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How Much Math Do We Really Need?
Pickens writes "G.V. Ramanathan, a professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago, writes in the Washington Post that although a lot of effort and money has been spent to make mathematics seem essential, unlike literature, history, politics and music, math has little relevance to everybody's daily life. 'All the mathematics one needs in real life can be learned in early years without much fuss,' writes Ramanathan. 'Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.' Ramanathan says that the marketing of math has become similar to the marketing of creams to whiten teeth, gels to grow hair and regimens to build a beautiful body, but even with generous government grants over the past 25 years, countless courses, conferences, and books written on how to teach teachers to teach, where is the evidence that these efforts have helped students? A 2008 review by the Education Department found that the nation is at 'greater risk now' than it was in 1983, and the National Assessment of Educational Progress math scores for 17-year-olds have remained stagnant since the 1980s (PDF). Meanwhile those who do love math and science have been doing very well and our graduate schools are the best in the world. 'As for the rest, there is no obligation to love math any more than grammar, composition, curfew or washing up after dinner. Why create a need to make it palatable to all and spend taxpayers' money on pointless endeavors without demonstrable results or accountability?'"
We could use, at least, a basic understanding of probability..
One part of math all people should be required to understand is exponential growth.
It might make people realize that population growth, resource consumption, etc. can't keep increasing at current levels without severe corrections in the somewhat close future.
Speaking as someone with a degree in English Literature, I can safely say that I've only used math two times in my life: when learning it in school, when counting my kids at night, and when doing my taxes.
Math needs you.
Yes! How can statistics possibly be useful in today's world? Or an understanding of continuously changing variables, like mortgages?
If more people understood math at that level, a lot fewer of us would be constantly fooled by financial flim-flam and political bullshit.
I'm a professor at a liberal arts college. I feel that music and literature is important, but there's no way I can say it's strictly more important than math or sciences. Equally important to being a well-rounded person? Sure.
Out of idle curiosity, when did "ramblings of a random guy" become "news"?
For me personally, learning advanced mathematics (calculus and beyond) has changed my thinking process from a purely creative, English-oriented one to an objective, analytical outlook. The true understanding of how mathematical principals work--what a derivative is and not merely how to calculate it--has shown me the power of mathematical, logical analysis. As an English major, I came to a point where I was not sure whether or not I wanted to continue taking math courses (as I will need almost no math beyond arithmetic in my life), but I came to the conclusion that the mindset mathematics gives me rather than the quantitative abilities it provides is what matters in my education, and I therefore encourage anybody to continue studying math well past the point in which the skills become irrelevant.
unlike literature, history, politics and music, math has little relevance to everybody's daily life.
Now we'll be comparing the uselessness of those subjects. Nice troll, though.
In base 4!
Nobodies Prefect
Tidbits for Techs Technology Blog
... as long as we replace it with logic and critical thinking. And finance. I don't care if someone can't do derivatives but everyone should understand the implications of credit card interest.
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
The one with that chick that is going to fix up her friend with the hunky mathematician. She tells her not to use her calculator so her calculus stays sharp. But she doesn't listen and uses her calculator all week, but the night before her big date she uses Crest Mathstrips and gets the hunky mathematician.
Math is not just calculations. Even people who do not need to apply mathematics in their day to day lives need it to understand what they're working with. Math ist structure and logic. If you don't know math, you can't know mechanics, physics, chemistry, computers, accounting. You may be able to do what you're told in any of these fields, but to know what you're doing you need math.
Why teach History? Few people need that in their daily life or jobs. Why teach music? Other arts? Science? Few people need Chemistry or Physics in their daily lives... etc.
Because Mathematics, like the rest, increase our fundamental understanding of the world around us. It's part of creating critically thinking individuals who have more to give back to society than a simple job skill they learned at an early age. Or at least give them the opportunity... take away fundamental education, they no longer have the choice.
How does literature or music get labeled as essential and not math? We learn math so we can build things that let us have time to create literature and music. Sure not everyone needs it (though probability would certainly help), but no one *needs* literature or music, its just the sort of thing we *want*. Some day when we finish automating all the jobs we'll all get to devote all our time to creating art... for our robotic overlords.
refactor the law, its bloated, confusing and unmaintainable.
A knowledge of math does not simply improve your ability to solve math problems. It is not the direct application of mathematics on everyday life that is most beneficial, but the analytical and conceptual skill set gained by learning higher level math. The real benefit is that when you study "literature, history, politics and music," you can actually conceptualize the complex interconnections and processes at work in a truly quantifiable way.
I learned computer programming at a very young age, and today, as an electrical engineering student, I am at a great advantage over my peers because of my ability to conceptualize and understand processes. The core of that is my learned ability with mathematics, both algebraic and algorithmic. It also spills over into my humanities courses, where the method of formalizing concepts central to the field of mathematics vastly improves my ability to synthesize complex texts. Of course, that's partly because nothing is as hard to understand as undocumented code, and partly because I have the mathematical foundation to build and conceptualize systems.
If anything, we need to push mathematics younger and younger, and complement that with computer programming courses. I know my 2 year old son will be getting weekly lessons from me on these subjects when he grows up, without question.
If the rest of the country continues to decline on the international standard of education, I know that at least my children will not.
When you're afraid to download music illegally in your own home, then the terrorists have won!
Does education in "literature, history, politics and music" have any "demonstrable results or accountability"? Indeed, in my profession, I use my math education on a daily (if not hourly) basis, while I can't remember a single instance of literature, history, politics and music having any utility or relevance. My sister, a nursing student, has seen much of her class drop away because they couldn't do the simple math that they need for their job.
Math can be useful for much more professions than pretty much any subject taught in school, short of basic reading skills. Literature, history, politics and music are, frankly, just enrichments.
am glad I was taught math. I wouldn't be able to do half the stuff I do right now if I hadn't been.
Music and literature may be popular, but they are hardly essential. And history's importance mainly comes from informing politics.
Do most people need to know multivariable calculus? No. But one thing most people are missing is an understanding of basic statistics and logic. Statisticians don't help much. Courses need to be more than just memorizing a bunch of statistical formulas. People need to understand why basic statistical reasoning works. If people don't have that basic philosophical understanding of why statistics work, then they'll just forget all about the formulas they were forced to memorize after the course is over.
These types of courses should be essential for all, but they aren't even available until college--and even then they're optional.
Most people don't directly use anything they learn in school. This goes deep into specialized programs such as engineering, even--the lessons from textbooks just are not applied directly. Does that mean all those programs are a waste of time? Might as well get people fresh out of HS. They'll be four years younger (and cheaper!) and not be especially behind in terms of what they have to learn.
Of course, what I propose above is ridiculous! Degree programs are about training people how to learn that field, not necessarily for teaching them the field directly. An employer doesn't look at a high GPA as a sign that you already know so much. They see it as that you are capable of learning, doing so at a high level, and caring enough to do so.
People need mathematics not because they're going to go out and compute all these things every day. Even engineers don't use all that much math beyond algebra on a daily basis. Rather, mathematics is a logical progression of steps. There are a list of rules and operations one can do, and needs to choose which of those to apply and then do so correctly. Every day, people are confronted with systems full of rules they have to follow, and need to know how to maneuver through those systems optimally. Mathematics teaches that.
It's unfortunate that most people never get to the truly higher mathematics, where proofs are taught. Being able to see the subtlety in arguments (and language!) is an invaluable skill for anyone. The rigor and logic of proof-based mathematics would be far more valuable than the symbol manipulation of lower levels. However, most people never get to that level, having given up far before then. At times I wonder whether the whole of people is actually capable of doing it.
Speaking as someone with a degree in Physics, I can safely say that I've only used literary analysis one time in my life: when learning it in school.
Yeah, like why bother? We're all going to die anyway. I did not RTFA but the summary is horribly defeatist in tone.
http://www.acetonestudio.com
They spend too much time teaching crap and instead skip over the important stuff
Why the f... did I learn trigonometric equations ins high school?! Really... Polynomial equation solving?!
Derivatives would be much more useful. And don't beat around the bush on limits, etc, that's math "self-indulgence", go directly to derivatives, simple, done
If they cut the crap and stick with the essentials, then maybe people will learn better. Maybe can they shave a year from the school curriculum so that students can go and study what interests them.
how long until
May be one can learn from people in :
http://hi-in.facebook.com/topic.php?uid=2204624701&topic=9478
Math is important for understanding why math is important. Which in turn allows you to see that math is important for being able to reason in a structured and abstract way about the world. Many people confuse math with arithmethic, algebra, trigonometry and calculus because these were all labeled math when they were students. Nothing could be farther from the truth. At its foundation, math is very closely tied with logic in that it is deductive rather than inductive, and you use it to prove complex assertions by stitching together smaller components you already know are true. The fact that with this system you can go on and prove the validity of the theoretical tools that you use to build a bridge that stays up or to make an airplane that flies or even to understand the best way to invest your own money is what makes math not only important but also amazing...
My book: Friendly F#, fun with game development and XNA; my game: Galaxy Wars by VSTeam; my gamedev language: Casanova.
The languages we know affect what thoughts we can think. While it is very zen to say that words hide meaning, empirical evidence seems to indicate that we cannot conceive of ideas that we do not have language to express. Math can express most anything which allows for thoughts right up to the limits of our hardware. It seems like this is also a good reason to learn a human language with different roots than your native one, but I have not done that yet, so I couldn't say.
refactor the law, its bloated, confusing and unmaintainable.
Obviously we all need some math (and as many here - myself included - are engineers, we know that a small portition of the people need more math)... But how much? Really, does average person ever have to deal with integrals, derivations... or nearly any other area of abstract algebra... after graduating? Everyone needs some very basich math (when shopping, dealing with loans, etc... But the type of math needed for that sort of things have been dealt with by sixth grade. If the point is that many still don't know them well enough, teaching more advanced subjects doesn't seem like a good solution.
Math should be taught for it's application of logic, not the memorization of formulas and algorithms. The average person DOES need to be able to apply logic on a daily basis. Certainly people do not use the quadratic equation daily, but the same mental abilities to derive the formula are useful on a daily basis.
Due to current culture, people do need to understand statistics. This is because mainstream media uses people's lack of fundamental understanding of statistics to confuse them.
Calculus is filled with contrived application like related rates. Get rid of those! Many integration techniques are important for theoretical reasons and have been removed. Get rid of most of the garbage about area and volume of surfaces of revolution. One would be adequete - \int \pi f(x)^2 dx. Shells and washers are riduculous. I could go on and on...
I use math (including some advanced stuff) every day. And, I am not talking about work. Literature, history, politics and music, not so much.
What happens in an advanced industrial society where most people are functionally innumerate, and have difficulty reading tables and graphs?
Does democracy work correctly when people cannot evaluate economic data for themselves, but merely vote along religious/ethnic/ideological lines?
If the campaign ads for these midterms are any indication, it's a no.
I guess it takes a mathematician to say what most people instinctively know: beyond basic math education, there is zero burning need for much math education when it comes to most people. We DO need some expanded math education, but not the kind that government and industry pushes in high schools and colleges so relentlessly. Most people forced to take Trigonometry, Calculus, etc, will only resent it it, hate the experience, and never use what they learn. The quite insane push to force more students into science and engineering... and the predictably dismal results of that push... should be abolished, and stat. Those that love advanced math, or merely those that are curious, will never need a government sponsored ad campaign to take a calculus class.
So what kinds of math DO most people need more of in High School? Practical maths dealing everyday problems, especially finances. Perhaps if more people knew how to calculate a simple mortgage, governments and banks and interested parties wouldn't have been able to sell subprime loans so easily. Getting the average man to understand interest rates will have a far more positive effect then making him sit through an algebra class he neither needs nor cares about.
Life is hard, and the world is cruel
As a programmer, I find I am using math almost constantly, including the calculus and linear algebra courses I took in post secondary. A broad knowledge of math has been helpful to me in inventing ways to model certain types of problems I've had occasion to run into that I suspect would have taken me much longer to write (and probably been much less elegant) otherwise.
On a more general note, I have met more than a disconcerting number of grown adults who cannot divide a three-digit number by 2 without using a calculator, or even just add a pair of 2 digit numbers in their head. Is it essential? Well, probably not... but if you don't bother to learn the basics you are going to inevitably come across as someone who should never have been allowed to graduate high school. Judgemental? Possibly. It's still reality though.
File under 'M' for 'Manic ranting'
Danica McKellar said so, and she's prettier than G.V. Ramanathan.
answer: none.
we survived without math thousands of years ago, so obviously it's not needed.
hint:
it depends on what you need.
anyway, it's a stupid question since 99.9% of today's technology and advance in any field requires strong math.
You are a professor at a liberal arts college and ask when did "ramblings of a random guy" become "news"? What did I miss here? The world is full of news about new books, which do contain such ramblings. But, true they may not always be the "News for nerds, Stuff that matters" that we all thirst for, but still are regarded as news.
In todays world, especially the financial world, math has become very important actually, where math used to be applied to calculate break-even its now used to gobber up that that promille. I'm thankfull to the business world allowing me to skip moral concerns over to my new paradigm "get filthy rich", it has really worked! Who needs snare theory anyways?
The ability to solve for X is applicable in at least one aspect of just about everyone's life. You quilt, you have some known elements you want to include, and you need to know how big your other pieces need to be. You ride motorcycles and you want to change your bike's acceleration characteristics...how big a gear do you need? You do absolutely anything involving money over a long period of time.
I've never had any sort of science or engineering job, but I've never gone 6 months without using SOMETHING from Algebra 1 or Algebra 2. You just have to be able to recognize when it can help. (I've rarely used anything beyond that, though.)
I listen to music.
I am forced to hear people yammer about politics occasionally on NPR
As for history and literature - probably the furthest thing from relevant in my day-to-day life.
As an engineer and programmer - math is with me all the time.
As a "average joe" - it's with me every time I pay for something or tell time. Even if *I'm* not doing it - its often some machine I'm directly involved with that does.
The two words that summarized where the whole article was coming from, were: "Professor" and "Emeritus"
Exactly. It's not like when I apply to an IT position they'll quiz me on the deeper meanings of The Great Gatsby. All of my English and composition classes have focused around this type of analysis, which is highly specialized and irrelevant for most everyone.
SSC
I've felt this way for a long time now, only about many other subjects that are mandatory in the school system as well. Instead of just teaching the essentials in the early years and allowing them to choose their classes in high school, they force you to take classes which have nothing to do with your desired profession. This likely increases the amount of failures because failing one of these non-essential subjects (which you aren't interested in) could cause you to fail an entire year. If you attempt to do well in one of these classes which you do not need, you will end up devoting a lot of time and effort for... something that you do not need. If people later change their mind about their desired profession, that is their own choice. They do that currently, and many of them have to relearn what they need for their desired profession, anyway, because when you don't use something, it is easily forgettable (even in a short amount of time). Sadly, many people think that more mandatory classes and tedious work will somehow make everyone more intelligent, but in reality, much of their time goes to waste memorizing this information which is not useful to them (which they forget soon enough because they do not use it, anyway).
Filthy, filthy copyrapists!
You must be a terrible physicist. As an electrical engineer, I need literary analysis every time I read a technical paper, and I needed composition skills last time I submitted one for publication.
When you're afraid to download music illegally in your own home, then the terrorists have won!
Math is important for understanding statistics, probablity and financial literacy. It's also important for understanding queues; A good foundation in mathematics should include probability, basic statistics, some finance (interest rates, compound growth, mark-up, mark-down, ROI), fractions, percentages and a bit of symbolic arithmetic (aka, high school algebra). Understanding sets (union, intersection) doesn't hurt. The population would be less easily bamboozled if they had a basic grasp of math. And, yes I think numeracy is important for most white collar (and many blue collar) jobs. Most jobs in the 21st century are going to require high school math or better.
I know Ramanathan as the author of a series of study manuals for the preliminary examinations for actuarial science in the US. It honestly surprises me that someone of that level of mathematical knowledge would make such a poorly reasoned argument. As such I must consider the possibility that this is some kind of cynical elitist ploy to retain mathematics as the language of the privileged and well-educated, much like Latin hundreds of years ago. But this too seems too sinister a line of thought to entertain--and somewhat contradictory, given what I know of him.
Nevertheless, the logic is unsound. Mathematics is not merely computation or abstract manipulation of symbols. It is a way of thinking that not only fosters an understanding of the importance of logical reasoning, but also the necessity to substantiate and quantify one's empirical observations. That is to say, mathematics is the foundation of science. To say that most people don't need anything more than the most basic knowledge of math is like saying people don't need the ability to think critically.
The reason why we learn mathematics is not just to perform work with it, but to learn how to think logically and behave rationally. If there should be any doubt about this, just look at the state of mathematics education in the US today, and compare that to how appropriately we assess things like the relative risk of terrorist threats versus being in a car accident; or how well people understand what happened with the Wall Street bailouts; or even something as basic as compound interest as it applies to making payments on credit cards. I think the evidence is overwhelming to support the notion that people suffer from innumeracy, not too much mathematics. And given that Ramanathan writes study manuals for actuarial candidates, I find his lack of understanding of this point to be all the more remarkable.
The article summary posted brings two issues and treats them as one - the value of teaching mathematics, and the value of "teaching how to teach" mathematics. The two can be related, but they are not one and the same. One might contend that learning mathematics has limited value; but for a person who must do just that, learning how to teach mathematics is requisite for the job.
Why stop at math? We don't need to know much about chemistry, physics, biology, engineering, or anything besides how to change the batteries in the remote. An operative word here is "need". In some sense all we "need" do is stuff food in our mouths and breathe. Now, change the "need" to some zeroth law about seeing the species as a whole progress, and suddenly a general awareness of math at a deeper level becomes quite important. I find the original author's thesis to be narrow, cynical, and with a subtle complacency to separate of the populace into Brahmans and non-Brahmans.
I do wish that there was a course for Math that started with Physics instead of starting with number theory which is really what most math is connected to and then after that Algebra is taught as an abstract set of rules and tricks, rather than a set of powerful tools for logic and problem solving. Get rid of exercises in favor of nothing but "word problems" That will make the classes a lot more worth while. Calculus in physics is so easy and so cool, but lots of times you don't get to see that until you have reached collage physics which is just stupid. With those modes of thinking in place, nothing is out of reach.
Not only they have been consistently high ranked in programming competitions, they are also becoming a reference of scientific and engineering work, not least because of their high standards in math on high-school and beyond.
...for the emeritus professor, but he did not become "emeritus" early enough.
And did he seriously use "taxpayer dollars" as an argument? Is he trolling for local office or something? The entire debate over the usefulness of any form of learning is ultimately predicated over the false assumption that this learning needs to be justified. An educated nation is one that is more productive, more aware, and ultimately happier than its massively illiterate counterparts, irrespective of the moaning of certain truck drivers, soccer moms and ex-professors over enforced learning. I've yet to observe many happy, illiterate nations - in fact the only things they tend to excel at are genocidal warfare and mass starvation.
People, pay attention: no one cares about your objections to learning math; you don't like it, tough. You like your 9-5, do you? Somehow I don't hear you bitching and moaning how we should do away with work. Shove your ignorant objections and STOP getting in the way of those of us who can actually think, 'cause you know what? In the end, you'll be the sad marginalia in the history books emblematic of a "more ignorant age". The rest of us will be praised for advancing humanity.
So, again: stop getting in our way. You are not important. Neither are your opinions. Quit trolling from the pulpit. Btw, fundamentalist Christian ministers, you hearing me? That goes double for you.
I take it you don't get published much in physics journals?
People try to do really dumb stuff (at a national and global level) when they don't understand the maths of what they're going. Drill Drill Drill springs to mind. A little maths goes a long way.
Having said that, getting rid of the hard stuff from school would provide a larger underclass to exploit, which is quite handy from a corporate point of view.
Education, funnily enough isn't just about what's needed.
Deleted
A basic understanding of mathematical proof and logic does more for critical thinking skills than the entire student career of humanities courses.
What the humanities actually teaches is empathy. But very few of its practitioners actually make the distinction between understanding someone's point of view and knowing whether that view is demonstrably right or wrong.
Let's cover the basics first please.
These days simple addition and subtraction seems to pose an intractable problem for the majority of people.
"90% of this game is one-half mental"
Seriously, though: Large scale serious problems like global warming, ecological services calculations, etc require
a deep and broad grasp of math and logic.
Understanding geopolitical problems and economic problems
at a fundamental level requires understanding of the math of complex systems.
In short:
- If you want to be in charge, and do the wrong things, you can get by without math and without believing in what
math and science say about the world.
- If you want to be in charge and do the right things, you need deep insight into mathematical and scientific
explanations of aspects of the world and aspects of collective societal behavior.
- If you want to vote for the people who will do the wrong things on the big problems and opportunities, you
can get by without math.
