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?'"
A little more (Score:5, Insightful)
We could use, at least, a basic understanding of probability..
Exponential growth (Score:5, Insightful)
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.
What World Does He Live On? (Score:5, Insightful)
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"?
The way we think (Score:5, Insightful)
Re:A little more (Score:5, Insightful)
Math is about logical thinking (Score:2, Insightful)
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 anything else? (Score:5, Insightful)
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.
Math is not an end (Score:4, Insightful)
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.
Confusing popularity with importance (Score:5, Insightful)
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.
Re:Not much literature either (Score:5, Insightful)
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.
Why bother? (Score:2, Insightful)
Math is recursively important (Score:5, Insightful)
Language (Score:5, Insightful)
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.
Re:Not much (Score:5, Insightful)
How much do you understand the budgets you pay taxes on, rates of growth in government and private economy, trends in your home value? Do you know how much you pay in interest on your loans, vs paying in full a little later? Have you considered how much you'd save by changing how your home is heated and powered, with an upfront investment? Do you have any idea how your IRA/401k is performing, or how you'd do if you reallocated its investments? Do you know how your gas mileage varies with different driving patterns or gas octanes?
You would if you used math.
I kinda agree with him (Score:4, Insightful)
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.
Re:What World Does He Live On? (Score:5, Insightful)
I've just gotten all my math courses complete for college, so I can safely say that much of what I learned will never be needed. Calculus? Important to know the principles of it, but it won't be critical to working in the modern world, and I definitely won't need to know the formula for integrating trigonometric functions off the top of my head. Trigonometry? Not of much use, unless I go into engineering. Even some of the higher algebra is needless memorization - I will never need to mathematically prove the Quadratic Formula. Statistics? Yeah, that's important, and they spend all of one term teaching it, while making me take three classes on calculus.
You want kids to learn important math - stop making us memorize things we don't really even need to know. Trim calculus and formal proofs down to the fundamental theory, maybe a bit of practical, and then load up on the statistics, the logic theory (best place to put it, really). With calculators and computers, nobody needs to know math itself. What we need to know is how to think mathematically, and knowing (sec x)' = sec x * tan x doesn't do anything for that.
Re:Exponential growth (Score:3, Insightful)
That's still relatively basic math. I think the message is that people don't really need to understand calculus, but they do need to understand things like exponents, single variable equation solving, and the general concepts behind statistics (population vs sample, general best practices for conducting a study [and thus how to determine if a study is even remotely unbiased], margin of error).
Understanding of derivatives and integrals isn't needed for everyday life, but those basics can very well be used.
Math doesn't suck (Score:5, Insightful)
Re:Why anything else? (Score:5, Insightful)
Mathematics is the language of science. (all science)
If people do not understand math, they are scientifically illiterate.
Applied science (technology) is what enables our free societies to work.
If only a few people know the language of science, then only a few people will control it. This is not a good state of affairs for freedom.
Precisely (Score:4, Insightful)
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).
Re:A little more (Score:5, Insightful)
"Lottery is a tax on people who are bad at math."
Re:Not much literature either (Score:2, Insightful)
Is this some kind of ploy? (Score:5, Insightful)
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.
don't know much about... (Score:5, Insightful)
Re:What World Does He Live On? (Score:3, Insightful)
Trim calculus and formal proofs down to the fundamental theory.
Yes, get rid of the actual derivations, because memorizing without understanding is obviously better than actually learning anything.
Wot no Google? (Score:3, Insightful)
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.
Re:Math is not an end (Score:5, Insightful)
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.
Re:The way we think (Score:5, Insightful)
Indeed. I have a mathematical background, but many years ago considered going to law school. I spoke to several practicing lawyers about the experience; one of the questions I wanted to know was how much my undergraduate degree would put me at a disadvantage compared to those with history, political science, or literature degrees.
