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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?'"
... 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.
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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.
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
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.
-- Technology for the sake of technology is as pathetic as eschewing technology because it's technology.
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.
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.
"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?
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.
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.)
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.
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.
The higher the technology, the sharper that two-edged sword.
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.
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.
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!
99% of the legal profession exists outside of jury trials.
It's ironic that, in order to actually believe your statement, one must not have a very firm grasp of probability.
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.
Use of the words "good", "bad" or "evil" is almost invariably the result of oversimplification.