- If you want to vote for the people who will do the right things on the big problems and opportunities, you need lots
of math to figure out who's probably on the best track to viable solutions.
Where are we going and why are we in a handbasket?
Perhaps this guy wants us all to fall prey to crap PR and marketing, price gouging, and all kinds of other bullshit.
Is that the derivative is one. (Yes, I agree mathematician make limits way more complex when they could just say the limit is the answer to the question "Where does it look like it's going?" Still the derivative is a limit so I'd think having some idea about limits makes you understand where the derivative comes from and not "Because that's what Stone Cold Isaac Newton said so.")
Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge.
But those aren't the skills that most English classes are teaching!
English classes seem focused on being able to analyze fiction and characters. I once got an A on a paper I wrote about transmissions that was maybe the worst paper I have ever written but the teacher was confused by the technical side and gave me the credit. In my English classes there has been a complete lack of technical literacy.
Highly improbable, statistically, his conclusions just don't square with me. I figure that his probability of being correct is inversely proportional to the ratio of conclusions drawn from assumptions made.
Math is easy to mark and as long as it is schools will be in love with it.
Speaking as someone with a degree in Physics, I can safely say that I've only used literary analysis one time in my life: when learning it in school.
That explains why so many physicists don't understand that Schroedinger's Cat thought experiment was a literary euphemism for sex.
I think you are talking about a different form of analysis. The sort of analysis that you would do on a technical paper would be a technical analysis, verification of facts, etc... not a literary one. Literary analysis involves explaining a work of fiction or poetry by means of interpretation based on the specific linguistic expressions or structural tools used by the author.
File under 'M' for 'Manic ranting'
The math people really need to survive in a very dynamic society involves probability, statistics, and estimation. Schools rarely teach how to estimate something within 10-20%, yet that's an enormously valuable skill. Being able to decide what to throw out of an estimation without losing too much accuracy is essential.
Kids should know enough probability to estimate the odds on the local lottery. They should know what an "expectation" is, and what zero-sum and negative-sum games are and how to recognize them. They should be able to calculate the odds of dying in a terrorist attack and in an auto accident. They should know the risk/reward calculation for various career choices. They need to understand the concept of exposure to interest rate variations in loans and investments.
Plane geometry, Euclid proof style, could probably be dropped with no loss. (I've done animation physics engines and GPS calculations, and I didn't use that stuff. Analytical geometry, yes; straightedge and compass proofs, no.)
This is completely missing the point. All that you are taught in school is basically useless in real life. It's just a mechanism to tell if you're smart.
A lot of companies hire math phds to make them do things completely unrelated to their thesis. They do that because they know that since the person succeeded at some very advanced work, they should be capable to do well anything a bit complicated that they throw at them.
Hmmm.... I wonder what would have happened if this guy would have lived circa 1853 right before Bernhard Riemann invented calculus on smooth manifolds, also known as Riemannian Geometry. Maybe Riemann would have been discouraged and scrapped his work. Too bad, since that work, which had no useful applications at the time, would turn out to be the core mathematics Einstein needed to complete General Relativity some 61 years later.
Math is the language that describes the universe. Stop pursuing new heights in math an you will never reach new heights in reality.
jdb2
Well, the summary IS the article. Seriously. Just in more words. It doesn't make the point that we need art as much as academics. It's just against math. What did math do, run over his dog and crash his car?
There is no -1 Disagree.
http://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools ... The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, "It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal 'home schooling' of children.""
"When Less is More: The Case for Teaching Less Math in Schools by Peter Gray; In an experiment, children who were taught less learned more.
See also:
http://www.newciv.org/whole/schoolteacher.txt
http://www.holtgws.com/whatisunschoolin.html
And some posts I made to the p2presearch list concerning education (it would take years to read through all the embedded links on Gatto, Holt, Goodstein, Schmidt, Honigman, Lewellyn, etc.):
* [p2p-research] College Daze links (was Re: : FlossedBk, "Free/Libre and Open Source Solutions for Education")
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-October/005379.htm
* [p2p-research] The Higher Educational Bubble Continues to Grow
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005584.html
* [p2p-research] Rebutting Communique from an Absent Future (was Re: Information on student protests)
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/006005.html
For the record, I've always loved math and think it can be a very fun and worthwhile profession or hobby. I love broccoli too, but forcefeeding endless amounts of it to people till bursting despite the tears and protests would be cruel and probably would result in them not eating broccoli when no one was looking. How do we get people to enjoy thinking well and eating healthy? Good question. But people do have answers, if you look.
http://www.educationrevolution.org/
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
as an engineer all I can say is thank heavens for spell checkers
'All the mathematics one needs in real life can be learned in early years without much fuss,'
Wow, what a load of BS.
My wife taught "College Algebra" for a few semesters.
She was astounded when early on, she was working with a student during office hours on a fairly simple problem. A shirt costs 29.50. You have a coupon for 15% off. How much will the shirt cost you? The resulting answer was more than the original price.
Additionally, she was working with a student, and reduced the problem down to seven times four. The student's response? "Hold on, let me get my calculator"
While the current teaching methods being experimented with may not be working, I think that the professor is wrong in his suggestion that we basically throw up our hands and give up. It just means that we have to try other things to reach such students.
the hard part about taxes is the rules that change each year. Not the the math part and the tax pros (not the HR block guys) keep up on all the new rules and they are able to help you to get the best refund or the lowest tax to pay.
So the higher you can raise that denominator, the better off society will be in the long term, because effectively, we're all making the decisions by electing our leaders, and if the bulk of the population is ignorant of the effects of exponential growth, disaster will eventually ensue.
That's why our public education was originally created - to have an educated electorate. Then somehow over the years, our education became job training - even at the university level.
Whenever I hear a business leader complain that our schools aren't producing "educated workers" my blood boils - and I can understand the folks who rant about "corporatism".
RIP America
July 4, 1776 - September 11, 2001
Based on the low, low standards this guy seesm to be advocating, most individuals don't need to be able to read more than the back of a cereal packet, have any clue about any foreign languages, be able to write anything their spell-checkers won't fix or learn any manual skills: such as cooking (we've got microwaves), handyman (can drive to the home centre) or anything more than turning on the TV or the computer.
So what's the point in staying at school past age 10?
politicians are like babies' nappies: they should both be changed regularly and for the same reasons
Learning maths and all the 'complicated' things, isn't done just for the sake of knowing how to do those, but to put you in the mindframe for learning and analysing the world around us in a certain way.
/. user, why do you ask?
I'm in ICT, and I actually find ways of using computer structures and algorithms (and the mindset) for my day to day life. Yes I'm a
Yes, it's important to understand how that 5 Ohm resistor represents the the resistance faced by the paper's author during his early days of obscurity.
I'm pretty sure the GP is referring to the interpretation of symbolism and metaphor for hidden meaning that most literary courses focus on, which would be entirely lacking in any technical paper.
I use math quite often in my career. Just the other day I had to write a piece of code that determined the margin of error between the actual GPS coordinates of a cellular phone and the coordinates that the phone was returning. The equation I used was as follows.
sqrt((N1*cos(True Lat x)*(True Long y - Long y))^2 + (N1*(True Lat x - Lat x))^2)
Granted it is a simple Algebra equation but it is still Algebra so don't throw all of those math book thumpers under the bus just yet.
Many great artists have used math and geometry in their works, like the Golden section. While perhaps not as much, math is also used in music.
For those who missed the joke, parent was being disingenuous, which in this case is funny as that's the crime the article's author was committing. We all use literary analysis every time we read a news site, watch a movie, or myriad other situations every day; but just like with math we're not tested on it by writing an essay or an equation. Doesn't mean we don't need both. (On a side note, this use of saying the opposite of what you actually mean is true irony.)
Unless I'm reading too much into the parent post, then he's just an asshat ;)
Let me guess, your are Frensh? In my experience technical papers written in English are usually quite usefull as the writer used some words and was done with. Perhaps sometimes a few puns too much but otherwise not much making it hard to read. While in Frensh people like to literary
papers, not repeating a single word but always insisting to use another one to avoid duplication....
(Well, also may happen elsewhere. Some math schoolbook was once printed in which a lector
without asking anyone replaced every second instance of "real numbers" with "actual numbers"
shortly before print).
The way I learned it is you count up from what is owed to what was paid -1, then figure out cents separately. You see this demonstrated with some cashiers. I'd also say whole number math actually is pretty easy, now if I was writing programs that interacted with the financial investment market it would have to be better than that.
We may not be doing lots of long-hand calculations on paper, but we certainly do use the concepts of set-theory, calculus and general math every day. When it becomes a necessity to keep tabs on, say, how much money you have in the bank, or understanding what the speedometer in your car means, or that jumping off a cliff will mean you accelerate until you hit the bottom, you stop thinking of it as 'math' and as just common sense. And while I admit to being a bit of a nerd, I may not sit down with a math book, I do enjoy some aspects of physics and it becomes more fulfilling to at least have a rough understanding of the math in the books I read or the lectures I watch.
I figured this out early on, when a classmate at university, gave all sorts of answers which the professor loved and ate up. The problem was that the student never even read the books.
He got an A
Please see relevant XKCD cartoon - imposter
http://xkcd.com/451/
..........FULL STOP.
who actually needed math skills and who didn't this would be great, but we don't. If we de-emphasize math education in this country, then we will surely diminish the future supply of mathematicians and scientists.
The biggest problem we have had lately is the financial crisis. Yet we it is asked if we should stop pushing math?
From the article it appears that the real problem is that the people making math curriculum don't have a good enough understanding of math to actually allow most of to comprehend how math is important.
History? How often does that get used outside of school? Science? Art? Literature? Geography? Once you get the basics of reading, writing, and math down, you can function in society. But I'd rather not have a society full of people that can just barely get by. I mean, we are TRYING to teach way more than the basics, and look how dumb our country is!
Don't forget to include religion in the, what math can't express, unless of course one is arguing how many angels can fit on the head of a pin?
Shai Schticks:"You don't make peace with friends, you make peace with enemies"
Some math schoolbook was once printed in which a lector without asking anyone replaced every second instance of "real numbers" with "actual numbers" shortly before print.
That is quite possibly the most awesome thing ever.
When you're afraid to download music illegally in your own home, then the terrorists have won!
You may just have had an advantage from natural talent and experience? Or maybe you just eat a better diet or exercise more than others?
http://www.alternativeratreatments.com/eat-to-live.html
You can see another post I made for links about alternative education.
http://science.slashdot.org/comments.pl?sid=1847578&cid=34081206
But basically, most young children tend to learn best through interactions with people, nature, exposure to a waide variety of experiences including music and stories, and basic things like playing with sand, water, and blocks. It is on those sorts of things that more advanced thinking is built. Trying to put the cart before the horse may lead to less success, not more. It has been hypothesized that the reason many kids are doing worse in math and science and criticial thinking is that those sorts of general early experiences have been curtailed in favor of early academics focusing on things like early print literacy or early drill of math concepts. So, you might want to research this more, including reading stuff by John Holt (a mathematical person who also studied alternative education).
http://holtgws.com/
With that said, there are things you can do, like pointing out things. I've pointed out examples of recursion to my kid from a young age (like trucks carrying trucks). And math has been a daily thing by pointing out examples of it in our daily life, including when working with LEGOs. But that is not the same as "lessons" in any kind of formal sense.
A good open-ended site for young kids to learn through play as an example:
http://www.poissonrouge.com/
I agree with you that programming is a good way to approach math. As people talked about on the Python edusig list, "math" can really just be seen as a subset of computation and programming in general (at least within the bounds of whatever most schools teach).
I can also wonder if getting kids indoors more at an early age has made them vitamin D deficient which has led to some learning difficulties? So, even if you use computers with a kid a lot, make sure that everyone is getting enough vitamin D.
http://www.vitamindcouncil.org/treatment.shtml
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Funny, that. I too did The Great Gatsby for English Lit, and decided that its deeper meaning was that reading books on the theory of programming languages was more fun than many people admit. Hell, even "Perl for Dummies" was not that boring!
Sent from my ASR33 using ASCII
The reason adults aren't using the math they learned in school on a daily basis is because the math they learned in school focuses too much on algebra and pre-calc and not enough on statistics. And I say this as a college physics professor, who has a vested interest in encouraging algebra and pre-calc.
Stats is, (well, should be), at the core of every news article you read or watch on TV, at the core of almost every memo you write at work. Good statistical analysis should be at the heart of every political debate you see on TV, and every major economic decision your family makes.
Too often, we're making decisions based on gut instinct, political principle, and anecdotal evidence, and it's causing us to make bad decisions at every level from individual to global. The only cure for this is more stats.
Just try to do any intelligent mechanical, aeronautical, or electrical engineering without a whole lot of interesting math. The "Computer Programming" many of you like to call "Computer Science" isn't engineering.
Finite stress analysis? Navier-Stokes? Just Maxwell's equations require basic calculus, and that you use every day and don't get taught in elementary school.
Interestingly enough, Tom Magliozzi, of "Click and Clack, the Tappet Brothers" similarly lambasts his own math education. For him, though, I have a simple riposte - He fixes cars. If a connecting rod in an engine is broken, he just buys a new one and bolts it in. But when it comes to an entirely new engine, built from scratch, for as cheap and as light as is consonant with the strength required, you need a heck of a lot of math to make the right connecting rod.
AC.
PS - I should also throw in Nevil Shute's (pen name) comment: "Engineering is the art of doing for a shilling what any clown can do for a pound."
(At the time, he was using Olde Englishe Currencie)
I'm pretty sure the GP is referring to the interpretation of symbolism and metaphor for hidden meaning that most literary courses focus on, which would be entirely lacking in any technical paper.
Unless that paper is on string theory.
For more of the history of school: http://www.johntaylorgatto.com/underground/toc1.htm
A key section is here:
http://www.lewrockwell.com/gatto/gatto-uhae-16.html
as part of another archive:
http://www.lewrockwell.com/gatto/gatto-arch.html
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
If you think sex is putting the pussy in the box, you're doing it wrong.
I have used math only 3 times in my entire life. Once in elementary school and the second counting my kids every night. And third...Oops...did I just miss a count? Oh well, my math is week anyway.
Because not knowing is clearly better than knowing.
Hello again, Dr. Freud! How's your research into necrozoöphilia coming along? Oh, it's rather dead? That's what she sa-!... No, I understand. Not funny. I'll let you get back to being dead and all.
For the most part we fail to tell people WHY they should care about math. Early on, in public schools, approaches such as connected math, come up with all these cute stories that most students do not really care about. In the context of our Scalable Game Design project we teach middle school kids how to make games. Suddenly we get these 12 year old kids who NEED to be able to build better AI into their games. The teacher indicated that these kids do not care about math. One week later they build video games implementing sophisticated AI based on diffusion equations and actually start to enjoy math. Why? Because, for the first time in their life math actually solves THEIR problem and not the one made up by the teacher or the text book. "Excuse me, I need better AI!" http://www.cs.colorado.edu/~ralex/papers/PDF/SIGGRAPH_06_Excuseme.pdf
They problem with math education is that it is taught in a sort of vacuum. Students don't see the necessity of math until much later in their lives when it's too late. People try all sorts of methods to teach math, but what we really need to teach, I feel, is the necessity of math. We need to wow students young to show them that math can be useful.
That said I think that we should introduce logic and geometry at younger ages and geometry needs to play a more natural role than doing those retarded column proofs that scar 10th graders so much. Math was invented to help explain the world around us, to help keep count of that which is important to us, but it has been divorced from that in education. Sure we have those asinine word problems, but again these problems rarely connect with their target audience.
If you look at higher math so much of it has very deep connections to geometric structure as well as critical logic skills. So it makes no sense to me that these ideas are taught in compartmentalized nature and that all the areas of math are so segregated. Plus Logic and critical thinking are skills that cross all areas of life.
In conclusion, we need to be showing children how and why math is important, not just trying to beat the rules of arithmetic and fractions into their aching and confused brains.
I don't care what you say, all I need is my Wumpabet soup.
'All the mathematics one needs in real life can be learned in early years without much fuss,' writes Ramanathan. 'Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.'
They're just wasting their time and government resources. And don't forget to point out that experts have determined that Information Technology doesn't matter..
Well, I must admit that I'm not very familiar with the system in USA. (I live in Finland, myself) I don't know how much math is mandatory over there and just wrote the post on some assumptions...
Could someone from that side of the pond enlighten us europeans about the subject? If a person wants a bachelor's degree in some field that isn't very math oriented... What is the minium amount of math that they need to know? (Both in theory and whether they really know it well when graduating or not)
No then it would be (n+1) at which point the OP would have the first "infinite post". Two was a good call
what an out-of-touch twit. then again, UChi is fairly famous for "odd" faculty.
numeracy is what's needed: that people are comfortable with quantitative reasoning. the specific mathematical techniques are irrelevant, but yes, people really do need better ability to understand issues in a quantitative way. climate change, sub-prime mortgages, this week's discount on cans of soup, fluoridating water, innoculations and autism, the list goes on forever. you can't be a competent human without understanding conditional probability, for instance.
the education system does an incredibly poor job of this, producing adults who struggle and fail to find structure and place in a big, confusing world, and for lack of comfort with analytic, quantitative approaches, latch on to religious/emotional/ideological movements like the Tea Party.
The economics of it are a bit sticky. If only say 5% of students will use a fair amount of math in their careers, then the money spent educating the other 95% is essentially wasted. That's a lot of education resources. However, it's hard to know up-front who that 5% is.
Perhaps we can take that 95% of the money and create some kind a kind of just-in-time education. People forget anyhow. Just make sure students have enough basic theory to pick up industry-specific details later when they actually need it.
One argument is that math teaches logic and reasoning. While that may be true, there may be other topics that do that same, such as logic and reasoning courses.
Further, as we ship physical factory production overseas, our jobs tend to use less "physical" math such as geometry, and needs instead have shifted toward marketing-centric fields that require probability, statistics, logic, and set theory. Our material may need an adjustment to fit our new role.
Table-ized A.I.
Heck, I would just be happy if people learned who has the burden of proof for a claim. If I got 2 cent every time I was asked to prove something do not exists, where as the one *pretending* something exists don't feel they have the bruden of proof.... Or if ONLY people would understand the difference between anecdte/personal experience and evidence...
C. Sagan : A demon haunted world:
http://www.amazon.com/gp/product/0345409469/
visit randi.org
Literary analysis involves explaining a work of fiction or poetry by means of interpretation based on the specific linguistic expressions or structural tools used by the author.
This is especially useful when the work isn't written in your native language, like converting between English and Old English, or English and French, or French and Russian, or English and Physicist, or Physicist and Management, or Physicist and Chemist, etc. Or, equivalently, when you just aren't on the same wavelength, such as 10 hours of sleep nightly vs 10 cups of coffee nightly.
It's not quite that estranged as a topic.
/Joking?
I agree with the premise of this article. Unless going into a science and engineering field, or accounting, etc, one doesn't need anything more advanced than basic elements from geometry, algebra and trig.
Seriously, even in the practice of doing engineering work, how often do you actually DO an integral, a derivative, or a laplace transform?
Yet all of these were drilled into me at engineering school.
Good? Yes? No? Maybe. That's the debate brought up in this article.
However, I think this is a non-issue. In my rural midwest high school, it was pretty straightforward - if you were NOT going to college, you didn't even HAVE TO take advanced english and math. If you WERE going on, you could take a max of calculus and took the advanced english class.
So, no, not everyone needs math.I'm not even sure how much math is needed for engineers, either.
Laplace transforms by hand? Seriously? Powerful, yes, but I still remember the brain pain. And haven't done one since my "analysis of dynamic systems" course.
With the advent of computer algebra and things like FEA and other advanced simulations, will there be an evolution into a new era where the advanced math is quaint and extremely unusual, like going from the horse and buggy to the automobile?
Flappinbooger isn't my real name
No: you're just reading the wrong journals.
Said Schroedinger," isn't this fun
Shot a cat in a box with a gun
I'll be sure it survives
'Cause the cat has nine lives
And I'll only be using just one."
Schroedinger should not have done that
It was cruel "playing God" with a cat
Which, by the way, mister
Belonged to your sister
The next time please make it a rat.
Said Schroedinger poison is nifty
To dispose of this cat, God is shifty
We can't tell if it died
Till we all peer inside
And the odds are at just that, 50/50.
The cat in the box still has growth
Or it's dead, and infested with sloth
One should not get unnerved
Till the cat is observed
It's a superposition of both.
So that is the way that you tell it
Leave a cat in a box with a pellet
Should the trigger let go
The poison will flow
And you'll know the cat's dead when you smell it.
Said Schroedinger, "let Physics advance
Though it might be kitty's last dance
When we open the box
Be prepared for some shocks
But there's only a 50% chance."
Said Schroedinger, "let's take a chance
Though it might be kitty's last dance."