Invariably, the answer was that a strong math background, as opposed to social sciences or humanities, turns out to be a strength. Engineers, and mathematicians usually do best in law school. People with a strong math education understand logical argument, whether it be in symbols and numbers, or in words. The emotional, rhetoric-laden argument style that humanities teaches doesn't hold water in the legal profession, because judges are usually very sharp and aren't going to fall for that shit.
So yes, mathematics education is critically important because it teaches you how to solve problems and answer questions with reason, not feelings.
Re:The problem is (Score:5, Insightful)
If you can't, or don't, understand the relatively simple concepts behind trigonometry and polynomials, you aren't ready for calculus.
Re:Not much literature either (Score:1, Insightful)
But those aren't the skills that most English classes are teaching!
English classes seem focused on being able to analyze fiction and characters. I once got an A on a paper I wrote about transmissions that was maybe the worst paper I have ever written but the teacher was confused by the technical side and gave me the credit. In my English classes there has been a complete lack of technical literacy.
Re:What World Does He Live On? (Score:5, Insightful)
With calculators and computers, nobody needs to know math itself.
With dictionaries, nobody needs to learn vocabulary.
Re:Not much (Score:3, Insightful)
Re:Not much literature either (Score:5, Insightful)
Math is the foundaton for physics yet to be (Score:5, Insightful)
Math is the language that describes the universe. Stop pursuing new heights in math an you will never reach new heights in reality.
jdb2
What schools were for.... (Score:4, Insightful)
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".
Re:Not much literature either (Score:1, Insightful)
Yes, it's important to understand how that 5 Ohm resistor represents the the resistance faced by the paper's author during his early days of obscurity.
I'm pretty sure the GP is referring to the interpretation of symbolism and metaphor for hidden meaning that most literary courses focus on, which would be entirely lacking in any technical paper.
Re:Precisely (Score:3, Insightful)
Not all of us knew what we wanted to do in middle school.
I thought through middle school and high school that I wanted to be a professional musician, but after one year of that in college I decided to study chemistry, which I wouldn't have known I liked had I not been forced to take it in high school, nor would I be able to study it had I not been forced to go through trigonometry and advanced algebra.
tl;dr You're required to study different subjects in school because there can only be so many firemen and veterinarians in the world.
Re:Exponential growth (Score:3, Insightful)
I, for one, hope they continue to teach calculus in schools.
Everything you learn up to calculus is basically arithmetic. With algebra, you get into some more complicated math, but it still seems like just adding and multiplying, which you've been doing for years by then. It's not really very interesting.
But calculus, oh boy. There is some interesting mathematics in there. In fact, I'd say that this is the first exposure students get to "real" math, with analysis rolled in for fun. Not to mention with calculus you get to start solving complicated, interesting problems that are actually useful to solve, like acceleration and velocity calculations, the first introduction of new operators since 1st grade, and the more existential problems like the completeness of reals.
If we drop calculus, all we end up teaching kids about math in schools is the boring stuff, and I fear that's what they'll think. Boring is not what math is about! We need to teach students calculus because it's the first real introduction to the type mathematics you work on as a mathematician.
I liked math before, but after calculus, I loved it. Now I'm working on a physics/math double major, and the physics is looking less and less interesting.
Re:Not much (Score:2, Insightful)
Re:What we do/don't need in Calculus. (Score:3, Insightful)
"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.
Re:A little more (Score:3, Insightful)
We could use, at least, a basic understanding of probability..
I don't know. All the math gives you is measure theory and some operations on sets. What you're talking about is getting outside the purview of mathematics. Now you're talking about philosophy, almost metaphysics...
Me, I "get" Kolmogorov's axioms, but I still don't truly understand how they map to reality -- or why we should believe that they do. And among people who do believe that probability theory describes reality, there isn't even really agreement; you've got Bayesians (and isn't this point of view anthropocentric?) and frequentists (is "statistical significance" or lack thereof actually significant?) and nobody really seems to have a handle on what all this stuff means.
