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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.
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.
... 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.
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
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.
Danica McKellar said so, and she's prettier than G.V. Ramanathan.
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!
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.
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.
...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.
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
"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?
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.)
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.
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
That reminds me!
The article looks at math from an anti-capitalist angle:
"Unfortunately, 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.
There are three steps to this kind of aggressive marketing. The first is to convince people that white teeth, a full head of hair and a sculpted physique are essential to a good life. The second is to embarrass those who do not possess them. The third is to make people think that, since a good life is their right, they must buy these products."
Now go ahead guys and gals, have fun with this:
http://en.wikipedia.org/wiki/Soviet_Student_Olympiads
http://www.kidsmathbooks.com/2010/10/2nd-all-soviet-union-mathematical.html
I mean, why is he targeting the left wingers with his anti intellectual propaganda?
Je me souviens.
If anything, you've just proven the real corollary of the research in the article, and not the one in the article.
Math is a hard, specialised tool. Essential for many distinct types of specialists. It's what they call "fundamental".
Nonspecialists don't need it. They don't understand why specialists need so many variants of it. They don't understand how rigorous math can be useful is so many different ways to different specialists.
Is it the fault of the specialists?
Is it the fault of the public?
Not really, the public can't seem to grasp the idea that the benefit to mankind is in the details, and wonders why we need something that has no generalists.
Medecine and engineering are doing fine in the public view, because they can be understood, without the details, or so the public thinks.
If you understand math without the details, you're back at a grade school level, precisely because that's the point in the curriculum where they start preparing you for the different math specialties, and you're starting to get the grounding into the differences.
You invest in math education precisely to get the specialists, and to get research done in the specialties. Proving the return of specialties is harder but it still has to be done.
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
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.
"To everyone else it's a waste of time which could be spent far better learning things which might ever be useful to them."
Exactly what? Grammar, history, geography, physics, basketball? Which one of these is important or useful?
In mathematics the basics are not about being directly important. They prepare your mind for the harder stuff. One of the basic things to learn is exactly that there are things that are NOT easily translated into direct day-to-day practice, but this doesn't mean they are useless. Mathematics is all about abstraction and manipulation of symbols.
On the other hand I agree with you that basic math courses need a major overhaul. Probability theory is a must, I do not even understand why they havent included it in the first place.
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.
Eh, but you also have to remember that getting into high schools in China is not guaranteed and students have to test for placement so the population of high school students is going to be self limiting. If only your most promising students are in high school then it is going to be easier for you to show strong scores at a global level. The same argument cant be made for Japan where high school is not compulsorily and students have to test to get into the high school of their choice.
The same without forcing kids to waste huge numbers of hours.
Let them use those hours learning something else(I know, I know, it's heresy to suggest that other subjects might be more useful than math for some people.) rather than pissing their time away on something they don't need.
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!
The author's point, however is valid. We spend a large amount of time and money teaching people a lot of crap that most of them will never use. I'd venture a guess that less then 10% of the population needs any advanced math at all. The number may be higher, but I doubt it. Given that something on the order of 25-30% of the population of the US has an undergraduate degree, and of those 25-30% only the smaller number with a degree in science, math, engineering or an "applied science" like medical people, ever use any advanced math at all. For the vast majority of the rest, a few courses in basic statistics would probably be all the math they ever need beyond arithmetic.
The problem is that we don't *know* in 7th or 8th grade who is likely to need more math 5 or 6 years down the line. Most kids, if you tell them in 7th grade that they can stop taking math, they're going to. Then they hit junior or senior year of high school, realize they want to be an engineer, and they have none of the needed mathematical background. Basically we teach 4-5 years of advanced math to every student in the country, so that the 10-15% if them who will actually need it, have it. It's wasteful as Hell, but I can't think of a better way to do it without forcing life altering career choices on 13-14 year olds.
I don't need a million points of light, just two points of multi-mode fiber and a 10 Gig-E router.