"The poor cat," he then joked
"is alive, or it's croaked"
But you can't know these things in advance.
(more)
Bio questions? Ask me to start a Q&A journal. Computer analogies available for most topics!
Frankly, I am much more disturbed to think that people don't know what is happening in the world around them and how to deal with it than if they can solve complex mathematical problems. I meet so many people who can't logically reason their way through a problem...if x then then y, therefore z is best course of action. Thoughts like that are surprisingly scarce in a large portion of the population. Mathematics need to emphasize more of the logic and problem solving than the memorization of formulas. Conversely, the other arts like English, history, etc. need to teach students how to apply that logic to real world situations. I don't think schools are teaching necessarily too much math...I think they are teaching it in the wrong way.
It's not just about performing calculations. Math courses teach things like deductive reasoning, which is used by everyone (or should be) in everyday walks of life!
I need literary analysis every time I read a technical paper
I was going to mod you funny, but since you have a +5 Insightful I'm starting to think nobody here actually knows what literary analysis is...
It's not reading comprehension! No, it's about interpreting symbolism, etc. Usually it's sort of a game you play, where you either try to find a particular political message (Marxist, feminist schools of criticism) in a work, or just create a contradiction between the work and itself (deconstructionism)...
You must be a terrible physicist. As an electrical engineer, I need literary analysis every time I read a technical paper, and I needed composition skills last time I submitted one for publication.
I tend to agree. Having been a software guy for about thirty years, I can tell you this: I've known a lot of engineers (in all fields) who got into it because they were good with technology but lacking in verbal skills, who chose their career believing they were excused from any need to communicate with anyone or anything. That would usually last until they got their first real job, and got told to write a hundred page project proposal all by themselves.
... all are just tools. The majority of human beings will never have a need, as long as they live, for higher mathematics ... but there are few people who cannot benefit from the ability to communicate.
That would often result in a few remedial English classes. Mathematics, spoken and written language
The higher the technology, the sharper that two-edged sword.
I am a physicist. You cannot write a technical paper effectively with just facts and data. If you do not know how to convey the ideas properly, no one will want to read it, and if they do, they'll either get bored and stop, or not understand it. No, writing a paper that no one can understand is not a strength or proof of your intelligence.
Almost every person who I know who lacks a good understanding of math is broke.
To me it looks like they go together.
Knowing everything about literature, art, history, football stats, is useless if you can't feed your kids
People know how to do better: http://www.educationrevolution.org/
We don't for all sorts fo reasons related to social power (see John Taylor Gatto).
See also my essay on learning "on demand" instead of learning "just in case":
"Why Educational Technology Has Failed Schools"
http://patapata.sourceforge.net/WhyEducationalTechnologyHasFailedSchools.html
Education can have several goals in this descending order:
* To help a person grow as a person
* To help a person be a good citizen
* To shape a person into someone elses' vision of a good consumer and good worker and, for a few, a good obedient professional with the "right" politics
Those three aspects of "education" are regularly confused, and usually most of formal schooling (especially when test-driven) has to do with the last of the three which is often at odds with the first two.
See also for how the third aspect goes on into grad school:
http://disciplinedminds.tripod.com/
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
I remember being reprimanded in an English class during a lesson on Shakespeare...
So, what do you think Shakespeare was really saying in this line here?
Miss, maybe he was just a writer who saw the value of sex and violence in putting bums on seats?
That didn't go down well at all...
If God forks the Universe every time you roll a die, he'd better have a damned good memory.
I can safely say that I've never used literary analysis, even in school. English classes amounted to nothing more than making things up out of whole cloth. That can in no way be described as "analysis".
Want to frustrate an English professor? When he says that some motif in a book is a symbol for something, ask him how he knows it's a symbol at all.
Give me Classic Slashdot or give me death!
BTW please shoot them SPAMMERS!1
Yes, there are people that do not use math at work. It is because they can only get jobs that require no math skills. The reasoning behind the article is faulty. I have very little doubt that it is very much like the rising tide lifting all boats. If our population were more educated in every field, not the least of which is math, then we would experience an increase in the quality of life whereas the less education the worse it will be for all of us.
We are in an era in which "educated" takes on a whole new meaning. As early as 1985 I am aware of one company that after interviewing people with a liberal arts diploma simply labeled their file with uneducated and trashed the applications. Expectations now can be very high and very restrictive. People wanting to earn a living had best acquire a love of academia.
Yeah but your print commands look pretty shabby when they come out "Dood, just cleek the buttawn"
Speaking as someone who has a degree in English Literature, I can safely say I use the maths every day. Although I should preface that I work as an analyst and the fields of mathematics I do the most research result in receiving an inordinate amount of CIA recruiting adverts from google adsense. On the upside, I can google "eclipse" and get zero vampire results.
That I ended up in a maths intensive vocation is not unusual. I didn't realise it at the time, but as a kid I had freakish abilities. I just thought it was not unusual. Actually, I believed my teachers who thought I was retarded. I could score 99th percentile on the maths portions of standardised testing, I just couldn't read, write or speak and was severely withdrawn.
Part of this was due to the fact that my father taught me the three R's at an early age and let me write left handed. At school I was required to switch to be right handed. Much later, a teacher advised me to try typing and it helped a lot.
Rather than pursue an Honours Engineering course at University of Illinois, I majored in Lit and Philosophy at a small liberal arts college to become a part of society. I had a fear of becoming an alienated scientist bullied by the same jocks from school into making nuclear weapons.
One could argue that there's no need to pursue literacy beyond the basics. And the author of the article mentions this. But really, what a dismal waste of one's life. It reminds me of the cliché Italian mobster who justifies a sociopath existence banking on a deathbed prayer can absolve him and get him to heaven -- it shows a true lack of understanding in the concept of statistics and risk analysis that someone in that line of work will even have a death bed beyond an unexpectedly cold sidewalk.
Society as it is far too unaware and lost. Literature, Science and Math are what glue our society together. Without it, there's just bread and circus and a general abuse of nerds. Do we really want a culture that would murder Archimedes or make a lampshade out of Einstein or Godel? It's not like we're that removed from that culture of violence today.
Life without intellectual stimulation is a banquet of white bread and margarine washed down with kool-aid while watching the football on the big screen. You can say it's adequate, but it's not my cup of tea.
Yes, one may rarely use the quadratic equation in everyday life, but that doesn't mean the neuron pathways developed in learning this formula doesn't help one make more rational and strategically better decisions in subject matter far removed from the ethereal world of numbers.
Math is neither an art, nor a science; it is the magic that holds the two hemispheres together; writing code seems to be a composite of both: poetry with numbers.
Sure one could do without either, but as Calvin's tiger Hobbes said, without it would be "nasty, brutish and short." For society's sake, we need more maths. I teach junior high economics and personal budgeting through JA and believe me when the teacher asks you quietly after class how to calculate percentages, you know mathematics is not valued enough in our culture.
Something to consider today, the birthday of John Keats, a man who so beautifully combined poetry and science to envision discoveries, such as the workings of the nervous system, not to be revealed through the scientific method for some time later.
Generally, I like to think I know where my dick is. Somehow I don't think that the question of whether or not it's in a box applies until I've had at least a fifth, and probably more.
Perhaps he's surreptitiously trying to increase America's reliance on H1-B visa candidates?
People making the case for "foo was important, but not bar" are advocating that we remove bar from the curriculum. I think they are making the opposite case by doing this. Only in hindsight can they know what they think of as important and interesting. The existence of several such foos and bars tells me that people take different things away from math education, and so what should we leave out?
I see this all the time in my classroom. We learned how to factor polynomials by grouping and one of the kids said it was baller. It's always surprising which topics appeal to students, and when it happens, you can see that a little switch has been flipped in their brain. So to speak.
On the other hand, I have students who protest to me that when you square -3 you get -9 because the calculator said so. I don't think the simple resulting GIGO lesson could be taught without a way to explain why the answer is actually 9. People proposing to leave the math to the calculator or computer are sending us down that road.
We spend a lot of times in school enforcing the notion that students should respect authority. I say that students need to learn to detect authority first. Math is one subject where nothing is true simply because I said so. Of course the students can trust that I will convey true statements to them, and they can also verify me independently.
> One part of math all people should be required to understand is exponential growth.
Then you should teach them about the S-curve, because exponentials will just keep going up.
I'm of the opinion that people should learn more math. If you can't find a way to use it in your daily life, you're not trying. Even my grandmother constantly comes to me to ask for a bit of help with geometry in her sewing. Simple things like "how big will the diagonal be" on this piece of fabric, or other things of that nature. I frequently merge sort RL papers out of piles that were already sorted. I do all kinds of estimates for how long things really take and keep track of how far off I was so that I know how reliable my estimates are. That's an application of statistics.
But nobody will appreciate the use of that unless they learn to do it for themselves. Merely studying it is no good, you have to use it.
Granted, the math we teach (and the way it's taught) are about as useful to most people as a lead balloon. But as other people have pointed out, literary analysis is about as useful to engineers and physicists as a, well, lead balloon. The problem is that if you wait until people have declared a major in college to start teaching them literary analysis or, more importantly, math, it's too damned late. Between high school and college I had four years of calculus or higher (I'm an aerospace engineer). Could that have been compressed? Maybe. But unless the suggestion is to track people as engineers when they're in grade school, there's no way I could have learned all the math I needed if I'd waited until I'd declared. I know some countries do start dividing people that early. But since I also have a degree in medieval history, I have to wonder whether such a system would have denied me the necessary math or the necessary history/writing backgrounds. In my view, possibly being "overprepared" was essential to actually being prepared for the career I've chosen (and at 30, I still haven't decided which I'm going to be when I grow up).
The problem may be that one needs more skills than one used to. The world is more complex. This means that one of two things has to happen: we either spend more total time in school, or something gets chopped. (A third approach is to somehow speed up learning, but that's another topic.)
Yes, everything is important, but something must go when the plate gets too full. Hard decisions must be made, and this author is at least asking the hard questions needed to get the culling started. Analysis of what people actually do at work is a good starting point.
Table-ized A.I.
It's fun to deride abstract academic concepts as irrelevant to the modern world. Those with such a shortsighted view fail to see that most engineered technologies depend heavily on mathematics. Nothing in our modern world would exist without math. No cell phones. No iPods. Even more mundane things like constructing buildings to withstand the elements and keep the occupants safe requires an application of mathematics at some point. The poor buildings that collapsed in the Haiti quake were slapped together by people who had equal disdain and ignorance of mathematics and how to apply it. They reaped what they sowed. Even the lowly construction worker needs some mathematical background to measure and assemble things properly.
Is this the world Ramanathan wants us to live in? Maybe he only sees the need for certain elites who understand how everything works. I'm reminded of certain episodes of Star Trek where an imperiled planet of people are slaves to technology that they don't understand. That's not the path we need to go down. It's already bad enough that the Western world is becoming dependent on the scientific and engineering prowess of the Asian nations.
I am becoming gerund, destroyer of verbs.
Man, my humanities courses must have been a total waste, since all I learned was how to figure out what things actually meant, rather than making up things for them to mean.
When you're afraid to download music illegally in your own home, then the terrorists have won!
If you really think about it most people only really ever need to know basics they learn before college. If you have a solid understand of math, english, science, history and health then you'll do well later in life whether you continue learning or not. That's why I think it's a shame that a lot of schools just pass kids through the basics so they can get a degree.
Even if you do well in your degree you'll still struggle without the basics. I've a few people that have absolutely appalling spelling in jobs and yes they get by but people also think less of them because they do stupid things like spell through as threw and pretty as pritty or, in the case of one guy, spells something as somethink. They'll never move up because people view them as morons whether or not they have a degree.
Well, a statistics professor I happened to listen to, some time ago, illustrated the need for math with just one example :
http://en.wikipedia.org/wiki/Simpson's_paradox
A little more math could make voters a little less dumb.
Cheers...
A lot of comments are arguing that Math makes you think in a different or better way even if you don't use it.
To accept that as a reason for teaching more math, you have to believe that other subjects of study do NOT encourage you to think in a different or better way.
I suggest that if we forced 1000 people to study math full time and 1000 other people to study whatever they want, that people who learn to think critically and make good decisions will emerge in similar numbers from both groups.
---Bless those silly trolls---
Your post is ironic as you are trying to conflate skills related to fiction with those related to exposition.
You seem to be suffering from the very affliction you're accusing the Physicist of.
A Pirate and a Puritan look the same on a balance sheet.
Robin is 22 and leaves the house for work at Quick Burger at 3:30 PM. Jack leaves school at 2:30 carrying a laptop and 2 math books, and arrives at home for study at 3:15. He stops on the way to get a burger and pays 99 cents plus tax. If Robin rings up 78 burgers each hour, and Jack spends 6 years in college, how many employees will be affected Jack's analysis when he's the Operations Research consultant for Quick Burger Corp? ADDITIONAL BONUS: Would Jack like fries with that?
You might think that things like art, music, and writing are the creative subjects. Well, maybe. But math is a subject that requires real creativity, and yet also a hard framework within which to evaluate what you're doing. So, for instance, if you're trying to prove Pythagoras' Theorem, there's several ways to start. Each way requires some lateral thinking to get to the proof, but there's a lot of ways to do it wrong. With arts, there's a lot written about different tastes (romantic, post-modern, classical, etc...) but there's rarely a satisfying right/wrong about it. It allows you to make a bit less effort, because the intermediate product (eg half finished canvas, a story with an undeveloped character...) is also arguably "a good piece of art." With math, you can be creative, but within a certain framework which constrains you.
As for needing it, well, someone already mentioned probability and statistics. Without knowing something about this, your decisions become very difficult to justify. Should you take a mortgage? Buy some stocks? Get a degree? Have kids? Buy a TV? I'm not saying there's a formula for deciding all these things, but often people make decisions that are downright irrational. Have a look at Kahnemann/Tversky for some scenarios that are completely irrational, but avoidable if you had a good numerical think about them.
Finally, for the young, study math because there's lots of people who don't know any, and will need you. Math related stuff like software engineering, finance, engineering, etc seem like witchcraft to people who don't know any math.
For my situation I would say "a lot more" based on the way I got my ass handed to me in the first year of grad school by the Indian, French and Chinese students.
The american students were at a clear and significant disadvantage here. Learning Galerkin's method for the first time while everyone else was treating it as a "refresher" sucked big time.
Now the irony is that I don't really use this stuff in my job now, but the fact still remains that these non-american students are at an advantage. Like it or not, the schools teaching engineering tend to focus on mathematics as an important subject (rightfully so!), so if your behind you peers....good luck to you! If you start off at a disadvantage in school, that tends to extend to the job market.
I see a strong correlation between aptitude in mathematics and numbers of H1B visas granted in the workplace. Is it the 'cause? Well who know's but i'd be willing to bet...
Yeah, we need to eliminate mathematics from education because the economist's wet dream of Homo economicus is already working too well. What's sad is to see a statistician write this. For shame, for absolute shame. Statistics are quoted in every newspaper and on every TV station every day, mostly to the befuddlement of the general public.
The problem is that we don't want an educated public who regards the following paper as common sense:
Lies, Damned Lies, and Medical Science
Or course what I'm saying is not original to me. Dweebs everywhere are catching on.
Arthur Benjamin's formula for changing math education
Although I would say that the principle of calculus is important. The problem with calculus is that we can't resist testing ugly mechanics. I guess we have our grade three spelling teacher to thank for that. Great literature, but can't spell during a flood of inspiration? Go to the back of the class.
Jane Austen's famous prose may not be hers after all
Regurgitating trig identities as evidence of grasping calculus has an electric chair utility function in the non-engineering population. But seriously, 16% of American GDP spent on health care, largely at the mercy of corporate observational studies, and a statistician is arguing that math education is overrated. Oh, the humanity! How about the general population having the vaguest clue about long tails and concentration of risk?
What Alan Greenspan got wrong is that while heads-up poker is a zero sum game and self interest carries the day, multiparty poker is subject to implicit collusion. You just need one weak player at the table bleeding a big stack for the poker sharks at the table to lick their chops collectively and organize for a division of spoils.
In the world of Goldman Sachs, the chump at the table is the average wage slave trying to save for retirement with no mathematical tools whatsoever. "Listen, here's the thing. If you can't spot the sucker in the first half hour at the table, then you ARE the sucker." So, after one viewing of Fox News, you're expected to know the score. If the general public wasn't trained by public education to play over their heads, the financial elite might be subject to the market discipline of having to play at a table of equals. The horror! The horror!
Williard: They told me that you had gone totally insane, and that your market discipline was unsound.
Goldman: Is my market discipline unsound?
Williard: I don't see any market discipline at all, sir.
Goldman: Who needs discipline when education is bliss?
Williard: These savages have K12?
Photographer: One through nine, no maybes, no supposes, no fractions.
Williard: Are you giving up America for a Playmate of the Month?
Goldman: Playmate of the Year, chief, Playmate of the Year.
Williard: What's in it for the crew?
Goldman: Would you believe 'sloppy seconds'?
Willard: You're the asshole of the world, major!
Playmate of the Year: Who are you?
Cleaned out: I'm next, ma'am.
Playmate: Are you crazy, Goddammit? Don't you think it's a little risky for your 401(k)?
Willard: Charlie Brown didn't get much USO. He was dug in too deep or bleeding too fast. His idea of great retirement was cold grits and a little bush meat. He had only two ways home: death, or bingo, the largest risk his education had trained him to comprehend.
I think we use quite some math every day, while universal lessons like "my system is better than yours and therefore you will use it too, even if I have to beat it into your system"...
Oh wait. That is still general practice all over the world.
Never mind then. Forget about math. History really works!!!
Privacy is terrorism.
Just because people today 'don't use' something in their daily lives, does not mean you can conclude it's not important. As many before have noted here, a solid understanding of algebra and calculus underpins understanding of statistics, finance, physics and on and on. While I agree the way math is taught to the 'general' track of students in school needs to change, it's just ridiculous to relegate the masses to ignorance by reducing math requirements any further than they are.
That mp3 player you're using? Your cellphone? That wouldn't work without data compression of the audio. Conveniently, after being sampled that audio is converted to the frequency domain to
permit higher compression rates. Fourier series are used for that. Pure math.
Secure payments over the internet? Hey, those private/public key encryption algorithms wouldn't be so secure without proper math to back them up.
Sure, you can do data compression with simple sigma-delta encoding and use ROT13 encoding for your encryption. But for the *seriously cool* stuff a good dose of maths indispensable as it generally makes things "better". And these are just the first two examples that come to mind.
The point is, you need to show students the practical applications of the subject you're teaching to pique their interest. Although I'm still not a big fan of *doing* maths myself, that doesn't mean it's irrelevant to my daily life. When the moment comes I need it, at least I'll know where to turn.
I have said this before, and no one is listening, I cant believe they teach math to mere mortals. The only people who need math are the PROGRAMMERS who write software the rest of the world relies on, and random physics geeks. I got an engineering degree, and all the work we do relies on the software we use, and physical tests. Who needs math? I have to ask myself that question nearly daily at work. No one uses it!!!
All those detractors with quite "technical" view even at literary analysis... while, if certain level of drive to uncover non-apparent meanings in our surroundings was a bit more widespread, the world could probably be a bit nicer too.
One that hath name thou can not otter
IMO we would be a lot better off if we spent less time on teaching kids stuff like that, and a lot more on teaching them about logic, how to tear apart political bullshit, which is related but different. And maybe we could dial back a bit on the math in exchange for giving them a solid _understanding_ of the math they actually are taught, instead of "sausage stuffing" them with as much as possible in the shortest possible time, and a solid grip on how to apply it to the real world.
Yeah, I guess I can keep dreaming.
It's only specialized and irrelevant in the same sense that graphing lines to learn about the cartesian plane is specialized and irrelevant.
Have a nice day!
Stupid much?
That was the idea, he means that why should we learn anything about literature, after all, for example he never had to use literary analysis, so then we are wasting time teaching kids that skill as well...
The importance of math is because you may be in a situation where you will have to figure something out for yourself and by that I don't necessarily mean that you need to build a house in the middle of the wilderness. So the importance of knowing math is...and I can't stress this enough...being able to do it. So in the case of just knowing the 'principles' of calculus nothing could be further from the truth. The importance of Calc is being able to integrate and differentiate and recognize problems where they apply. Seriously just knowing lim h->0 for f(x+h) - f(x)/h isn't going to help you actually perform much calculus. Unless you relish deriving the chain rule from scratch...which is IMHO one of the prime reasons for memorizing things in math - when the derivation is rather difficult. As for saying things like "I don't need X" well that from where I stand is the fault of the educational system insofar as it has taught you that life's problems come in convenient little packages. Difficult functions exist because the world is messy.
