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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.
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.
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.
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.
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.
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.
Nah. That claim was once made for teaching Latin in public schools. It's still made for teaching Euclidean plane geometry.
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.
Not all of us want to study literature and music. I especially hate it when the prof looks down on what you like to read/listen to as "not music/literature".
SSC
If the purpose of your schools is to provide your people with vocational skills, you end up with people with vocations. If the purpose of your schools is to provide your people with intellectual skills, you end up with intellectuals.
I would much rather have learned Latin than Spanish.
When you're afraid to download music illegally in your own home, then the terrorists have won!
"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?
If you can't, or don't, understand the relatively simple concepts behind trigonometry and polynomials, you aren't ready for calculus.
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'
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
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
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.
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.
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.
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!
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.
Even people that go on to college can benefit from votech skills. A lot of this stuff works out to be basic survival skills in a highly technological society where being able to fix your house or your car or your TV is of considerable advantage. It helps even if you don't want to do the work yourself. It allows you to understand the work well enough to properly judge it and shop for it as a consumer.
It's like anything else that seems unecessary in education. Understanding the world allows people to make better informed choices.
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.
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.
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.
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.