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How Much Math Do We Really Need?
Pickens writes "G.V. Ramanathan, a professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago, writes in the Washington Post that although a lot of effort and money has been spent to make mathematics seem essential, unlike literature, history, politics and music, math has little relevance to everybody's daily life. 'All the mathematics one needs in real life can be learned in early years without much fuss,' writes Ramanathan. 'Most adults have no contact with math at work, nor do they curl up with an algebra book for relaxation.' Ramanathan says that the marketing of math has become similar to the marketing of creams to whiten teeth, gels to grow hair and regimens to build a beautiful body, but even with generous government grants over the past 25 years, countless courses, conferences, and books written on how to teach teachers to teach, where is the evidence that these efforts have helped students? A 2008 review by the Education Department found that the nation is at 'greater risk now' than it was in 1983, and the National Assessment of Educational Progress math scores for 17-year-olds have remained stagnant since the 1980s (PDF). Meanwhile those who do love math and science have been doing very well and our graduate schools are the best in the world. 'As for the rest, there is no obligation to love math any more than grammar, composition, curfew or washing up after dinner. Why create a need to make it palatable to all and spend taxpayers' money on pointless endeavors without demonstrable results or accountability?'"
We could use, at least, a basic understanding of probability..
One part of math all people should be required to understand is exponential growth.
It might make people realize that population growth, resource consumption, etc. can't keep increasing at current levels without severe corrections in the somewhat close future.
Yes! How can statistics possibly be useful in today's world? Or an understanding of continuously changing variables, like mortgages?
If more people understood math at that level, a lot fewer of us would be constantly fooled by financial flim-flam and political bullshit.
I'm a professor at a liberal arts college. I feel that music and literature is important, but there's no way I can say it's strictly more important than math or sciences. Equally important to being a well-rounded person? Sure.
Out of idle curiosity, when did "ramblings of a random guy" become "news"?
For me personally, learning advanced mathematics (calculus and beyond) has changed my thinking process from a purely creative, English-oriented one to an objective, analytical outlook. The true understanding of how mathematical principals work--what a derivative is and not merely how to calculate it--has shown me the power of mathematical, logical analysis. As an English major, I came to a point where I was not sure whether or not I wanted to continue taking math courses (as I will need almost no math beyond arithmetic in my life), but I came to the conclusion that the mindset mathematics gives me rather than the quantitative abilities it provides is what matters in my education, and I therefore encourage anybody to continue studying math well past the point in which the skills become irrelevant.
Why teach History? Few people need that in their daily life or jobs. Why teach music? Other arts? Science? Few people need Chemistry or Physics in their daily lives... etc.
Because Mathematics, like the rest, increase our fundamental understanding of the world around us. It's part of creating critically thinking individuals who have more to give back to society than a simple job skill they learned at an early age. Or at least give them the opportunity... take away fundamental education, they no longer have the choice.
Music and literature may be popular, but they are hardly essential. And history's importance mainly comes from informing politics.
Do most people need to know multivariable calculus? No. But one thing most people are missing is an understanding of basic statistics and logic. Statisticians don't help much. Courses need to be more than just memorizing a bunch of statistical formulas. People need to understand why basic statistical reasoning works. If people don't have that basic philosophical understanding of why statistics work, then they'll just forget all about the formulas they were forced to memorize after the course is over.
These types of courses should be essential for all, but they aren't even available until college--and even then they're optional.
Speaking as someone with a degree in Physics, I can safely say that I've only used literary analysis one time in my life: when learning it in school.
Math is important for understanding why math is important. Which in turn allows you to see that math is important for being able to reason in a structured and abstract way about the world. Many people confuse math with arithmethic, algebra, trigonometry and calculus because these were all labeled math when they were students. Nothing could be farther from the truth. At its foundation, math is very closely tied with logic in that it is deductive rather than inductive, and you use it to prove complex assertions by stitching together smaller components you already know are true. The fact that with this system you can go on and prove the validity of the theoretical tools that you use to build a bridge that stays up or to make an airplane that flies or even to understand the best way to invest your own money is what makes math not only important but also amazing...