One of my relatives went to a technical school and never took any math beyond addition/subtraction multiplication and division and I remember trying to explain algebra to them. In doing so I realized that much of what they did in life with math was rote memorization. From doing their taxes to converting from Fahrenheit to Celsius. They didn't realize that if you know some things about the system you are trying to model you can "create your own formulas". He couldn't recognize a problem as algebraic and didn't have the tools to solve it.
People I've worked with have shown the same issue with probability. The understood that the odds of the lottery were bad and flipping a coin was good but when faced with a moderately complex problem (i.e. like how to replace a usage based model with a fixed rate model in a way that we don't lose money) it was difficult to communicate to them. They didn't recognize to problem as probabilistic and didn't have the tools to solve it.
I've seen people who had some algebra calculate it over and over again to see how it changes over time. They didn't recognize a calculus problem and they didn't have the tools to solve it.
From where I stand not learning to DO math means putting yourself in the position of having to know by rote every math solution which is beyond your ability. Even then, you probably don't know enough to make any changes to that solution...I can't count the number of times I've read product literature where someone has compared some performance metric for a specific item against the average for some grouping of items.
There are dozens of examples of where we need better and more vocational Mathematical skills.
As a sucker for buy-one-get-one-free offers and 3 for 2's I regularly find that my till receipt reveals that I've been incorrectly billed.
When paying in cash, the number of times I start counting my change and get offered more that the staff "accidentally" failed to give me is astounding.
Schools fail to teach the most key mathematical skill that children need when they grow up - how to budget. The debt society that we live in is driven most of all by the inability of so many people to understand the Micawber Principle - "Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery."
Just because Mathematics is a pure subject http://xkcd.com/435/ it doesn't mean that it doesn't underpin almost every other subject in some way.
that you have a naive grasp of math:
Math is closely tied with logic but not arithmetic, algebra, trig, or calculus? Why is it, then, that systems such as PRA (arithmetic) are so fundamental to logic?
Math is deductive, not inductive? LOL. Nice one. Since you like logic so much, have you ever heard of inductive logic?
Your approach is very much a deconstructive one, which misses the point of most of the in-house debate over the issues in math today, such as debate over axioms.
I'll agree that math is amazing, though.
This is some kind of meta-joke about you missing the intent of the post you're replying to, isn't it?
The emotional, rhetoric-laden argument style that humanities teaches doesn't hold water in the legal profession, because judges are usually very sharp and aren't going to fall for that shit.
Is that claim also valid for the jury?
Cardinal Richleau famously decreed "Control the langauge, control the people" and was the basis for his establishing L'Acadamie Francais which to this day enforces what can and cannot be used as a word in the French langauge. I believe there is still a legal ban on the word "Le Weekend".
Arch-Romantic and symboliste genius Arthur Rimbaud, inspiration for the film series Rambo, saw this sameinsight from the other perspective: change your language, change your life. This insight led him to abandon his incredible literary achievements at 17 to go off an lead a life of adventure, travel, gun running and decadence.
If it language doesn't change perception, why is so much effort put into double speak? The verbal Frankensteins created by today's spin doctors would make Orwell blush or more likely vomit. And it's done at such a granular level it goes unnoticed. I remember reading an interesting thesis that the word 'like' was injected into the hippie subculture to weaken their mindset on the simple premise you may recall from poetry class that a simile is much weaker than a metaphor. Whether it was intentionally planted or evolved organically, it was like totally bogus in helping the like counterculture gain any like credibility.
Both words and numbers can hide meaning. Nothing zen to it other than the basic premise of maya or all things are an illusion. But even the Buddhists find enlightenment in contemplating words. Basho's frog comes to mind.
The enlightened however are able to see there is truth in everything, even lies. Particularly lies. Something the counterculture of the 60's / 70's could perhaps grasp but not express. Much of this was due to a lack of mathematical understanding and poor verbal skills that left them inarticulate and ineffective.
Vietnam was a military failure much in part as it was based on faulty maths much based on Game Theory and the Prisoner's Dilemma and other works of paranoid schizophrenic John Nash. While Nash's works hold critical insight, those who attempted to apply them had little grasp on what those insights were. Where Nash realised insight in numbers, the pentagon just saw them as something to punch into adding machines. It wasn't necessarily garbage in garbage out, but just the wholesale download of data into the garbage disposal for shredding with the results interpreted by certifed tea leaf readers.
Body counts and other meaningless quota systems gamed the system against victory because the theory failed to recognise that humans are not calculators. Sure some weird freaks are, and until recently the word calculator referred not to machines but to someone good at calculating numbers. Overall, most humans are bad with numbers but good at lazy (different than the greedy that was used to incorrectly apply game theory) and being able to build odd logic systems when forced to meet meaningless imaginary goals such as quotas. Numbers are easy to fudge, and if you don't fudge them you can always get bonus points in the body counts by killing anyone and labelling them as enemy afterwards. The mathematical results did little to realise the martial goals originally set out upon.
One thing I have found strange in all the recent talk in the US regarding healthcare is that it seems much of the mess we're in was a result of these same bad maths strategy of Vietnam were later applied to the US Healthcare system when Robert Macnamera played his same numbers game as consultant for the US and later at the invitation of Margaret Thatcher in the 80's to apply his 'wizardry' to the UK system. Both applications were utter failures worse than Vietnam. But like there were no hippies, like complaining. Instead, they turned to alternative medicine which is based on even less reliable principles.
That's not funny, that's a perspective that has value, even if it may not be the whole story. Bad teaching.
1) move the decimal over one space to the left
2) multiply the first digit by 2
3) a)was the service bad? pick the result of 1)
b)was the service good? pick the result of 2)
c)was the service really good? stop being fucking lazy and multiply the whole damned thing by 2 and round up
Personally my step 2) is "divide the original by 5" but I'm weird
Yeah. Everyone knows that the Globe was standing room only.
I'm not sure Prof. Ramanathan's essay is coherent. I'm extremely wary of a thesis posed as a question: "How much math do you really need in everyday life?" Also, there's a shit-ton of elderly, loopy/cranky professor emeritus (retired) types out there writing on how their whole discipline has totally lost its way from the old days.
So, I can't tell exactly what his recommendation is. Is it to cut off math education after a certain point? Would he make algebra non-required in the high school educational system? Or is it to just give up on perceived attempts to make people "love" math with contrived examples? The "question posed as thesis" leaves these issues all tangled up. Apparently, a coherent argument wasn't necessary for the Washington Post to get some publicity for a retired crank whacking his own discipline.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
math has little relevance to everybody's daily life.
I disagree. I think part of the problem is math is taught in such an abstract manner. Aside from a few story problems there is little effort to apply math to the real world in the classroom.
Why aren't vectors taught when you learn triangles? Why are Calculus I and Physics I separate classes?
I think story problems should be the base for teaching mathematics. At what age can a kid understand scales and balance compared to the '=' sign?
Many people don't use math to determine whether buying more is cheaper, they just assume. This doesn't mean math is unnecessary. It just means that it's not applied.
This guy is argueing that math, that he understands, isn't all that needed... this argument has been done before. Someone with a chauffeur driven car cannot judge the need for public transport, so that is why ministers with chauffeur driven cars are in charge of it. People with high income and private healthcare cannot judge the need for free healthcare, so that is who we put in charge. The rich cannot represent the views of the poor, that is why every media star earns more then a million.
You CANNOT say that math doesn't matter all that much if you got a perfect grasp for it. Because you cannot imagine what it is like NOT to have a grasp of it. I was in England once when they still had the old currency system. There I was, reasonably intelligent kid and I had to hold up my hand with the change to have the shop keeper pick out the right coins because I didn't know the math. Suddenly I was an idiot. Well more then usual. If you do not grasp math, then you are helpless against the countless ads that try to sell you stuff cheaply when in fact they are more expensive. How can you deal with supermarkets that don't list the unit price if you can't do the math and see if 1 kilo at 2.50 is better then half a kilo at 1.15 (yes, BBC watchdog showed that british supermarkets do pull this one).
And gosh, the rich who tend to get better education don't have to worry about pennies in the supermarket, but the poor with bad education do... see the problem?
The less likely you are to be good at math, the more likely you are to need it. This isn't about people being able to calculate the height of a tree, it is about understanding numbers, about understanding MONEY.
Basically, this prof is saying that in this day and age, a solid understanding about money isn't important... gosh, wonder what his angle is. Daddy owns a supermarket? Teaparty supporter?
MMO Quests are like orgasms:
You may solo them, I prefer them in a group.
no. just no.
Writing SA's on how a drum represents Emily Dickinsons conflict with society is 100% useless.
Completely and utterly usless.
No redeeming qualities whatsoever.
It didn't help me understand anything later life in any way shape or form.
It didn't help me understand any news items I read today.
There was no hidden understanding conveyed.
it was useless in every way.
on the other hand reading simple lists of common logical fallacies(which was not part of any english class I ever took ) did help me to understand and judge news items I read today.
There are a few very good reasons to be worried about mathematics.
The first is that a lot of kids are growing up and getting out of school without the basic abilities to balance a check book. This is something I'm able to teach a child with Down Syndrome. Why is this important? We operate in a capitalist society. Statistical mathematics can give someone an edge. If the population as a whole can't even get percentages and averages down, don't you think people who are able to grasp these concepts can take advantage of the fact?
Second, once you get into Algebra and Geometry, you are dealing with spatial relationships, how you can use math to relate to the world. You are working the basic calculating ability of the mind, allowing it to expand in its abilities. A chess player is great with a level playing field. Try to get the same to deal with modern littoral warfare, or anything since WWII, and he will need a grasp on spatial relationships.
Finally, you are exercising the MIND. It has been proven that people working games that deal with mathematics keep active areas that are linked to Alzheimer's and Parkinson's. If you don't use the various synapses, they have been proven to atrophy over time. This can create obstructions and slowing of basic thinking, not just higher thought. Remember, once you stop progressing, however slowly, you are on the road to death.
Doing pushups is physical exercise.
Doing math is mental exercise; it teaches problem solving.
The issue here is that there are a lot of different branches of mathematics, and only one of them is being taught in schools.
Algebra: The concepts behind basic algebra ("Algebra I") are essential for anyone doing any sort of mathematics, so you can't really get rid of this. From what I remember of my Algebra II and Trigonometry classes, nothing there is a prerequisite for any other branches except calculus. It is essential for someone going to college for a scientific degree to know trigonometry, though. It is probably unnecessary to teach everyone trigonometry or "advanced" algebra*.
Geometry: Used as a didactic tool to teach logic, reasoning and proof. "Math without numbers" might attract people who would not otherwise enjoy mathematics. Teaching proof to high school students sounds great conceptually, but from what I have heard attempts are made near-constantly in this direction by math education theoreticians and never catch on. Note that while geometry actually does do the "develop students' logic and reasoning" which everyone says math is good for, algebra generally is not taught this way: rather, it is presented as a series of magical formulas. Certainly there is nothing even close to a "proof-based math course" in high school except geometry.
Calculus: Essential for anyone going into science, unimportant for everyone else. The algebra -> calculus line is the one primarily taught in schools, which is very convenient for future scientists and engineers and annoying for everyone else.
Statistics and probability: A basic understanding of statistics is essential for understanding current events, politics and the news, since statistics are everywhere and one must learn to judge whether they mislead.
Discrete mathematics: Way cooler than calculus, but probably not suitable for high schoolers, as it is not very relevant to people outside mathematics.
"Life economics": I'm not too knowledgeable about this, but from what I have heard, a lot of schools have a "life skills" course. This probably includes basic knowledge about compound interest, buying versus renting, and other economic skills which ultimately stem from mathematics.
Given this overview, I personally came to the conclusion that the best way to teach high schoolers math would be to require a basic algebra course, a geometry course (maybe), and a "useful math" course, which would include basic statistics, basic probability, compound interest, investing, and other ways students will probably actually use math even if they don't go on to become scientists or engineers.
Of course, this does nothing to fix the related problem that many students do not find more theoretical math interesting, limiting the number of people who go into math and science. But as long as most of the math teachers out there don't even like math, we'll just have to live with students not liking it either.
Speaking as someone with a degree in Physics, I can safely say that I've only used literary analysis one time in my life: when learning it in school.
I was thinking much the same thing. Other than to inculcate reading skills and the very narrow case of teaching how to write persuasively, I'm not sure there's any reason to teach literature in school. It's a form of entertainment involving few transferable skills. There are much stronger arguments for teaching music, though even then not as a core subject.
Mind you, I love literature: I have over 2000 books in my house and a degree in English literature. I've also spent the last twenty years working as a software engineer, and I've never had occasion to resort to my knowledge of literature for any practical purpose. Someone will inevitably object that literature teaches us about human nature, but that is quite frankly bullshit. Psychology and sociology teach us about human nature; literature just teaches us about writers' ideas of human nature. Literature as a compulsory subject is an archaic hangover from the time when only the aristocracy had access to education, and its function was to prepare students for aristocratic social norms.
I don't have any problem with curtailing math instruction with the proviso that it should be offered for those who are interested, and preferably taught by a better grade of teacher than the current lot. If I'd had even one math teacher in high school who knew what the applications of the subject were, I'd have been much more interested. As it was, I had to wait until college to discover the applications, and even that was entirely self-guided.
What I would like to replace compulsory higher math with is formal logic and, as several other posters have suggested, basic statistics. Everyone can get a lot of mileage out of logic and statistics no matter what they end up doing as adults: even fast-food employees get to vote. If they never discover the brilliance of F. Scott Fitzgerald, that's their loss, but the world will go on.
Proud member of the Weirdo-American community.
You mean making stuff up that the author didn't even do on purpose.
I guess it's as much a sham as psychology.
Yes. The Bible has already made it clear that the value of pi is 3.0. There is certainly no need for mathematicians to try to confuse people.
I didn't go very high in math in my early school years; later in life I regret it... as it's been a lot more work catching up!
Math is much more than essential, it's vital. It also needs to be taught in different ways so that it appeals to kids of different backgrounds.
My teachers in school were dreadfully boring; I spent more time drawing cartoons of them than listening. But had they used a different approach, if they went into art and programming and .. maybe things would have been different.
Math is everywhere, whether we like it or not. I admit, now a days I even see math as "beautiful" from a certain perspective. The great masters of art knew this.
Just my 2 cents.
See A Mathematician's Lament, by Paul Lockhart. At least follow that link, even if you ignore the rest of what I write.
I was taking community college courses until recently. Initially, my plan was to take the prerequisites for a computer science degree, then transfer. I found the computer related courses interesting and generally well within my abilities; in particular, I found programming courses very easy, even the ones in which I was sitting next to professional software developers who were brushing up their skills. The courses on mathematics were quite another story. In my first semester as a (returning) full time student, I found I spent over 90% of my study time on Calculus I.
What really struck me as puzzling was that on the one hand, I could not keep up with the complex transformations on the chalkboard and the homework assignments that the other students could. On the other hand, outside of that classroom, I found that the same students showed no particular intellectual strengths beyond mine; those that were in the same programming classes that I was in weren't as good as I was at programming, or even at understanding the mathematical applications of programming. The students showed no curiosity about nor enthusiasm for mathematics; for that matter, neither did the instructors. Yet I was curious and enthusiastic about mathematics. I actually have read books on algebra for pleasure.
Years ago, when I was in college for the first time, I was an English major; for years afterwards, I was astonished when I would meet former classmates who couldn't remember any of the literature we'd studied together. Now, I find that when I talk to engineers and developers, I'm astonished that many of them remember little mathematics beyond basic algebra.
I understand Lockhart's point to be that the model for teaching mathematics is at odds with the nature of mathematics; that we waste years of students' time teaching them gibberish, which they will not remember or use, while discouraging those that would actually love mathematics from actually encountering the subject. The way mathematics is taught now is something like the way Latin used to be taught: its necessity is exaggerated, those elements that are necessary are passed over quickly, and both its real utility and its intellectual appeal is buried under tons of meaningless busywork.
One part of math all people should be required to understand is exponential growth.
It might make people realize that population growth, resource consumption, etc. can't keep increasing at current levels...
Since most countries these days are experiencing negative population growth, a statement like yours shows that a good understanding of math is pointless for people that are not properly trained to feed proper inputs into the equations.
Far better that we expend energy directing students to properly apply critical thinking and understand how to research facts.
"There is more worth loving than we have strength to love." - Brian Jay Stanley
Expect to see more and more articles like this as republicans get on with gutting the educational system in America., which they see as why we have so many leftists and socialists. Why do Americans need any education at all, the Chinese and foreigners are going to be the only ones with jobs anyway? Lets get rid of the department of education, all public higher education, all expenditures for libraries, all scholarships. We can't afford these things any more anyway. Let other countries that have favorable balance of payments provide the world with education. You just don't need an education to vote the straight republican ticket or to watch Glen Beck. You just need to know your place.
Civilization? We don't need no stinking civilization.
Wait... what relevance does literature have to everyday life? What good is it, aside from making and catching references that other people who have read the same literature understand (Math works as well for this, as XKCD has shown ad nauseum). History? I'll grant you it's important, but not in the "everyday life" sense. There are plenty of people doing just fine today who don't know what the Soviet Union was, never mind such "ancient history" as WWI. Politics? Great for water-cooler arguments, not so useful for much else. Music? Mere entertainment, and certainly nothing in a music class is at all relevant to most people's every day life.
So what do they teach you in school which is useful in everyday life?
1) Reading. If you're totally illiterate, you're at a serious disadvantage.
2) Math. Not the sort he's talking about, but basic arithmetic. If you don't know enough math to make change, you've got problems.
3) Geography. Not world geography, just the basic stuff like how to read a map.
4) Whatever's needed for your particular vocation.
As for his complaint about contrived examples in calculus texts... so what? If students learn better if they think of a nap of a cone as a martini glass, that's good (if they don't, it's just silly). Pretty much any example you put in a math book is going to be contrived, because real problems tend to be too complex to illustrate the particular technique being highlighted. Physics textbooks have been doing this forever, with frictionless pulleys, weightless ropes, spherical cows, etc, and nobody seems to be upset about that.
For me, as a math whiz, i just did it, straight through to trig and prob/stat in high school, 800 math sat. i stopped in the middle of calculus in college, when my interests focused more on the humanities and psychology. i am biased towards math as a diversion and a way of modeling the world. But i am in a minority. my father was a frickin rocket scientist. I really didnt know i would not become a scientist, so learning it was fine, good discipline and all, but now almost none of my math past decimals, fractions, simple algebra and word problems is utterly useless to me. I suspect that our educational system is designed to ferret out the asperger leaning math savants, to get them into industry and the military (nuclear weapons design for one). For most of us, i believe, the educational system is a total failure. you either get into a phd track and pray you can maintain your focus, or you just live with stupid debts and wonder why you did what you did. we need practical math education, as part of a real world based learning system, where problems from our lives are solved with educational tools. math: taxes, understanding economics, understanding science reporting, understanding polls, making budgets for a family or small business. a multi tiered educational track, with each track leading to good jobs. my high school was later nearly decertified due to having a twin track system where the less gifted (read:black) were put into a failure oriented track. seriously, and this was Berkeley High in the 80's. Oh, and we need free college education or its equivalent. And none of this will happen. there is no hope to reform or reinvent our educational system. most of us are now low grade morons, having grown up with the equivalent of alcohol in our blood surrogate. (and if you dont get the reference, its only proof i am right). dumb, dumber, dumbest. go to a thrift store, note some of the serious topics that Mass Market books covered in the 50's, 60' and 70's. now its all vampire romance novels. Im not even sure i trust anyone to build anything anymore, like the new Bay Bridge. oh, and you kids get off my lawn.
You hear about the person who didn't rely on anecdotal evidence to support his belief system?
Speaking as someone with a degree in Physics, I can safely say that I've only used literary analysis one time in my life: when learning it in school.
But how does the antiproton feel about the collision?
You are not a brain: http://books.google.com/books?id=2oV61CeDx-YC
Nonsense, it's not a ploy. The fact is that education policymakers everywhere are questioning whether the curricula being taught to today's students has enough relevance to the job skills that the market is looking for.
As we all know, there is no shortage of grads suffering from crushing debt while facing difficulties getting hired.
As such, it's imperative for educators to be asking hard questions that are relevant to economic realities.
In the meantime, there are basic and critical skills that people don't graduate with.
I call it preparing people to go to college who will never go. You shouldn't be trying to teach calculus to somebody who's 80% likely to drop out of high school, much less attend college.
My basic list:
Addition, Subtraction, multiplication, and division. Counting(as in change), and some geometry(figure out how many square feet of wall you have so you can buy the correct amount of paint). How to keep track of a checkbook/budget. Familiarity with 'cost of capital' so they at least understand the different costs of lower payments now vs fewer payments.
Use the time saved to make sure they know how to do things like cook, clean, take care of basic maintenance, understand why messing with electricity can be bad, etc... Preferably get them started with a trade.
