How Much Math Do We Really Need? 1153
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?'"
Less math would be fine with me... (Score:5, Interesting)
... 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.
essential (Score:4, Interesting)
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.
Demonstrable results (Score:3, Interesting)
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.
The Art of Thinking (Score:2, Interesting)
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.
The problem is (Score:4, Interesting)
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.
Re:Less math would be fine with me... (Score:4, Interesting)
In my experience, you can't teach a person to think. It doesn't matter whether you try it with math, logic, or MBA "critical thinking"; those who already know how to think will pass your courses, those who don't will fail them, and guess which you are going to count if you don't know much about statistics and have an agenda to pursue?
Re:What World Does He Live On? (Score:4, Interesting)
Formal proof is very important - if taught well, it teaches people to think in different way.
One of most enlightening moments when i was at university was excercise where we were given few claims and told to prove/disprove them formally.
Re:Math is not an end (Score:5, Interesting)
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.
Re:essential (Score:5, Interesting)
With all lack of respect... (Score:2, Interesting)
...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.
Re:Why anything else? (Score:5, Interesting)
Why teach History? Few people need that in their daily life or jobs.
Yeah, until you start voting for TEA party candidates because you've never heard of the Know Nothings.
Science? Few people need Chemistry or Physics in their daily lives... etc.
Basic chemistry and physics could save you from mixing two common household items (or leaving them around for the kids to find) that don't react well together, or from not realizing what role momentum has to play when doing certain 'jackass' style stunts or driving. Those things can save your life.
Math? Up to a certain point, math is incredibly useful in everyday life. The trick is to find out what that certain point IS. Like others have said, probability and statistics are probably higher up there than most people would think, as far as being useful in your daily life. Having to do geometric proofs? No, let's not be silly. Calculus is useless for the vast majority of people (I've taken engineering-level calculus, so I'm not speaking from a position of ignorance here on that).
I think a much more practical program that helps people do what they will ALL need to do is better, and let them specialize as they wish. Everyone should be able to do their taxes, understand basic economic theory for when it comes time to vote, etc. The problem is not that people take too much math, because I believe most people only get as far as basic algebra in the U.S. by the time they're out of high school, but that people aren't learning how to apply it to the real world, and they aren't being taught anywhere NEAR enough of the other stuff with the real world applications, as they should be.
If we had a good public education system in this country, I doubt the TEA Party, whose candidates seem to evince a spectacular lack of understanding of the U.S. Constition, either wouldn't exist, or their preferred candidates would be very, very different. When you claim to be all about enforcing the Constitution, and one of your most highly-visible candidates doesn't know where the concept of 'Separation of Church and State' comes from, that's pretty telling.
Teaching economics and social theory and international trade, etc., would all be very valuable in trying to recover from our current mess, and preventing it from happening again.
But I think the most valuable lessons that could be taught would be in real world politics. Everything that's going wrong starts with a corrupt-by-design system we have, and until we fix that, we're not going to fix anything else without simply shifting the corruption into other forms.
Keeping the populace uneducated in useful things (rather than having everyone learn Calculus in high school) seems like a pretty good way to keep the status quo.
A lot more than we have (Score:5, Interesting)
"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.
Re:Exponential growth (Score:4, Interesting)
I see another angle of this "how much math do we really need?" notion.
If we all lived in a country, like China, where we didn't pick our leaders, then no, we really don't need to understand much math, and we don't even need to understand exponential growth, because theoretically, smarter, better-educated people are studying those issues you list and making decisions for everyone. This is why China can get away with a one-child-per-couple policy even though I'm sure it's not exactly popular.
However, in democratic countries like ours, every moron has a vote, so politicians pander to the lowest common denominator. 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.
Probability, statistics, and estimation (Score:4, Interesting)
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.)
Extend the question (Score:3, Interesting)
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?
Re:What we do/don't need in Calculus. (Score:5, Interesting)
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.
Re:A little more (Score:3, Interesting)
Oh it works.... most of the time... and assuming you have a really big pile of money.
though the *everyone loses* 00 slot in the wheel makes it a bad choice for roulette.
It's better than what most people do, which is the exact opposite.
"I won again? I must be having a winning streak! everything on black!"
increasing your bet every time you win(what a lot of people do) close to guarantees losing it all.
Doubling your bet every time you lose almost guarantees you'll win but you're risking orders of magnitude more than your greatest possible gains and the "almost" bit will bite you in the arse eventually.
Re:A little more (Score:4, Interesting)
Understanding it and applying it aren't the same thing. I know lots of people who are much much much better at maths than I am and still can't get their head around the concept of coincidence.
Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house. -- Robert A. Heinlein
I once read that quote to my father, who studied nuclear physics at the University of Rome, and had been an electronics engineer for much of his career, and I remember him saying, "Well, I'm sure he believes that." Personally, speaking as a software engineer, I do wish I had studied more higher math in college, because it would help me do more. More and better mental tools rarely hurt. But, to be honest, that really hasn't affected my earning power in the slightest.
Re:What schools were for.... (history) (Score:5, Interesting)
For more of the history of school: http://www.johntaylorgatto.com/underground/toc1.htm [johntaylorgatto.com]
A key section is here:
http://www.lewrockwell.com/gatto/gatto-uhae-16.html [lewrockwell.com]
as part of another archive:
http://www.lewrockwell.com/gatto/gatto-arch.html [lewrockwell.com]
Re:What we do/don't need in Calculus. (Score:5, Interesting)
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.
How to do better...(growth, civics, or obedience?) (Score:4, Interesting)
People know how to do better: http://www.educationrevolution.org/ [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 [sourceforge.net]
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/ [tripod.com]
Bread and Circus or Godel and Bach? (Score:5, Interesting)
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.
Re:Eng. Lit is BullShiat, but fun (Score:5, Interesting)
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.
Re:The way we think (Score:4, Interesting)
99% of the legal profession exists outside of jury trials.
Re:A little more (Score:5, Interesting)
The important value isn't the expected value of one's net winnings (perhaps -$0.50 for the lottery player and $0 for the abstainer), but the expectation of the utility of one's net winnings (for example, u(0-1)*(1-1/2000000)+u(1000000-1)*1/2000000 versus u(0) ).
The arrogance inherent in your statement becomes glaringly obvious in these terms. Implicitly, you are claiming knowledge of the utility of money to lottery players, while simultaneously denying such knowledge to the lottery players themselves.
Re:What we do/don't need in Calculus. (Score:3, Interesting)
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.
Re:What we do/don't need in Calculus. (Score:3, Interesting)
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.
Re:What we do/don't need in Calculus. (Score:3, Interesting)
>>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.
Re:What we do/don't need in Calculus. (Score:3, Interesting)
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.
Re:What we do/don't need in Calculus. (Score:3, Interesting)
Yes, Fermi problems. http://en.wikipedia.org/wiki/Fermi_problem [wikipedia.org]
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.
Re:What schools were for.... (history) (Score:3, Interesting)
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.