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.
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.
Bullshit is never fun. Making shit up is really uncomfortable for those of use who care about intellectual honesty. Never mind the fact that they never teach you how to do it. English class consists of example after example of bullshit, and then they expect you to do the same. But they never teach you a method, or give you any way to check your answers. Personally, I found English classes (once we stopped doing grammar/spelling) to be mentally abusive.
Give me Classic Slashdot or give me death!
The problem of history, economics and political science is that many of the sources are actually the work of "manipulative talking heads".
With Math, or anything else probably, it's now so much "how much you know" but "how well you know it". It's the old "quality" versus "quantity" problem. There are plenty of concepts that would be useful to understand just from a basic life skills perspective that most people simply don't get. Something as simple as compound interest is lost on most people and that's a pretty basic mathematical idea. Applied math can be a very handy thing. However, most maths education goes out of it's way to avoid any sort of real world relevance at all.
A Pirate and a Puritan look the same on a balance sheet.
I'd add "order of magnitude estimation" to that list, becuase I find it regularly useful to make ballpark guesses about various issues. So, being able to do something like this, just to make something up as a calculation of the mass of the Earth:
The Earth is about 8000 miles across, but let's call it 10,000 in round numbers. It's a sphere, but if it were a cube, it would have a volume of 10K time 10K time 10K, or about 1,000,000,000,000 cubic miles. A mile is about 5000 feet, so a cubic mile is about 75,000,000,000 cubic feet, or about 100 billion cubic feet in round numbers. A bag of dirt is about a cubic foot and weighs about 40 pounds, but lets call it 100 pounds in round numbers and accounting for rock. So a cubic mile of Earth weighs about 10,000 billion pounds. So, the Earth weighs about 10 thousand billion trillion pounds. Or about 5 billion trillion tons.
Let's check how close I got? :-)
http://science.howstuffworks.com/environmental/earth/geophysics/planet-earth-weigh.htm
6,000,000,000,000,000,000,000,000 (6E+24) kilograms.
10,000,000,000,000,000,000,000,000 pounds (so, a little low if divided by 2.2)
10,000 * 1,000,000,000 * 1,000,000,000,000
Pretty close! :-)
Anyway, while that's a complicated calculation, and with big rounding errors in various places (compressed molten rock must weigh quite a bit more than topsoil since I rounded up a bunch), the more people who can do that sort of thing, the more people can make sense of a lot of public policy issues like comparing NASA's budget to the DOD budget, or understanding the amount of the economy goint to social security relative to education, or guessing how feasible some technical proposal is, and so on. The devil is in the details, of course, but order of magnitude estimation at least can put a sort of ballpark fence around the details. I used just facts I knew (diameter of the Earth, weight of a bag of soil) without precise details to get close. Often, in public policy, close is all you need to have a feel for the basics of a situation and to fact check what you are being told.
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Teaching math isn't about teaching a specific skill that everyone will use, it's about teaching how to approach problems quantitatively. At least it should be. As someone pointed out in a post further down, a lot of us don't use literary analysis in day to day life either but the reason to learn it is that learning different topics that require critical and logical thinking will arm students with better methods to approach problems with.
A physicist may well benefit a great deal from from having gone to English class in high school. Sure they only use make use of the basics, like correct spelling and grammar, every day but the style of critical thinking that is exercised in literary analysis is additional tool that they have. Similarly, math teaches and practices a way of approaching problems that other subjects don't address.
Someone who has an education in only a range of topics that is limited to their interests will be a flat, bland and incapable person.
So if this is the future...where's my jet pack?
I can't think of a better way to do it
Teach it to them when they do need it.
Personally I find most branches of maths to be mind numbingly boring and utterly irrelevant. Until the times I need them to solve an actual problem. In which case they suddenly become interesting and useful, and a whole lot easier to grasp beyond rote learning for a test.
