Slashdot Mirror
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.
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 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.
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.
When you're afraid to download music illegally in your own home, then the terrorists have won!
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.
Yeah, like why bother? We're all going to die anyway. I did not RTFA but the summary is horribly defeatist in tone.
http://www.acetonestudio.com
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.
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.
--
make install -not war
Obviously we all need some math (and as many here - myself included - are engineers, we know that a small portition of the people need more math)... But how much? Really, does average person ever have to deal with integrals, derivations... or nearly any other area of abstract algebra... after graduating? Everyone needs some very basich math (when shopping, dealing with loans, etc... But the type of math needed for that sort of things have been dealt with by sixth grade. If the point is that many still don't know them well enough, teaching more advanced subjects doesn't seem like a good solution.
Danica McKellar said so, and she's prettier than G.V. Ramanathan.
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).
Filthy, filthy copyrapists!
You must be a terrible physicist. As an electrical engineer, I need literary analysis every time I read a technical paper, and I needed composition skills last time I submitted one for publication.
When you're afraid to download music illegally in your own home, then the terrorists have won!
I know Ramanathan as the author of a series of study manuals for the preliminary examinations for actuarial science in the US. It honestly surprises me that someone of that level of mathematical knowledge would make such a poorly reasoned argument. As such I must consider the possibility that this is some kind of cynical elitist ploy to retain mathematics as the language of the privileged and well-educated, much like Latin hundreds of years ago. But this too seems too sinister a line of thought to entertain--and somewhat contradictory, given what I know of him.
Nevertheless, the logic is unsound. Mathematics is not merely computation or abstract manipulation of symbols. It is a way of thinking that not only fosters an understanding of the importance of logical reasoning, but also the necessity to substantiate and quantify one's empirical observations. That is to say, mathematics is the foundation of science. To say that most people don't need anything more than the most basic knowledge of math is like saying people don't need the ability to think critically.
The reason why we learn mathematics is not just to perform work with it, but to learn how to think logically and behave rationally. If there should be any doubt about this, just look at the state of mathematics education in the US today, and compare that to how appropriately we assess things like the relative risk of terrorist threats versus being in a car accident; or how well people understand what happened with the Wall Street bailouts; or even something as basic as compound interest as it applies to making payments on credit cards. I think the evidence is overwhelming to support the notion that people suffer from innumeracy, not too much mathematics. And given that Ramanathan writes study manuals for actuarial candidates, I find his lack of understanding of this point to be all the more remarkable.
Why stop at math? We don't need to know much about chemistry, physics, biology, engineering, or anything besides how to change the batteries in the remote. An operative word here is "need". In some sense all we "need" do is stuff food in our mouths and breathe. Now, change the "need" to some zeroth law about seeing the species as a whole progress, and suddenly a general awareness of math at a deeper level becomes quite important. I find the original author's thesis to be narrow, cynical, and with a subtle complacency to separate of the populace into Brahmans and non-Brahmans.
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.
Deleted
If you can't, or don't, understand the relatively simple concepts behind trigonometry and polynomials, you aren't ready for calculus.
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.
I thought the same thing when I first read that post. But I heard the on coming whooshing sound early enough to divert it.
I want to shoot the messenger!
I think you are talking about a different form of analysis. The sort of analysis that you would do on a technical paper would be a technical analysis, verification of facts, etc... not a literary one. Literary analysis involves explaining a work of fiction or poetry by means of interpretation based on the specific linguistic expressions or structural tools used by the author.
File under 'M' for 'Manic ranting'
Hmmm.... I wonder what would have happened if this guy would have lived circa 1853 right before Bernhard Riemann invented calculus on smooth manifolds, also known as Riemannian Geometry. Maybe Riemann would have been discouraged and scrapped his work. Too bad, since that work, which had no useful applications at the time, would turn out to be the core mathematics Einstein needed to complete General Relativity some 61 years later.
Math is the language that describes the universe. Stop pursuing new heights in math an you will never reach new heights in reality.
jdb2
So the higher you can raise that denominator, the better off society will be in the long term, because effectively, we're all making the decisions by electing our leaders, and if the bulk of the population is ignorant of the effects of exponential growth, disaster will eventually ensue.