My book: Friendly F#, fun with game development and XNA; my game: Galaxy Wars by VSTeam; my gamedev language: Casanova.
The languages we know affect what thoughts we can think. While it is very zen to say that words hide meaning, empirical evidence seems to indicate that we cannot conceive of ideas that we do not have language to express. Math can express most anything which allows for thoughts right up to the limits of our hardware. It seems like this is also a good reason to learn a human language with different roots than your native one, but I have not done that yet, so I couldn't say.
refactor the law, its bloated, confusing and unmaintainable.
If the purpose of your schools is to provide your people with vocational skills, you end up with people with vocations. If the purpose of your schools is to provide your people with intellectual skills, you end up with intellectuals.
I would much rather have learned Latin than Spanish.
When you're afraid to download music illegally in your own home, then the terrorists have won!
With Math, or anything else probably, it's now so much "how much you know" but "how well you know it". It's the old "quality" versus "quantity" problem. There are plenty of concepts that would be useful to understand just from a basic life skills perspective that most people simply don't get. Something as simple as compound interest is lost on most people and that's a pretty basic mathematical idea. Applied math can be a very handy thing. However, most maths education goes out of it's way to avoid any sort of real world relevance at all.
A Pirate and a Puritan look the same on a balance sheet.
I'd add "order of magnitude estimation" to that list, becuase I find it regularly useful to make ballpark guesses about various issues. So, being able to do something like this, just to make something up as a calculation of the mass of the Earth:
The Earth is about 8000 miles across, but let's call it 10,000 in round numbers. It's a sphere, but if it were a cube, it would have a volume of 10K time 10K time 10K, or about 1,000,000,000,000 cubic miles. A mile is about 5000 feet, so a cubic mile is about 75,000,000,000 cubic feet, or about 100 billion cubic feet in round numbers. A bag of dirt is about a cubic foot and weighs about 40 pounds, but lets call it 100 pounds in round numbers and accounting for rock. So a cubic mile of Earth weighs about 10,000 billion pounds. So, the Earth weighs about 10 thousand billion trillion pounds. Or about 5 billion trillion tons.
Let's check how close I got? :-)
http://science.howstuffworks.com/environmental/earth/geophysics/planet-earth-weigh.htm
6,000,000,000,000,000,000,000,000 (6E+24) kilograms.
10,000,000,000,000,000,000,000,000 pounds (so, a little low if divided by 2.2)
10,000 * 1,000,000,000 * 1,000,000,000,000
Pretty close! :-)
Anyway, while that's a complicated calculation, and with big rounding errors in various places (compressed molten rock must weigh quite a bit more than topsoil since I rounded up a bunch), the more people who can do that sort of thing, the more people can make sense of a lot of public policy issues like comparing NASA's budget to the DOD budget, or understanding the amount of the economy goint to social security relative to education, or guessing how feasible some technical proposal is, and so on. The devil is in the details, of course, but order of magnitude estimation at least can put a sort of ballpark fence around the details. I used just facts I knew (diameter of the Earth, weight of a bag of soil) without precise details to get close. Often, in public policy, close is all you need to have a feel for the basics of a situation and to fact check what you are being told.
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Teaching math isn't about teaching a specific skill that everyone will use, it's about teaching how to approach problems quantitatively. At least it should be. As someone pointed out in a post further down, a lot of us don't use literary analysis in day to day life either but the reason to learn it is that learning different topics that require critical and logical thinking will arm students with better methods to approach problems with.
A physicist may well benefit a great deal from from having gone to English class in high school. Sure they only use make use of the basics, like correct spelling and grammar, every day but the style of critical thinking that is exercised in literary analysis is additional tool that they have. Similarly, math teaches and practices a way of approaching problems that other subjects don't address.
Someone who has an education in only a range of topics that is limited to their interests will be a flat, bland and incapable person.
So if this is the future...where's my jet pack?