If they're shaping up to be good at math, have the drive to attend college, THEN worry about teaching them the advanced stuff. Germany has/had a three tier system, why shouldn't we?
I don't read AC A human right
I would think the promulgation of competence for abstract thinking, which is inherant in mathematical thinking, is neccessary for the furtherance of a modern postindustrial society.
It is clear to me however that this tendency has been vastly overdone. Everyone should be exposed to it however, so those with a facile ability can be winnowed out and cultivated.
This should be done early on, those not winnowed out for further development should be inculcated with earthy wisdoms.
And YOU the MOD'ster, rtfp before you score me a measly 1, AGAIN damit.....
Republicans will work to send most jobs overseas anyway.
Too many mathematicians sitting idle on the street corner could simply lead to trouble or worse, a lot of theorems and proofs. Everyone knows republicans have no use for either theorems or proofs, especially since you can now hire an Indian mathematician to produce them at less than half the cost.
What business should have to pay a mathematician when they could get a tax break instead?
At the age of ~13 the school I went to (in the UK, under a Grammar school system) decided that 2/3 of the pupils didn't need any maths education beyond basic arithmetic so I and many others left school with a certificate in arithmetic that even the local college didn't recognise. I then had to go to college and night school (over 3 years) to get the equivalent qualifications and knowledge that I would have had if I'd been lucky enough to be in the other 1/3 of the students in my school. After 3 more years at night school I was able to go to university where I got a degree in Mathematics. All this despite the fact that teachers and schools had decided that I had no need for any maths education. I've learned never to trust an education system that decides what skills a child needs at an early age. Schools should give student an education that broadens their choices, not deny those choice in the belief that they know what a child will need to know in the future.
I can't believe how many posters missed your point. "Ha, you moron, exponential growth can't continue forever!" Yeah, that's exactly the point. Re-read the comment.
Mathematics is the language of science. (all science)
This is utterly and completely false. It is used in some aspects of some sciences to highly varying degrees. To say it is the fundamental language of science is absolute rubbish. The only "math" that is universally necessary in science is the logic required to formulate and test a solid hypothesis.
...are we scared yet?
you need to read A Mathematician's Lament
Tell me you don't need math. When you say everyday life I LOL, because every damn day I use basic algebra (IT management). I program in C/C++ w/ mix of electrical engineering, tell me I don't need math.
The biggest problem with the US is that this country feels that the four essential skills that have put this country behind other industrialized nations are not needed: Science, Math, Engineering, Technology. This nation is sadly SMET-o-phobic...
I guess when you were learning electrical engineering, composition, and literary analysis you didn't have time to learn how to not make childish insults.
I'd agree with you on composition skills, although parent poster said nothing about composition.
But literary analysis is a completely different field from technical reading. Literary analysis has to do with analyzing literature for things like themes, motives, symbols, etc. You probably learned this in high school, like most people. Reading a technical paper is about understanding new theories, models, or ideas and finding out what results some people have achieved in a field. There may be search for hidden meanings like the drawbacks of an approach that the paper's authors don't come out and say, but I think you learn to spot this through experience in academia and your field, and not from having studied literature.
I sense this 'professor' may not be a good teacher if he can't show the practicality of the material he's teaching to his students Although perhaps he needs to clarify what does superficially appear to be him condoning a 'dumbing-down' of education which is meant to be to teach people to think for them selves logically rather than fill people with a bunch of facts and formulas that, I agree, may not be used by most. Though in an educational environment, they are absolutely relevant.
Any day now, you will be replaced by a more capable electronic calculator. Since you don't have the necessary understanding, you won't be needed at the cutting edge of science and technology. The money society spends on you can be put to much better use, say a tax cut for the wealthy who will generate jobs and advanced technology in foreign countries and big profits can be had.
And a much more insightful point than he probably realised when he made it. Shakespeare would never have seen himself as any kind of literary figurehead - he was a working playwright, in a competitive environment with an audience that didn't treat the theatre as somewhere to sit quietly with your date while you pretended you understood. Elizabethan audiences demanded blood, guts, and emotion from their theatre-going, and Shakespeare gave them it in spades.
[FUCK BETA]
It's even more than that. Without math, your ability to understand physics is compromised; and without physics basic and very practical things like your driving skills are going to suffer. People are *really* a lot better drivers when they can bring a realistic understanding of traction, inertia, kinetic energy and so forth to the driver's seat. But that's not all. Polls completely bewilder and mislead their readers without basic statistics; lotteries rob the probability-impaired (hence the joke, "lotteries are a tax for the math-impaired); people who don't have a good, intuitive understanding of what thousand, million, billion and trillion mean relative to each other are inherently incapable of forming useful opinions on federal budget issues (and consequently, are likely to vote in a random, haphazard manner more driven by crap like fox news than sense); it even leads to poor military strategy, an excellent example of which can presently be found in the Iraq war.
The pachyderm in the parlor, however, is the fact that if you take an IQ 100 person (or lower) and try to teach them math beyond the basics, you're not often going to get very far. People aren't born equal in capacity, and we can't fix that by applying more pressure to their foreheads, which is about what forced math classes do.
It's that whole thing about teaching pigs to dance. It wastes your time, and it annoys the pig.
I've fallen off your lawn, and I can't get up.
"Why create a need to make it palatable to all and spend taxpayers' money on pointless endeavors without demonstrable results or accountability?" ... You're just gonna be proles, anyway. Why bother to teach slaves to read or do math? That's why they call it "unskilled" labor in the work camps where the Fabian Socialists put you when you're unable to justify the cost of your existance to the government.
I wonder just how much of his own money he's willing to give to pay people not to work?
As a programmer, I find I use nothing more advanced than simple addition, subtraction, etc five nines of the time.
Logic yes. Advanced maths? Nope.
Sig Battery depleted. Reverting to safe mode.
Most of the things you learn in school and college are mostly useless. Except reading, writing and a bit or arithmetic, nothing is really too useful for the majority of people. Most of the things you need for most of the jobs out there you have to learn at the job, anyway. Most of the concepts we'll meet in daily life are never even touched in school. You don't learn about insurance, or what's a bill, or a receipt, or a mortgage, or car mechanics or home repairs. But we learn about biology (why? what has biology to be so widely taught? agreed we are living things, but still), lots of history (interesting, sure, but useful? only if you are Indiana Jones, I suppose), physics (you'll learn all you need about gravitation by age five, anyway), literature (that's more useful than math?).
The syllabuses we trod in our life seem at best random and at worst residual accumulation of pet topics from a long genealogy of teachers. Most of it comes from forgotten times, where you could really grasp ALL the human knowledge of the time, so no selection was needed. Since that's no longer the case, some selection is overdue, for math and for all the rest of topics. But it seems like once installed in the syllabus, there is no way of getting something thrown out. And it should be a continuous work in progress, year in and year out, selecting what must come in and what must go out.
The best that can be said of today's education is not about what we learn, because we forget that soon, but how that learning teaches us to better ways of thinking. In this regard, Mathematics should be considered fundamental. Perhaps an instinctive suspicion of that is what keeps Math in our schools, who knows?
Rome taught me patience and assiduous application to detail. Virtues which temper the boldness of great, general views.
I think it's glaringly clear that the author was being facetious. Looking around at today' society, we need more emphasis on logic and deduction.
Most folks here seem to be saying that math is important to learn due to it's importance to other subjects; i.e. mathematical subjects like probability, logic, economics, or even non-mathematical subjects like English or law. It's been said here that if we learned the correct maths, we'd understand these higher subjects earlier and be harder for politicos to dupe.
It would seem to me that ditching some of the higher math in favor of integrating probability into math studies, logic into science studies and deeper economics studies during high school years would be quite a bit more valuable than ever learning geometry, trig, or calculus. At the very least, if math is so important to other subjects, why is there no grade school education focused on how these subjects tie into each other? Do we need to call in James Burke to develop a course for students to understand the practical applications beyond calculating your tips? Does anyone remember the single semester spent on economics in high school? I sure don't. And the reason is because our education is a joke.
For example, the math system used during my high school years was the UC Davis system. There were a ton of problems with it, but the biggest was a lack of examples from which to study with. On the surface this was bad enough, but the Davis system expected students to use applied learning to figure out more complicated problems in each chapter. With zero lessons on applied learning. Nor any labeling for which questions were more complex and required students to jump ahead and just figure it out. Oh yeah, and there were no answers included as the entire system was photocopied and students were expected to keep the pages in three ring binders.
Additionally, most folks are in their respective corners on education, in the red or blue trunks and ready to duke it out. They've all got someone to blame for our terrible school system, but when's the last time you heard someone bitch that a D is no longer a failing grade? That some students must learn without having a real book(physical or electronic)? No one politician or party has these things as their core concern regarding education because it's not germane to their ideology.
After years of being passed with D's and little to no help from my schools(at least till high school), I had piss poor grades because I spent all my time struggling with math. I was decent in science and history because I love science and history. I was decent in English because I love to read, thank god for my parents. I tested at a tenth grade reading level in the fifth and no one that knows me thinks I'm stupid - but my grades show someone that loved band and didn't give a shit about anything else.
Student tutors tried but I needed more help than they could give, which was too little and too late anyway. Had it not been for the help of a friend who was a math major in college, I'd never have passed on time. What schools need is less politics, and students need professional tutoring, real consequences for failing and real incentives for success. The best part of high school for me was electives, and at least I performed well in most of those subjects. However, almost none of it was real world experience, and I've only learned later in life that I don't want a career in computers. Career guidance is a joke, and everyone knows it. Career integrated electives showing what it takes to make it, which courses are important and how to integrate them, the duties of various professions and what to expect from a life in a given field will help students to succeed. I'd have had a good idea in high school that computers were not for me. I expect the argument will arise that this is just too difficult, but most of this information is not hidden, we read articles about the ins and outs of professions all the time. If more time was spent helping students to choose careers, I guarantee we'd have better performance from them.
As it is, I'll be studying for my CCNA to stay competitive over the next few years while I re-gear for the profession I really want. For now I suggest we provide students with basic necessities before we start with the gasbag ideologies.
E.g., http://www.thefreelibrary.com/Mathematics+and+academic+success+in+three+disciplines%3A+engineering,...-a0219062371
Math is the foundation of modeling all processes we can't hold in our two hands.
Forget competence with computers. Who would need that in the 21st century?
Forget probability. Forget statistics. Forget risk. Forget data. Forget the ability to make rational decisions in public policy, economics, medicine, or any field requiring understanding of an aggregate. And of course, forget any understanding of science.
Who needs any of that?
Having said that, there is plenty wrong with math education in school. Besides the clear failure to teach what they try to teach, they're generally trying to teach the wrong things. Kids are still basically learning how to use the slide rule. Everything is about analytic hand calculation, which computers do just fine.
People need understanding of modeling, process, data, process, statistics. Math is the language of understanding reality. Those who understand that language use it all the time, every day as the fundamental building blocks of their thought. Those who don't understand that language don't know what they're missing, just as monkeys don't understand what they're missing lacking a spoken language.
Math puts a person two languages away from flinging poo on the savannah. And probably, one language away from the Dark Ages.
Obscure elegance at the expense of clarity is the bane of programming.
I work as a patent attorney. My background is EE, but we do an awful lot of MechE patent applications. I was told that when I applied for the job. You know what really won the interviewers over for me? The fact that I took two years of drafting way back in high school -- the old-fashioned kind with paper and pencil where you really have to visualize the object you're drafting.
Math as much as reading and writing is learned early in life. And if you don't use these skill much, you are not becoming better in reading or math. While there are people which survive without reading skills nobody would claim that reading is not so important. Same applies to math. You don't need it. Some people can even live without calculus. But they could live better with math.
For example, when people would understand set theory and building classes, they would understand tagging, marking elements with attributes and finally understand folders in computer systems. With simple logic they could proof that most political and media statements are plain lies. Yes most people feel that way, but they cannot act on it as they have no understanding of the concepts. Furthermore they could understand the structure of modern economics (which affects everyone) and see the problems with it.
Well you probably don't purposefully analyze papers on a literary level, but you hopefully do (and definitely should) on a subconscious level. Understanding the way people use language to convey feelings helps make it clear what biases they have -- look at any scandal involving seemingly objective medical papers put out by pharma companies if you don't believe that "objective" studies can have biases and half-truths behind scientific conclusions. Even in dense technical writing people still use language intentionally and pointedly and understanding how scientific papers portray their own biases is far more important than understanding Dickens -- but they use the same skills, which are more easily taught through him.
Hmm. Notice the name "G.V. Ramanathan". I wonder if he wants to keep Americans dumb. Indians are getting ahead because they value education and studying the hard stuff, so much so the poor will even study under street lamps. We could learn something from having those values, not just saying we do.
Sarcasm aside, he has a point, but I have a better one.
My disciplines use a math requirement as a "weed out course", usually Calculus. There are many people in many fields who struggle through that weed out class in their education and then go on to never use any math other than arithmetic.
My point, the better one, is that all of the sciences, engineering, technical related fields, the highest paying careers and the careers with the most power to change things run on mathematics. If you are strong in math, any of those fields are yours for the choosing.
The fact is math education sucks.
Up until the beginning of highschool most children don't get taught anything but arithmetic. Then when they get to higher mathematics they usually get a teacher who is math geek and a lousy communicator. It is taught sink or swim without making students realize that math is a language. It is also taught with very little exposure, not enough to learn even a natural language much less an abstract one. Europeans speak several languages well, but they start as small children and are continuously exposed to it. American kids get higher mathematics thrown at them, poorly taught and at a fast pace, for the first time in their teens. Then we wonder why most don't do well. Only a few talented ones are and they aren't necessarily good educators. Then the cycle continues.
All the mathematics one needs in real life can be learned in early years without much fuss
Profs in my university were pretty open that factually we need very little math in our lives. Yet it helps developing brains and making people generally smarter.
Similarly, one can try to say that we do not need to study literature: who the hell cares about an ancient writing by some brit? Yet, everybody acknowledges the role of the literature because it directly influences our communication skills. I wish it was that simple with the math too.
All hope abandon ye who enter here.
" unlike literature, history, politics and music, math has little relevance to everybody's daily life."
Ha! Literature and history and MUSIC?
You have it completely backwards. Math is the most useful of any of those.
I would argue that in a world of high technology, where people rely on GPSes and nukes to keep them safe, it is very dangerous to have people handling things which they don't quite understand. Am I arguing for absolute comprehension at every level? Certainly not. However, the popularity of lotteries, and the constant examples of people getting screwed on loans leads me to believe we aren't teaching enough of the *necessary* subjects.
Others here have already gone into how higher math has given them another perspective and expanded their minds. Still others here have gone over how those in power don't necessarily want people better educated (about anything, not just math) because it wouldn't benefit those in power (probably be detrimental to their power). I will say this: you have to realize that people (even smart people) only have so many hours in the day and so many months in their life, they can't learn everything. You have to pick and choose. Would I say drop higher math altogether? No. Would I be in favor of swapping statistics, probability and logic for calculus? Definitely.
Nathan's blog
What an idiot. By his logic, we need no math. You can "get by" even if you never have formal education and know zero math. I hope this professor is jobless soon.
I stopped believing the "they don't need math" argument years ago when it became necessary to give an impromptu lesson to my department on how to calculate period-over-period percentage sales growth. Half the group couldn't do it on their own.
I think we should be handing meth to every man, woman, and child!
I think basic algbra (sorry, they spent so much time teaching me geometry they forgot to teach me how to spell) is all people really need in life.
Anything after that isn't overly necessary for most people.
I could be wrong of course, but in my life, even with doing computer programing, I never needed very complicated math.
Problem solving though, they should teach more of, imo.
but i've been out of school for 20 or so years and i have no idea what they teach anymore, since I don't have kids. But i imagine they are still using the same text books I did. (that should be a joke, but sadly, it's probably not.)
Be seeing you...
What mathematics a programmer needs varies substantially on the work they do. Writing a physics simulation program? Algebra is essential, and calculus may be essential, but may be optional depending on what is being simulated, and the techniques used.
When writing a program to manipulate images, Linear algebra can be very helpful, especially for simple transformations. If you are writing a program to find an optimal schedule of buses for a city, then linear programming is what you need.
On the other hand, if you are writing a basic online store and you can get by with arithmetic (except in so far as Relational Algebra is the basis of the DB being used, etc). Writing a simple (non-physics based) computer game may involve very little math.
Writing a compiler? The important parser techniques etc can be described using math, but a very abstract one, far more abstract than calculus or even set theory.
Stylish sheet to fix many problems in Slashdot's D3: https://gist.github.com/801524
Okay, I read a bit of it, and I've got to say that this is one of the most insanely stupid pieces of tripe I think I've ever read.
Universal education is one of the cornerstones of an advanced society, and responsible for untold inventiveness and ingenuity. Without it, we'd be doubtlessly stuck a hundred years or more in the past, because most of the great thinkers of our time would have been too busy tending the farms to have become accomplished.
I'm going to go out on a limb here... You're one of these "government is evil" schmucks, aren't you? It all sounds good, unless you happen to be one of the poor saps who gets left behind in the dust because your parents are stupidly suspicious of all of those people with that fancy schmancy learnin'.
Has he ever wondered, why Poles and Russians are better programmers than many other nations. And as in Poland secondary school math was not compulsory for over a decade, one could trace the quality of programmers at different age levels.
Maybe the problem is that not enough people know enough math or we wouldn't have so many people borrowing more then they need and we would not have had to go through the latest economic issues.You will notice that those of us who can add are doing just fine.
I tried to count the times in a day (except at work since that is all math) I use math and I can't count that high. From checking tire pressure on my car to making breakfast to what change should i get back when buying a cup of coffee. It's amazing how often the checkout girl gets it wrong. Maybe she needs more math training. Nope most people trust the stupid machine and get ripped off.
My wife when asked said she doesn't use math but a little prompting and she quickly realized how often she does.
Take a little time, think about what you are doing and use a little more math and you will end up living better for it.
Many adults need a lot of the skills which are trained in math, in their daily life and in their jobs. To believe that math is about learning how to add just shows the mediocre understanding of the guy. In the same way reading a text in literature will not bring me a direct gain of knowledge. Reading literature is not important to learn the literature by heart but to learn how to understand and classify texts and get some basic knowledge about their structure, so that one is not puzzled when the storyline of a TV drama is slightly more complicated than normal.
In history its not necessary to remember when Rome was founded, but its helpful to remember that big empires grow and come down with time, and that truth evolves with time.
In math you learn that a problem can be abstracted, and that, using a set of fixed rules problems can be transformed and analyzed, and that, when done right such an approach can reduce the effort to understand and solve a task. Understanding that things like Markov chains exist may help the Manager to ask the right questions. Understanding that there is an algorithm to protect you data helps you to formulate the task. Understanding that complex systems exhibit long-term dynamics help you to understand and ignore when a politician bullshits (e.g. the economy goes up/down *since the election* so it *must* be connected). Understanding probability enables you to understand studies and elections.
All our modern life is built on math. Understanding the pattern of it helps. I am pissed of when people complain that i did not read enough classic literature, but on the other hand done even know basic mathematics known 4000Years ago.
I have always wondered why children's books spend so much effort teaching preschoolers about lions and tigers and hippotomuses, and other such exotic things.
I am anarch of all I survey.
A more than substantial part of elegance *IS* clarity and simplicity, so the notion of obfuscated elegance is sort of a contradiction in terms.
File under 'M' for 'Manic ranting'
Homogenized, Pasteurized 2% Skim Math.
It has fewer calories than a fraction of Pi, and gets safely pasteurized with degrees instead of radians!
It also weighs less with the metric system, so we sell it by the gallon instead.
Question: Why does one need a head? Answer: One eats with it.
But they also haven't learned the math they need!
Some have already listed here the utility of probability and statistics, and I would add to that simple and compound interest.
Most people don't need to know how to "solve for x" in the Algebra I & II sense, nor do they need trigonometry, or basic newtonian mechanics and elementary calculus. But pretty much everyone needs to know how their savings account works, how insurance premiums and risk (on a basic level) are calculated, how slot machines and the lottery work, how to save for retirement, whether the maintenance plan on their car was worth it, and enough arithmetic to save money on their groceries.
This is where I get my recommended daily allowance of "Foot in Mouth."
The central pit, or courtyard, was standing room only, but it was surrounded by three tiers of stadium seating.
What about at the university level? Is it fair that most schools require English and history classes as part of the core gen-eds, but not math? Isn't the point of high school to get a general education?
Sure and while we are at it lets get rid of history, literature, languages, music. Most people don't need any of that stuff either right?
We don't teach people maths because it is useful, we teach it so we have a citizenry which minimally engaged with the big questions of our time by being informed of the big questions of the past. We teach these things to enhance the human spirit.
You're obviously correct, it didn't help you; but that's probably more to do with you being an asshat than any lack of value of a liberal arts education. For the educable among us, well, we take something from everything. Today I learned that some douchebags think that their experiences apply to everybody, and that if it's not in their experience, it can't exist.