That's why our public education was originally created - to have an educated electorate. Then somehow over the years, our education became job training - even at the university level.
Whenever I hear a business leader complain that our schools aren't producing "educated workers" my blood boils - and I can understand the folks who rant about "corporatism".
RIP America
July 4, 1776 - September 11, 2001
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.
I know you just said you have an English Lit major, but as a tangent, I believe that the best critics in the disciplines of the social sciences, Literary Critics for instance, will do a great deal for their discourse if they learn as much mathematics and science as possible. There has been a long recorded mutual hostility and ignorance between the two worlds -- the hard and soft sciences -- and it's projects like John Brockman's Edge, ones trying to advance C.P. Snow's Third Culture concept, for example, that will push not just math further, but literature, art criticism, and philosophy. Most philosophers of the twenty-first century are aware of this (not just people like Alain Badiou or Irigaray, who get railed on for invoking math in interpretive ways, but see Katherine Malabou's essays on brain plasticity and philosophy -- this is where we need to take Writing), most lit-heads are still, unfortunately, not. /rant
"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.
The problem of history, economics and political science is that many of the sources are actually the work of "manipulative talking heads".
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?
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.
"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.
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.
Craft Beer Programming T-shirts
Mathematics is the language of science. (all science)
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.
...are we scared yet?
It's even more than that. Without math, your ability to understand physics is compromised; and without physics basic and very practical things like your driving skills are going to suffer. People are *really* a lot better drivers when they can bring a realistic understanding of traction, inertia, kinetic energy and so forth to the driver's seat. But that's not all. Polls completely bewilder and mislead their readers without basic statistics; lotteries rob the probability-impaired (hence the joke, "lotteries are a tax for the math-impaired); people who don't have a good, intuitive understanding of what thousand, million, billion and trillion mean relative to each other are inherently incapable of forming useful opinions on federal budget issues (and consequently, are likely to vote in a random, haphazard manner more driven by crap like fox news than sense); it even leads to poor military strategy, an excellent example of which can presently be found in the Iraq war.
The pachyderm in the parlor, however, is the fact that if you take an IQ 100 person (or lower) and try to teach them math beyond the basics, you're not often going to get very far. People aren't born equal in capacity, and we can't fix that by applying more pressure to their foreheads, which is about what forced math classes do.
It's that whole thing about teaching pigs to dance. It wastes your time, and it annoys the pig.
I've fallen off your lawn, and I can't get up.
We should be pushing for everyone to learn differential equations by the time they finish high school.
ROFLMAO.
"I don't know, therefore Aliens" Wafflebox1
No.
I went to high school 6 years ago, and we learned nothing. Absolutely nothing at all. The entire day was a complete and utter waste. The problem was the pace. Everyone assumes kids are stupid, so they teach us slowly. If they did a better job teaching, it would be trivial to reach a meaningful depth in every subject.
I'm not promoting math at the expensive of other subjects. I'm saying every subject is woefully under taught.
Actually, I think we should pull back on subjects like "standardized test preparation." We're taught to pass idiotic tests, so all we ever learn is idiocy.
When you're afraid to download music illegally in your own home, then the terrorists have won!
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.
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.
I've fallen off your lawn, and I can't get up.
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.
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.
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.
"I may disagree with what you say, but I will defend unto the death your right to say it." -- Voltaire
Wow, way to close your mind to scientific research based on your own preconceived notions. Based on that, I hereby relegate you to the 'dumb' category.
Qxe4
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?
"I don't know, therefore Aliens" Wafflebox1
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.
Can you be Even More Awesome?!
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.
For more of the history of school: http://www.johntaylorgatto.com/underground/toc1.htm
If you are an educator then the book linked above is a must read. The chapter entitled Intellectual Espionage is a must read for those who love standardised testing.
The new right fascists are bilingual. They speak English and Bullshit.
In theory that all sounds good, but what about money spent on rent before buying your home? How would you factor that in? Surely that damages how much money you actually saved?
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=
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.