At least I don't.
Re:A little more (Score:3, Insightful)
But then the casinos would all collapse...
And nothing of value was lost.
Re:A little more (Score:4, Insightful)
Re:A little more (Score:5, Insightful)
and statistics... Wouldn't want everyone freaking out after every low-n medical study that comes out(IE "SMOKING MAKES YOU HEALTHIER!").
Funny you should mention statistics (and have it buried in the word salad here). Basic statistics isn't hard but doesn't seem to be taught anywhere other than statistics courses (obviously I could be wrong but I don't see any general trend towards teaching stats).
Even in pre Med, statistics is way behind calculus (which you won't use much) and Algebra (likewise). Understanding virtually all current medical literature requires a fairly good grasp of statistics. Otherwise you're left to the mercy of the authors which is never a good situation.
I've taught remedial stats in residency programs. Really shouldn't have to to that. Of course I said the same after teaching basic English sentence structure as a grad student while TA'ing undergrad biology courses...
Re:What we do/don't need in Calculus. (Score:4, Insightful)
The problem of history, economics and political science is that many of the sources are actually the work of "manipulative talking heads".
Re:What we do/don't need in Calculus. (Score:5, Insightful)
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.
Re:Wot no Google? (Score:5, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:5, Insightful)
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 [howstuffworks.com]
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.
Re:What we do/don't need in Calculus. (Score:5, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:5, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
"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.
Re:What schools were for.... (Score:3, Insightful)
Funny you should say that - I dropped out of A-level maths (a combined pure and applied course) because I was crap at it.
A few years later, I was doing a placement in a school and the head of physics - who believed that papers were getting easier - showed me a physics A-level paper. I didn't think it looked that challenging, even allowing for my dismal attempt at A-level maths.
(For those who don't know, A-level physics and applied maths in the UK were - at least at the time - very similar).
I've already alluded to it elsewhere in this topic, but I think the biggest problem with education is the number of conflicting requirements. "All children should leave with basic qualifications" clashes horribly with "Basic qualifications must mean something" unless you can dramatically up the standard of teaching and the ability of the pupils. IMV, it's easier to lower the standard of the qualification and quietly ignore the bit about qualifications having any meaning.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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.
Rubbish! (Score:2, Insightful)
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.
Need does not equal capacity (Score:5, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
We should be pushing for everyone to learn differential equations by the time they finish high school.
ROFLMAO.
Re:What we do/don't need in Calculus. (Score:5, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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.
Re:Why anything else? (Score:3, Insightful)
True story about a practical application of what I learned in chemistry.
A friend of mine started a cooking oil fire in his kitchen. The residue from the fire was a thick, slimy sludge which got over everything. He got it on his hands, and nothing h tried would get it off (soap, detergent, scalding hot water, scrubbing with an abrasive pad). As he was subjecting his hand to increasingly nasty stuff, I sat and thought about the problem, and remembered "like dissolves like." I took out the cooking oil and handed it to him, saying, "try a hair of the dog." It worked perfectly.
Although I am not a scientist myself, one of my regular pleasures over the thirty years since I got out of high school has been following developments in science through Science News and Scientific American, and other publications for the general public. I think this makes me a better, more informed citizen. I might possibly be just as well informed now had I never studied physics, biology, chemistry or four years of math in high school. But it hasn't hurt me.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:5, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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.
Re:Less math would be fine with me... (Score:3, Insightful)
Re:A little more (Score:3, Insightful)
I study a lot of statistics as a part of my course, and recently I've been reviewing some medical literature. Not so much the sciency stuff, just their statistical method, data, conclusions, reporting, etc. After going through a pile of this stuff, I have a feeling most doctors either don't understand statistics, or are ignoring the data and concluding whatever they want. A friend of mine who is studying medicine was telling me how they don't really cover statistics much, or at least not like I do. Their coverage of statistics, is here's an application which generates these statistics for you. You take this number and if it's less than this, you're good. So for instance they learn something like "If p-value is less than alpha then it's true". It was really amazing to me, though it might just be this school. Hell, I even had to help my doctor when he was going over some material.
