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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.
Speaking as someone with a degree in English Literature, I can safely say that I've only used math two times in my life: when learning it in school, when counting my kids at night, and when doing my taxes.
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.
unlike literature, history, politics and music, math has little relevance to everybody's daily life.
Now we'll be comparing the uselessness of those subjects. Nice troll, though.
In base 4!
Nobodies Prefect
Tidbits for Techs Technology Blog
... as long as we replace it with logic and critical thinking. And finance. I don't care if someone can't do derivatives but everyone should understand the implications of credit card interest.
Dear Slashdot: next time you want to mess with the site, add a rich-text editor for comments.
The one with that chick that is going to fix up her friend with the hunky mathematician. She tells her not to use her calculator so her calculus stays sharp. But she doesn't listen and uses her calculator all week, but the night before her big date she uses Crest Mathstrips and gets the hunky mathematician.
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.
How does literature or music get labeled as essential and not math? We learn math so we can build things that let us have time to create literature and music. Sure not everyone needs it (though probability would certainly help), but no one *needs* literature or music, its just the sort of thing we *want*. Some day when we finish automating all the jobs we'll all get to devote all our time to creating art... for our robotic overlords.
refactor the law, its bloated, confusing and unmaintainable.
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!
Does education in "literature, history, politics and music" have any "demonstrable results or accountability"? Indeed, in my profession, I use my math education on a daily (if not hourly) basis, while I can't remember a single instance of literature, history, politics and music having any utility or relevance. My sister, a nursing student, has seen much of her class drop away because they couldn't do the simple math that they need for their job.
Math can be useful for much more professions than pretty much any subject taught in school, short of basic reading skills. Literature, history, politics and music are, frankly, just enrichments.
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.
Most people don't directly use anything they learn in school. This goes deep into specialized programs such as engineering, even--the lessons from textbooks just are not applied directly. Does that mean all those programs are a waste of time? Might as well get people fresh out of HS. They'll be four years younger (and cheaper!) and not be especially behind in terms of what they have to learn.
Of course, what I propose above is ridiculous! Degree programs are about training people how to learn that field, not necessarily for teaching them the field directly. An employer doesn't look at a high GPA as a sign that you already know so much. They see it as that you are capable of learning, doing so at a high level, and caring enough to do so.
People need mathematics not because they're going to go out and compute all these things every day. Even engineers don't use all that much math beyond algebra on a daily basis. Rather, mathematics is a logical progression of steps. There are a list of rules and operations one can do, and needs to choose which of those to apply and then do so correctly. Every day, people are confronted with systems full of rules they have to follow, and need to know how to maneuver through those systems optimally. Mathematics teaches that.
It's unfortunate that most people never get to the truly higher mathematics, where proofs are taught. Being able to see the subtlety in arguments (and language!) is an invaluable skill for anyone. The rigor and logic of proof-based mathematics would be far more valuable than the symbol manipulation of lower levels. However, most people never get to that level, having given up far before then. At times I wonder whether the whole of people is actually capable of doing it.
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
They spend too much time teaching crap and instead skip over the important stuff
Why the f... did I learn trigonometric equations ins high school?! Really... Polynomial equation solving?!
Derivatives would be much more useful. And don't beat around the bush on limits, etc, that's math "self-indulgence", go directly to derivatives, simple, done
If they cut the crap and stick with the essentials, then maybe people will learn better. Maybe can they shave a year from the school curriculum so that students can go and study what interests them.
how long until
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.
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.
I use math (including some advanced stuff) every day. And, I am not talking about work. Literature, history, politics and music, not so much.
I guess it takes a mathematician to say what most people instinctively know: beyond basic math education, there is zero burning need for much math education when it comes to most people. We DO need some expanded math education, but not the kind that government and industry pushes in high schools and colleges so relentlessly. Most people forced to take Trigonometry, Calculus, etc, will only resent it it, hate the experience, and never use what they learn. The quite insane push to force more students into science and engineering... and the predictably dismal results of that push... should be abolished, and stat. Those that love advanced math, or merely those that are curious, will never need a government sponsored ad campaign to take a calculus class.
So what kinds of math DO most people need more of in High School? Practical maths dealing everyday problems, especially finances. Perhaps if more people knew how to calculate a simple mortgage, governments and banks and interested parties wouldn't have been able to sell subprime loans so easily. Getting the average man to understand interest rates will have a far more positive effect then making him sit through an algebra class he neither needs nor cares about.
Life is hard, and the world is cruel
As a programmer, I find I am using math almost constantly, including the calculus and linear algebra courses I took in post secondary. A broad knowledge of math has been helpful to me in inventing ways to model certain types of problems I've had occasion to run into that I suspect would have taken me much longer to write (and probably been much less elegant) otherwise.
On a more general note, I have met more than a disconcerting number of grown adults who cannot divide a three-digit number by 2 without using a calculator, or even just add a pair of 2 digit numbers in their head. Is it essential? Well, probably not... but if you don't bother to learn the basics you are going to inevitably come across as someone who should never have been allowed to graduate high school. Judgemental? Possibly. It's still reality though.
File under 'M' for 'Manic ranting'
I don't know, we need a lot of that weird volume stuff for electromagnetics. Maybe your mathematics courses were tailored to cover all the basics students at your school needed for higher level courses in more rigorous disciplines. I know that's how they pick what to put in the curriculum at my school.
When you're afraid to download music illegally in your own home, then the terrorists have won!
Danica McKellar said so, and she's prettier than G.V. Ramanathan.
You are a professor at a liberal arts college and ask when did "ramblings of a random guy" become "news"? What did I miss here? The world is full of news about new books, which do contain such ramblings. But, true they may not always be the "News for nerds, Stuff that matters" that we all thirst for, but still are regarded as news.
The ability to solve for X is applicable in at least one aspect of just about everyone's life. You quilt, you have some known elements you want to include, and you need to know how big your other pieces need to be. You ride motorcycles and you want to change your bike's acceleration characteristics...how big a gear do you need? You do absolutely anything involving money over a long period of time.
I've never had any sort of science or engineering job, but I've never gone 6 months without using SOMETHING from Algebra 1 or Algebra 2. You just have to be able to recognize when it can help. (I've rarely used anything beyond that, though.)
I listen to music.
I am forced to hear people yammer about politics occasionally on NPR
As for history and literature - probably the furthest thing from relevant in my day-to-day life.
As an engineer and programmer - math is with me all the time.
As a "average joe" - it's with me every time I pay for something or tell time. Even if *I'm* not doing it - its often some machine I'm directly involved with that does.
The two words that summarized where the whole article was coming from, were: "Professor" and "Emeritus"
Exactly. It's not like when I apply to an IT position they'll quiz me on the deeper meanings of The Great Gatsby. All of my English and composition classes have focused around this type of analysis, which is highly specialized and irrelevant for most everyone.
SSC
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!
Math is important for understanding statistics, probablity and financial literacy. It's also important for understanding queues; A good foundation in mathematics should include probability, basic statistics, some finance (interest rates, compound growth, mark-up, mark-down, ROI), fractions, percentages and a bit of symbolic arithmetic (aka, high school algebra). Understanding sets (union, intersection) doesn't hurt. The population would be less easily bamboozled if they had a basic grasp of math. And, yes I think numeracy is important for most white collar (and many blue collar) jobs. Most jobs in the 21st century are going to require high school math or better.
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.
I do wish that there was a course for Math that started with Physics instead of starting with number theory which is really what most math is connected to and then after that Algebra is taught as an abstract set of rules and tricks, rather than a set of powerful tools for logic and problem solving. Get rid of exercises in favor of nothing but "word problems" That will make the classes a lot more worth while. Calculus in physics is so easy and so cool, but lots of times you don't get to see that until you have reached collage physics which is just stupid. With those modes of thinking in place, nothing is out of reach.
...for the emeritus professor, but he did not become "emeritus" early enough.
And did he seriously use "taxpayer dollars" as an argument? Is he trolling for local office or something? The entire debate over the usefulness of any form of learning is ultimately predicated over the false assumption that this learning needs to be justified. An educated nation is one that is more productive, more aware, and ultimately happier than its massively illiterate counterparts, irrespective of the moaning of certain truck drivers, soccer moms and ex-professors over enforced learning. I've yet to observe many happy, illiterate nations - in fact the only things they tend to excel at are genocidal warfare and mass starvation.
People, pay attention: no one cares about your objections to learning math; you don't like it, tough. You like your 9-5, do you? Somehow I don't hear you bitching and moaning how we should do away with work. Shove your ignorant objections and STOP getting in the way of those of us who can actually think, 'cause you know what? In the end, you'll be the sad marginalia in the history books emblematic of a "more ignorant age". The rest of us will be praised for advancing humanity.
So, again: stop getting in our way. You are not important. Neither are your opinions. Quit trolling from the pulpit. Btw, fundamentalist Christian ministers, you hearing me? That goes double for you.
There is one problem, though. Achieving a really useful level of math needs about 15 years. Now trim the math from basic education and you are harming those who actually want to use it professionally later. It is like piano -- you have to start learning very early to be able to reach the top. While I understand that this increases the pressure on those students who will never use it, but I think that is an acceptable tradeoff.
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
A basic understanding of mathematical proof and logic does more for critical thinking skills than the entire student career of humanities courses.
What the humanities actually teaches is empathy. But very few of its practitioners actually make the distinction between understanding someone's point of view and knowing whether that view is demonstrably right or wrong.
Let's cover the basics first please.
These days simple addition and subtraction seems to pose an intractable problem for the majority of people.
"90% of this game is one-half mental"
Seriously, though: Large scale serious problems like global warming, ecological services calculations, etc require
a deep and broad grasp of math and logic.
Understanding geopolitical problems and economic problems
at a fundamental level requires understanding of the math of complex systems.
In short:
- If you want to be in charge, and do the wrong things, you can get by without math and without believing in what
math and science say about the world.
- If you want to be in charge and do the right things, you need deep insight into mathematical and scientific
explanations of aspects of the world and aspects of collective societal behavior.
- If you want to vote for the people who will do the wrong things on the big problems and opportunities, you
can get by without math.
- If you want to vote for the people who will do the right things on the big problems and opportunities, you need lots
of math to figure out who's probably on the best track to viable solutions.
Where are we going and why are we in a handbasket?
Is that the derivative is one. (Yes, I agree mathematician make limits way more complex when they could just say the limit is the answer to the question "Where does it look like it's going?" Still the derivative is a limit so I'd think having some idea about limits makes you understand where the derivative comes from and not "Because that's what Stone Cold Isaac Newton said so.")
Did you know 80 to 90% of the moderators on slashdot wouldn't recognize a troll even if one dragged them under a bridge.
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.
Highly improbable, statistically, his conclusions just don't square with me. I figure that his probability of being correct is inversely proportional to the ratio of conclusions drawn from assumptions made.
Math is easy to mark and as long as it is schools will be in love with it.
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.
That explains why so many physicists don't understand that Schroedinger's Cat thought experiment was a literary euphemism for sex.
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'
The math people really need to survive in a very dynamic society involves probability, statistics, and estimation. Schools rarely teach how to estimate something within 10-20%, yet that's an enormously valuable skill. Being able to decide what to throw out of an estimation without losing too much accuracy is essential.
Kids should know enough probability to estimate the odds on the local lottery. They should know what an "expectation" is, and what zero-sum and negative-sum games are and how to recognize them. They should be able to calculate the odds of dying in a terrorist attack and in an auto accident. They should know the risk/reward calculation for various career choices. They need to understand the concept of exposure to interest rate variations in loans and investments.
Plane geometry, Euclid proof style, could probably be dropped with no loss. (I've done animation physics engines and GPS calculations, and I didn't use that stuff. Analytical geometry, yes; straightedge and compass proofs, no.)
This is completely missing the point. All that you are taught in school is basically useless in real life. It's just a mechanism to tell if you're smart.
A lot of companies hire math phds to make them do things completely unrelated to their thesis. They do that because they know that since the person succeeded at some very advanced work, they should be capable to do well anything a bit complicated that they throw at them.
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
Well, the summary IS the article. Seriously. Just in more words. It doesn't make the point that we need art as much as academics. It's just against math. What did math do, run over his dog and crash his car?
There is no -1 Disagree.
http://www.psychologytoday.com/blog/freedom-learn/201003/when-less-is-more-the-case-teaching-less-math-in-schools ... The school that Kenschaft visited happened to be in a very poor district, with mostly African American kids, so at first she figured that the worst teachers must have been assigned to that school, and she theorized that this was why African Americans do even more poorly than white Americans on math tests. But then she went into some schools in wealthy districts, with mostly white kids, and found that the mathematics knowledge of teachers there was equally pathetic. She concluded that nobody could be learning much math in school and, "It appears that the higher scores of the affluent districts are not due to superior teaching but to the supplementary informal 'home schooling' of children.""
"When Less is More: The Case for Teaching Less Math in Schools by Peter Gray; In an experiment, children who were taught less learned more.
See also:
http://www.newciv.org/whole/schoolteacher.txt
http://www.holtgws.com/whatisunschoolin.html
And some posts I made to the p2presearch list concerning education (it would take years to read through all the embedded links on Gatto, Holt, Goodstein, Schmidt, Honigman, Lewellyn, etc.):
* [p2p-research] College Daze links (was Re: : FlossedBk, "Free/Libre and Open Source Solutions for Education")
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-October/005379.htm
* [p2p-research] The Higher Educational Bubble Continues to Grow
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/005584.html
* [p2p-research] Rebutting Communique from an Absent Future (was Re: Information on student protests)
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-November/006005.html
For the record, I've always loved math and think it can be a very fun and worthwhile profession or hobby. I love broccoli too, but forcefeeding endless amounts of it to people till bursting despite the tears and protests would be cruel and probably would result in them not eating broccoli when no one was looking. How do we get people to enjoy thinking well and eating healthy? Good question. But people do have answers, if you look.
http://www.educationrevolution.org/
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
as an engineer all I can say is thank heavens for spell checkers
'All the mathematics one needs in real life can be learned in early years without much fuss,'
Wow, what a load of BS.
My wife taught "College Algebra" for a few semesters.
She was astounded when early on, she was working with a student during office hours on a fairly simple problem. A shirt costs 29.50. You have a coupon for 15% off. How much will the shirt cost you? The resulting answer was more than the original price.
Additionally, she was working with a student, and reduced the problem down to seven times four. The student's response? "Hold on, let me get my calculator"
While the current teaching methods being experimented with may not be working, I think that the professor is wrong in his suggestion that we basically throw up our hands and give up. It just means that we have to try other things to reach such students.
the hard part about taxes is the rules that change each year. Not the the math part and the tax pros (not the HR block guys) keep up on all the new rules and they are able to help you to get the best refund or the lowest tax to pay.
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
Based on the low, low standards this guy seesm to be advocating, most individuals don't need to be able to read more than the back of a cereal packet, have any clue about any foreign languages, be able to write anything their spell-checkers won't fix or learn any manual skills: such as cooking (we've got microwaves), handyman (can drive to the home centre) or anything more than turning on the TV or the computer.
So what's the point in staying at school past age 10?
politicians are like babies' nappies: they should both be changed regularly and for the same reasons
Learning maths and all the 'complicated' things, isn't done just for the sake of knowing how to do those, but to put you in the mindframe for learning and analysing the world around us in a certain way.
/. user, why do you ask?
I'm in ICT, and I actually find ways of using computer structures and algorithms (and the mindset) for my day to day life. Yes I'm a
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 use math quite often in my career. Just the other day I had to write a piece of code that determined the margin of error between the actual GPS coordinates of a cellular phone and the coordinates that the phone was returning. The equation I used was as follows.
sqrt((N1*cos(True Lat x)*(True Long y - Long y))^2 + (N1*(True Lat x - Lat x))^2)
Granted it is a simple Algebra equation but it is still Algebra so don't throw all of those math book thumpers under the bus just yet.