Integrating the necessary maths into the disciplines that actually need them might perhaps take some more time, but I think it'd be less of a waste of time than the current situation and probably yield easier learning of the maths useful in those disciplines.
"Someone who has an education in only a range of topics that is limited to their interests will be a flat, bland and incapable person."
Citation needed. More importantly, does it really matter? Plenty of people are boring, have limited interests and are very good at what they do.
"Similarly, math teaches and practices a way of approaching problems that other subjects don't address."
And these would be what exactly? Sorry, but logical thinking and criticial reasoning is the same regardless of specialty. Only the vocabulary changes. And no one is suggesting that we stop teaching math or english or history. But most people don't need calculus. That includes most people who take it.
The difference between english and math is that everybody has to communicate. Not everybody has to use advanced math. But virtually everybody could use math that deals with everyday life. And we ignore that because we are too busy teaching advanced math.
Teach it to them when they do need it.
That's nice in principle, but poor in practice. There are some fields of mathematics that can be taught from scratch with little requirement for much other math outside of that little field. Those are few and far between however. If you've had any experience trying to teach math, even to people who need it, who don't have the necessary background, you'll understand. It is an extremely frustrating process for the student, because the reality is that mathematics is one of those subjects that is very hard to pick up later, and is certainly hard to pick up piecemeal.
I'm glad that you managed to picm up the bits and pieces required, but in my experience teaching math, you are the exceptional student: most have a great deal of difficulty picking it up -- instead they require labourious coverage of the pre-requisites which, unfortunately can take years -- it's not a very practical way to go about it.
Craft Beer Programming T-shirts
We should be pushing to bring everyone up, not pulling back to give everyone the bare minimum.
I don't think that's what OP wrote or meant.
Everyone, even those who "can't do math", in a modern society needs to *understand* percentages, orders of magnitude, estimation and basic statistics.
While I never use calculus at work, and obviously never at home, I frequently use the 4 items mentions above at work and I *constantly* use it while watching basketball and American Football.
It's also vital when thinking about how to reduce government budget deficits: eliminating the Corporation for Public Broadcasting's US$422M sounds great, but it's only 1.2% of 1% of the budget.
"I don't know, therefore Aliens" Wafflebox1
I see the big problem with math education is how it is taught. To be honest, there is no reason whatsoever we can't have taught kids basic differential equations by the time they hit 8th grade. The problem is we force students to memorize a bunch of obscure math that although we will use later in specialties, is totally pointless, out of context, and relatively useless at that point. And it is by rote and not by concept. In case you haven't noticed, memorizing vast amounts of crap is hard, but learning lots of new concepts is easy. If math was taught in order, in a contextually relevant way, first conceptual and then practical, there is no reason at all that we couldn't have 8th graders beating out the average college graduate. It doesn't have to be expensive, it doesn't have to be so terrible, it is just that it is done in such a terrible manner that it appears wasteful as it is currently done.
Plus, to be honest, a knowledge of extremely advanced math could come in handy to virtually everyone. I get really tired of watching our system be a kind of stagnation in most fields. If everyone had an advanced education out of high school, everyone would be able to advance their field. Plumbers, welders, residential contractors, auto repairmen, any profession at all could be improved by a knowledgeable worker in that field, even if just new and interesting ways to fix things. We could easily be living in a world where everyone advances society, not just about 10% of us.
Where is the mod rating for "scary"? Also,
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?
I think this is a question of definitions. I consider having a basic knowledge of various schools of logic and mathematics such as you list to be the bare minimum, and much less than we should be teaching. We should be pushing for everyone to learn differential equations by the time they finish high school. The problem is that people are afraid of math, not that they really can't do it. Less math won't fix that.
When you're afraid to download music illegally in your own home, then the terrorists have won!
>>We spend a large amount of time and money teaching people a lot of crap that most of them will never use.