Ah more lies from the under and un educated
I find that I use trigonometry all the time (realistically, two or three times a year). I can't say the same for politics.
Math reaches into nearly every career. Even if the steps you take to solve your domain specific problem doesn't look like high school algebra does not mean it isn't directly related to it. Chemists, pharmacist, doctors, nurses, dentists, metallurgist, and accounts all have highly specialized forms of math in their jobs.
“Common sense is not so common.” — Voltaire
In a world where computers are becoming more and more integral every day into every profession, machines that for all intents and purposes just do maths really fast, are you really saying that knowledge of maths isn't a useful skill? In the 19th century it may have been useless, but the world has been moving from superstition and physical skill into a world of logic and intelligence since then; if maths isn't a good skill to have in that world I don't know what is.
The people at my old job thought I was a math genius and entrusted me with multi-million dollar budgets to allocate at my own discretion. Little did they know I was just doing Algebra. BWAHAHA!
Accountability is a marketing buzz word in the USA and is so loaded and abused that it has lost meaning.
The real accountability is the end result of the nation slipping behind in engineering etc or the people who are good at it leaving to go to other nations. Everything else is just a silly braindead metric which can't be proven to be effective at indicating much of anything (maybe you could reasonably argue for a scientific study having some validity and relevance but these do not actually influence education policy here. Science could prove removing sports doubles results and nothing would change.)
Look, some kids won't learn it the way you want when you want to test for it. I've seen too many illiterate kids "slip bye" only to make HUGE leaps forward when they find the right conditions -- making one think all those years were a waste when it should have just been delayed until the right time. Ultimately, its a logistics issue, we can't have individually customized education with emotional counseling (which all could use and some can not succeed without it.)
Me, I find the biggest supporters of "Accountability" are themselves some of the most irresponsible (and often unaccountable) people that I know. Americans themselves are some of the least accountable people in the world today; I'm from here, live here, and I'm honest - that is the bitter truth.
The difficulty is that this is Schroedinger we're talking about. There isn't so much subtext as... text. See
here and here.
Kids are taught to solve stupid problems like robots. That's not Math at all. Math is about creating purely imaginary constructs, asking questions about them, and figuring out how to answer those questions. It's both creative, logical, and engaging. Judging by the reasoning abilities (or lack thereof) of 99.9999% of people I encounter, the world needs lots and lots more Math--real Math. See "A Mathematician's Lament".
Practically anyone can be called to Jury duty.
Increasingly often, technical experts presents forensic evidence in terms of probability, like DNA evidence.
When the jury does not understand the maths, this can lead to wrongful convictions, which is a serious matter.
Nick
And here a retired English teacher I know and a professional writing instructor both have said almost the same thing you did, quite openly. Shakespeare has lots of sexual innuendo and gratuitous violence. After all, what is the point of Rosencrantz and Guildenstern? To up the body count in Hamlet.
"I may disagree with what you say, but I will defend unto the death your right to say it." -- Voltaire
This is amusing. A professor of Math probably doesn't remember that Math is the only subject in schools that teaches kids logic, critical thinking, and problem solving skills. There is no other subject that offers this to children. It isn't about memorization or learning stuff that you "need to know" it is about the greater need to know how to take the "rules" or "facts" around us and combine them in a logical manner to discover new things or solve problems.
A typical guy who got a job just for the paycheck. How can a math prof like that motivate any student to learn? I feel sorry for those students in his class... Do they need to pay to go to his class?
yes, *my* experiences are meaningless but *your* experiences apply to everyone or at least everyone who counts or is educable.
you're absolutely right!
pulling random things out of the air and pretending they're what the author really meant is sooooo useful.
Try a fun little game:
watch a film by some serious director, do your literary analysis and then have someone else watch with the directors commentary turned on and tick off points from your analysis.
oh?
what is that?
that doesn't count?
because apparently even if the director/author/poet personally says straight out that no, their use of some church bells is not a symbol for neo-colonialism or whatever else you've dreamed up that doesn't count because everyone makes their own meaning.
http://xkcd.com/451/
The Mathemetician's Apology
Schroedinger's Cat is not a euphemism, it is simply as close to sex as most physicists will ever get.
The US government have made it clear that we have no inalienable rights; any we do not defend vigorously will be taken.
Considering that many of the labourers I work with (construction industry) have difficulty figuring out quarter, eighth or sixteenths of a inch on a measuring tape -- I'm very hard pressed to give any credence to the idea that we should be teaching less math in school.
"Grab them by the pussy" -- President of the United States of America
Universal education is indeed one of the cornerstones of an advanced society.
However, what he have now is not "education", but indoctrination. Our school systems aren't aimed at educating our youth, but rather preparing them for dead-end careers and being ill-informed voters who can't exercise critical thinking.
And yes, the government is evil, our government. Not all governments are evil, but ours is. The governments in small European countries like Switzerland and Sweden seem like they manage to do a decent job of not being evil, and proving proper governmental services to their populations, but the American government is bloated and evil. If you ask me, the only way to fix it is to break up the country into a bunch of smaller countries. One giant country, with too much power, is simply unable to avoid having a giant government which becomes corrupt and self-serving. Just as giant corporations are generally bad, giant governments are too. Having a giant country like ours with a tiny government simply wouldn't work too well, so the answer is to not have a giant country in the first place, and break it up into smaller countries.
Studying maths just for the sake of knowledge is pointless, mathematics per se can't produce any knowledge for the simple reason that its axioms are arbitrary. They are picked for convenience, because ZFC gives the richest most interesting mathematical structures that we know of. Use another set of axioms and you will develop different mathematics. Therefore its byproducts can't be the reason why it's interesting to study maths.
The reason to study mathematics is quite different, mathematics teaches you rigour in reasoning. That by itself is so valuable that it justifies all the hours spent studying them.
that's why u r asking this question
we always say ' we dun need sth sth.....while we like sth sth'
but....that 'we' is only individual...
this world is individually grouped only..........not really a 'team'.....that 's why we r 'balancing' ourselves to 'how much do we need'.......
becoz we can't own them all..........personally.........
becoz we dun have 'teams'........we only have 'person's..........
> nor do they curl up with an algebra book for relaxation
Is it a pun? ...
I think algebra book don't teach vector calculus
Depends what you mean by "test-driven". It's a well known fact that the more you give students, the more they retain the knowledge. Testing their recall and reasoning skills under pressure improves the retention of that knowledge and those skills.
Higher Logics: where programming meets science.
i think the problem is math is taught backwards, if at all correctly. I have never once in class found out how or why the formula's and expressions and equations were created. Never. Yet, almost all math I've found has had real-world implications, even in theory to the mathematicians who created it. In my experience, this was even more evident in higher-math courses such as calculus, where proofs were done with the same attitude as simple arithmetic. it got to a point where you didnt ask why, you just did the work and handed it in, knowing the theories and concepts with no real way to think about them. Were it not for my luck in several corresponding courses in calculus, biology, and several string theory and game theory specials courtesy of the Disovery Channel and PBS, I doubt I would ever have thought of the simple beauty of math and it as the ultimate language. Math is the one connecting function of everything, even in say, literature, timing is key to a great story, now how do you express time and its relations to other times? Math is important, theoretical math doubly so: Experimental and theoretical math is the boundary pusher of math and science, the two go hand-in-hand at that level. this is the concept that is lost when math becomes commonplace. all math started as a radical new idea of thinking, of explaining and analyzing. to me theoretical math is the benchmark that shows the boundary of human thought. To me somebody who cannot realize the importance of math, especially theoretical math and its relation to science has no right using a computer, which is above all designed to aide in these respects. we have computers to do math.... i.e. we give them rules and an equation to solve. we are now free to become creative mathematicians because we dont have to do the legwork until we get the right answer from the computer.
While I'm not familiar with the pricing of tickets at the globe, at the time there was a much bigger division between first class and third class tickets generally. So pandering to the masses was probably less effective.
I don't know about the deep meta-analysis, but I agree that scientific papers use many of the same skills as literature. Having written more than my fair share of published scientific papers, and having been on the other side as a reviewer quite a few times, I can't stress how important it is that a manuscript needs to tell a damn story. It needs to have a point, and each paragraph needs to sell the reader on that idea. Perhaps it's not Dickens, but a paper that doesn't tell a story that the reader can follow ends up on the scrap heap in a hurry.
Math is a foundation of pretty much everything else in sciences. Moreover, math teaches you how to think about abstract concepts, how to reason logically, how to rigorously prove theorems, and so on. Now, Joe Sixpack doesn't really need math all that much, beyond basic arithmetics. But even Joe could benefit from deeper understanding of it, to avoid getting pwned by banks, real estate agents, car dealers, insurance companies, stock brokers and so on.
If in other sciences we should arrive at certainty without doubt, and truth without error, it would behoove us to place the foundations of knowledge in mathematics.
-- Roger Bacon
Ramanathan is right and wrong. Wrong that we don't need to teach math; right that we're teaching the wrong kind. Calculus, and even trigonometry, are powerful mathematical frameworks that few people will ever use. On the other hand, logical, statistical, and economical reasoning are essential to daily life. Euclidean geometry is a beautiful way to teach logical reasoning, but most schools get caught up in the geometry and fail to recognize the value of teaching people to reason logically _in general_. A course on "statistical fallacies in the newspapers" would be way more valuable than a course on differentiation and integration (and the source material is limitless). Nowadays, given the prevalence on computation in everyone's life, a course on basic programming would also be of greater general value than the math we teach now.
The sun is setting on America, and I have this gloomy feeling that we're going to see a lot more articles like this: we don't need math, Engineering is dying career, college is overrated, it's better to just learn to work with your hands, etc. Maybe I'm jumping at shadows, but this is how I imagine things will go as our youth are converted into low cost portable labor.
It's not that everyone will learn differential equations. You don't finish high school unless you do.
Those who can't do math don't graduate. I expect them to drop out or continue on for another year, though I admit it would be more cool to have them go on stage at the graduation and perform sepuku when their name is called.
I can't think of a better way to do it
Teach it to them when they do need it.
Or show them what it can be used for, before teaching it.
(ie. Make them need it sooner.)
By giving students interesting problems to solve (that can only be solved using maths) before teaching, their attention will be held that much better.
In my experience this practice is common among good teachers, but uncommon among bad teachers.
Some subjects are harder to teach than others, and require better teaching skills. Such teaching skills can be taught.
A good teacher can even lift a students mental blocks.
On October 1st, George M. Phillip, the president of the New York State University at Albany, announced that the French, Russian, Italian, Classics and Theater departments were to be eliminated by 2012.
Humanities and social science programs in the UK face an 80% reduction in government funds for research and teaching. The reduction is interpreted as attempt to steer the UK educational system toward a for-profit model--a move that will force many institutions to close and that will transform all but the elite universities into technical schools.
Could this sustained assault on the public education system and the university itself be a misapplication of mathematics? Now that the development of mathematical methods with the potential to raise the level of political and economic discourse above ideological debate appears within reach, the public education system is faced with massive cutbacks on a global scale. The institution of tenure must defend itself against the adventitious imposition of market based-criteria of faculty productivity. Administrators relentlessly expanding their domain of responsibility and resentful of their support role fantasize "upstreaming" faculty research to themselves. Adherents of the "build to strength" philosophy wreak havoc on their institutions by eliminating departments deemed to be under-performing--typically the humanities and social sciences--as this is the most expedient way to terminate tenured faculty.
But now it appears that mathematics is next.
In my opinion, the greatest value of math is in college preparation. Based on my conversations with students at several college campuses, fear of math seems like the number one reason a lot of people do not go into engineering or science majors in college. It's part of the reason we have so many people going into liberal arts majors like mass communication or political science instead of CS, engineering, or sciences. While one needs just some knowledge of algebra for real life applications, it's really important that as many kids as possible are taught pre-calculus, and even calculus in high school, and that they're taught it well. Just my $0.02.
How bout Imaginary numbers. WTF. Never used those.
The question in the title "How much math do we really need?" is really the author, Mr. Ramanathan expressing a low opinion of his students, a low opinion of a textbook he used in his classes and a low valuation of all students.
The pesky word "need" is the pivot point for his sophistry.
If your educational model is to create truly educated men and women, you need at least a quality geometry course and four years of college level mathematics.
(See the curriculum provided by the great books colleges, St. John's College at Santa Fe and Annapolis.)
In my opinion, the two great fields of mathematics are: Calculus (based on limit theorems) and Topology (based on Euler's polyhedron theorem). The calculus has been over emphasized and topology has been seriously neglected.
To be real specific, the high school curriculum could really benefit from a topology course that would cover knot theory (with matrix math), paper folding (with solution of equations), lattices, symbolic logic, network theory (with walks), and surfaces(with klein bottles), and an introduction to fractals. It could be parallel to Algebra I.
Topology has both the beauty of pure math and a wealth of applications. Unlike calculus, in knot theory for instance, after a couple days' study a student can encounter unproven theorems.
Right there: obvious things that nobody has been able to prove in 50 years! Yeah, how does that affect the development of your "educated person"?
It seems your education didn't provide much about evolution.
Those who prioritize "issues facing our planet" over reproduction are severely selected against. If family size is even slightly inheritable, we'll be back to huge families in no time. Family size shrunk because of changes in the environment (primarily birth control) but it can go right back to being large. There are existing individuals who have mental traits that encourage large family size. In not very many generations, they will become predominant.
Squalor is the norm for all life forms, humans included.
I did find that I had to use Calculus once, about 12 years afterward in the real world.
I had to calculate summations; learned in Calculus II.
Either I could do it in Excel, and take 50 pages to calculate it, or I could summarize it into a nice little Calculus formula.
I couldn't figure out how to create the formula at the time, so I went ahead with the brute force method and created 50 pages of Excel to get my answer. Thank heavens for Excel.
Then the following day, I looked at the problem again, and derived my simple formula to solve my problem. A skill which I had once learned 12 years prior in some Calculus class I took in College; while questioning, when the heck was I ever going to use such a knowledge in my life.
Now, I can plug that formula into a program, and it will help me solve more questions that would take me 200 pages of Excel to brute force calculate.
Times like that is when you appreciate the beauty of math.
The median pay for an engineer is above the median pay for a worker. Therefore, we have a shortage of engineers.
That proof is legitimate for any field that doesn't involve bidding wars for superstars and/or a fixed number of positions. It's wrong for things like pro sports, but it works perfectly well for anything normal.
Hey - how much do we even need to read? Does History really have any relevance for anyone anymore? Why should anyone need to write? All anyone needs is an XBox, and some beer. No one needs skill or expertise - except perhaps a few who are interested in programming the entertainment systems, or workerbots.
sheesh.
On a stack-based calculator, you should get 100.
When you press "+", you get a stack underflow error. Continuing on as if nothing had happened, you enter the "10". When you press "*" you get another stack underflow error. Continuing on as if nothing had happened, you enter the "100". That just sits there. (you are supposed to do "100 ENTER 10 * 5 +" instead)
Getting 1500 would be really defective. Are such calculators actually sold?
For more of the history of school: http://www.johntaylorgatto.com/underground/toc1.htm
If you are an educator then the book linked above is a must read. The chapter entitled Intellectual Espionage is a must read for those who love standardised testing.
The new right fascists are bilingual. They speak English and Bullshit.
Calculus (and some other advanced math in specialized schools) was included into secondary education course. Students and teachers were moaning, but somehow struggled through. There were no noticeable impact on common workers, but engineering college students were a lot better prepared, and had easier life (advantage they used to drink more). Education ministry of modern democratic Russia decided that advanced math is harmful for working people, Russia don't need many engineers anyway, and advanced math was removed form curriculum.
Thank God for that. I no longer feel ashamed of being horny whenever I see roadkill.
The new right fascists are bilingual. They speak English and Bullshit.
Unlike literature, history, politics and music, math has little relevance to everyday life.
It just seems like lots of people are missing this point. Another point that's getting missed is
That courses such as "Quantitative Reasoning" improve critical thinking is an unsubstantiated myth.
This may or may not be true, but many of the counter-arguments I've read take it as given that math courses improve critical thinking. Personally, I tend to agree with the article, but it doesn't provide enough evidence to truly convince me. That is, I run both inductive and deductive reasoning when considering arguments; my inductive reasoner says "yeah, I think that's right" and my deductive reasoner says "but it's not rigorous enough to really say".
Right, because high school students make such good choices about their futures. Like about whether to make babies.
Math is *already* a filter in the U.S. school system, and people who opt out of it are denying themselves entry into a huge swathe of well-paying jobs. And in the U.S., way too many people subscribe to the myth that the ability to do high-school-level math is a matter of in-built talent, so they get one bad grade and conclude that their brains aren't built for math and they stop trying.
Math is actually one of the things kids can do pretty well, because it does not rely on knowledge about the world.
I think notion that people don't use math in their lives is very much misguided. Example of compound interest in another post above was an excellent point. We think we don't need and don't use math, but that's only until we go to a bank for a loan, try to check our bill from a vendor, endeavor on a nontrivial household construction project requiring some geometry, or try to understand something about politics and economics around us. Then we remember and apply our math skills, but somehow this doesn't factor in the argument about "uselessness" of math education.
What people mean is not always what they say. If one wants to simply know what they said, anyone can just read it. One may want to conclude that they meant nothing beyond that, and that's fine... but that's not generally the point of literary analysis... it's to search for any deeper meaning beyond the literal words themselves.
File under 'M' for 'Manic ranting'
First of all, probability at an elementary and high school level is generally a matter of motion for nearly all students which take exams on it. If you doubt this, check out the massive number of people gambling online. The fact is, people don't grasp even the slightest concepts of probability in relationship to mathematics. People get excited over statements like "a 500% better chance to win!", but first of all, they don't ask "better than what?" and "what were the original chances". That 500% better chance actually just made it so that they still would have a better chance of getting hit by lightning... in their shower... in a sealed underground bunker... with water provided by an underground storage reserve.
There are many people who use probability for the majority of their decisions all day, every day but couldn't calculate the number of possible outcomes from a roll of a pair of dice. They don't understand probability, but they do survive based on subconscious decisions such as "If I start walking across the street now, the car driving at me will have a chance to see me, then will manage to stop in time to not turn me into roadkill". This is a probability related gamble, but it's based on experience as opposed to pure probability logic.
This is a topic that we often call common sense (or lack-thereof). Even an uneducated coal miner will teach it to his children. It is often something we learn through experience. If we actually took the time to calculate out whether the car will have a chance to stop or not, we could just wait for the car to pass instead... and the 50 cars following it.
I personally prefer that we focus more on boolean logic and discrete math with kids at a young age. Let us force them to learn how to think past a single level. The average person has the ability to identify cause and result at a single level, but can not cope with any complexity introduced by conditions when calculating a second level. For example "If I go to school today, I'll see my friend Jesse" is easy to understand. "If I skip school today AND wait beside the building on 3rd, but NOT between 1pm and 2pm when the principal passes there on his way to and from lunch, the I can see Jesse AND NOT have to take my math exam OR eat a terrible cafeteria lunch" is far more complex.
Demorgan's theorem is one of the most useful topics in solving daily life problems. We often waste a tremendous amount of time waiting for condition A and condition B to be true when we could instead take a moment to verify that either condition A or condition B are not true.
I have personally spent ages waiting to go do something because the person I'd like to go do it with insists on waiting for either two positive or two negative conditions to be true. When you try to explain the simple laws of logic to the person who is forcing you to wait, you might end up losing a friend for making them feel stupid over their flawed logic.
So, forget probability which is hopeless to teach anyone anyway and focus instead on logic which should be taught side by side with addition and subtraction from the time a child can write their names.
Even though we'll never really teach it to the people who never learn it at any age, it will teach them to subconsciously think more intelligently. Beat logic into their heads from a young age and maybe when they're making plans or decisions, they'll actually think things through a bit better without even knowing it.
That being said, as a father of a 7 and an 8 year old, I talk with teachers in schools, teachers who are parents etc... quite often. Some of these are even math teachers and frankly, I find that most teachers are utterly incapable of teaching logic to anyone since they haven't learned it themselves. Such and insanely easy topic is incredibly complex for the majority of people out there.
I am not sure what AGW stands for (I tried to google with the "define: AGW" but I doubt you meant American Glass Works) but based on the context, I think that it has something to do with the climage change (perhaps... [Something] Global Warming]). Anyways, we really don't need integrals for that.
Anyone who looks at Global Land-Ocean Temperature Index (or data from meteorological stations or any other relevant climate graph) can clearly see that temperatures are going up, they weren't doing so over a century ago and they're certainly doing so faster than some 80 years ago. And that they're doing that despite the fact that there is occasionally (like now) some 2-3 years during which the temperature stays stable (or even drops very slightly).
