse Analyst/Programmer Case Western Reserve University On Mon, Aug 6, 2012 at 12:33 AM, meekerdb <meekerdb@verizon.net> wrote:
Why concentrate on the quadratic. Everyone deals with loans and interest rates and investments. I'd say exponentials and logarithms are more widely useful than polynomials.
Brent Meeker
On 8/5/2012 4:52 PM, Henry Baker wrote:
I keep hoping that someone will do a better job rebutting the Times editorial. But I haven't even been able to come up with a good elementary example for the use of the quadratic formula. (Perhaps the best uses of the quadratic formula come with trig; but somehow, I can't see convincing the general population about trigonometry.)
Maybe he's right, after all... ;-)
At 05:42 AM 8/4/2012, Robert Baillie wrote:
Many of you might find this article interesting:
http://www.dailykos.com/story/2012/08/03/1109331/-In-Laymen-s-Terms-a-segue-...
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From: Warren Smith <warren.wds@gmail.com>
To: math-fun@mailman.xmission.com Sent: Monday, July 30, 2012 10:03 AM Subject: [math-fun] Is algebra necessary?
For what it is worth, I think it would be absolutely absurd to allow getting a CS college degree without knowing calculus.
I also have a hard time accepting the idea that general people do not need to know and should not be taught algebra. But the best argument for that stance might be (which is not mentioned at all in the newspaper of course) the advent of software like mathematica. I think that technology like that PERHAPS could be used to completely change traditional math education and both speed it up and make it better. Optimally, you'd learn the principles and ideas while skipping the drudgery and errors. I'm not sure if that goal is feasible, but I am fairly sure that the educators and software writers haven't yet put in a high quality attempt to accomplish it. There have been low-quality attempts which I never saw convincing evidence worked better than 1950s style teaching and may work worse. One thing I'd like to see in education is controlled experiments, like educate class #K with method #K. This would be easy to do in large universities. But I've never seen any ever do it. _______________________________________________
I'd like to see the same principle applied to grades K-12: school A uses method A, school B uses method B, etc. But instead of making the children be guinea pigs, families get to freely choose schools. And, the selection of different methods is not dictated by the educational establishment and teachers unions.
-- Gene
I totally agree that, instead of debating the best way to teach math, many educationa experiments need to be performed. Perhaps none so radical that they risk leaving the students virtually without the knowledge to be conveyed. And with large enough samples that accidents of who's teaching what won't noticeable affect results. --Dan On 2012-07-31, at 9:15 AM, Eugene Salamin wrote:
I'd like to see the same principle applied to grades K-12: school A uses method A, school B uses method B, etc. But instead of making the children be guinea pigs, families get to freely choose schools. And, the selection of different methods is not dictated by the educational establishment and teachers unions.
This experiment is being performed as we speak. Unfortunately, most of the interesting parts are being conducted in Far Eastern languages. China now has a middle class approx. the same size as the U.S. and the E.U. -- approx. 300M people. But China is graduating 5-10x the number of engineers that the U.S./E.U. are. We can argue about the quality, but there are one heck of a lot of intelligent people in a population of 1.3-1.6 billion. The _only_ thing the U.S. has going for it right now are its demographics: the U.S. population is still growing, while that of the E.U. is not being replaced, and the Chinese demographics are going to turn completely upside down in 2020. Whatever problem the US/EU is going to have with a graying population is going to be magnified enormously in China, as its "one child policy" becomes "one child to support large numbers of retirees" policy. Too bad that political scientists can't solve this equation; they don't know a polynomial from an exponential. (Supposedly true story from the 1980's debate on "Star Wars": one of the scientists testified that some number needed to be 10^20 instead of 10^10; one of the politicians said "we're half way there, then!".) At 11:47 AM 7/31/2012, Dan Asimov wrote:
I totally agree that, instead of debating the best way to teach math, many educationa experiments need to be performed. Perhaps none so radical that they risk leaving the students virtually without the knowledge to be conveyed. And with large enough samples that accidents of who's teaching what won't noticeable affect results.
--Dan
On 2012-07-31, at 9:15 AM, Eugene Salamin wrote:
I'd like to see the same principle applied to grades K-12: school A uses method A, school B uses method B, etc. But instead of making the children be guinea pigs, families get to freely choose schools. And, the selection of different methods is not dictated by the educational establishment and teachers unions.
participants (11)
-
Adam P. Goucher -
Charles Greathouse -
Dan Asimov -
Dave Makin -
Eugene Salamin -
Henry Baker -
meekerdb -
Mike Stay -
Robert Baillie -
Victor Miller -
Warren Smith