That reminds me!
The article looks at math from an anti-capitalist angle:
"Unfortunately, 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.
There are three steps to this kind of aggressive marketing. The first is to convince people that white teeth, a full head of hair and a sculpted physique are essential to a good life. The second is to embarrass those who do not possess them. The third is to make people think that, since a good life is their right, they must buy these products."
Now go ahead guys and gals, have fun with this:
http://en.wikipedia.org/wiki/Soviet_Student_Olympiads
http://www.kidsmathbooks.com/2010/10/2nd-all-soviet-union-mathematical.html
I mean, why is he targeting the left wingers with his anti intellectual propaganda?
Je me souviens.
Many great artists have used math and geometry in their works, like the Golden section. While perhaps not as much, math is also used in music.
For those who missed the joke, parent was being disingenuous, which in this case is funny as that's the crime the article's author was committing. We all use literary analysis every time we read a news site, watch a movie, or myriad other situations every day; but just like with math we're not tested on it by writing an essay or an equation. Doesn't mean we don't need both. (On a side note, this use of saying the opposite of what you actually mean is true irony.)
Unless I'm reading too much into the parent post, then he's just an asshat ;)
Let me guess, your are Frensh? In my experience technical papers written in English are usually quite usefull as the writer used some words and was done with. Perhaps sometimes a few puns too much but otherwise not much making it hard to read. While in Frensh people like to literary
papers, not repeating a single word but always insisting to use another one to avoid duplication....
(Well, also may happen elsewhere. Some math schoolbook was once printed in which a lector
without asking anyone replaced every second instance of "real numbers" with "actual numbers"
shortly before print).
As a long term math nerd I have to say I agree with TFA.
Most of what was taught in school was completely useless.
now that doesn't mean that kids who *want* to do math shouldn't be able to, merely that requiring everyone to learn about Complex numbers or calculus is insane.
It even harms the kids who are good at math and want to do it because the teacher has to slow down for the kids who have no talent for math, aren't going to go into a math related profession and shouldn't be forced to learn about the square roots of negative numbers or quadratic equations.
Addition, subtraction, multiplication and division.
These are the only ones which are utterly essential to most people.
percentages , basic volumes and areas and very very basic probability are all I can find in the more advanced part of the curriculum with almost universal applications.
funnily enough probability wasn't a mandatory part of my math course when I was in school.
It's an acceptable tradeoff to people who like math or eventually use it.
To everyone else it's a waste of time which could be spent far better learning things which might ever be useful to them.
We may not be doing lots of long-hand calculations on paper, but we certainly do use the concepts of set-theory, calculus and general math every day. When it becomes a necessity to keep tabs on, say, how much money you have in the bank, or understanding what the speedometer in your car means, or that jumping off a cliff will mean you accelerate until you hit the bottom, you stop thinking of it as 'math' and as just common sense. And while I admit to being a bit of a nerd, I may not sit down with a math book, I do enjoy some aspects of physics and it becomes more fulfilling to at least have a rough understanding of the math in the books I read or the lectures I watch.
I figured this out early on, when a classmate at university, gave all sorts of answers which the professor loved and ate up. The problem was that the student never even read the books.
He got an A
Please see relevant XKCD cartoon - imposter
http://xkcd.com/451/
..........FULL STOP.
who actually needed math skills and who didn't this would be great, but we don't. If we de-emphasize math education in this country, then we will surely diminish the future supply of mathematicians and scientists.
If anything, you've just proven the real corollary of the research in the article, and not the one in the article.
Math is a hard, specialised tool. Essential for many distinct types of specialists. It's what they call "fundamental".
Nonspecialists don't need it. They don't understand why specialists need so many variants of it. They don't understand how rigorous math can be useful is so many different ways to different specialists.
Is it the fault of the specialists?
Is it the fault of the public?
Not really, the public can't seem to grasp the idea that the benefit to mankind is in the details, and wonders why we need something that has no generalists.
Medecine and engineering are doing fine in the public view, because they can be understood, without the details, or so the public thinks.
If you understand math without the details, you're back at a grade school level, precisely because that's the point in the curriculum where they start preparing you for the different math specialties, and you're starting to get the grounding into the differences.
You invest in math education precisely to get the specialists, and to get research done in the specialties. Proving the return of specialties is harder but it still has to be done.
History? How often does that get used outside of school? Science? Art? Literature? Geography? Once you get the basics of reading, writing, and math down, you can function in society. But I'd rather not have a society full of people that can just barely get by. I mean, we are TRYING to teach way more than the basics, and look how dumb our country is!
Don't forget to include religion in the, what math can't express, unless of course one is arguing how many angels can fit on the head of a pin?
Shai Schticks:"You don't make peace with friends, you make peace with enemies"
Some math schoolbook was once printed in which a lector without asking anyone replaced every second instance of "real numbers" with "actual numbers" shortly before print.
That is quite possibly the most awesome thing ever.
When you're afraid to download music illegally in your own home, then the terrorists have won!
You may just have had an advantage from natural talent and experience? Or maybe you just eat a better diet or exercise more than others?
http://www.alternativeratreatments.com/eat-to-live.html
You can see another post I made for links about alternative education.
http://science.slashdot.org/comments.pl?sid=1847578&cid=34081206
But basically, most young children tend to learn best through interactions with people, nature, exposure to a waide variety of experiences including music and stories, and basic things like playing with sand, water, and blocks. It is on those sorts of things that more advanced thinking is built. Trying to put the cart before the horse may lead to less success, not more. It has been hypothesized that the reason many kids are doing worse in math and science and criticial thinking is that those sorts of general early experiences have been curtailed in favor of early academics focusing on things like early print literacy or early drill of math concepts. So, you might want to research this more, including reading stuff by John Holt (a mathematical person who also studied alternative education).
http://holtgws.com/
With that said, there are things you can do, like pointing out things. I've pointed out examples of recursion to my kid from a young age (like trucks carrying trucks). And math has been a daily thing by pointing out examples of it in our daily life, including when working with LEGOs. But that is not the same as "lessons" in any kind of formal sense.
A good open-ended site for young kids to learn through play as an example:
http://www.poissonrouge.com/
I agree with you that programming is a good way to approach math. As people talked about on the Python edusig list, "math" can really just be seen as a subset of computation and programming in general (at least within the bounds of whatever most schools teach).
I can also wonder if getting kids indoors more at an early age has made them vitamin D deficient which has led to some learning difficulties? So, even if you use computers with a kid a lot, make sure that everyone is getting enough vitamin D.
http://www.vitamindcouncil.org/treatment.shtml
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Funny, that. I too did The Great Gatsby for English Lit, and decided that its deeper meaning was that reading books on the theory of programming languages was more fun than many people admit. Hell, even "Perl for Dummies" was not that boring!
Sent from my ASR33 using ASCII
The reason adults aren't using the math they learned in school on a daily basis is because the math they learned in school focuses too much on algebra and pre-calc and not enough on statistics. And I say this as a college physics professor, who has a vested interest in encouraging algebra and pre-calc.
Stats is, (well, should be), at the core of every news article you read or watch on TV, at the core of almost every memo you write at work. Good statistical analysis should be at the heart of every political debate you see on TV, and every major economic decision your family makes.
Too often, we're making decisions based on gut instinct, political principle, and anecdotal evidence, and it's causing us to make bad decisions at every level from individual to global. The only cure for this is more stats.
Devil in the details.
If you include addition and subtraction of fractions(my clarification), percentages, basic volumes and areas and very basic probability then you are basically going to leave math unchanged until (US) high school (about age 14).
In my experience kids who don't like math basically manage to skate in high school.
They take freshman pre-algebra (review of what they should already know e.g. +-*/) and a very weak algebra sophomore year.
Re-take pre-algebra (same review +-*/) freshman year in college, flunk business math soph year, switch to liberal arts major.
Basically your saying keep things the same.
John McAfee 'It was like that time I hired that Bangkok prostitute; to do my taxes, while I fucked my accountant'
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.
Unless that paper is on string theory.
"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.
For more of the history of school: http://www.johntaylorgatto.com/underground/toc1.htm
A key section is here:
http://www.lewrockwell.com/gatto/gatto-uhae-16.html
as part of another archive:
http://www.lewrockwell.com/gatto/gatto-arch.html
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
If you think sex is putting the pussy in the box, you're doing it wrong.
Because not knowing is clearly better than knowing.
Hello again, Dr. Freud! How's your research into necrozoöphilia coming along? Oh, it's rather dead? That's what she sa-!... No, I understand. Not funny. I'll let you get back to being dead and all.
For the most part we fail to tell people WHY they should care about math. Early on, in public schools, approaches such as connected math, come up with all these cute stories that most students do not really care about. In the context of our Scalable Game Design project we teach middle school kids how to make games. Suddenly we get these 12 year old kids who NEED to be able to build better AI into their games. The teacher indicated that these kids do not care about math. One week later they build video games implementing sophisticated AI based on diffusion equations and actually start to enjoy math. Why? Because, for the first time in their life math actually solves THEIR problem and not the one made up by the teacher or the text book. "Excuse me, I need better AI!" http://www.cs.colorado.edu/~ralex/papers/PDF/SIGGRAPH_06_Excuseme.pdf
They problem with math education is that it is taught in a sort of vacuum. Students don't see the necessity of math until much later in their lives when it's too late. People try all sorts of methods to teach math, but what we really need to teach, I feel, is the necessity of math. We need to wow students young to show them that math can be useful.
That said I think that we should introduce logic and geometry at younger ages and geometry needs to play a more natural role than doing those retarded column proofs that scar 10th graders so much. Math was invented to help explain the world around us, to help keep count of that which is important to us, but it has been divorced from that in education. Sure we have those asinine word problems, but again these problems rarely connect with their target audience.
If you look at higher math so much of it has very deep connections to geometric structure as well as critical logic skills. So it makes no sense to me that these ideas are taught in compartmentalized nature and that all the areas of math are so segregated. Plus Logic and critical thinking are skills that cross all areas of life.
In conclusion, we need to be showing children how and why math is important, not just trying to beat the rules of arithmetic and fractions into their aching and confused brains.
I don't care what you say, all I need is my Wumpabet soup.
All the nonsense with the anti-vaccine says Medecine is not doing ok in the public view.
Engineering has the defense that people generally don't need to know the details, merely know that the magic box works.
I'm all for investing in math education but much of it is nothing but a waste of time for the vast majority of the kids involved.
Let the kids who have no talent for math and no inclination towards math based professions drop it once they have the basics.
Knowledge of imaginary numbers and differentiation will never help them in any way shape or form. Ever.
An extra few hours of languages, woodworking, literature or whatever else they're actually interested in will do them far more good.
I *am* a math nerd and I'm in a profession which uses math extensively yet I know damn well that it really is nothing more than a waste of time for most people after the basics of addition, subtraction, multiplication and division have been covered.
Throw in some percentages, fractions and probability and you've got pretty much all the math a normal person needs to get through life.
Eh, but you also have to remember that getting into high schools in China is not guaranteed and students have to test for placement so the population of high school students is going to be self limiting. If only your most promising students are in high school then it is going to be easier for you to show strong scores at a global level. The same argument cant be made for Japan where high school is not compulsorily and students have to test to get into the high school of their choice.
No then it would be (n+1) at which point the OP would have the first "infinite post". Two was a good call
The same without forcing kids to waste huge numbers of hours.
Let them use those hours learning something else(I know, I know, it's heresy to suggest that other subjects might be more useful than math for some people.) rather than pissing their time away on something they don't need.
what an out-of-touch twit. then again, UChi is fairly famous for "odd" faculty.
numeracy is what's needed: that people are comfortable with quantitative reasoning. the specific mathematical techniques are irrelevant, but yes, people really do need better ability to understand issues in a quantitative way. climate change, sub-prime mortgages, this week's discount on cans of soup, fluoridating water, innoculations and autism, the list goes on forever. you can't be a competent human without understanding conditional probability, for instance.
the education system does an incredibly poor job of this, producing adults who struggle and fail to find structure and place in a big, confusing world, and for lack of comfort with analytic, quantitative approaches, latch on to religious/emotional/ideological movements like the Tea Party.
Depends on their major, but in most cases, if you aren't going for a degree in the sciences or engineering then most schools really don't require much math beyond basic calculus as part of the core curriculum. In some cases they might go a bit farther, but in other cases there might actually be less if you are going for a humanities degree where students might not even have to take calculus courses.
The economics of it are a bit sticky. If only say 5% of students will use a fair amount of math in their careers, then the money spent educating the other 95% is essentially wasted. That's a lot of education resources. However, it's hard to know up-front who that 5% is.
Perhaps we can take that 95% of the money and create some kind a kind of just-in-time education. People forget anyhow. Just make sure students have enough basic theory to pick up industry-specific details later when they actually need it.
One argument is that math teaches logic and reasoning. While that may be true, there may be other topics that do that same, such as logic and reasoning courses.
Further, as we ship physical factory production overseas, our jobs tend to use less "physical" math such as geometry, and needs instead have shifted toward marketing-centric fields that require probability, statistics, logic, and set theory. Our material may need an adjustment to fit our new role.
Table-ized A.I.
Languages? Insanely useful in many ways.
practical skills like woodworking or metalworking?
Grammar and history are probably more useful than imaginary numbers whatever else you could say about them.
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.
Which is fantastic if you're ever likely to go into a math related profession. For everyone else, far less useful.
Heck, I would just be happy if people learned who has the burden of proof for a claim. If I got 2 cent every time I was asked to prove something do not exists, where as the one *pretending* something exists don't feel they have the bruden of proof.... Or if ONLY people would understand the difference between anecdte/personal experience and evidence...
C. Sagan : A demon haunted world:
http://www.amazon.com/gp/product/0345409469/
visit randi.org
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.
This is especially useful when the work isn't written in your native language, like converting between English and Old English, or English and French, or French and Russian, or English and Physicist, or Physicist and Management, or Physicist and Chemist, etc. Or, equivalently, when you just aren't on the same wavelength, such as 10 hours of sleep nightly vs 10 cups of coffee nightly.
It's not quite that estranged as a topic.
/Joking?
I agree with the premise of this article. Unless going into a science and engineering field, or accounting, etc, one doesn't need anything more advanced than basic elements from geometry, algebra and trig.
Seriously, even in the practice of doing engineering work, how often do you actually DO an integral, a derivative, or a laplace transform?
Yet all of these were drilled into me at engineering school.
Good? Yes? No? Maybe. That's the debate brought up in this article.
However, I think this is a non-issue. In my rural midwest high school, it was pretty straightforward - if you were NOT going to college, you didn't even HAVE TO take advanced english and math. If you WERE going on, you could take a max of calculus and took the advanced english class.
So, no, not everyone needs math.I'm not even sure how much math is needed for engineers, either.
Laplace transforms by hand? Seriously? Powerful, yes, but I still remember the brain pain. And haven't done one since my "analysis of dynamic systems" course.
With the advent of computer algebra and things like FEA and other advanced simulations, will there be an evolution into a new era where the advanced math is quaint and extremely unusual, like going from the horse and buggy to the automobile?
Flappinbooger isn't my real name
No: you're just reading the wrong journals.
Said Schroedinger," isn't this fun
Shot a cat in a box with a gun
I'll be sure it survives
'Cause the cat has nine lives
And I'll only be using just one."
Schroedinger should not have done that
It was cruel "playing God" with a cat
Which, by the way, mister
Belonged to your sister
The next time please make it a rat.