This is a horrible way of thinking about it. A friend of my father's is a EE Professor at USC, who has studied all sorts of high level mathematics. He freely admits he's probably never going to use 90% of them, but what's important in life is improving your toolbox so that you can solve the broadest range of problems possible. This doesn't just mean math, either - he passed the bar not too long ago because he found that not having a background in law had screwed him over pretty badly. So he worked to improve himself.
The key point here is that as a high school student, you're not going to know where you're going to end up, or what opportunities will be opened/missed by having/not-having certain skills. Our school system should try to fill out that toolbox with the most commonly used tools... and in that respect, I do think that we're focusing on the wrong kinds of math. Algebra is certainly a useful skill to have (not only as a foundation for all advanced math, but even in real life), but trig, geometry and calculus... maybe not as much as probability and statistics.
Other critically important things in real life that we don't teach in schools:
Economics (especially managing personal finance and business management skills)
Public speaking (or even just learning to speak in front of small audiences)
Leadership / Management Skills (or interpersonal Skills in general)
I think history is also critically important, since understanding your place in the world and how you got there renders you immune to a lot of the manipulation that politicians put on an ignorant populace, and you don't look like a moron at a company picnic when your boss asks for your insight on possibly expanding into communist China.
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.
We should be pushing for everyone to learn differential equations by the time they finish high school.
ROFLMAO.
"I don't know, therefore Aliens" Wafflebox1
No.
I went to high school 6 years ago, and we learned nothing. Absolutely nothing at all. The entire day was a complete and utter waste. The problem was the pace. Everyone assumes kids are stupid, so they teach us slowly. If they did a better job teaching, it would be trivial to reach a meaningful depth in every subject.
I'm not promoting math at the expensive of other subjects. I'm saying every subject is woefully under taught.
Actually, I think we should pull back on subjects like "standardized test preparation." We're taught to pass idiotic tests, so all we ever learn is idiocy.
When you're afraid to download music illegally in your own home, then the terrorists have won!
Personally, I found English classes (once we stopped doing grammar/spelling) to be mentally abusive.
If we s/English/foreign language/g then I'm right there with you.
I was a foreign language major because I'm good at learning languages. I hadn't really considered or understood that this was essentially the same thing as being an English major (ie. basket weaving) except in different languages. My Great Moment of Disenchantment came when I decided to teach this one professor a lesson once and for all. More references, more references, I'll show you more references! So I didn't read the book at all, and my big paper was one continuous series of citations from random people's doctoral theses and so on. 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. I was impressed with how horrific this paper was, because it was the utmost extreme exercise in not thinking and not having any original thoughts or genuine insights whatsoever.
The result?
(Everybody probably already saw this coming...)
"Fantastic! A++ This is your BEST work EVER! Why can't you ALWAYS write papers this good! This is what I have been trying to get you to do all along!!"
And that, boys and girls, is why I was a truck driver for 15 years after college.
Yes, but that's exactly the situation. That's why there are so many credit card users and mortgaged-to-the-hilt home"owners" in the US; because people really don't understand compound interest. Anyone who does and has even a lick of sense will never let a lender get into that kind of position over them... it's just a highly accelerated way to transfer your money to the already-rich.
You know how many people run a credit card up to the limit and then pay the minimum? Most of them. And that is a recipe for financial destruction. Which the banks are happy to cook up for anyone they can entice into the deal with access to a shiny new whatever.
Likewise, you know how many people get a mortgage and then pay only the suggested payment? Most of them. And how many about shit themselves when they find out they have very little equity when the payment book has half the coupons gone? Again, most of them.
It's basic math, and in this society (in the US, I mean), understanding these things before you get in trouble is usually one key difference between the haves and the have-nots.
I've fallen off your lawn, and I can't get up.
The key point here is that as a high school student, you're not going to know where you're going to end up, or what opportunities will be opened/missed by having/not-having certain skills.
Chances are that if you hate algebra and struggle to pass it, then a life in engineering or the physical sciences isn't going to be your cup of tea.