I don't think that one can make any argument against the fact that a rapid climate change is happening. Rather, those who used to deny it now tend to claim "Oh, but there have been other times in history, during which temperatures have gone up without us"... Which is, of course, irrelevant. If we deem significant climate change to be catastrophic and can scientifically show that something we do at least contributes to it, we should probably try to do less of that.
I must say that I do agree with the article. Math departments are much larger than they need to be, thanks to the notion that everyone needs to learn lots of math. The public has been duped, and though it benefits me directly by giving me more opportunities for jobs, it is unfair to require so many people in nontechnical subjects to take math that they'll never need. It's noteworthy that the author only came out with this after he retired from being a math professor. I can tell you that there are many math professors still teaching who feel the same way, but can't come out and say so for obvious reasons, which is why I'm posting this as an AC.
With out Math? What does it mean?
Math is and has been foremost about solving problems. Real world problems. Get to the moon type problems.
How do you balance you checkbook type problems?
When are we going to get there type problems.
When are we going to get to a society that values Economic and Social competencies as well as cultural awarness?
Certainly not watching TVs Jersey Shore.
Professor is brilliant. Slow news day.
Professor is a blathering idiot! Slashdot front page news! Get it while its hot!
We certainly need only a small ratio of people with high mathematic, logic and scientific skills. But we do need them, starting their education at an adult age is too late (they won't think without accent), and you can't determine in advance which crops turn out good.
Some of the most important scientific contributions have come from "slow starters". Because it is not just enough to be proficient in math. You also need to be proficient in what you want to apply it to.
So, yes sure, but we can't help it.
"unlike literature, history, politics and music, math has little relevance to everybody's daily life" - i agree maths has very little relevance to who's going to win X factor, what the next overpriced Apple fashion accessory will be or how much meat Lady Gaga is wearing to the next premiere. It is of course the basis of every technological leap made by human kind throughout history but that's not important.....
Because you never know who will be left holding the bag of our unsustainable consumer lifestyle.
We need people that know to much, not know to little.
This is like passengers on the titanic burning the life boats because "We're crusing along fine aren't we?"
The peak oil hits, people have to fend for themselves and they can't even do technical things cause they lack the math mindset..
The original version had the cat on a pedestal.
the style of critical thinking that is exercised in literary analysis
"Agree with teacher" is a kind of critical thinking?
Then maybe I didn't get the message. I would be happy if you would explain to me the point and purpose of literary analysis, or some of the take-away messages that can be applied in my life.
For comparison, history is "a video running in a loop, in which a small group of people try to dominate and extract resources from a much larger group of people" (paraphrasing Brett Veinotte of schoolsucks.podomatic.com). The point of studying history is to learn how to affect societal change and how people might try to extract resources from you.
Advanced math in school useful in support for education of big number of engineers. Otherwise it has no impact.
Kids don't know why they're learning higher math, and they don't have any incentive to learn it except for the "if you don't, you fail school"
If you give kids problems to solve which they find interesting and fun, then they will learn the math they need in a couple of weeks.
If they have no interest, then no amount of math lessons will give them the interest, and you'll be just making yet another disenfranchised youth who believes the system is shit.
What we need to teach kids is problem solving, information research and workflow optimisation, as well as basic useful skills we all need to work as a society (reading, writing, statistics, fact-checking, the scientific method).
More than one. Here in the civilised world, we have "Maths" because we do more than one sum. :-)
I'm pretty sure I've related this story on here before, but here goes again.
I used to work for West Australian Police (as a civilian) and one of the things I used to do was look after juvenile delinquents. I had a high school kid with me one day who tried telling me that maths was crap and he didn't need to learn it etc.
I asked him, 'If you were offered a job for $400 a week or one that paid $50 an hour for 40 hours work a week, which would you take?'
He insisted the $400 a week job was worth more than the $50 an hour x 40 hours job. I had to explain to him that the $50 an hour x 40 hours a week was $2000 a week. He still insisted for a while that the $400 a week job was more. It was hell trying to get him to think it through.
But, the main point is, how relevant is the maths we are teaching now a days to what they will use. Many will need at least basic skills and they will need those skills re-inforced as they go through school. If an average kid in High School can't tell the difference in pay between a $400 a week job and a $2000 a week job, then society has failed. Good skills in the areas that they will use in every day situations (like not getting ripped off for change or bank interest etc) is important. Learning how to calculate the area under a curve using calculus, less so for the average student.
Sure enough, the cow costume was hanging up next to the superhero outfit and sailors uniform. (S,Spud)
http://xkcd.com/263/
When I asked my third grade teacher what use I could possibly make of Venn diagrams in everyday life, she told me "when it happens, you'll be happy that you know them." It's been almost thirty years and I'm still waiting for that day when I face a problem on the street or at work that can ONLY be resolved by a Venn diagram...
And how do we know who needs it? 99% of women don't need any formal education, they just need to do the dishes and cooking. So education is wasted on them.
And 99% of men's education is wasted, since you don't need much to operate a lathe or dig a trench.
But like the "90% of Application X is covered by Application Y", we don't know who the 1% the education will be useful for will be until we've tried teaching 100% of them.
Without educated women, Mme Curie wouldn't have made her discoveries. Not educating all women would have been a waste.
It isn't a tin frying pan for a start.
Maybe there's no coincidence between soaring national/state/provincial/city/personal debt and lack of maths skillz.
Well everyone thinks, while some1 is in school, that he will never need maths again. 10% of those start studying mathematics. Same happened with me...and to the topic, yes in everypart of this strange world we need maths.
http://www.wowcast.de
How do you know that there's interesting stuff in german that hasn't been translated (never mind "never will")?
If you know it's interesting, then you must have understood it in German. If so, you can translate and put it out there. Of course, the "owner" may not want you making a translation, but then the problem isn't the interestingness or germanity but the assholery of the owner of the work in question.
If you don't understand german, then how do you know it's interesting?
I hate to tell you this, but your core premises are wrong. Continuing to argue with you would be like trying to convince a creationist that evolution is correct; you're so whacked that it won't do any good.
The real shame of it is that it's people like you who are doing real damage to the country, always criticizing with no productive ideas, trying to tear down the very institutions that DO work well and that made it great.
It would be nice if all the people exposed to political ads and then voting would have a basic understanding of statistics.
I've long felt that math teaching would be much more successful if there was more context ie what could I use matricies /for/
I recall the many happy hours I spent optimising ship/mecha/whatever design and that started me toying with the idea for a game (computer or board) that could put maths into some sort of context (for boys at least :-)
The main element of the MathFleet Battles would be and intentionally complex the ship design system set up in such a way as to allow many optimal ship designs and many many more non optimal ones. The rules would imply (but not state) questions like:-
The optimal battleship shape is a sphere, but the Meson Cannon is a long spinal mount weapon which increaces power with length what is the optimal shape for the ship.
The probability drive has a 2/3 chance of hoping the ship in a random direction forward and a 1/3 chance Drives come in a number of models with different jump lengths, jump frequency's and power consumption. Which is the best one for your particular ship.
How many mine dispensers do you need to have a reasonable chance of hitting a following ship if each mine has a 1% chance of hitting.
The object of the game would for groups to design be best ship they can and the try and blow up the opposition.
A group that had worked out that if they could would out that if they had X mine dispensers would give them a 65% hit chance and still leave enough room to pack a dozen extra medium lasers, which, between the systems would give a 95% hit chance
If you help me find the Time Masheen, I'll pay you like 4 billion dollars.
...
Methinks the troll tag on this article is most appropriate. I almost spit my Cheerios on the floor yesterday when I read Dr. Ramanathan's article in my local fish wrap. I'm guessing his intent was to proffer the most basic straw man so as to spur discussion as to how to make math education more effective in modern society. I offer this forum as my first point of evidence.
US2B
except I would change it to read: unlike math, literature, history, politics and music have little relevance to everybody's daily life.
If you are not allowed to question your government then the government has answered your question.
I would rather see grades 1 - 8 focus on essential life skills rather then math, literature, geography, history, etc. I think children are not being prepared for reality, only some idea that they have to learn the 3 R's of education "or else". By focusing on life skills I think a student will typically find school more fun and less taxing, and thus possibly want to continue with high school and beyond. These life skills should also include arts, such as music, so a student can get a well rounded exposure to other things other then math and science. How many virtuosos are being lost simply because they never have had a chance to touch an instrument or have a chance to build other skills and talents. I think the current academia program in North American have students "burnt out" by the time they hit grade 9 making continued learning a chore and something they want to avoid. Sending an 8 year old home with 20 pounds of books and 4 hours homework is not ideal to success.
Make the first 8 grades "fun" while constructive so by the end of it the student can "get by" easily through life. Start to focus on pure academia by high school, ultimately allowing the student what course in life to proceed whether they want to pursue higher education or get into the working force earlier with some essential skill they have already learned.
The weight of the Earth comes in useful in calculating how many space habitats you could build from it. :-)
Let's see:
http://en.wikipedia.org/wiki/O'Neill_cylinder
http://www.newworldencyclopedia.org/entry/Space_habitat
http://ramblingsonthefutureofhumanity.blogspot.com/2009/10/designing-space-habitat.html
You can support 15 million people with a habitat requiring 3000 million metric tons of mass (if I got that right), or about
3 billion tons. (One could also ballpark that mass calculation, but I won't right now, just by thinking about a shell of six feet deep material with some surface area.)
The Earth weighs, as above, about 5 billion trillion imperial tons (close enough to metric tons). So, if we vandalized and vaporized the Earth to build space habitats (not that we know how yet), we could build a trillion space habitats that each support 15 million people. Or, that would be about 15 billion billion people, or about a billion times more people than the Earth supports now. I have not double checked that, but it sounds more or less right within a thousand or so. :-)
Anyway, while I don't recommend disassembling the Earth to make way for a space habitat(or hyperspace) bypass, as there are plenty of asteroids and moons in the solar system that are easier to use for mass, and it makes sense to preserve Earth as a historical landmark to our past, this points out that people like William Catton who are spouting imminent danger from "overpopulation" are more just lacking basic math skills and some imagination. :-)
"[p2p-research] Earth's carrying capacity and Catton"
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-August/004123.html
"Bottleneck: Humanity's Impending Impasse, by William R. Catton, Jr."
http://www.theoildrum.com/node/5954
Contrast with someone who though the empowered human imagination was the ultimate resource:
http://www.juliansimon.com/writings/Ultimate_Resource/
These calculations have life-and-death consequences as relate to human wars and decisions about having children or abortions. Seriously. Whether someone is stockpiling ammo for the "overpopulation die-off" or trying to get a job at NASA or private or volunteer efforts to build space habitats or even just design better solar panels hinges on this sort of basic math.
The consequences that flow from this simple calculation about the weight of the Earth and the weight of a space habitat in comparison are politically profound. They suggest we should not be fighting over oil as a form of dogma-driven collective "suicide" but instead should be putting a lot of time and effort in developing a serious space program and other advanced technology, but from an abundance paradigm where the wealth is widely shared, not a scarcity paradigm where wealth is tightly hoarded. See also my essay:
http://www.pdfernhout.net/recognizing-irony-is-a-key-to-transcending-militarism.html
"There is a fundamental mismatch between 21st century reality and 20th century security thinking. Those "security" agencies are using those tools of abundance, cooperation, and sharing mainly from a mindset of scarcity, competition, and secrecy. Given the power of 21st century technology as an amplifier (including as weapons of mass destruction), a scarcity-based ap
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Most Americans, hell even most Europeans probably don't know enough about recent history to understand this reference of yours. You succeeded in sending a cold shiver down my spine, though, FWIW.
Ancient Greece and Ancient Rome did not have compulsory education, were they not "advanced" for their time?
The Haudenosaunee (Iroquois) had no compulsory schooling as we know it hundreds of years ago, but the USA borrowed ideas from their society for its constitution.
The USA did not have compulsory education for most of the 1700s and 1800s. Was US American not advanced for its time? Was it perhaps in some ways more advanced back then, as Gatto suggests, with more independent self-educated people with a higher degree of literacy?
Anyway, another reply by someone else (who you may have confused with me?) makes a related point.
There are lots of better educational alternatives than compulsory mainstream public schooling listed here:
http://www.educationrevolution.org/
Why not just give the money that now goes to compulsory schools directly to the parents to let them decide how to spend it on their children's behalf? A related specific proposal:
http://www.pdfernhout.net/towards-a-post-scarcity-new-york-state-of-mind.html
And if you say, you can't trust the parents to look out for their own children's interests, then what does that say about the value of thirteen years of compulsory schooling?
Anyway, there are lots of alternative ideas out there if you look around with an open mind. But the whole point of compulsory schooling is to close people's minds and distract them. That may not be the intentional purpose of most schoolteachers, but it is the end result of the systemic process, and as Gatto suggests, that process is doing exactly what it was designed to do, so if you give it more resources, it will only dumb people down faster and more comprehensively.
See also from a previous vice-provost of Caltech and a previous editor of Physics today that say related things:
http://www.its.caltech.edu/~dg/crunch_art.html
http://www.disciplined-minds.com/
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
G.V. Ramanathan expresses a common ethnocentric egotistical point of view of Academics. Math is more than equations and numbers it leverages brain power by giving the possessor the power to think and make decisions in quantitative rather than qualitative terms. Second those gifted with math abilities do make it through a educational system that teaches math so poorly that it creates mental illness. Everyone has the ability to learn math, which is after all merely a language. The problem is that the ability to learn languages must be exercised before it atrophies. I do agree that the approach to encouraging math is flawed, Kindergartners should be graphing lines instead of learning to do calculations. The need is for math is much greater in today's information age than in the industrial age. In fact math is as important in the information age as reading literacy was to the industrial age. Math ignorance leads to science ignorance which today is seen in the climate debate. This debate is not scientific but political and only exists because of math illiteracy of the American public..
And who decides what knowledge or skills (including unquestioned immediate obedience to authority as exemplified in classrooms?) are important to a child's present or future, or the present or future of the culture they live in?
Who picks the hoops a person is forced to jump through (in a democracy)? The person? His or her parents? Neighbors? Elected officials in the community? Big foundations? How should these different voices be balanced in a democracy? What are we trying to achieve as a culture? Do some of these voices (business concerns?) have a stronger influence than others (like Gatto suggest)?
What different views are there on this?
http://www.mindfully.org/Reform/2003/Compulsory-Schooling-AnarchistMar03.htm
"The history of the development of Western schooling is a complex and meandering thing, but I think it is worth looking at in a very abbreviated form here. A little insight into the logics and basis for contemporary compulsory schooling might be useful to social ecologists."
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
The question of what to learn, or who decides it, is irrelevant. The point is simply that testing has been proven to improve retention. You can argue social policies all you like, but it won't change this basic fact.
Higher Logics: where programming meets science.
WTF? I just gave you a productive idea in my previous post: break up the country.
And exactly what institution that works well did I tear down? Our education system in the USA is an utter disaster. The only governmental institution that really works well in the USA (I know the libertarians will disagree) is the USPS. They deliver my small packages across the country in 2 days for far less money than UPS and Fedex want, and they don't break them like UPS does to everything.
If you think our pre-college education system works well, then you are an idiot. Your idiotic post definitely deserves the Flamebait mod it got.
I feel that music and literature is important
But which literature? The high school that I attended forces six tragedies by one British playwright on all students. It also forces students to read love-drama novels when their brains are not yet formed enough to understand the motivations of the characters. Under what criteria do those who set the required reading list decide which works are The Classics(tm)?
There are lots of areas we need more math in, but probably not what you think. Logic would be the first one, yes probability and statistics (80% of all statistics are made up) ... not all math is about numbers after all. Oh yeah, I'm always surprised by how little people seem to understand of geometry. No, I don't mean proofs, I mean shapes, filling spaces, general concepts like that.
Yes, I am one of those who likes to curl up with a good Algebra book. But it is amazing how much of this stuff could be used every day if people knew it.
We all use literary analysis every time we read a news site, watch a movie, or myriad other situations every day
Then why do literature teachers teach literary analysis on novels, short stories, and poems, rather than on news sites, movies, or other situations?
apparently even if the director/author/poet personally says straight out that no, their use of some church bells is not a symbol for neo-colonialism or whatever else you've dreamed up that doesn't count because everyone makes their own meaning.
In other words, death of the author. But in the real world, it's difficult to apply death of the author in the literary criticism sense until 70 years after the death of the author in the legal sense because the author or the author's estate still has the exclusive right against certain reinterpretations.
Does anyone NEED math in their life? I'm sure you could get by without it and survive...but you're guaranteed to live a lot worse! Probability, basic accounting practices, decimal/fractional math, and other basic stuff we learned early on may seem simple and basic enough, but few people understand it well enough to use it to their advantage in life! Taking out a mortgage? You'll be in bad shape if you don't understand all the types of loans out there, the benefits of each, and be able to determine which is the best deal for your house. Our mortgage crisis wasn't caused by well-educated Americans making careful and thoughtful decisions! Out shopping? Being able to compare prices and quickly do that basic decimal math in your head (and add or subtract percentages) can save a lot of money in the long run! Beyond all the simple economic examples, I like being able to read the news, whether it's politics, science, or economics, and have a clue what's really going on. Math isn't just for test scores and educational grants, it's so people can understand the world. Understanding math allows people to solve problems better and to apply analytical skills to the world around them instead of judging based on biases, rumor, or the opinions of others. It's lack of science and math knowledge that's allowing people to hold ignorant beliefs and make poor decisions, whether on a mortgage, or on who to vote for in an upcoming election. Will the average guy need Calculus for anything...nope. Will they need alot of other math skills in order to live their lives the best they can? Most definitely!
I had citations everywhere, and everything was either a direct quote or a paraphrase. The extent to which I injected original thought or analysis into this work consisted of conjunctions, articles, and perhaps a two- or three-word connecting phrase in a couple of places.
So in other words, you made it look like a Wikipedia featured article.
Is algebra advanced ? probability ? statistics ? geometry (volumes, areas etc) ? proving things ? calculus ? diff eq ? I don't think we teach (in the US) any advanced math in HS, except for AP calculus ! Maybe you can be a little bit more specific ?
Strangely, our teachers loved mentioning how this part or that part were just dirty jokes to get cheap laughs from the bums.
Some years ago, I helped a colleague at work, who was attending a night-school accounting course, who had no idea how to calculate a simple proportion sum.
(If 5 apples cost $4.00, how much do 12 apples cost? 12 apples cost more than 5, so it's 12 / 5 x 4.00 / 1 = 48.00 / 5 = where's my calculator? ummm $9.60)
He'd passed senior high-school and been accepted into the course on his results.
I don't think things that "simple" are taught any more, as a simple stand-alone arithmetic tool ... something I learnt in primary school (elementary school).
So maybe, to keep it useful and relevant to daily life, more Arithmetic to a higher level needs to be taught (possibly in the simplistic repetitive rote manner it always was taught) and perhaps a greater level of interest in higher Mathematics will result.
Don't blame me, it's usually 2 in the morning when I post
The weight of the Earth comes in useful in calculating how many space habitats you could build from it.
No it does not. The mass of the Earth might be useful to know though. Since imperial units like pounds and tons measure weight, not mass, you cannot use the normal conversion of one metric ton (mass) to imperial ton (weight) for this because it assumes a constant gravitational field of 9.81m/s^2 which is clearly not the case when dealing with space habitats.
When it comes to constructing real-world things maths alone is not enough and you do actually need some basic physics as well.
Education can have several goals in this descending order:
* To help a person grow as a person
* To help a person be a good citizen
* To shape a person into someone elses' vision of a good consumer and good worker and, for a few, a good obedient professional with the "right" politics
I don't find these categories helpful. The third simply informs the first and second.
The Daddy casts sleep on the Baby. The Baby resists!
See what I mean about arguing with "government is evil" pricks? Pointless. No matter what I say, you've already zealously started with a false premise, and nothing anyone says will change your mind.
I do indeed think that our pre-college education system works very well. It has--and continues to--turn out some of the most brilliant minds that the world has ever known. But because it's not perfect, in your demented little world, it's "an utter disaster." Yes, there's definitely idiocy going on, but it's not on my part.
Personally, I've had experience with both public and private school. Both had upsides and downsides. In the end, I chose to leave the private school I was attending because I realized the simple notion that which school you attend has little to do with success and happiness in life. It mostly depends on how well your parents train you for dealing with the real world, and how much you take personal responsibility for your own education, both book-wise and common sense-wise.
I can't speak to the former in your case because I don't know you, but based on your posts, I can definitely speak to the latter. You have very little common sense.
So tell me, in your educational utopia, what happens after we've dismantled the public education system? I can tell you, because we've been there. You pretty much took over whatever job your parents were doing because there was little to no opportunity to do anything else. Only the rich people could afford to send their kids to school or pay for private tutors. Will you be the one to explain to poor people how in this land of so-called "opportunity," you're looking to take away the one great opportunity equalizer among different social classes we have away from them?