Said Schroedinger poison is nifty
To dispose of this cat, God is shifty
We can't tell if it died
Till we all peer inside
And the odds are at just that, 50/50.
The cat in the box still has growth
Or it's dead, and infested with sloth
One should not get unnerved
Till the cat is observed
It's a superposition of both.
So that is the way that you tell it
Leave a cat in a box with a pellet
Should the trigger let go
The poison will flow
And you'll know the cat's dead when you smell it.
Said Schroedinger, "let Physics advance
Though it might be kitty's last dance
When we open the box
Be prepared for some shocks
But there's only a 50% chance."
Said Schroedinger, "let's take a chance
Though it might be kitty's last dance."
"The poor cat," he then joked
"is alive, or it's croaked"
But you can't know these things in advance.
(more)
Bio questions? Ask me to start a Q&A journal. Computer analogies available for most topics!
Frankly, I am much more disturbed to think that people don't know what is happening in the world around them and how to deal with it than if they can solve complex mathematical problems. I meet so many people who can't logically reason their way through a problem...if x then then y, therefore z is best course of action. Thoughts like that are surprisingly scarce in a large portion of the population. Mathematics need to emphasize more of the logic and problem solving than the memorization of formulas. Conversely, the other arts like English, history, etc. need to teach students how to apply that logic to real world situations. I don't think schools are teaching necessarily too much math...I think they are teaching it in the wrong way.
The author's point, however is valid. We spend a large amount of time and money teaching people a lot of crap that most of them will never use. I'd venture a guess that less then 10% of the population needs any advanced math at all. The number may be higher, but I doubt it. Given that something on the order of 25-30% of the population of the US has an undergraduate degree, and of those 25-30% only the smaller number with a degree in science, math, engineering or an "applied science" like medical people, ever use any advanced math at all. For the vast majority of the rest, a few courses in basic statistics would probably be all the math they ever need beyond arithmetic.
The problem is that we don't *know* in 7th or 8th grade who is likely to need more math 5 or 6 years down the line. Most kids, if you tell them in 7th grade that they can stop taking math, they're going to. Then they hit junior or senior year of high school, realize they want to be an engineer, and they have none of the needed mathematical background. Basically we teach 4-5 years of advanced math to every student in the country, so that the 10-15% if them who will actually need it, have it. It's wasteful as Hell, but I can't think of a better way to do it without forcing life altering career choices on 13-14 year olds.
I don't need a million points of light, just two points of multi-mode fiber and a 10 Gig-E router.
Well, changing things after age 14 would still save us some money. I remember being taught quadratic equations after age 14. We don't need those. Exponents don't seem useful. I'm sure that there are more.
I seem to remember reading about how boys don't need to be taught much math until grade 7. If we could cut math out of all those years, and still keep the students well prepared for life, then I'd say that we did a good job.
testing out my trending skills
Based on how many people actually listen to Glen Beck, Bill O'Reilly and other manipulative talking heads, I would say some more history, economics, and political science/civics wouldn't hurt.
Laissez lire, et laissez danser; ces deux amusements ne feront jamais de mal au monde. - Voltaire
I need literary analysis every time I read a technical paper
I was going to mod you funny, but since you have a +5 Insightful I'm starting to think nobody here actually knows what literary analysis is...
It's not reading comprehension! No, it's about interpreting symbolism, etc. Usually it's sort of a game you play, where you either try to find a particular political message (Marxist, feminist schools of criticism) in a work, or just create a contradiction between the work and itself (deconstructionism)...
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.
I tend to agree. Having been a software guy for about thirty years, I can tell you this: I've known a lot of engineers (in all fields) who got into it because they were good with technology but lacking in verbal skills, who chose their career believing they were excused from any need to communicate with anyone or anything. That would usually last until they got their first real job, and got told to write a hundred page project proposal all by themselves.
... all are just tools. The majority of human beings will never have a need, as long as they live, for higher mathematics ... but there are few people who cannot benefit from the ability to communicate.
That would often result in a few remedial English classes. Mathematics, spoken and written language
The higher the technology, the sharper that two-edged sword.
People know how to do better: http://www.educationrevolution.org/
We don't for all sorts fo reasons related to social power (see John Taylor Gatto).
See also my essay on learning "on demand" instead of learning "just in case":
"Why Educational Technology Has Failed Schools"
http://patapata.sourceforge.net/WhyEducationalTechnologyHasFailedSchools.html
Education can have several goals in this descending order:
* To help a person grow as a person
* To help a person be a good citizen
* To shape a person into someone elses' vision of a good consumer and good worker and, for a few, a good obedient professional with the "right" politics
Those three aspects of "education" are regularly confused, and usually most of formal schooling (especially when test-driven) has to do with the last of the three which is often at odds with the first two.
See also for how the third aspect goes on into grad school:
http://disciplinedminds.tripod.com/
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
I remember being reprimanded in an English class during a lesson on Shakespeare...
So, what do you think Shakespeare was really saying in this line here?
Miss, maybe he was just a writer who saw the value of sex and violence in putting bums on seats?
That didn't go down well at all...
If God forks the Universe every time you roll a die, he'd better have a damned good memory.
surely you mean *after* grade 7?
a lot of math is useless to most people but the early basic stuff is utterly essential.
You'd also have to make sure the kids who *want* to do math can keep doing it since they're the ones who are going to go on to be the engineers, statisticians, mathematicians etc.
I can safely say that I've never used literary analysis, even in school. English classes amounted to nothing more than making things up out of whole cloth. That can in no way be described as "analysis".
Want to frustrate an English professor? When he says that some motif in a book is a symbol for something, ask him how he knows it's a symbol at all.
Give me Classic Slashdot or give me death!
BTW please shoot them SPAMMERS!1
Probability theory is too abstract for people if they haven't already gotten enough math to understand at least basic combinatorics and simple algebra. If all you've fed them is fractions, real numbers, and +-*/, prob. theory won't stick and they will get lost. Or worse, they'll think they'll understand it and get manipulated even more.
Laissez lire, et laissez danser; ces deux amusements ne feront jamais de mal au monde. - Voltaire
Yes, there are people that do not use math at work. It is because they can only get jobs that require no math skills. The reasoning behind the article is faulty. I have very little doubt that it is very much like the rising tide lifting all boats. If our population were more educated in every field, not the least of which is math, then we would experience an increase in the quality of life whereas the less education the worse it will be for all of us.
We are in an era in which "educated" takes on a whole new meaning. As early as 1985 I am aware of one company that after interviewing people with a liberal arts diploma simply labeled their file with uneducated and trashed the applications. Expectations now can be very high and very restrictive. People wanting to earn a living had best acquire a love of academia.
Yeah but your print commands look pretty shabby when they come out "Dood, just cleek the buttawn"
Speaking as someone who has a degree in English Literature, I can safely say I use the maths every day. Although I should preface that I work as an analyst and the fields of mathematics I do the most research result in receiving an inordinate amount of CIA recruiting adverts from google adsense. On the upside, I can google "eclipse" and get zero vampire results.
That I ended up in a maths intensive vocation is not unusual. I didn't realise it at the time, but as a kid I had freakish abilities. I just thought it was not unusual. Actually, I believed my teachers who thought I was retarded. I could score 99th percentile on the maths portions of standardised testing, I just couldn't read, write or speak and was severely withdrawn.
Part of this was due to the fact that my father taught me the three R's at an early age and let me write left handed. At school I was required to switch to be right handed. Much later, a teacher advised me to try typing and it helped a lot.
Rather than pursue an Honours Engineering course at University of Illinois, I majored in Lit and Philosophy at a small liberal arts college to become a part of society. I had a fear of becoming an alienated scientist bullied by the same jocks from school into making nuclear weapons.
One could argue that there's no need to pursue literacy beyond the basics. And the author of the article mentions this. But really, what a dismal waste of one's life. It reminds me of the cliché Italian mobster who justifies a sociopath existence banking on a deathbed prayer can absolve him and get him to heaven -- it shows a true lack of understanding in the concept of statistics and risk analysis that someone in that line of work will even have a death bed beyond an unexpectedly cold sidewalk.
Society as it is far too unaware and lost. Literature, Science and Math are what glue our society together. Without it, there's just bread and circus and a general abuse of nerds. Do we really want a culture that would murder Archimedes or make a lampshade out of Einstein or Godel? It's not like we're that removed from that culture of violence today.
Life without intellectual stimulation is a banquet of white bread and margarine washed down with kool-aid while watching the football on the big screen. You can say it's adequate, but it's not my cup of tea.
Yes, one may rarely use the quadratic equation in everyday life, but that doesn't mean the neuron pathways developed in learning this formula doesn't help one make more rational and strategically better decisions in subject matter far removed from the ethereal world of numbers.
Math is neither an art, nor a science; it is the magic that holds the two hemispheres together; writing code seems to be a composite of both: poetry with numbers.
Sure one could do without either, but as Calvin's tiger Hobbes said, without it would be "nasty, brutish and short." For society's sake, we need more maths. I teach junior high economics and personal budgeting through JA and believe me when the teacher asks you quietly after class how to calculate percentages, you know mathematics is not valued enough in our culture.
Something to consider today, the birthday of John Keats, a man who so beautifully combined poetry and science to envision discoveries, such as the workings of the nervous system, not to be revealed through the scientific method for some time later.
"Languages?"
I give you that one. You cannot have enough of languages (applies to programming languages, too ;) ).
"practical skills like woodworking or metalworking?"
Um, they actually teach those things in my country -- in primary schools definitely, and then in higher schools were the children not interested in math and such go.
"Grammar and history are probably more useful than imaginary numbers whatever else you could say about them."
Imaginary numbers are not taught under university (at least in my country), history is not that relevant for most students at all -- they do not make the mental leap from "boring past events" to the current world around them. Exactly the same problem that they have with mathematics.
"Which is fantastic if you're ever likely to go into a math related profession. For everyone else, far less useful."
That is true but I also had to learn a lot of stuff that I never used since -- it was a tradeoff for me, too. But as time progresses, students specialize more and more, so I do not see this as a huge problem. Also, it is quite common that young people do not realize what they really want to do at about their 20th birthday.
Generally, I like to think I know where my dick is. Somehow I don't think that the question of whether or not it's in a box applies until I've had at least a fifth, and probably more.
The problem of history, economics and political science is that many of the sources are actually the work of "manipulative talking heads".
The problem may be that one needs more skills than one used to. The world is more complex. This means that one of two things has to happen: we either spend more total time in school, or something gets chopped. (A third approach is to somehow speed up learning, but that's another topic.)
Yes, everything is important, but something must go when the plate gets too full. Hard decisions must be made, and this author is at least asking the hard questions needed to get the culling started. Analysis of what people actually do at work is a good starting point.
Table-ized A.I.
It's fun to deride abstract academic concepts as irrelevant to the modern world. Those with such a shortsighted view fail to see that most engineered technologies depend heavily on mathematics. Nothing in our modern world would exist without math. No cell phones. No iPods. Even more mundane things like constructing buildings to withstand the elements and keep the occupants safe requires an application of mathematics at some point. The poor buildings that collapsed in the Haiti quake were slapped together by people who had equal disdain and ignorance of mathematics and how to apply it. They reaped what they sowed. Even the lowly construction worker needs some mathematical background to measure and assemble things properly.
Is this the world Ramanathan wants us to live in? Maybe he only sees the need for certain elites who understand how everything works. I'm reminded of certain episodes of Star Trek where an imperiled planet of people are slaves to technology that they don't understand. That's not the path we need to go down. It's already bad enough that the Western world is becoming dependent on the scientific and engineering prowess of the Asian nations.
I am becoming gerund, destroyer of verbs.
Man, my humanities courses must have been a total waste, since all I learned was how to figure out what things actually meant, rather than making up things for them to mean.
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.
"Most people don't need the math."
Let's be honest. Strictly speaking most people do not need ANY of what they learn in school except reading and writing and basic algebra.
As a software engineer, I the most advanced math I have had to use was Trig.
Out of curiosity (not sarcasm) what Trig are you using as a software engineer.
"Educate the mind but never at the expense of the soul."~Blessed Basil Moreau
If you really think about it most people only really ever need to know basics they learn before college. If you have a solid understand of math, english, science, history and health then you'll do well later in life whether you continue learning or not. That's why I think it's a shame that a lot of schools just pass kids through the basics so they can get a degree.
Even if you do well in your degree you'll still struggle without the basics. I've a few people that have absolutely appalling spelling in jobs and yes they get by but people also think less of them because they do stupid things like spell through as threw and pretty as pritty or, in the case of one guy, spells something as somethink. They'll never move up because people view them as morons whether or not they have a degree.
I agree. My personal experience is that courses, systems do not really matter. What matters are good teachers. If a school system is good, then it encourages the talented to become teachers and allows them to do their best.
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.
A lot of comments are arguing that Math makes you think in a different or better way even if you don't use it.
To accept that as a reason for teaching more math, you have to believe that other subjects of study do NOT encourage you to think in a different or better way.
I suggest that if we forced 1000 people to study math full time and 1000 other people to study whatever they want, that people who learn to think critically and make good decisions will emerge in similar numbers from both groups.
---Bless those silly trolls---
Your post is ironic as you are trying to conflate skills related to fiction with those related to exposition.
You seem to be suffering from the very affliction you're accusing the Physicist of.
A Pirate and a Puritan look the same on a balance sheet.
Robin is 22 and leaves the house for work at Quick Burger at 3:30 PM. Jack leaves school at 2:30 carrying a laptop and 2 math books, and arrives at home for study at 3:15. He stops on the way to get a burger and pays 99 cents plus tax. If Robin rings up 78 burgers each hour, and Jack spends 6 years in college, how many employees will be affected Jack's analysis when he's the Operations Research consultant for Quick Burger Corp? ADDITIONAL BONUS: Would Jack like fries with that?
You might think that things like art, music, and writing are the creative subjects. Well, maybe. But math is a subject that requires real creativity, and yet also a hard framework within which to evaluate what you're doing. So, for instance, if you're trying to prove Pythagoras' Theorem, there's several ways to start. Each way requires some lateral thinking to get to the proof, but there's a lot of ways to do it wrong. With arts, there's a lot written about different tastes (romantic, post-modern, classical, etc...) but there's rarely a satisfying right/wrong about it. It allows you to make a bit less effort, because the intermediate product (eg half finished canvas, a story with an undeveloped character...) is also arguably "a good piece of art." With math, you can be creative, but within a certain framework which constrains you.
As for needing it, well, someone already mentioned probability and statistics. Without knowing something about this, your decisions become very difficult to justify. Should you take a mortgage? Buy some stocks? Get a degree? Have kids? Buy a TV? I'm not saying there's a formula for deciding all these things, but often people make decisions that are downright irrational. Have a look at Kahnemann/Tversky for some scenarios that are completely irrational, but avoidable if you had a good numerical think about them.
Finally, for the young, study math because there's lots of people who don't know any, and will need you. Math related stuff like software engineering, finance, engineering, etc seem like witchcraft to people who don't know any math.
For my situation I would say "a lot more" based on the way I got my ass handed to me in the first year of grad school by the Indian, French and Chinese students.
The american students were at a clear and significant disadvantage here. Learning Galerkin's method for the first time while everyone else was treating it as a "refresher" sucked big time.
Now the irony is that I don't really use this stuff in my job now, but the fact still remains that these non-american students are at an advantage. Like it or not, the schools teaching engineering tend to focus on mathematics as an important subject (rightfully so!), so if your behind you peers....good luck to you! If you start off at a disadvantage in school, that tends to extend to the job market.