So, why make somebody try to prepare for a handful of careers that they are unlikely to pursue, and if they do pursue them most likely they'll never be able to outcompete somebody mediocre to above-average in a country that pays 1/3rd the US wage?
If you want to be successful, you need to find a career that you can excel at - not one where you can barely get a job, because with current trends you won't get a job.
Whoosh! No matter what the term of your loan is, if you pay it off at the coupon rate, you're shooting yourself in the foot. Even getting a little ahead, early on, saves huge amounts of money later when the excess in the payment is applied to the principal. Try a few sample calculations and you'll see.
Looky here: 100k for 30 years at 6.5%; you pay 227,544.49 via monthly payments of $632.07; the lender gets $127,544.49 extra out of your ass because you "want it now."
But if you pay $100 extra a month ($732.07) - skip the DirectTV and the Starbucks, perhaps - you will come out $45,000.00 ahead, and the loan payments will end 9 years earlier.
If you can get your $100,000 at 6% for 15 years, you pay $151,894.23 via monthly payments of $843.86; the lender gets $51,894 extra because you want it now.
But if you pay $100 extra a month ($943.86) you will come out $9,115 ahead, and the loan payments will end 2 years, 4 mo. earlier.
So clearly, the higher your loan, the more that $100 per month will mean to you in the end. And of course, if you can bolster it with $1000 or $2500 here and there (instead of that flat screen TV or the down payment on that new car - and paid into the loan as early as possible) you'll save HUGE amounts more.
Also, people are a darned sight better off if they save their money until they have enough and then simply buy the house, cutting the lenders out entirely. In the above 30 year example, it is possible to avoid paying $127,544.49; putting away the exact same amount ($632.07) means you'll have your $100,000 in 13.x years - faster than your 15 year loan and $50,000 cheaper. If you can do it without starbucks and DirecTV ($732.07), you'll have your $100000 in 11.x years and still $50,000.00 cheaper.
Furthermore, if the individual saves their money and invests it (thus becoming a lender, rather than a borrower), they'll be even better off.
Mortgages are just like credit cards. The lenders dangle the "you can have it now" hook, and people will snap at that bait without ever thinking it through. It's the consumer mentality "gotta have it" destroying the "you'd be better off if you created, and followed, a plan that led to early financial security" fact.
And yes, I bought my home for cash; and yes, I'm far ahead of most people financially. What I didn't do was accept the idea that I "needed" to own a home when I didn't actually have the money. That's just bogus social conditioning that can be thrown off in any number of creative ways. Interest is only your friend if you are the lender. Otherwise, it is the single most corrosive financial technique in anyone's arsenal, barring the actual social conditioning that gets people suckered into paying it.
I've fallen off your lawn, and I can't get up.
One of the things I found frustrating about calculus was that we had a lot of drill, with little or no explanation of what we were being drilled upon.
For instance, I remember spending about two weeks on l'Hospital's rule, in two different classes. One instructor laboriously worked through proofs, and was scrupulous about terminology. The other instructor offered cute mnemonic devices. The same textbook was used both times: a paragraph introducing l'Hospital's rule talked about a "struggle" between two derivatives with an uncertain conclusion. It was clearly an incomplete thought.
Later, it dawned on me that it amounted to, "If you can't work out what happens when comparing two rates of change, try comparing the rates of change of the rates of change. Recurse as needed." That, some of the caveats, and a few illustrative sketches would have explained it clearly in a single lecture; a handful of problems would have verified that I understood it. Instead, I got weeks of confusing lectures and about a hundred increasingly complicated problems that drilled me on a procedure that, at that point, I didn't understand.
If you don't understand the point of the procedure, how are you to recognize when it would be useful to apply it, if it's outside the context of a homework problem set or an exam? Yet there never seemed to be any concern with whether we understood mathematics conceptually, only whether we could grind through meaningless assignments.
And you're going to be crippled when you get your ideal job as a middle manager of a business and you can't do algebra to calculate how many widgets you need to buy and sell each month.