Re:Exponential growth (Score:3, Insightful)
Not exactly. The problem is that if you don't take proactive measures to reduce the population, a lot of destruction will occur that could otherwise be avoided.
Look what happens if some animal species (for instance, deer) is allowed to overpopulate because it doesn't have any remaining natural predators. They multiply too fast, and eat all the available food. Then they have a giant starvation event. It's even possible they all go extinct in that area because there's no food for any of them. If they're lucky, a few will survive, and the food will grow back the next season (if they didn't kill the plants by eating too much), but what if they're not lucky, and the whole population starves?
That's what we're facing: a massive die-off event, and the end of civilization as a result (if not total extinction). Sure, civilization might come back in 1000 years, like it did after the fall of the Roman Empire, but do we really want to go through another 1000-year long Dark Ages, and lose most of the knowledge and technology we've gained thus far, waiting ages for it to be rediscovered (if ever)? Also, humans facing resource shortages frequently start wars, which cause immense amounts of destruction.
It's a lot better to proactively manage resources effectively, and achieve an equilibrium state where civilization can exist in harmony with the environment, so that humans don't have to go through any such periods.
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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?
Re:essential (Score:3, Insightful)
Unless you're listening to white noise or John Cage, and reading UUencoded dumps of /dev/random, you should feel free to tell your professor that that's what they used to say about whatever it is the HE thinks is music.
There's a reason that you like to listen to it, and making sounds you'll want to listen to is basically the goal of music theory. Similarly, making works you'll want to read is the point of literature. So there's something to learn from it if you'll just look.
But, keep in mind that filling your belly is the point of a Big Mac, and lots of people like those, as well, but they're not nearly as nourishing as other things you could eat, some of which might take some getting used to, at first. In other words, there's a lot you can learn from your professor, too.
everybody will have as many kids as they can (Score:3, Insightful)
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.
Seconded (in a big way) (Score:2, Insightful)
For more of the history of school: http://www.johntaylorgatto.com/underground/toc1.htm [johntaylorgatto.com]
If you are an educator then the book linked above is a must read. The chapter entitled Intellectual Espionage [johntaylorgatto.com] is a must read for those who love standardised testing.
Re:Need does not equal capacity (Score:3, Insightful)
Even at the amateur level, the drivers have a firm understanding of the physics. Could they crank out the equations? Probably not, but they could certainly explain the underpinnings.
I'm not quite sure one can have "a firm understanding of the physics" without being able to "crank out the equations".
Either that or "firm understanding of the physics" doesn't mean what I interpret it as. Because if you take out the maths and equations, there's not a lot left that can really be called "Physics".
The biggest reason most drivers are awful is because they're not paying attention. In nearly every case, for street driving, by the time you need to be overly concerned about how the physics works (eg: stopping distances or losing traction on a corner), you've already failed as a driver. "Good driving" is about 50% attitude, 30% experience and 20% skill.
Re:What we do/don't need in Calculus. (Score:2, Insightful)
Re:What we do/don't need in Calculus. (Score:3, Insightful)
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=
Re:What we do/don't need in Calculus. (Score:1, Insightful)
6.5% makes that example look terrifying. At the current 4.5% (or lower) rates that saves you 45k in the 30 year example. 4% at 15 years saves you 19k on the example and you are now "paying" 33k to get a house 11 years early. 2.2k per year. On a house. And in most markets, there is almost no room for housing prices to go lower. That house in 11 years is going to be worth at least as much as it is now, most likely more.
Also, I assume you aren't living for free wherever you are now? Are you renting? Might as well burn that money. Rent on a 100k house in my area is going to be in the 750-900 range - BUY A HOUSE. If you are living for free and can tolerate the situation, then do that and save.