I see a strong correlation between aptitude in mathematics and numbers of H1B visas granted in the workplace. Is it the 'cause? Well who know's but i'd be willing to bet...
Yeah, we need to eliminate mathematics from education because the economist's wet dream of Homo economicus is already working too well. What's sad is to see a statistician write this. For shame, for absolute shame. Statistics are quoted in every newspaper and on every TV station every day, mostly to the befuddlement of the general public.
The problem is that we don't want an educated public who regards the following paper as common sense:
Lies, Damned Lies, and Medical Science
Or course what I'm saying is not original to me. Dweebs everywhere are catching on.
Arthur Benjamin's formula for changing math education
Although I would say that the principle of calculus is important. The problem with calculus is that we can't resist testing ugly mechanics. I guess we have our grade three spelling teacher to thank for that. Great literature, but can't spell during a flood of inspiration? Go to the back of the class.
Jane Austen's famous prose may not be hers after all
Regurgitating trig identities as evidence of grasping calculus has an electric chair utility function in the non-engineering population. But seriously, 16% of American GDP spent on health care, largely at the mercy of corporate observational studies, and a statistician is arguing that math education is overrated. Oh, the humanity! How about the general population having the vaguest clue about long tails and concentration of risk?
What Alan Greenspan got wrong is that while heads-up poker is a zero sum game and self interest carries the day, multiparty poker is subject to implicit collusion. You just need one weak player at the table bleeding a big stack for the poker sharks at the table to lick their chops collectively and organize for a division of spoils.
In the world of Goldman Sachs, the chump at the table is the average wage slave trying to save for retirement with no mathematical tools whatsoever. "Listen, here's the thing. If you can't spot the sucker in the first half hour at the table, then you ARE the sucker." So, after one viewing of Fox News, you're expected to know the score. If the general public wasn't trained by public education to play over their heads, the financial elite might be subject to the market discipline of having to play at a table of equals. The horror! The horror!
Williard: They told me that you had gone totally insane, and that your market discipline was unsound.
Goldman: Is my market discipline unsound?
Williard: I don't see any market discipline at all, sir.
Goldman: Who needs discipline when education is bliss?
Williard: These savages have K12?
Photographer: One through nine, no maybes, no supposes, no fractions.
Williard: Are you giving up America for a Playmate of the Month?
Goldman: Playmate of the Year, chief, Playmate of the Year.
Williard: What's in it for the crew?
Goldman: Would you believe 'sloppy seconds'?
Willard: You're the asshole of the world, major!
Playmate of the Year: Who are you?
Cleaned out: I'm next, ma'am.
Playmate: Are you crazy, Goddammit? Don't you think it's a little risky for your 401(k)?
Willard: Charlie Brown didn't get much USO. He was dug in too deep or bleeding too fast. His idea of great retirement was cold grits and a little bush meat. He had only two ways home: death, or bingo, the largest risk his education had trained him to comprehend.
I think we use quite some math every day, while universal lessons like "my system is better than yours and therefore you will use it too, even if I have to beat it into your system"...
Oh wait. That is still general practice all over the world.
Never mind then. Forget about math. History really works!!!
Privacy is terrorism.
Just because people today 'don't use' something in their daily lives, does not mean you can conclude it's not important. As many before have noted here, a solid understanding of algebra and calculus underpins understanding of statistics, finance, physics and on and on. While I agree the way math is taught to the 'general' track of students in school needs to change, it's just ridiculous to relegate the masses to ignorance by reducing math requirements any further than they are.
All those detractors with quite "technical" view even at literary analysis... while, if certain level of drive to uncover non-apparent meanings in our surroundings was a bit more widespread, the world could probably be a bit nicer too.
One that hath name thou can not otter
It's only specialized and irrelevant in the same sense that graphing lines to learn about the cartesian plane is specialized and irrelevant.
Have a nice day!
The importance of math is because you may be in a situation where you will have to figure something out for yourself and by that I don't necessarily mean that you need to build a house in the middle of the wilderness. So the importance of knowing math is...and I can't stress this enough...being able to do it. So in the case of just knowing the 'principles' of calculus nothing could be further from the truth. The importance of Calc is being able to integrate and differentiate and recognize problems where they apply. Seriously just knowing lim h->0 for f(x+h) - f(x)/h isn't going to help you actually perform much calculus. Unless you relish deriving the chain rule from scratch...which is IMHO one of the prime reasons for memorizing things in math - when the derivation is rather difficult. As for saying things like "I don't need X" well that from where I stand is the fault of the educational system insofar as it has taught you that life's problems come in convenient little packages. Difficult functions exist because the world is messy.
One of my relatives went to a technical school and never took any math beyond addition/subtraction multiplication and division and I remember trying to explain algebra to them. In doing so I realized that much of what they did in life with math was rote memorization. From doing their taxes to converting from Fahrenheit to Celsius. They didn't realize that if you know some things about the system you are trying to model you can "create your own formulas". He couldn't recognize a problem as algebraic and didn't have the tools to solve it.
People I've worked with have shown the same issue with probability. The understood that the odds of the lottery were bad and flipping a coin was good but when faced with a moderately complex problem (i.e. like how to replace a usage based model with a fixed rate model in a way that we don't lose money) it was difficult to communicate to them. They didn't recognize to problem as probabilistic and didn't have the tools to solve it.
I've seen people who had some algebra calculate it over and over again to see how it changes over time. They didn't recognize a calculus problem and they didn't have the tools to solve it.
From where I stand not learning to DO math means putting yourself in the position of having to know by rote every math solution which is beyond your ability. Even then, you probably don't know enough to make any changes to that solution...I can't count the number of times I've read product literature where someone has compared some performance metric for a specific item against the average for some grouping of items.
There are dozens of examples of where we need better and more vocational Mathematical skills.
As a sucker for buy-one-get-one-free offers and 3 for 2's I regularly find that my till receipt reveals that I've been incorrectly billed.
When paying in cash, the number of times I start counting my change and get offered more that the staff "accidentally" failed to give me is astounding.
Schools fail to teach the most key mathematical skill that children need when they grow up - how to budget. The debt society that we live in is driven most of all by the inability of so many people to understand the Micawber Principle - "Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery."
Just because Mathematics is a pure subject http://xkcd.com/435/ it doesn't mean that it doesn't underpin almost every other subject in some way.
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?
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.
Is that claim also valid for the jury?
Holy crap, if someone doesn't know what the effect of compound interest is, that's like not understanding that sharp objects can hurt you. Please take my money mr. moneylender.
"Um, they actually teach those things in my country"
I meant putting more hours into those things rather than differentiation.
"Imaginary numbers are not taught under university "
oh they are here.
I'm sure there's cruft in almost any countries math courses.
"But as time progresses, students specialize more and more, so I do not see this as a huge problem. Also, it is quite common that young people do not realize what they really want to do at about their 20th birthday."
The kids who know exactly what they want to do shouldn't suffer for the ones who have an inability to make an decisions.
If you really detest math and have no talent for it you're not going to go into a maths based profession unless you're a reall glutton for punishment.
The problem is that we don't *know* in 7th or 8th grade who is likely to need more math 5 or 6 years down the line. Most kids, if you tell them in 7th grade that they can stop taking math, they're going to. Then they hit junior or senior year of high school, realize they want to be an engineer, and they have none of the needed mathematical background. Basically we teach 4-5 years of advanced math to every student in the country, so that the 10-15% if them who will actually need it, have it. It's wasteful as Hell, but I can't think of a better way to do it without forcing life altering career choices on 13-14 year olds.
Maybe if you're not interested in math as a 13 or 14 year old, you shouldn't go on to be an engineer, or a scientist, or whatever. I don't say that to be a troll, what if it's true though? Maybe the population as a whole would have a considerably higher job satisfaction rate if they listened a little more carefully to their interests at that age. Maybe that guy who is drudging through his life as an electrical engineer was really "supposed" to be a graphic designer for a high tech consumer product manufacturer. He knew he was into high tech gadgets, and he had all that math, so he got pushed into being an EE, but he really was more into designing how people used them then in designing how they functioned. Just a thought.
Cardinal Richleau famously decreed "Control the langauge, control the people" and was the basis for his establishing L'Acadamie Francais which to this day enforces what can and cannot be used as a word in the French langauge. I believe there is still a legal ban on the word "Le Weekend".
Arch-Romantic and symboliste genius Arthur Rimbaud, inspiration for the film series Rambo, saw this sameinsight from the other perspective: change your language, change your life. This insight led him to abandon his incredible literary achievements at 17 to go off an lead a life of adventure, travel, gun running and decadence.
If it language doesn't change perception, why is so much effort put into double speak? The verbal Frankensteins created by today's spin doctors would make Orwell blush or more likely vomit. And it's done at such a granular level it goes unnoticed. I remember reading an interesting thesis that the word 'like' was injected into the hippie subculture to weaken their mindset on the simple premise you may recall from poetry class that a simile is much weaker than a metaphor. Whether it was intentionally planted or evolved organically, it was like totally bogus in helping the like counterculture gain any like credibility.
Both words and numbers can hide meaning. Nothing zen to it other than the basic premise of maya or all things are an illusion. But even the Buddhists find enlightenment in contemplating words. Basho's frog comes to mind.
The enlightened however are able to see there is truth in everything, even lies. Particularly lies. Something the counterculture of the 60's / 70's could perhaps grasp but not express. Much of this was due to a lack of mathematical understanding and poor verbal skills that left them inarticulate and ineffective.
Vietnam was a military failure much in part as it was based on faulty maths much based on Game Theory and the Prisoner's Dilemma and other works of paranoid schizophrenic John Nash. While Nash's works hold critical insight, those who attempted to apply them had little grasp on what those insights were. Where Nash realised insight in numbers, the pentagon just saw them as something to punch into adding machines. It wasn't necessarily garbage in garbage out, but just the wholesale download of data into the garbage disposal for shredding with the results interpreted by certifed tea leaf readers.
Body counts and other meaningless quota systems gamed the system against victory because the theory failed to recognise that humans are not calculators. Sure some weird freaks are, and until recently the word calculator referred not to machines but to someone good at calculating numbers. Overall, most humans are bad with numbers but good at lazy (different than the greedy that was used to incorrectly apply game theory) and being able to build odd logic systems when forced to meet meaningless imaginary goals such as quotas. Numbers are easy to fudge, and if you don't fudge them you can always get bonus points in the body counts by killing anyone and labelling them as enemy afterwards. The mathematical results did little to realise the martial goals originally set out upon.
One thing I have found strange in all the recent talk in the US regarding healthcare is that it seems much of the mess we're in was a result of these same bad maths strategy of Vietnam were later applied to the US Healthcare system when Robert Macnamera played his same numbers game as consultant for the US and later at the invitation of Margaret Thatcher in the 80's to apply his 'wizardry' to the UK system. Both applications were utter failures worse than Vietnam. But like there were no hippies, like complaining. Instead, they turned to alternative medicine which is based on even less reliable principles.
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.
That's not funny, that's a perspective that has value, even if it may not be the whole story. Bad teaching.
Yes, my big problem with how history is taught where I live is that all the focus is on "how other countries have screwed over ours in the past" and glosses over "how my country has screwed over other countries".
self described "Patriots" should never be allowed to choose a history curriculum.
they view their own country through rose tinted glasses.
Are there many schools that even require calculus for all students? Having taught at both a large state university and a small liberal arts college (that's my sample, so it's limited), neither required students take any math if they didn't want to and didn't need to in order to take their other requirements. In both cases, math classes did satisfy general education distribution requirements, but there are options to avoid the math department if one desires. And it's certainly true neither school required calculus for everyone.
1) move the decimal over one space to the left
2) multiply the first digit by 2
3) a)was the service bad? pick the result of 1)
b)was the service good? pick the result of 2)
c)was the service really good? stop being fucking lazy and multiply the whole damned thing by 2 and round up
Personally my step 2) is "divide the original by 5" but I'm weird
Let the kids who have no talent for math and no inclination towards math based professions drop it once they have the basics.
The problem with that is you end up magnifying the intellectual disparity between the educated and the uneducated, which is never good. We should be pushing to bring everyone up, not pulling back to give everyone the bare minimum.
Of course, that's sort of the "Star Trek" future where no one is a janitor.
When you're afraid to download music illegally in your own home, then the terrorists have won!
Because when your software says that it requires 1000 gallons of fuel, you still need to know if it means 1000 litres.
Because if your software costs £1600 per seat, you still need to know what that means for your department's budget.
Because you need to know that increasing each dimension by 6% might increase the mass by much more than that and that it won't scale linearly if your dimensions differ.
If you think you don't use maths, you probably do. If you think you use a little, you probably use a lot. If you know you use an awful lot, you're probably not far wrong. Maths is *NOT* arithmetic. It's units, dimensions, scales, percentages, and billions of other things.
I don't *WANT* an engineer who doesn't know that the ideal place to put up a cell tower is probably not equi-distance from all the others. I don't want an engineer who can't spot when the software mistakes inches and centimetres (NASA spacecraft have been TAKEN DOWN by such errors because "the computer must know what I mean"). I don't want an engineer who is reliant on tools that they don't understand and, thus, don't know when they are faulty. I *really* don't want an engineer who doesn't have a basic understanding of mathematics designing anything that moves, rotates, exerts pressure, stress or anything else. Yes, a computer can do an awful lot of the work for you but it's like spellcheckers - now we have spellcheckers we can just throw all that literacy stuff out of the window, yes?! NO! Computers are labour-saving machines, not intelligent. They will blindly follow stupid orders even if you don't know they are stupid yourself. And mathematics and programming don't have as much in common as you think - having a knowledge of one is helpful in the other but expert mathematicians are usually terrible programmers and vice versa.
If you rely on software to do your job, that means we can effectively obsolete your entire industry by just automating the part you do, right? If that sounds stupid, that's what it sounds like when you say you don't need to know maths.
Yeah. Everyone knows that the Globe was standing room only.
"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.
I'm not sure Prof. Ramanathan's essay is coherent. I'm extremely wary of a thesis posed as a question: "How much math do you really need in everyday life?" Also, there's a shit-ton of elderly, loopy/cranky professor emeritus (retired) types out there writing on how their whole discipline has totally lost its way from the old days.
So, I can't tell exactly what his recommendation is. Is it to cut off math education after a certain point? Would he make algebra non-required in the high school educational system? Or is it to just give up on perceived attempts to make people "love" math with contrived examples? The "question posed as thesis" leaves these issues all tangled up. Apparently, a coherent argument wasn't necessary for the Washington Post to get some publicity for a retired crank whacking his own discipline.
We know where leadership by an anti-intellectual "strongman" who scapegoats minorities and likes boisterous rallies goes
math has little relevance to everybody's daily life.
I disagree. I think part of the problem is math is taught in such an abstract manner. Aside from a few story problems there is little effort to apply math to the real world in the classroom.
Why aren't vectors taught when you learn triangles? Why are Calculus I and Physics I separate classes?
I think story problems should be the base for teaching mathematics. At what age can a kid understand scales and balance compared to the '=' sign?
Many people don't use math to determine whether buying more is cheaper, they just assume. This doesn't mean math is unnecessary. It just means that it's not applied.
Thank you! I wish I had some mod points for you...
This guy is argueing that math, that he understands, isn't all that needed... this argument has been done before. Someone with a chauffeur driven car cannot judge the need for public transport, so that is why ministers with chauffeur driven cars are in charge of it. People with high income and private healthcare cannot judge the need for free healthcare, so that is who we put in charge. The rich cannot represent the views of the poor, that is why every media star earns more then a million.