I dunno - I don't see too many middle managers at my workplace using algebra at all. At the most they use spreadsheets to evaluate math - never having to solve for a variable.
Don't get me wrong - I use it all the time, and I appreciate having that tool in my toolbox. But, I minored in math and majored in the physical sciences and I'm not really the target of the article.
COULD the average person use algebra? Sure! Will they ever use it? No. So, what exactly is the point of spending lots of tax dollars trying to teach it to them?
I don't think the author of the article is suggesting that we get rid of math education. His point is that we shouldn't cram it down people's throats, or try to spend a fortune trying to get people who don't like math to learn it.
I couldn't disagree more.
Fractions are used constantly. So are decimals. You may not realize it. You not even think about how you use it. But simple things like manipulating money, adjusting recipes, all use decimals and fractions. Understanding sale prices uses percentages.
Volume and area is only a tiny bit less used, but ask a general contractor how often they use the concept of area. How big is that yard? How much tile is needed to do that floor, or that bathroom? How much fence to enclose that yard? How many square inches of window is needed for that particular window (used in pricing windows).
The problem isn't that people don't use math, but people learn the math and use it intuitively and claim they never use it at all. "Pizza and money" is what I learned as how to explain most math problems. (Pizza is for fractions and geometric problems, money for decimals and percentages).
A classic problem today done by an actual math teacher in a community college. "Someone tell me your credit card rate. Okay, someone else tell me your current balance. Okay, someone else tell me your minimum payment. Now let's calculate how long it takes to pay that off at that rate, and how much you will spend." Eyes light up when the problem is done.
A lot of algebra is learned not for the reason you think, but for learning how to set up problems. I don't do much traditional math in my job today, but I use the concept of setting up problems all the time, not just at work. I even use it when cooking and the recipe needs adjusting. Without the middle school algebra, or even some of the high school algebra, setting up those problems is very difficult, and knowing that you set it up correctly is very hard.
I found in high school, only those truly interested in math took Calculus. In college, calculus was required for many majors because the basic material of the course required at least some understanding of calculus concepts. Then again, I was dismayed to learn that in some states, it was possible (if difficult) to be certified as a math teacher to teach calculus, without ever having taken it, including have the degree in education.
Finally, math doesn't just teach math, it teaches how to think. Analytical thinking ought to be fundamental.
"I may disagree with what you say, but I will defend unto the death your right to say it." -- Voltaire
Yes, Fermi problems. http://en.wikipedia.org/wiki/Fermi_problem
The classic Fermi problem is, "How many piano tuners are there in Chicago?"
Fermi's wife Laura wrote a biography called Atoms in the Kitchen, which described how they used to sit around the dinner table and Enrico would ask questions like, "Tin melts at 232 degrees C, olive oil boils at 300 degrees C, so how come you can boil olive oil in a tin frying pan?"
Answer: It's not the olive oil boiling, it's absorbed water. (Anyway that was his explanation.)
And they couldn't look things up in the Internet back in those days.
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.
We need to teach math with a calculator and Google. Because let's be honest you aren't ever going to be blah blah
No. We must teach "manual" math, because (IMNSHO) that's a precursor (and integral to) to understanding math.
Remember a few weeks ago the article about most American kids not knowing what the "=" sign means because they are so used to calculators?
"I don't know, therefore Aliens" Wafflebox1
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.
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.
In theory that all sounds good, but what about money spent on rent before buying your home? How would you factor that in? Surely that damages how much money you actually saved?
Actually not a bad idea; even if you have no interest in being a doctor, knowing something about Latin - which is a partial basis for the English language - will help improve your English skills.
In general, learning another language improves your skills in your native language. Assuming you're learning more than catchphrases, anyway.
Latin is also useful for those who deal with legal documents, BTW. Probably more so than medical professions. It's also useful in biology and related science fields.
=Smidge=