"I'm sorry, Timmy. You used to be able to learn calculus in high school for free so that you could become the engineer you wanted to be. But in 2010, Grishnakh declared that the government was evil, your parents who work at the local 7-11 can't even teach you basic math, let alone calculus, and of course your family is too poor to pay for you to have a private tutor. Oh well, c'est la vie! Oops, sorry, I forgot that you've never learned French, either. That means, 'That's life.' Oh, no, I didn't mean that no one can be an engineer, that privilege is reserved only for kids of families of means. C'est ta vie--that's your life!"
Yes, we tried it that way, and it didn't work very well. Thus, we tried it another way, and we became one of the most well-educated and universally-educated countries on the planet in a very short time. Now because of some irrational hatred or paranoia, you want to tear it all down. The result is predictable, because again, we've been there: most kids will not get an education, and the general level of intelligence of the population as a whole will dramatically go down. If you think this is a good thing, you're either so rich that it wouldn't matter to you or you're so stupid for listening to rich people pushing that agenda that you don't know better. Either way, you clearly do not have the best interest of our country at heart, and thus your opinion holds no weight to me.
Only idiots buy into the whole "government is evil" pablum that is being foisted by and upon people like you. Only a total tool actually tries to tear down an institution that has provided immeasurable opportunity to countless people.
Tell you what, if government is so evil, how about putting your damned money where your mouth is? Stop driving on those cushy government-provided roads and interstates. Go mix some arsenic in your water and take some drags off your tailpipe, since the government is what sets environmental standards for how clean our water and air must be. If your house catches on fire, don't bother calling that socialist bastion of evil fire department. Let me know where you live so I can come rob you, secure in knowing that you'd never dream of calling those evil police on me. Mix some poison i
I have an education in electrical engineering. Yet I can think of only one time in my professional life I ever had to solve a differential equation, and by that time I had to look up how to do it since I mainly forgot the the details. But differential equations can help you understand transistor physics.
My experience with vector calculus enabled me to understand important concepts such a coaxial cable and antenna design. I also learned a great deal of applied Real and Complex analysis in terms of Laplace and Fourier transforms, but I never had an actual "analysis" math course. I don't typically solve transforms any more, but my knowledge that they exist inform my understanding of video and audio compression and signal equalization techniques.
In high school, I had an awesome combo of synchronized calculus with physics, which truly helps you understand both.
So I think often math is a tool to understand technology, even if you are more of a technology user than developer.
On the other hand, I think everyone could use more probability and statistics knowledge, as we do have to deal with understanding financial, economic, and political statistics on a regular basis.
People do need to know math. The bankers who sold people sub-prime mortgages, and people who bought them did not know math or did not know it well enough. They bought mortgages they couldn't afford because they didn't understand interests rates and basic addition and subtraction (Algebra II level knowledge in my HS). Is the financial crises and subsequent recession a result of bad math or lack of math knowledge, I think so. I suspect that the same intellectually lazy people who in school said they would never need math so why learn it (as if this were common knowledge or revealed truth) are the same people who have facing enormous credit card debt, debt in general (the new norm in our society), or entered into loans that they couldn't pay. Indeed it is surprising that a nation that shuns math so much finds itself in massive debt.
People need more math, not less. This man teaches actuarial courses, actuaries are paid well for their knowledge. Even actuaries just entering the job market are paid handsomely. If anything people need math for practical purposes, like making a living.
You, sir, have a good question. Literary analysis is, by definition, the analysis of literature, so it's taught on literature. I was unclear in saying that it's used all over. The skills used in literary analysis are used all the time. It's our ability to interpret, analogize, and make inferences about meaning that make communication richer than simple communication of action. Listen to or read Carl Sagan's works for a great example of how very intricate and exciting scientific ideas can be communicated in a rich and interesting way that would not be possible without skills which are often described as "interdisciplinary". My overarching message was just that all studies are important; yes, to varying degrees to different people due to both their work and aptitude. But if we completely ignore any subject we do so at our own peril.
I never said government is evil, only OUR government. There's plenty of governments that work quite decently, but they happen to be in smaller countries.
I do indeed think that our pre-college education system works very well. It has--and continues to--turn out some of the most brilliant minds that the world has ever known. But because it's not perfect, in your demented little world, it's "an utter disaster." Yes, there's definitely idiocy going on, but it's not on my part.
No, you're an idiot, and I don't think many people will disagree with me on this. The American education system is consistently ranked at the very bottom of industrialized countries'. The brilliant minds coming out of it are coming out in spite of the education system. Moreover, many of the "brilliant minds" in America are coming from PRIVATE schools, not the government-run public schools.
In the end, I chose to leave the private school I was attending because I realized the simple notion that which school you attend has little to do with success and happiness in life. It mostly depends on how well your parents train you for dealing with the real world, and how much you take personal responsibility for your own education, both book-wise and common sense-wise.
According to your logic, then, we don't need schools at all! Or at least we shouldn't worry about making them any good, because it's all up to the kids and parents. I'm glad more enlightened countries don't take your laissez-faire attitude.
So tell me, in your educational utopia, what happens after we've dismantled the public education system?
And this here is the proof that you are an idiot. I never said anything about dismantling the public education system, and I actually said that a good public education system is necessary for an advanced society. Do you even bother to read the things you reply to? Or do you just read one line and assume someone is another stereotypical right-winger?
My proposal is to break up the country into smaller countries, and let them rebuild their school systems, hopefully along the lines of the successful schools in countries like Germany and other European countries. It can't be done in America as it is now, because the country and government are too big and too corrupt, and that can only be fixed by downsizing. Just like you can't fix a monopoly by any method other than breaking it up, so it is with nations.
Tell you what, if government is so evil, how about putting your damned money where your mouth is? Stop driving on those cushy government-provided roads and interstates.
Here I am, advocating that we copy the socialist Europeans, and you're calling me an anti-government right-winger. Are you beginning to see why you're an idiot yet?
Jesus, you really are stupid, as is anyone who modded you "Insightful."
Sorry, but you're the stupid one here. You can't even coherently reply to anything I've said, and instead put words in my mouth. Moron.
Literary analysis is, by definition, the analysis of literature, so it's taught on literature. I was unclear in saying that it's used all over. The skills used in literary analysis are used all the time.
Then why is only literary analysis taught in K-12 school, not news analysis, film analysis, or the over 9000 other fields you implied? I imagine that students will be more eager to learn if they can see more immediate applications.
LOL. I remember this argument in college. And you are correct, everybody makes their own meaning (more so on post modern and later literature, but that's the point of that genre, no?). So? Did you have a bad experience with a professor who got upset that you didn't see the same meaning?
I was actually part of the very experiment you described (again, in college). We found that interpretations varied widely. It was both frustrating and fun. It taught most of us that even when given the same input, people would come to hugely different (and often equally logically valid) conclusions. One reason for this is past experiences. Knowing all this helps me all the time; how else can you explain logical, reasoned analysis of the same input leading to both Smart Conservatives and Smart Liberals? Both have equally defensible points logically, but their starting interpretations of the data are so divergent that they're unlikely to agree. If you can find the divergences, one can better figure out how to re-frame the starting arguments to bring them both to a more agreeable position.
Example: Randall Munroe. I interpret that comic as a dig against literary analysis, but not a definitive one. Randall appears to see everything in life through the lens of mathematics, making Deconstructionism, a highly interpretive practice which is heavily influenced by Philosophy, as unintelligible to him as mathematics above 7 dimensions was to me. However, I can appreciate both his frustration and see how he can be just like the nincompoops who think that since they don't understand the equations behind how quantum foam behaves near an event horizon that it's both useless and meaningless (just in reverse). We all do it sometimes, and it doesn't make me dislike XKCD (it is the only comic I read religiously), but it seems we have different takes on this strip.
I'd like to give you an answer, but I haven't had enough math to figure it out.
Judging by the number of people participating in state-funded lotteries, math education is somewhat lacking.
http://tvtropes.org/pmwiki/pmwiki.php/Main/MoreDakka
Never enuff Dakka, never enuff maths. People just get taught mathematics in a sucky way. Learn it properly and you use it for *everything*. Who hasn't heard of the kid who counted their steps, or figured out the number of tiles in the pavement, ie, folks who even use maths for silly idle stuff?
There's a book about folks like that, called Cryptonomicon. Shortening wars and saving millions of lives sounds like a good application ;-)
Math applies to every single aspect of not just your life, but your entire existence.. People just prefer the path of least resistance (to guess) instead of actually trying to figure out the truth of things.
BeauHD. Worst editor since kdawson.
Did you have a bad experience with a professor who got upset that you didn't see the same meaning?
Nope, I just recognise it as about as useful as a glass hammer.
Actual psychology would be far more useful for simply understanding people and their points of view.
It taught most of us that even when given the same input, people would come to hugely different (and often equally logically valid) conclusions.
in other news water is wet and ducks go quack.
did you doubt this or something?
how else can you explain logical, reasoned analysis of the same input leading to both Smart Conservatives and Smart Liberals?
You get the same divergence between people with even mildly different precepts.
Again.
water, wet, ducks, quack.
The view tends to be quite common amongst people who actually deal with genuinely understanding the nuts and bolts of the universe.
Try reading "A map of the cat" by feynman and his brush with philosophy.
In the Graduate College dining room at Princeton everybody used to sit with his own group. I sat with the physicists, but after a bit I thought: It would be nice to see what the rest of the world is doing, so I'll sit for a week or two in each of the other groups.
When I sat with the philosophers I listened to them discuss very seriously a book called Process and Reality by Whitehead. They were using words in a funny way, and I couldn't quite understand what they were saying. Now I didn't want to interrupt them in their own conversation and keep asking them to explain something, and on the few occasions that I did, they'd try to explain it to me, but I still didn't get it. Finally they invited me to come to their seminar.
They had a seminar that was like, a class. It had been meeting once a week to discuss a new chapter out of Process and Reality - some guy would give a report on it and then there would be a discussion. I went to this seminar promising myself to keep my mouth shut, reminding myself that I didn't know anything about the subject, and I was going there just to watch.
What happened there was typical - so typical that it was unbelievable, but true. First of all, I sat there without saying anything, which is almost unbelievable, but also true. A student gave a report on the chapter to be studied that week. In it Whitehead kept using the words "essential object" in a particular technical way that presumably he had defined, but that I didn't understand.
After some discussion as to what "essential object" meant, the professor leading the seminar said something meant to clarify things and drew something that looked like lightning bolts on the blackboard. "Mr. Feynman," he said, "would you say an electron is an 'essential object'?"
Well, now I was in trouble. I admitted that I hadn't read the book, so I had no idea of what Whitehead meant by the phrase; I had only come to watch. "But," I said, "I'll try to answer the professor's question if you will first answer a question from me, so I can have a better idea of what 'essential object' means.
What I had intended to do was to find out whether they thought theoretical constructs were essential objects. The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. I wanted to make the idea of a theory clear by analogy. In the case of the brick, my next question was going to be, "What about the inside of the brick?" - and I would then point out that no one has ever seen the inside of a brick. Every time you break the brick, you only see the surface. That the brick has an inside is a simple theory which helps us understand things better. The theory of electrons is analogous. So I began by asking, "Is a brick an essential object?"
Th
Sorry, old episode, out of date, so are you.
You're welcome.
Well, if you liked those, here are some other links accumulated from some years of homeschooling/unschooling... :-)
At a somewhat older age, this site on learning to read is interesting:
http://www.starfall.com/
We also like the original Electric Company with some episodes available on DVD:
http://en.wikipedia.org/wiki/The_Electric_Company_(1971_TV_series)
And it looks like there is a new version but I don't know how good it is:
http://today.msnbc.msn.com/id/28675624
But don't sweat "early reading". A kid is learning all the time. If they learn to read nature and computers and blocks and people and social situations and sand and water and pets and so on for seven to ten years (while listening to you read stories and other information aloud), they are learning in general a lot more than they would by trying to learn such things from books and other print media on the computer. If a kid wants to learn to read early (age two to four), fine. And of course, all kids should probably be exposed to reading material and the power of the written word (like adding things to shopping lists, or making signs). But if you go back two hundred years, learning to read at a later age was quite common, and kids catch up very fast. Don't let a stupid schooling lockstep age-focused paradigm harm your kid. Some kids also learn best to read by writing first (John Holt talks about this -- and how if you kid expresses an interest in writing, even just by scribbling stuff with no relation to regular letters, build on that). Note also that late reading in a homechooling/unschooling situation (where kids make their own choices) is different than late reading in a school-based print-based academic environment (where late reading is often a sign of some underlying health issue or just a broad, often justified, rejection of the authoritarian school paradigm, and problem piles upon problem if you can't read).
Contrast the probably true as far as it goes for compelled schooled children:
"Waiting Rarely Works: Late Bloomers Usually Just Wilt"
http://www.readingrockets.org/article/11360
"In the simplest terms, these studies ask: Do struggling readers catch up? The data from the studies are clear: Late bloomers are rare; skill deficits are almost always what prevent children from blooming as readers. This research may be counter-intuitive to elementary teachers who have seen late-bloomers in their own classes or heard about them from colleagues. But statistically speaking, such students are rare. (Actually, as we'll see, there is nearly a 90 percent chance that a poor reader in first grade will remain a poor reader.)"
with what happen when early reading is not emphasized because the environment is more flexible:
"Children Teach Themselves to Read"
http://www.psychologytoday.com/blog/freedom-learn/201002/children-teach-themselves-read
"In marked contrast to all this frenzy about teaching reading stands the view of people involved in the "unschooling" movement and the Sudbury "non-school" school movement, who claim that reading need not be taught at all! As long as kids grow up in a literate society, surrounded by people who read, they will learn to read. They may ask some questions along the way and get a few pointers from others who already know how to read, but they will take the initiative in all of this and orchestrate the entire process themselves. This is individualized learning, but it does not require brain imaging or cognitive scientists, and it requires little effort on the part of anyone other than the child who is l
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
What's interesting about these sorts of discussions is that they are much more approachable for everyone than if we were arguing over calculus type things. And, these sorts of calculation are sometimes much more amenable to reasonable discussions and amendments and improvements related to bounds than overly precise ones about exact outcomes.
As Freeman Dyson said:
http://www.edge.org/3rd_culture/dysonf07/dysonf07_index.html
"As a scientist I do not have much faith in predictions. Science is organized unpredictability. The best scientists like to arrange things in an experiment to be as unpredictable as possible, and then they do the experiment to see what will happen. You might say that if something is predictable then it is not science. When I make predictions, I am not speaking as a scientist. I am speaking as a story-teller, and my predictions are science-fiction rather than science. The predictions of science-fiction writers are notoriously inaccurate. Their purpose is to imagine what might happen rather than to describe what will happen. I will be telling stories that challenge the prevailing dogmas of today. The prevailing dogmas may be right, but they still need to be challenged. I am proud to be a heretic. The world always needs heretics to challenge the prevailing orthodoxies. Since I am heretic, I am accustomed to being in the minority. If I could persuade everyone to agree with me, I would not be a heretic. We are lucky that we can be heretics today without any danger of being burned at the stake. But unfortunately I am an old heretic. Old heretics do not cut much ice. When you hear an old heretic talking, you can always say, "Too bad he has lost his marbles", and pass on. What the world needs is young heretics. I am hoping that one or two of the people who read this piece may fill that role."
Back of the envelope calculations can give us a better idea of the range and scale of possibility, even if someone probably needs to do more detailed calculations to really make things work. So, we can answer "Might it fly?" with ballpark figures, whereas, "What is the best way to make it fly, given certain constraints and goals?" might take calculus or something else (evolutionary annealing algorithms or whatever).
It's been said (Knuth) that "premature optimization is the root of all evil": :-)
http://en.wikipedia.org/wiki/Program_optimization
but related to that may be the notion that teaching people optimization techniques and high precision math (like calculus or even the full times table) as opposed to basic approximation (like working with only one degree of precision or round numbers) may be the root of all extreme dumbness and math illiteracy?
By the way, related to general errors in assumptions (or calculations), especially in relation to the LHC at CERN:
http://reason.com/archives/2008/09/02/a-1-in-1000-chance-of-gotterda
"At the Global Catastrophic Risk conference, Future of Humanity Institute research associate Toby Ord asked an interesting question: How certain should we be about safety when there could be a risk to the survival of the human species? As Ord argued, "When an expert provides a calculation of the probability of an outcome, they are really providing the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in their modeling of the problem, or a mistake in their calculations.""
There is also the risk of "social group think" perhaps leading to this:
"The CERN black hole"
http://www.youtube.com/watch?v=BXzugu39pKM
Seriously, the LHC cost billi
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Sure, you got me there. :-) Thanks.
And also a lot of great math comes from great physics, and is easier to understand that way. My young kid really liked the "derivative machine" cartoon in this series, as well as other animations connecting physics with the math (especially calculus) it inspired:
"The Mechanical Universe... and Beyond"
http://www.learner.org/resources/series42.html
With so many great resources, learning both math and physics can be a lot more fun at an early age than slogging through a lot of paperwork:
http://www.fun-motion.com/list-of-physics-games/
Other sciences are part of that too, from chemistry through psychology and zoology, etc.
A great resource on chemistry, and how it connects with various logical and practical challenges:
"The World of Chemistry"
http://www.learner.org/resources/series61.html
Even if at the end, Nobel Laurette Roald Hoffman extols the wonders of Bisphenol-A. :-)
http://www.chemicalsubstanceschimiques.gc.ca/challenge-defi/batch-lot-2/bisphenol-a/index-eng.php
"Canada is the first country in the world to take action on bisphenol A, thanks to our Chemicals Management Plan. This Plan was introduced in 2006 to review the safety of widely-used chemicals that have been in the marketplace for many years, and to update our knowledge and understanding of these chemicals."
I made something like this poem up once before (maybe I heard it before, too?). Here is another try at it:
The circle of knowledge, a poem by Paul D. Fernhout
All philosophy is anthropology; :-)
All anthropology is psychology;
All psychology is biology;
All biology is chemistry;
All chemistry is physics;
All physics is math;
All math is philosophy.
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
The difference comes down to the fact that how a person chooses to grow as an individual, or what a person should do to be a good friend, neighbor and citizen, may both have very little to do with how someone else wants to enslave that person to do work for them.
Of course, one person's view of being enslaved (say, to rabid nationalism or even just professional ethics that involve not taking a political position for a personal view of social justice) may be another person's view of progress and social uplift. And work as in "doing productive stuff" and "hard fun" and "making things happen" and "helping others" may well have many good qualities which are irrespective of who is defining the work (and the workplace) and who is getting the fruits of the work.
Still, ask yourself, what would be the "perfect" education for a slave these days? How far away are we from that with our public school system?
http://www.thewaronkids.com/
This is a typical example of the intent behind it connected to the "marketplace" and not personal growth (or even just citizenship):
"To fix US schools, panel says, start over"
http://www.csmonitor.com/2006/1215/p01s01-ussc.html
"What if the solution to American students' stagnant performance levels and the wide achievement gap between white and minority students wasn't more money, smaller schools, or any of the reforms proposed in recent years, but rather a new education system altogether? That's the conclusion of a bipartisan group of scholars and business leaders, school chancellors and education commissioners, and former cabinet secretaries and governors. They declare that America's public education system, designed to meet the needs of 100 years ago when the workplace revolved around an assembly line, is unsuited to today's global marketplace. Already, they warn, many Americans are in danger of falling behind and seeing their standard of living plummet."
While I completely agree with the title of the article that we should start over with our education system, I disagree with the approach as well as "the marketplace" as a primary aspiration. See my other posts on this article for unschooling alternatives).
http://slashdot.org/comments.pl?sid=1847578&cid=34099866
And see this for other real solutions to the jobs crisis transcending marketplace problems resulting from a combination of limited demand through saturation and the falling value of most paid humor labor due to robotics and other automation, better design, and voluntary social networks:
http://knol.google.com/k/paul-d-fernhout/beyond-a-jobless-recovery#Four_long(2D)term_heterodox_alternatives
It's true that eventually black slaves in the USA were kept from learning how to read (though that was not the case at first, only when they were getting uppity). But, what would you want a personal slave in the 21st century be able to do for you, and would reading, writing, and arithmetic be part of it? Sort your emails according to written criterion you supply? Drive your car while reading all the road signs and navigating efficiently? Be good in bed just the way you like it through extensive study of writings on the topic? Have brilliant engaging conversations about whatever you wanted to talk about based on being informed about current events? Build for you a comfortable house without a leaky roof by being able to follow blueprints precisely?
Remember, the Egyptians must have had many very technically skilled slaves (for the time) to build the pyramids. Slavery is not incompatible with some forms of learning. Even if eventually the slaves might choose to revolt in some way:
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.