You CANNOT say that math doesn't matter all that much if you got a perfect grasp for it. Because you cannot imagine what it is like NOT to have a grasp of it. I was in England once when they still had the old currency system. There I was, reasonably intelligent kid and I had to hold up my hand with the change to have the shop keeper pick out the right coins because I didn't know the math. Suddenly I was an idiot. Well more then usual. If you do not grasp math, then you are helpless against the countless ads that try to sell you stuff cheaply when in fact they are more expensive. How can you deal with supermarkets that don't list the unit price if you can't do the math and see if 1 kilo at 2.50 is better then half a kilo at 1.15 (yes, BBC watchdog showed that british supermarkets do pull this one).
And gosh, the rich who tend to get better education don't have to worry about pennies in the supermarket, but the poor with bad education do... see the problem?
The less likely you are to be good at math, the more likely you are to need it. This isn't about people being able to calculate the height of a tree, it is about understanding numbers, about understanding MONEY.
Basically, this prof is saying that in this day and age, a solid understanding about money isn't important... gosh, wonder what his angle is. Daddy owns a supermarket? Teaparty supporter?
MMO Quests are like orgasms:
You may solo them, I prefer them in a group.
"Let's be honest. Strictly speaking most people do not need ANY of what they learn in school except reading and writing and basic algebra."
Not true. Other subjects are taught so that students can be good citizens. I know this concept is rather outdated but it is extremely important. Democracy does not work if people are not well educated.
In any case, basic math is far more important than algebra.
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.
That sounds fine at a high level, but in practice you're going to be teaching lots of detail to people who will struggle with it and never use it again. In the meantime, there are basic and critical skills that people don't graduate with.
I never, not once, used the formula to factor a quadratic formula outside of school. I learned so much geometry in high school that I never touched again outside of school. It goes on and on. It got worse in college. It's just a huge waste of time to be teaching these topics in depth, unless there's a demonstrated need.
"It even harms the kids who are good at math and want to do it because the teacher has to slow down for the kids who have no talent for math, aren't going to go into a math related profession and shouldn't be forced to learn about the square roots of negative numbers or quadratic equations."
Returning for this sentence for a moment: my experience is that the best teachers were those who were actually able to close the gap between the students with different abilities.
no. just no.
Writing SA's on how a drum represents Emily Dickinsons conflict with society is 100% useless.
Completely and utterly usless.
No redeeming qualities whatsoever.
It didn't help me understand anything later life in any way shape or form.
It didn't help me understand any news items I read today.
There was no hidden understanding conveyed.
it was useless in every way.
on the other hand reading simple lists of common logical fallacies(which was not part of any english class I ever took ) did help me to understand and judge news items I read today.
There are a few very good reasons to be worried about mathematics.
The first is that a lot of kids are growing up and getting out of school without the basic abilities to balance a check book. This is something I'm able to teach a child with Down Syndrome. Why is this important? We operate in a capitalist society. Statistical mathematics can give someone an edge. If the population as a whole can't even get percentages and averages down, don't you think people who are able to grasp these concepts can take advantage of the fact?
Second, once you get into Algebra and Geometry, you are dealing with spatial relationships, how you can use math to relate to the world. You are working the basic calculating ability of the mind, allowing it to expand in its abilities. A chess player is great with a level playing field. Try to get the same to deal with modern littoral warfare, or anything since WWII, and he will need a grasp on spatial relationships.
Finally, you are exercising the MIND. It has been proven that people working games that deal with mathematics keep active areas that are linked to Alzheimer's and Parkinson's. If you don't use the various synapses, they have been proven to atrophy over time. This can create obstructions and slowing of basic thinking, not just higher thought. Remember, once you stop progressing, however slowly, you are on the road to death.
Vote Palin in the primaries 2012. Then the GOP will have no chance!
Brilliant. Party loyalist over the good of the country.
See my journal for slashdot ID's by year. Mine created in 2005. http://slashdot.org/journal/289875/slashdot-ids-by-year
"Democracy does not work if people are not well educated."
Exactly. Also, the best way to learn is not necessarily to learn always the things most relevant to your current work. There is a reason why most of us like games, puzzles, riddles, even though they are not directly applicable to the real world.
Doing pushups is physical exercise.
Doing math is mental exercise; it teaches problem solving.
Wish I had mod points at the moment. Great example.
Enrico Fermi was famous for doing calculations on the back of an envelope to get a feel for the scale of things. If more people did this we would get more reasoning about the relative significance of issues.
Thanks for your post.
What math you can use in life depends on what you know more than on your job. Sure, there are common calculations/algorithms that require trig or calculus, but you can usually palm them off on someone that knows how. My son called me up once for an arithmetic answer his calculator couldn't handle. But he needed it to complete a train of thought on a politics question. He could set up the problem but couldn't solve it, an interesting cusp where he knew just enough for the situation.
I had studied differential equations, but had never encountered differential forms until later in life. It really opened a new way of seeing a lot of the world, since it allowed me to visualize approximate solutions to so much of what happens around me. (Most of the world from economics to weather is in dynamic equilibrium, that takes difEq to understand)
In college I took "music appreciation" and learned stuff about music I was far from being able to perform. I wonder if a course like that could be developed that taught differential forms without teaching the skills for general integration, the mean value theorem without the proof or much probability calculation, etc. so kids could understand why some conclusions have much more solid support than others that dissolve into speculation on further study.
My friend's girlfriend thinks we should just print a bunch of money and not tell anybody about it to get rid of our National Debt. I tried explaining how that causes inflation, and why inflation is bad, a dozen different ways, but she still doesn't get it, and still thinks that's the answer to the problem.
Frustrating is not a strong enough word for it.
Security is mostly a superstition... Avoiding danger is no safer in the long run than outright exposure. - Helen Keller
The issue here is that there are a lot of different branches of mathematics, and only one of them is being taught in schools.
Algebra: The concepts behind basic algebra ("Algebra I") are essential for anyone doing any sort of mathematics, so you can't really get rid of this. From what I remember of my Algebra II and Trigonometry classes, nothing there is a prerequisite for any other branches except calculus. It is essential for someone going to college for a scientific degree to know trigonometry, though. It is probably unnecessary to teach everyone trigonometry or "advanced" algebra*.
Geometry: Used as a didactic tool to teach logic, reasoning and proof. "Math without numbers" might attract people who would not otherwise enjoy mathematics. Teaching proof to high school students sounds great conceptually, but from what I have heard attempts are made near-constantly in this direction by math education theoreticians and never catch on. Note that while geometry actually does do the "develop students' logic and reasoning" which everyone says math is good for, algebra generally is not taught this way: rather, it is presented as a series of magical formulas. Certainly there is nothing even close to a "proof-based math course" in high school except geometry.
Calculus: Essential for anyone going into science, unimportant for everyone else. The algebra -> calculus line is the one primarily taught in schools, which is very convenient for future scientists and engineers and annoying for everyone else.
Statistics and probability: A basic understanding of statistics is essential for understanding current events, politics and the news, since statistics are everywhere and one must learn to judge whether they mislead.
Discrete mathematics: Way cooler than calculus, but probably not suitable for high schoolers, as it is not very relevant to people outside mathematics.
"Life economics": I'm not too knowledgeable about this, but from what I have heard, a lot of schools have a "life skills" course. This probably includes basic knowledge about compound interest, buying versus renting, and other economic skills which ultimately stem from mathematics.
Given this overview, I personally came to the conclusion that the best way to teach high schoolers math would be to require a basic algebra course, a geometry course (maybe), and a "useful math" course, which would include basic statistics, basic probability, compound interest, investing, and other ways students will probably actually use math even if they don't go on to become scientists or engineers.
Of course, this does nothing to fix the related problem that many students do not find more theoretical math interesting, limiting the number of people who go into math and science. But as long as most of the math teachers out there don't even like math, we'll just have to live with students not liking it either.
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
"because of other people too stupid"
Not necessarily stupid, but they are likely uninterested victims of the mandatory advanced math classes.
Filthy, filthy copyrapists!
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.
I was thinking much the same thing. Other than to inculcate reading skills and the very narrow case of teaching how to write persuasively, I'm not sure there's any reason to teach literature in school. It's a form of entertainment involving few transferable skills. There are much stronger arguments for teaching music, though even then not as a core subject.
Mind you, I love literature: I have over 2000 books in my house and a degree in English literature. I've also spent the last twenty years working as a software engineer, and I've never had occasion to resort to my knowledge of literature for any practical purpose. Someone will inevitably object that literature teaches us about human nature, but that is quite frankly bullshit. Psychology and sociology teach us about human nature; literature just teaches us about writers' ideas of human nature. Literature as a compulsory subject is an archaic hangover from the time when only the aristocracy had access to education, and its function was to prepare students for aristocratic social norms.
I don't have any problem with curtailing math instruction with the proviso that it should be offered for those who are interested, and preferably taught by a better grade of teacher than the current lot. If I'd had even one math teacher in high school who knew what the applications of the subject were, I'd have been much more interested. As it was, I had to wait until college to discover the applications, and even that was entirely self-guided.
What I would like to replace compulsory higher math with is formal logic and, as several other posters have suggested, basic statistics. Everyone can get a lot of mileage out of logic and statistics no matter what they end up doing as adults: even fast-food employees get to vote. If they never discover the brilliance of F. Scott Fitzgerald, that's their loss, but the world will go on.
Proud member of the Weirdo-American community.
Knowing the ins and outs of your profession quantitatively is the difference between dying in middle management and retiring in corporate because, if you are only capable of understanding the basic day to day numbers of your operation, you are not going to be much use in long term strategic thinking.
We promoted a middle management guy at work last year who was promptly demoted when he asked more questions about the graphs at presentations than a freshman.
An Education is the Font of All Liberty
Work on software for maps (eg. roading in my case) and you need a lot of trig. In fact, I once had to calculate the direction of a perpendicular to a roadway so I whipped out my vector cross-product in 3D and reduced to 2D. The result was simple. Thing is, if I didn't know about it I simply couldn't use it (I wouldn't even know where to search for the solution since I couldn't ask the right questions).
In my spare time I do mods for games - mostly flight sims. Trig is essential all over the place. eg. calculate the indicated radar altimeter reading for an aircraft banked at 60 degrees. Its a basic trig problem. Or, calculate the slant range between your aircraft an your target, is this withing the Maverick seeker head limit? Does the line-of-sight between yourself and your wingman pass through a mountain and block radio comms? All require math.
We should be pushing to bring everyone up, not pulling back to give everyone the bare minimum.
I don't think that's what OP wrote or meant.
Everyone, even those who "can't do math", in a modern society needs to *understand* percentages, orders of magnitude, estimation and basic statistics.
While I never use calculus at work, and obviously never at home, I frequently use the 4 items mentions above at work and I *constantly* use it while watching basketball and American Football.
It's also vital when thinking about how to reduce government budget deficits: eliminating the Corporation for Public Broadcasting's US$422M sounds great, but it's only 1.2% of 1% of the budget.
"I don't know, therefore Aliens" Wafflebox1
You mean making stuff up that the author didn't even do on purpose.
I guess it's as much a sham as psychology.
Yes. The Bible has already made it clear that the value of pi is 3.0. There is certainly no need for mathematicians to try to confuse people.
So the kids who could be tearing far ahead have to loiter around waiting for the slow kids to catch up?
The *nicest* teachers were those who were actually able to close the gap between the students with different abilities.
Not the best teachers.
they're the ones who make the parents of the slow kids feel good because their little johnny isn't struggling.
meanwhile the kids who already understand it are getting more and more and more bored wasting time they could be spending learning waiting for their slower classmates.
A good trainer isn't one who has everyone running at the same miserably slow speed at the end of the year.
Abandoning the slowest entirely is bad but dragging back the most able is vastly worse.
that's what really awful teachers do.
I didn't go very high in math in my early school years; later in life I regret it... as it's been a lot more work catching up!
Math is much more than essential, it's vital. It also needs to be taught in different ways so that it appeals to kids of different backgrounds.
My teachers in school were dreadfully boring; I spent more time drawing cartoons of them than listening. But had they used a different approach, if they went into art and programming and .. maybe things would have been different.
Math is everywhere, whether we like it or not. I admit, now a days I even see math as "beautiful" from a certain perspective. The great masters of art knew this.
Just my 2 cents.
There's that guy sure. But the opposite side of the coin is me. If you'd made me choose at that age, I'd never have kept going in math. I *failed* Algebra I in eighth grade. It just wouldn't click. I tried, really hard in fact, but I couldn't understand the concepts. Then I took it again and it did click, and everything after it clicked too. I have no trouble with abstract mathematical concepts and got through a couple years of calculus just fine.
What happened? Well, one answer is biology. Supposedly people's capability for higher cognition jumps in the early teenage years. Happens to different people at different times. Apparently it happened to me a bit later than my course load dictated it should have.
There's a *lot* of biology going on in a young teenager. Capabilities are changing, growing, even making first appearances in early to mid adolescence. Beyond that, kids that age almost universally have a confidence problem, and tend to this that anything they aren't *awesome* at, they're *bad* at. All in all, it's a pretty terrible time for people to making decisions like the ones we're talking about.
I don't need a million points of light, just two points of multi-mode fiber and a 10 Gig-E router.
See A Mathematician's Lament, by Paul Lockhart. At least follow that link, even if you ignore the rest of what I write.
I was taking community college courses until recently. Initially, my plan was to take the prerequisites for a computer science degree, then transfer. I found the computer related courses interesting and generally well within my abilities; in particular, I found programming courses very easy, even the ones in which I was sitting next to professional software developers who were brushing up their skills. The courses on mathematics were quite another story. In my first semester as a (returning) full time student, I found I spent over 90% of my study time on Calculus I.
What really struck me as puzzling was that on the one hand, I could not keep up with the complex transformations on the chalkboard and the homework assignments that the other students could. On the other hand, outside of that classroom, I found that the same students showed no particular intellectual strengths beyond mine; those that were in the same programming classes that I was in weren't as good as I was at programming, or even at understanding the mathematical applications of programming. The students showed no curiosity about nor enthusiasm for mathematics; for that matter, neither did the instructors. Yet I was curious and enthusiastic about mathematics. I actually have read books on algebra for pleasure.
Years ago, when I was in college for the first time, I was an English major; for years afterwards, I was astonished when I would meet former classmates who couldn't remember any of the literature we'd studied together. Now, I find that when I talk to engineers and developers, I'm astonished that many of them remember little mathematics beyond basic algebra.
I understand Lockhart's point to be that the model for teaching mathematics is at odds with the nature of mathematics; that we waste years of students' time teaching them gibberish, which they will not remember or use, while discouraging those that would actually love mathematics from actually encountering the subject. The way mathematics is taught now is something like the way Latin used to be taught: its necessity is exaggerated, those elements that are necessary are passed over quickly, and both its real utility and its intellectual appeal is buried under tons of meaningless busywork.
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...
Since most countries these days are experiencing negative population growth, a statement like yours shows that a good understanding of math is pointless for people that are not properly trained to feed proper inputs into the equations.
Far better that we expend energy directing students to properly apply critical thinking and understand how to research facts.
"There is more worth loving than we have strength to love." - Brian Jay Stanley
Expect to see more and more articles like this as republicans get on with gutting the educational system in America., which they see as why we have so many leftists and socialists. Why do Americans need any education at all, the Chinese and foreigners are going to be the only ones with jobs anyway? Lets get rid of the department of education, all public higher education, all expenditures for libraries, all scholarships. We can't afford these things any more anyway. Let other countries that have favorable balance of payments provide the world with education. You just don't need an education to vote the straight republican ticket or to watch Glen Beck. You just need to know your place.
Civilization? We don't need no stinking civilization.
Wait... what relevance does literature have to everyday life? What good is it, aside from making and catching references that other people who have read the same literature understand (Math works as well for this, as XKCD has shown ad nauseum). History? I'll grant you it's important, but not in the "everyday life" sense. There are plenty of people doing just fine today who don't know what the Soviet Union was, never mind such "ancient history" as WWI. Politics? Great for water-cooler arguments, not so useful for much else. Music? Mere entertainment, and certainly nothing in a music class is at all relevant to most people's every day life.
So what do they teach you in school which is useful in everyday life?
1) Reading. If you're totally illiterate, you're at a serious disadvantage.
2) Math. Not the sort he's talking about, but basic arithmetic. If you don't know enough math to make change, you've got problems.
3) Geography. Not world geography, just the basic stuff like how to read a map.
4) Whatever's needed for your particular vocation.
As for his complaint about contrived examples in calculus texts... so what? If students learn better if they think of a nap of a cone as a martini glass, that's good (if they don't, it's just silly). Pretty much any example you put in a math book is going to be contrived, because real problems tend to be too complex to illustrate the particular technique being highlighted. Physics textbooks have been doing this forever, with frictionless pulleys, weightless ropes, spherical cows, etc, and nobody seems to be upset about that.
For me, as a math whiz, i just did it, straight through to trig and prob/stat in high school, 800 math sat. i stopped in the middle of calculus in college, when my interests focused more on the humanities and psychology. i am biased towards math as a diversion and a way of modeling the world. But i am in a minority. my father was a frickin rocket scientist. I really didnt know i would not become a scientist, so learning it was fine, good discipline and all, but now almost none of my math past decimals, fractions, simple algebra and word problems is utterly useless to me. I suspect that our educational system is designed to ferret out the asperger leaning math savants, to get them into industry and the military (nuclear weapons design for one). For most of us, i believe, the educational system is a total failure. you either get into a phd track and pray you can maintain your focus, or you just live with stupid debts and wonder why you did what you did. we need practical math education, as part of a real world based learning system, where problems from our lives are solved with educational tools. math: taxes, understanding economics, understanding science reporting, understanding polls, making budgets for a family or small business. a multi tiered educational track, with each track leading to good jobs. my high school was later nearly decertified due to having a twin track system where the less gifted (read:black) were put into a failure oriented track. seriously, and this was Berkeley High in the 80's. Oh, and we need free college education or its equivalent. And none of this will happen. there is no hope to reform or reinvent our educational system. most of us are now low grade morons, having grown up with the equivalent of alcohol in our blood surrogate. (and if you dont get the reference, its only proof i am right). dumb, dumber, dumbest. go to a thrift store, note some of the serious topics that Mass Market books covered in the 50's, 60' and 70's. now its all vampire romance novels. Im not even sure i trust anyone to build anything anymore, like the new Bay Bridge. oh, and you kids get off my lawn.
You hear about the person who didn't rely on anecdotal evidence to support his belief system?
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.
But how does the antiproton feel about the collision?
You are not a brain: http://books.google.com/books?id=2oV61CeDx-YC
Nonsense, it's not a ploy. The fact is that education policymakers everywhere are questioning whether the curricula being taught to today's students has enough relevance to the job skills that the market is looking for.
As we all know, there is no shortage of grads suffering from crushing debt while facing difficulties getting hired.
As such, it's imperative for educators to be asking hard questions that are relevant to economic realities.
Yea, we really don't need a lot of this stuff. Really the thing we should be concentrating of in schools is Public Speaking, Dancinging, and Athletics. These are the things that will help your average student get with a lot of girls and have lots of offspring. Everything else is just a bunch of fancy pants thinking forced upon us by the teachers unions.
In the meantime, there are basic and critical skills that people don't graduate with.
I call it preparing people to go to college who will never go. You shouldn't be trying to teach calculus to somebody who's 80% likely to drop out of high school, much less attend college.
My basic list:
Addition, Subtraction, multiplication, and division. Counting(as in change), and some geometry(figure out how many square feet of wall you have so you can buy the correct amount of paint). How to keep track of a checkbook/budget. Familiarity with 'cost of capital' so they at least understand the different costs of lower payments now vs fewer payments.
Use the time saved to make sure they know how to do things like cook, clean, take care of basic maintenance, understand why messing with electricity can be bad, etc... Preferably get them started with a trade.
If they're shaping up to be good at math, have the drive to attend college, THEN worry about teaching them the advanced stuff. Germany has/had a three tier system, why shouldn't we?
I don't read AC A human right
I would think the promulgation of competence for abstract thinking, which is inherant in mathematical thinking, is neccessary for the furtherance of a modern postindustrial society.
It is clear to me however that this tendency has been vastly overdone. Everyone should be exposed to it however, so those with a facile ability can be winnowed out and cultivated.
This should be done early on, those not winnowed out for further development should be inculcated with earthy wisdoms.
And YOU the MOD'ster, rtfp before you score me a measly 1, AGAIN damit.....
I see the big problem with math education is how it is taught. To be honest, there is no reason whatsoever we can't have taught kids basic differential equations by the time they hit 8th grade. The problem is we force students to memorize a bunch of obscure math that although we will use later in specialties, is totally pointless, out of context, and relatively useless at that point. And it is by rote and not by concept. In case you haven't noticed, memorizing vast amounts of crap is hard, but learning lots of new concepts is easy. If math was taught in order, in a contextually relevant way, first conceptual and then practical, there is no reason at all that we couldn't have 8th graders beating out the average college graduate. It doesn't have to be expensive, it doesn't have to be so terrible, it is just that it is done in such a terrible manner that it appears wasteful as it is currently done.
Plus, to be honest, a knowledge of extremely advanced math could come in handy to virtually everyone. I get really tired of watching our system be a kind of stagnation in most fields. If everyone had an advanced education out of high school, everyone would be able to advance their field. Plumbers, welders, residential contractors, auto repairmen, any profession at all could be improved by a knowledgeable worker in that field, even if just new and interesting ways to fix things. We could easily be living in a world where everyone advances society, not just about 10% of us.
Where is the mod rating for "scary"? Also,
Republicans will work to send most jobs overseas anyway.
Too many mathematicians sitting idle on the street corner could simply lead to trouble or worse, a lot of theorems and proofs. Everyone knows republicans have no use for either theorems or proofs, especially since you can now hire an Indian mathematician to produce them at less than half the cost.
What business should have to pay a mathematician when they could get a tax break instead?
At the age of ~13 the school I went to (in the UK, under a Grammar school system) decided that 2/3 of the pupils didn't need any maths education beyond basic arithmetic so I and many others left school with a certificate in arithmetic that even the local college didn't recognise. I then had to go to college and night school (over 3 years) to get the equivalent qualifications and knowledge that I would have had if I'd been lucky enough to be in the other 1/3 of the students in my school. After 3 more years at night school I was able to go to university where I got a degree in Mathematics. All this despite the fact that teachers and schools had decided that I had no need for any maths education. I've learned never to trust an education system that decides what skills a child needs at an early age. Schools should give student an education that broadens their choices, not deny those choice in the belief that they know what a child will need to know in the future.
I can't believe how many posters missed your point. "Ha, you moron, exponential growth can't continue forever!" Yeah, that's exactly the point. Re-read the comment.
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?
I guess when you were learning electrical engineering, composition, and literary analysis you didn't have time to learn how to not make childish insults.
I'd agree with you on composition skills, although parent poster said nothing about composition.
But literary analysis is a completely different field from technical reading. Literary analysis has to do with analyzing literature for things like themes, motives, symbols, etc. You probably learned this in high school, like most people. Reading a technical paper is about understanding new theories, models, or ideas and finding out what results some people have achieved in a field. There may be search for hidden meanings like the drawbacks of an approach that the paper's authors don't come out and say, but I think you learn to spot this through experience in academia and your field, and not from having studied literature.
I think this is a question of definitions. I consider having a basic knowledge of various schools of logic and mathematics such as you list to be the bare minimum, and much less than we should be teaching. We should be pushing for everyone to learn differential equations by the time they finish high school. The problem is that people are afraid of math, not that they really can't do it. Less math won't fix that.
When you're afraid to download music illegally in your own home, then the terrorists have won!
I sense this 'professor' may not be a good teacher if he can't show the practicality of the material he's teaching to his students Although perhaps he needs to clarify what does superficially appear to be him condoning a 'dumbing-down' of education which is meant to be to teach people to think for them selves logically rather than fill people with a bunch of facts and formulas that, I agree, may not be used by most. Though in an educational environment, they are absolutely relevant.
The fallacy you make is that "closing the gap" means "slowing down".
I guess it's just a matter of priorities. So a few people get the benefit of starting math at an early age despite thinking it's not what they'll want when they're older, how many more people will need to suffer through it needlessly? What's a worthwhile ratio? One to four? One to eight? One to one thousand? Hopefully someday there will be a better way that allows everyone to come out ahead...
Any day now, you will be replaced by a more capable electronic calculator. Since you don't have the necessary understanding, you won't be needed at the cutting edge of science and technology. The money society spends on you can be put to much better use, say a tax cut for the wealthy who will generate jobs and advanced technology in foreign countries and big profits can be had.
great to know the managers left are either knowledgeable or are quiet fools.
"Even a stubborn fool is thought to be wise if he keeps silent. He is considered intelligent if he keeps his lips sealed."
"He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever"
great choices there.
>>We spend a large amount of time and money teaching people a lot of crap that most of them will never use.
This is a horrible way of thinking about it. A friend of my father's is a EE Professor at USC, who has studied all sorts of high level mathematics. He freely admits he's probably never going to use 90% of them, but what's important in life is improving your toolbox so that you can solve the broadest range of problems possible. This doesn't just mean math, either - he passed the bar not too long ago because he found that not having a background in law had screwed him over pretty badly. So he worked to improve himself.
The key point here is that as a high school student, you're not going to know where you're going to end up, or what opportunities will be opened/missed by having/not-having certain skills. Our school system should try to fill out that toolbox with the most commonly used tools... and in that respect, I do think that we're focusing on the wrong kinds of math. Algebra is certainly a useful skill to have (not only as a foundation for all advanced math, but even in real life), but trig, geometry and calculus... maybe not as much as probability and statistics.
Other critically important things in real life that we don't teach in schools:
Economics (especially managing personal finance and business management skills)
Public speaking (or even just learning to speak in front of small audiences)
Leadership / Management Skills (or interpersonal Skills in general)
I think history is also critically important, since understanding your place in the world and how you got there renders you immune to a lot of the manipulation that politicians put on an ignorant populace, and you don't look like a moron at a company picnic when your boss asks for your insight on possibly expanding into communist China.
And a much more insightful point than he probably realised when he made it. Shakespeare would never have seen himself as any kind of literary figurehead - he was a working playwright, in a competitive environment with an audience that didn't treat the theatre as somewhere to sit quietly with your date while you pretended you understood. Elizabethan audiences demanded blood, guts, and emotion from their theatre-going, and Shakespeare gave them it in spades.
[FUCK BETA]
Which is insanely arrogant.
You speak as if you think the only knowledge worth having is your own.
Someone who doesn't waste their time learning math they don't want or need can spend the same time learning any number of other things.
You don't just send the kids home early, you spend that time teaching them something else.
How to write a good book, how to build a bookshelf, history, geography, design.
there is more in life than math.
I love math but I can recognize that.
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.
That's not true. Historians have to back up their claims with primary sources.
May the Maths Be with you!
As a programmer, I find I use nothing more advanced than simple addition, subtraction, etc five nines of the time.
Logic yes. Advanced maths? Nope.
Sig Battery depleted. Reverting to safe mode.
Right, so in your world the kids who are struggling the most and having the most problems are the ones most capable of learning fast?
if the slowest are to end up at an equal level then you either have to slow/stop the fastest or make the slowest far faster than the ones who are furthest ahead.
play with words however you like but you're either hobbling the best and brightest or making the least capable go faster than the most (while not applying the same methods to teaching the brightest to allow them to learn faster too).
Either way doing so would mean being an awful teacher.
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
Most of the things you learn in school and college are mostly useless. Except reading, writing and a bit or arithmetic, nothing is really too useful for the majority of people. Most of the things you need for most of the jobs out there you have to learn at the job, anyway. Most of the concepts we'll meet in daily life are never even touched in school. You don't learn about insurance, or what's a bill, or a receipt, or a mortgage, or car mechanics or home repairs. But we learn about biology (why? what has biology to be so widely taught? agreed we are living things, but still), lots of history (interesting, sure, but useful? only if you are Indiana Jones, I suppose), physics (you'll learn all you need about gravitation by age five, anyway), literature (that's more useful than math?).
The syllabuses we trod in our life seem at best random and at worst residual accumulation of pet topics from a long genealogy of teachers. Most of it comes from forgotten times, where you could really grasp ALL the human knowledge of the time, so no selection was needed. Since that's no longer the case, some selection is overdue, for math and for all the rest of topics. But it seems like once installed in the syllabus, there is no way of getting something thrown out. And it should be a continuous work in progress, year in and year out, selecting what must come in and what must go out.
The best that can be said of today's education is not about what we learn, because we forget that soon, but how that learning teaches us to better ways of thinking. In this regard, Mathematics should be considered fundamental. Perhaps an instinctive suspicion of that is what keeps Math in our schools, who knows?
Rome taught me patience and assiduous application to detail. Virtues which temper the boldness of great, general views.
When I was in Grade 7 or 8, we studied compound interest in math class (in Southern Ontario). My math classes didn't go out of their way to avoid relevance to the real world. Maybe that's why Canadians tend to score so much higher on math than Americans?
Most folks here seem to be saying that math is important to learn due to it's importance to other subjects; i.e. mathematical subjects like probability, logic, economics, or even non-mathematical subjects like English or law. It's been said here that if we learned the correct maths, we'd understand these higher subjects earlier and be harder for politicos to dupe.
It would seem to me that ditching some of the higher math in favor of integrating probability into math studies, logic into science studies and deeper economics studies during high school years would be quite a bit more valuable than ever learning geometry, trig, or calculus. At the very least, if math is so important to other subjects, why is there no grade school education focused on how these subjects tie into each other? Do we need to call in James Burke to develop a course for students to understand the practical applications beyond calculating your tips? Does anyone remember the single semester spent on economics in high school? I sure don't. And the reason is because our education is a joke.
For example, the math system used during my high school years was the UC Davis system. There were a ton of problems with it, but the biggest was a lack of examples from which to study with. On the surface this was bad enough, but the Davis system expected students to use applied learning to figure out more complicated problems in each chapter. With zero lessons on applied learning. Nor any labeling for which questions were more complex and required students to jump ahead and just figure it out. Oh yeah, and there were no answers included as the entire system was photocopied and students were expected to keep the pages in three ring binders.
Additionally, most folks are in their respective corners on education, in the red or blue trunks and ready to duke it out. They've all got someone to blame for our terrible school system, but when's the last time you heard someone bitch that a D is no longer a failing grade? That some students must learn without having a real book(physical or electronic)? No one politician or party has these things as their core concern regarding education because it's not germane to their ideology.
After years of being passed with D's and little to no help from my schools(at least till high school), I had piss poor grades because I spent all my time struggling with math. I was decent in science and history because I love science and history. I was decent in English because I love to read, thank god for my parents. I tested at a tenth grade reading level in the fifth and no one that knows me thinks I'm stupid - but my grades show someone that loved band and didn't give a shit about anything else.
Student tutors tried but I needed more help than they could give, which was too little and too late anyway. Had it not been for the help of a friend who was a math major in college, I'd never have passed on time. What schools need is less politics, and students need professional tutoring, real consequences for failing and real incentives for success. The best part of high school for me was electives, and at least I performed well in most of those subjects. However, almost none of it was real world experience, and I've only learned later in life that I don't want a career in computers. Career guidance is a joke, and everyone knows it. Career integrated electives showing what it takes to make it, which courses are important and how to integrate them, the duties of various professions and what to expect from a life in a given field will help students to succeed. I'd have had a good idea in high school that computers were not for me. I expect the argument will arise that this is just too difficult, but most of this information is not hidden, we read articles about the ins and outs of professions all the time. If more time was spent helping students to choose careers, I guarantee we'd have better performance from them.
As it is, I'll be studying for my CCNA to stay competitive over the next few years while I re-gear for the profession I really want. For now I suggest we provide students with basic necessities before we start with the gasbag ideologies.
Primary sources -- what makes them more reliable?
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!
E.g., http://www.thefreelibrary.com/Mathematics+and+academic+success+in+three+disciplines%3A+engineering,...-a0219062371
Yes, exactly. In my high school classes, the math teacher was going on about math (I presume) and I was thinking about tits and legs and what my band was going to practice that night.
A couple years later, I spent an entire summer studying math with a tutor, electronics (strictly because I was interested... and let me tell you, the missing math made itself felt, hence the tutor) and I really enjoyed myself. Which is not to say I didn't enjoy myself in math class -- I did. I just wasn't learning math.
Personally, I've always felt that schooling would be better off with basic schooling first, then a five (or so) year break from age 15 to 20 while your hormones rage, and then back to school until about 25. Of course, if you were so inclined, you could spend that five year break studying anything you liked, and certainly some would do that... but generally speaking, those years would be well spent, I think, outdoors, dating, and socializing - perhaps even working.
I've fallen off your lawn, and I can't get up.
Math is the foundation of modeling all processes we can't hold in our two hands.
Forget competence with computers. Who would need that in the 21st century?
Forget probability. Forget statistics. Forget risk. Forget data. Forget the ability to make rational decisions in public policy, economics, medicine, or any field requiring understanding of an aggregate. And of course, forget any understanding of science.
Who needs any of that?
Having said that, there is plenty wrong with math education in school. Besides the clear failure to teach what they try to teach, they're generally trying to teach the wrong things. Kids are still basically learning how to use the slide rule. Everything is about analytic hand calculation, which computers do just fine.
People need understanding of modeling, process, data, process, statistics. Math is the language of understanding reality. Those who understand that language use it all the time, every day as the fundamental building blocks of their thought. Those who don't understand that language don't know what they're missing, just as monkeys don't understand what they're missing lacking a spoken language.
Math puts a person two languages away from flinging poo on the savannah. And probably, one language away from the Dark Ages.
I'm currently a second year engineering student. In first year, we had several mature students (aged late 20's to late 60's) myself included. The people that survived were the ones who took advanced math courses in high school, or retained their prior knowledge of math. Those who did not have a strong math background dropped out fairly quickly, even though the first term math was considered a 'remedial' math course (covering basic algebra and trig, stuff I did in grade 10). Those with poor math backgrounds quickly floundered and failed out (a couple of the more tenacious types stuck on, but they had to re-take the course and are now severely behind).
But really, if we're only going to teach the basics to everyone and leave specialty courses to when you've chosen your field, then why not eliminate the need for English after grade 10 for those not pursuing a degree in it? get rid of all science classes for MBA and Economics students too; no more history classes unless you plan on being a history major or social science classes unless you're gonna be a sociologist.
The point of high school is to provide a well-rounded, general education is just about every academic discipline. To do this, a certain level of math proficiency is required. While I agree that calculus isn't necessary for most students, normal math classes all through will be. Even if you will never again have to sketch a parabola, or solve two unknowns in two equations, having a knowledge of math that is significantly higher than required will not only make the maths that you need to know for life much easier, it will also enable you to expand your horizons later in life if you choose to.
There is one problem, though. Achieving a really useful level of math needs about 15 years. Now trim the math from basic education and you are harming those who actually want to use it professionally later. It is like piano -- you have to start learning very early to be able to reach the top. While I understand that this increases the pressure on those students who will never use it, but I think that is an acceptable tradeoff.
So why aren't we making everyone learn how to play the piano?
Math as much as reading and writing is learned early in life. And if you don't use these skill much, you are not becoming better in reading or math. While there are people which survive without reading skills nobody would claim that reading is not so important. Same applies to math. You don't need it. Some people can even live without calculus. But they could live better with math.
For example, when people would understand set theory and building classes, they would understand tagging, marking elements with attributes and finally understand folders in computer systems. With simple logic they could proof that most political and media statements are plain lies. Yes most people feel that way, but they cannot act on it as they have no understanding of the concepts. Furthermore they could understand the structure of modern economics (which affects everyone) and see the problems with it.
You see, lack of smartness is just one cause of struggling, but there are others. There are many vectors for a student and you will see them in very different mixtures:
SmartnessDumbness
ConfidenceLack of confidence
BraveryCowardice, passiveness
Hard workingLaziness
InterestedUninterested, skeptic
Sense of safetyWorries, depression
etc...
I am a teacher, not a fucking judge. Who am I to decide which students deserve hours of work and who don't? I rather leave it to life and I do instead my best to do whatever to teach them. And I am no idealist, I know that there are children as stupid as a rock, still, I give a chance at least.
Here in France the mathematics are used only for selection, the entrance exams to top schools have a lot of maths, the best minds are suposed to excel in mathematics, but the alumini end up doing management anyway.
Why don't we?
All the mathematics one needs in real life can be learned in early years without much fuss
Profs in my university were pretty open that factually we need very little math in our lives. Yet it helps developing brains and making people generally smarter.
Similarly, one can try to say that we do not need to study literature: who the hell cares about an ancient writing by some brit? Yet, everybody acknowledges the role of the literature because it directly influences our communication skills. I wish it was that simple with the math too.
All hope abandon ye who enter here.
Surely you are familiar with the old phrase, history is written by the whiners?
Escher was the first MC and Giger invented the HR department.
Things that most people do need:
Geography. If we're going to invade someone, we ought to know where the hell the country is. Not "oooh, it's THE MIDDLE EAST. Somewhere east. In the middle."
History. Eg: Hey look, there have been huge economic booms and busts in the past. Hmm, I wonder if housing prices will climb forever?
Politics & Government : What does the Constitution say? What does it not say? How is it interpreted? What does "federalism" mean? How much does the US government spend on what?
Religion: What do people of other religions actually believe? Where do those beliefs come from? Eg: What exactly is the difference between Sunni and Shi'a Islam?
All of these seem practical to me. If you can't understand what's happening in the world, you don't know how to react to it.
I would argue that in a world of high technology, where people rely on GPSes and nukes to keep them safe, it is very dangerous to have people handling things which they don't quite understand. Am I arguing for absolute comprehension at every level? Certainly not. However, the popularity of lotteries, and the constant examples of people getting screwed on loans leads me to believe we aren't teaching enough of the *necessary* subjects.
Others here have already gone into how higher math has given them another perspective and expanded their minds. Still others here have gone over how those in power don't necessarily want people better educated (about anything, not just math) because it wouldn't benefit those in power (probably be detrimental to their power). I will say this: you have to realize that people (even smart people) only have so many hours in the day and so many months in their life, they can't learn everything. You have to pick and choose. Would I say drop higher math altogether? No. Would I be in favor of swapping statistics, probability and logic for calculus? Definitely.
Nathan's blog
Yes, but that's exactly the situation. That's why there are so many credit card users and mortgaged-to-the-hilt home"owners" in the US; because people really don't understand compound interest. Anyone who does and has even a lick of sense will never let a lender get into that kind of position over them... it's just a highly accelerated way to transfer your money to the already-rich.
You know how many people run a credit card up to the limit and then pay the minimum? Most of them. And that is a recipe for financial destruction. Which the banks are happy to cook up for anyone they can entice into the deal with access to a shiny new whatever.
Likewise, you know how many people get a mortgage and then pay only the suggested payment? Most of them. And how many about shit themselves when they find out they have very little equity when the payment book has half the coupons gone? Again, most of them.
It's basic math, and in this society (in the US, I mean), understanding these things before you get in trouble is usually one key difference between the haves and the have-nots.
I've fallen off your lawn, and I can't get up.
There is a misunderstanding here. My original comment was a reaction to the comment that "most people don't need the math". Following that same logic you end up realizing that most people do not use any (or most) of the stuff their learned -- so we should not teach it.
Of course I do not agree with this conclusion at all.
Nor, perhaps, where you are? Compulsory.
I've fallen off your lawn, and I can't get up.
"And I am no idealist, I know that there are children as stupid as a rock, still, I give a chance at least."
Which has nothing to do with "closing the gap"
Even if you fix the problems which are holding some of the slowest back the best and fastest should still keep charging ahead unless someone is hobbling them to make the parents of the struggling kids feel better about how small the gap is between them.
Not true. Most are acutely aware of the problems with America, especially the shitty things it did in the past to Africans and Native Americans, but still love the country anyway.
>>glosses over "how my country has screwed over other countries".
What decade did you take history? While your statement is true for the 50s or 60s, for anyone whose answer is after 1980 or so, believe me, the textbooks are filled with examples about how evil America is.
I stopped believing the "they don't need math" argument years ago when it became necessary to give an impromptu lesson to my department on how to calculate period-over-period percentage sales growth. Half the group couldn't do it on their own.
Ahh, gotcha.
To clarify my below comment, I use your running analogy:
- while two runners may run at the same speed, they may not start from the same position. I do not care who "wins" (is the fist) I care only how far they get at the end
- unlike running, it is not immediately obvious who runs faster
- running speed is not constant, but grows slowly. For some students it starts growing later but stronger and lets them close the gap
- some students are behind because of an injury -- you cure them and they will be as fast as the others
- unlike running, you are not alone
Of course there are guys that will never be up to the challenge. It is just quite complex to figure out which ones. Have you been to "class reunion" (is this the correct English term?) events? Which are the students who lived up to everyones expectations? Who were the ones that surprised you?
I personally think that assessing people is very hard, and most of us think that we are good judge of character. I keep a mental list on people I misjudged and that constantly reminds me how hard is to judge others.
I tend to go one step further and believe that there are political/financial motivations for this "negative emphasis" on not just mathematical, but all forms of rigorous logical education.
Firstly, it can be seen as trying to appeal to the "will of the majority" and the popular discourse of inclusionism, thus making the less educated people content in their place and giving them the illusion that all skills are created equal. Indeed, the portrayal of education itself as 'eugenicist' and 'classist' mean that even the intention to go into further education can become stigmatised, especially to the "majority" which popular rhetoric have placed as antithetical to the "upper class's" whims.
This has the function of allowing political and business interests to leverage this lack of understanding to manipulate the population based on faux-mathematics and faulty logic. We see this happening every day, in areas such as the economy and counterterrorism, and it seems to be working well. "Facts and figures" are treated like holy scriptures, and even their logical inconsistencies are accepted without question - creating a docile class of proles that publicists (who all along knew the power of numbers and rhetoric) can easily manipulate for their own means.
This is why maths - and other forms or logical education is important in this day and age: it encourages people to be analytical, logical and find out answers to themselves, something highly threatening to the current politics of ignorance. Knowledge is power, folks!
(Disclaimer: I'm a Gender/Cultural Studies major, former straight-Maths student.)
I think basic algbra (sorry, they spent so much time teaching me geometry they forgot to teach me how to spell) is all people really need in life.
Anything after that isn't overly necessary for most people.
I could be wrong of course, but in my life, even with doing computer programing, I never needed very complicated math.
Problem solving though, they should teach more of, imo.
but i've been out of school for 20 or so years and i have no idea what they teach anymore, since I don't have kids. But i imagine they are still using the same text books I did. (that should be a joke, but sadly, it's probably not.)
Be seeing you...
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.
Teach it to them when they do need it.
The problem is, by then, it's too late.
I am in my first year of my doctoral studies in computer science. The joke around here is that I'm "a minority", namely an American. 5% of my program is American. Now, there are two things to say about this. One is that our graduate schools and research institutions are extremely competitive, world-class places. That's a good thing. The other thing is that we Americans are benefiting from them, but by and large, not participating in them. I think this is extremely bad in the long run. What is very clear to me, though, by comparing the graduate population, which is largely international, with the ungraduate population, which is largely American, is that international students are far better prepared for their graduate studies.
I don't think we're incapable of doing science, but the sad fact is: you have to grind away for a LONG TIME before you get to the fun bits. And in a field like computer science, those fun and interesting bits don't really start to reveal themselves until you're comfortable with some advanced concepts. The field I am in now resembles very little of what thought it was before I started. The thing that kept me going was simply that I was curious. How most people would even get hooked into a field like mine without prior exposure to math or programming... I have no idea.
We don't make large public policy decisions for the benefit of the individual. We do it for society. Or, that's the way it's supposed to work, anyway.
What mathematics a programmer needs varies substantially on the work they do. Writing a physics simulation program? Algebra is essential, and calculus may be essential, but may be optional depending on what is being simulated, and the techniques used.
When writing a program to manipulate images, Linear algebra can be very helpful, especially for simple transformations. If you are writing a program to find an optimal schedule of buses for a city, then linear programming is what you need.
On the other hand, if you are writing a basic online store and you can get by with arithmetic (except in so far as Relational Algebra is the basis of the DB being used, etc). Writing a simple (non-physics based) computer game may involve very little math.
Writing a compiler? The important parser techniques etc can be described using math, but a very abstract one, far more abstract than calculus or even set theory.
Stylish sheet to fix many problems in Slashdot's D3: https://gist.github.com/801524
Okay, I read a bit of it, and I've got to say that this is one of the most insanely stupid pieces of tripe I think I've ever read.
Universal education is one of the cornerstones of an advanced society, and responsible for untold inventiveness and ingenuity. Without it, we'd be doubtlessly stuck a hundred years or more in the past, because most of the great thinkers of our time would have been too busy tending the farms to have become accomplished.
I'm going to go out on a limb here... You're one of these "government is evil" schmucks, aren't you? It all sounds good, unless you happen to be one of the poor saps who gets left behind in the dust because your parents are stupidly suspicious of all of those people with that fancy schmancy learnin'.
Likewise, you know how many people get a mortgage and then pay only the suggested payment? Most of them.
Then most people are smart - at least for most mortgages.
If you could really afford to pay off your 30-year loan in 15 years, then you almost always would have been better-off getting a 15-year loan. Since you're paying a premium on the loan (in the form of interest rates) to assume the long-term risk of rates changing, you shouldn't take out a longer-duration loan than you can afford. A 6% 15-year loan is a LOT cheaper than a 6.5% 30-year loan that you pay off in 15 years.
Now, if you can't get a better deal on the interest then of course it is in your interest to extend the duration (with no pre-payment penalty) and then make higher payments as you have opportunity - this gives you more financial flexibility over the long term.
I agree that those who are good at math will have advantages financially over those who are not. However, my wife took enough math in high school to in theory cover all these kinds of basic financial topics, but this would not be nearly as intuitive to her as it is to you and I. So, in that sense, it isn't doing her any good to have to have spent her time on it.
Has he ever wondered, why Poles and Russians are better programmers than many other nations. And as in Poland secondary school math was not compulsory for over a decade, one could trace the quality of programmers at different age levels.
I keep hearing the word "suffer" around here, but we're not talking about someone pulling out your toenails-- we're talking about mathematics.
People's experiences are shaped at least as much by their teachers as they are by the subject itself, and on that point, I think that most elementary school mathematics teachers are mindless automatons, teaching mathematics by rote. Yeah, that's dull. But let's put this in perspective: mathematics is the most powerful invention in the history of mankind. It is what allows us to understand our world, enables almost every facet of our modern lifestyle, and it will continue to be the thing that gives us control over our futures.
If you can't make that exciting, well, I think you suffer from a lack of imagination. The mathematics is not the problem.
How do you plan to teach economics without math?
Many adults need a lot of the skills which are trained in math, in their daily life and in their jobs. To believe that math is about learning how to add just shows the mediocre understanding of the guy. In the same way reading a text in literature will not bring me a direct gain of knowledge. Reading literature is not important to learn the literature by heart but to learn how to understand and classify texts and get some basic knowledge about their structure, so that one is not puzzled when the storyline of a TV drama is slightly more complicated than normal.
In history its not necessary to remember when Rome was founded, but its helpful to remember that big empires grow and come down with time, and that truth evolves with time.
In math you learn that a problem can be abstracted, and that, using a set of fixed rules problems can be transformed and analyzed, and that, when done right such an approach can reduce the effort to understand and solve a task. Understanding that things like Markov chains exist may help the Manager to ask the right questions. Understanding that there is an algorithm to protect you data helps you to formulate the task. Understanding that complex systems exhibit long-term dynamics help you to understand and ignore when a politician bullshits (e.g. the economy goes up/down *since the election* so it *must* be connected). Understanding probability enables you to understand studies and elections.
All our modern life is built on math. Understanding the pattern of it helps. I am pissed of when people complain that i did not read enough classic literature, but on the other hand done even know basic mathematics known 4000Years ago.
I have always wondered why children's books spend so much effort teaching preschoolers about lions and tigers and hippotomuses, and other such exotic things.
I am anarch of all I survey.
A more than substantial part of elegance *IS* clarity and simplicity, so the notion of obfuscated elegance is sort of a contradiction in terms.
File under 'M' for 'Manic ranting'
ny experience in school comprised of both, but fair point.
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You are of course, absolutely correct.
I can't agree at all with this premise that we don't need to know advanced math. Knowledge of how things move, change, and interact is of practical use all the time. And, being able to understand data and make predictions are important no matter what your job is.
I feel that saying that the usefulness of math is overrated is akin to saying that toilets are overrated. Sure, we got by just fine without them, but in a modern society with a large population, this is a crucially important ingredient for progress.
Understanding gradients is a good example here - it gives you a much more realistic perspective on everything from good real estate deals to good social skills. Gradients are invisible but you can see them everywhere if you have a solid understanding of math. Sure, teaching people how to take tests is overrated, but this is not an indictment of math, no way.
>>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.
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.
That's why I said it's important to have useful tools in your toolbox. Things like algebra aren't just used in engineering or the physical sciences.
>>So, why make somebody try to prepare for a handful of careers that they are unlikely to pursue
Since I was about five years old, I knew I'd be a computer science guy and prepared myself for college and a career in it since I was first allowed to make choices in my education. You know which two classes I've used the most in my 20 years of education? AP US History in high school and a literature class in college, followed by all of my computer science classes in college and earlier.
Don't follow my logic further than it was meant to go. I am talking about math, not all other subjects.
You can be an educated citizen without knowing advanced algebra. There are plenty of things that *should* be taught that aren't. Math is akin to computer programming, Chemistry/Physics, etc. Those are topics taught in high school. Great to take if you are interested in them, or would like to someday work in a field dealing with this. A complete waste of time if your post high school plans do not involve anything remotely related.
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Figured out an algorithm to calculate distances between lat/lng pairs. Yes, I know there are code snippets available online that you can just drop into place, but I wanted to figure it out. I did.
Another time I was asked to make some analog gauges in flash that represented home well a team was doing for the current day. At the time (it was 2003 so this whole story is IIRC) flash only supported radians for such a thing, so I had to take a percentage and express that in terms of radians. Couple that with the fact I had no clue about how to use flash and had never used actionscript, it was a fun task :)
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Question: Why does one need a head? Answer: One eats with it.
Oh, totally agreed. I have used plenty of math for hobby related stuff. Probably more math than I have used for work.
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But they also haven't learned the math they need!
Some have already listed here the utility of probability and statistics, and I would add to that simple and compound interest.
Most people don't need to know how to "solve for x" in the Algebra I & II sense, nor do they need trigonometry, or basic newtonian mechanics and elementary calculus. But pretty much everyone needs to know how their savings account works, how insurance premiums and risk (on a basic level) are calculated, how slot machines and the lottery work, how to save for retirement, whether the maintenance plan on their car was worth it, and enough arithmetic to save money on their groceries.
This is where I get my recommended daily allowance of "Foot in Mouth."
The central pit, or courtyard, was standing room only, but it was surrounded by three tiers of stadium seating.
What about at the university level? Is it fair that most schools require English and history classes as part of the core gen-eds, but not math? Isn't the point of high school to get a general education?
What party do you suppose I'm in favor of here? And how is voting in general not party loyalism over the good of the country?
When you're afraid to download music illegally in your own home, then the terrorists have won!
Sure and while we are at it lets get rid of history, literature, languages, music. Most people don't need any of that stuff either right?
We don't teach people maths because it is useful, we teach it so we have a citizenry which minimally engaged with the big questions of our time by being informed of the big questions of the past. We teach these things to enhance the human spirit.
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.
You're obviously correct, it didn't help you; but that's probably more to do with you being an asshat than any lack of value of a liberal arts education. For the educable among us, well, we take something from everything. Today I learned that some douchebags think that their experiences apply to everybody, and that if it's not in their experience, it can't exist.
Historians have to back up their claims with primary sources.
(Disclaimer: I'm not a historian, but I do sleep with one)
That's not precisely a fail-safe, since a "primary source" can be, if the history in question is recent enough (THISW is mostly focused on the civil rights movement, e.g.) just someone who "was there."
Short of taking care of the Southeastern United States with our own "B Ark" plan, it's not inconceivable that a late 21st century Historian could find a "primary source" that says that President Obama was a Repton and Jesus Christ ran in the 2016 election on a platform of putting an American flag on the sun.
This is not entirely so. The advantage of getting a longer mortgage with lower payments, even if the net interest rate is higher, is security in lean times. If you're in a good position now, make double payments. If you get laid off or incur unexpected expenses, then you can make single payments until you get back into a better position. Creating a 15- or 30-year plan with the assumption that nothing could possibly go wrong in that time is not a good idea.
Virtue finds and chooses the mean.
Aristotle, Ethica Nichomachea
This is the comment I was waiting to see. The entire discussion that I've read up until this point is incredibly biased. People arguing both the pros and cons of more or less math education were starting with considerations about the utility of a math education. Why are we settling for education merely as a pragmatic instrument? Yes, I understand that it costs money and that as things stand now, the cost/benefit analysis of education must consider how practical the knowledge will be. Must it be that way? Should it be that way? Some people like to solve logical problems; some people like to create beautiful music; some people like build furniture. Regardless of how much more or less useful any of these is than the others, why aren't we fighting to give people an opportunity to learn whatever skills they want to pursue whatever passions they want?
Virtue finds and chooses the mean.
Aristotle, Ethica Nichomachea
If the point of education is to produce competent employees who are "good at what they do", so that they can by efficient cogs in the machinery of production/consumption, then no, it doesn't really matter.
If the point of education is to produce well-rounded, intellectual-capable human beings, so that they can be effective citizens of a great democratic nation, then yes, it does matter. Boring people of limited interests show a failure of such a system.
Tom Swiss | the infamous tms | my blog
You cannot wash away blood with blood
I find that I use trigonometry all the time (realistically, two or three times a year). I can't say the same for politics.
Math reaches into nearly every career. Even if the steps you take to solve your domain specific problem doesn't look like high school algebra does not mean it isn't directly related to it. Chemists, pharmacist, doctors, nurses, dentists, metallurgist, and accounts all have highly specialized forms of math in their jobs.
“Common sense is not so common.” — Voltaire
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.
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.
I disagree with that. If you hold cash or non-productive assets when you have loans, then you're shooting yourself in the foot.
If all you can afford to pay is the coupon rate, then trying to pay more is reckless.
If you can trivially afford to pay the coupon rate, then chances are that your coupon rate isn't high enough. You're paying a higher interest rate to have a loan duration that is longer than you need it to be.
Of course, you shouldn't make your mortgage payments 60% of your income, because then if anything goes wrong you're sunk. However, if you have all kinds of extra cash to put into accelerated payments, then you probably took out the wrong loan.
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.
That depends a great deal on inflation rates and home values in the area. If home values are generally rising (often the case in developing areas on the periphery of developed areas), then paying rent for 20 years while you save up to pay cash for a home (assuming that you can ever save enough) could cost you more than the interest on a loan. Of course, if home values are going down then renting is great.
Now, once you have a loan you should of course try to pay it off quickly.
Since you threw out numbers, here are a few:
Suppose I borrow $200k at 6.5% interest with a 30-year term. I can pay it off at the coupon rate of $1264/month. Now, suppose I have extra cash, and pay $1742/month - now I'll pay it off in 15 years and save myself $142k. That sounds good, right?
Wrong. I could have instead taken a 15 year loan at maybe 6% interest instead. If I paid that at the coupon of $1688 I would pay $9700 less. If I went ahead and paid it at $1742/month I'd pay an additional $6k less.
The problem is that you're taking out a loan that is longer than you need. If you don't need 30 years to pay off a loan, then you can save a boatload with a shorter loan and a lower rate.
If you can pay it off in only a few years, you can of course make a very safe killing with an ARM (the adjustable rate would only barely kick in, and if it has a gradual ramp-up feature like most ARMs then even if Carter is back in office you'd still be paying a low rate the whole time you're making payments).
The bottom line is that you have to look at the big picture, and what you have, and what you need. Loans are not always a bad thing.
In a world where computers are becoming more and more integral every day into every profession, machines that for all intents and purposes just do maths really fast, are you really saying that knowledge of maths isn't a useful skill? In the 19th century it may have been useless, but the world has been moving from superstition and physical skill into a world of logic and intelligence since then; if maths isn't a good skill to have in that world I don't know what is.
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.
The Earth is about 8000 miles across, but let's call it 10,000 in round numbers.
10,000km please! Save the poor kids from having to know all the conversion factors. How many fluid pounds in a cubic furlong?
Imperial units are almost as bad as long division.
There is a difference between not knowing the difference between a mean and a rolling mean, but this guy did not know the difference between a mean and a median.
We don't tolerate fools and you can tell after a few meetings who knows what they are talking about and who is bullshitting.
An Education is the Font of All Liberty
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
The difficulty is that this is Schroedinger we're talking about. There isn't so much subtext as... text. See
here and here.
I would theorize that the higher a percentage of a society is that is exposed to higher maths the better off that society as a whole is in the long run.
I got the impression from the article that someone like a plumber really doesn't need higher maths for everyday life but in reality everyday life for him/her is plumbing. The better plumbers are going to be so because of their better understanding of plumbing because of the related math. Understanding angles, line sizes and flow capacity, system volume and pressure, etc. are a part of everyday life for them.
The same is true for mechanics, electricians, machinists, carpenters, etc., the many average people working blue collar careers. Their everyday life is what they do for a living and the better they are at the applicable maths they better they are at their trade. How many of them knew what their career path would turn out to be in their early years of school? How many could have followed their eventual career path as successfully without an early maths foundation to build on?
I can't really seem to think of many careers where an understanding of higher maths would not be a benefit. That said, it would seem the more mathematically educated our workforce is as a whole the better off our society is for all of us.
And here a retired English teacher I know and a professional writing instructor both have said almost the same thing you did, quite openly. Shakespeare has lots of sexual innuendo and gratuitous violence. After all, what is the point of Rosencrantz and Guildenstern? To up the body count in Hamlet.
"I may disagree with what you say, but I will defend unto the death your right to say it." -- Voltaire
Yes, Fermi problems. http://en.wikipedia.org/wiki/Fermi_problem
The classic Fermi problem is, "How many piano tuners are there in Chicago?"
Fermi's wife Laura wrote a biography called Atoms in the Kitchen, which described how they used to sit around the dinner table and Enrico would ask questions like, "Tin melts at 232 degrees C, olive oil boils at 300 degrees C, so how come you can boil olive oil in a tin frying pan?"
Answer: It's not the olive oil boiling, it's absorbed water. (Anyway that was his explanation.)
And they couldn't look things up in the Internet back in those days.
I would argue we should teach more math--but I think the distinction you made is important we need to teach "understanding" of math.
We need to teach math with a calculator and Google. Because let's be honest you aren't ever going to be locked in prison cell on a deserted island and need to engineer the next airliner.
On the other hand you need to be able to discern smell tests. So if we do have any math classes without calculators and Google it needs to be rapid fire, "about right" questions.
21x42 = 882
vs
20x40 = 8,820 or 88.
True/False type questions where the person would notice something that's "probably wrong" and double check. That's how the real world works. I can't remember the volume of a sphere or a cylinder. I can't even remember how to find the reflected vector of an incoming ray--and I'm a VFX artist doing computer rendering all day. I look that crap up when I need it. And I definitely don't do long hand division anymore but I can vague figure out about what a tip should be.
Then why did you talk about closing the gap?
If it is such then the difference between the best and worst is irrelevant and makes no sense as a metric or otherwise.
And that kind of basic stats takes what?
2 weeks to learn?
3?
but you kicked out the person who asked questions and tried to learn.
great management there.
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.
True. An engineer may benefit a great deal for having taken an English class that taught him how to organize his ideas and argue, as Roger Boisjoly did when he tried to convince Morton Thiokol management to cancel the Challenger launch. http://en.wikipedia.org/wiki/Challenger_disaster#Pre-launch_conditions_and_delays
Good scientists are just well-rounded guys who happen to know a lot about science.
You know which two classes I've used the most in my 20 years of education? AP US History in high school and a literature class in college,
Not surprising. Gerard Piel, the founding editor of the modern Scientific American, was a history major.
yes, *my* experiences are meaningless but *your* experiences apply to everyone or at least everyone who counts or is educable.
you're absolutely right!
pulling random things out of the air and pretending they're what the author really meant is sooooo useful.
Try a fun little game:
watch a film by some serious director, do your literary analysis and then have someone else watch with the directors commentary turned on and tick off points from your analysis.
oh?
what is that?
that doesn't count?
because apparently even if the director/author/poet personally says straight out that no, their use of some church bells is not a symbol for neo-colonialism or whatever else you've dreamed up that doesn't count because everyone makes their own meaning.
http://xkcd.com/451/
Here is the problem: most people don't really *get" an area of math until they have studied more advance areas. For example, a lot of people get through arithmetic by rote, and it finally "clicks" for them when they go on to study algebra. They understand algebra better after they've had calculus... you get the idea. I worked as a math tutor all the way through college (I was a math major) so I've seen it hundreds of times.
Now, as a technical draftsman, I don't use (or really remember)most of it. I live and die by arithmetic and trig, though. I'm actually glad I had 4 semesters of calculus, because it forced me to really understand arithmetic, trigonometry, and basic algebra.
The Mathemetician's Apology
Schroedinger's Cat is not a euphemism, it is simply as close to sex as most physicists will ever get.
The US government have made it clear that we have no inalienable rights; any we do not defend vigorously will be taken.
Considering that many of the labourers I work with (construction industry) have difficulty figuring out quarter, eighth or sixteenths of a inch on a measuring tape -- I'm very hard pressed to give any credence to the idea that we should be teaching less math in school.
"Grab them by the pussy" -- President of the United States of America
Universal education is indeed one of the cornerstones of an advanced society.
However, what he have now is not "education", but indoctrination. Our school systems aren't aimed at educating our youth, but rather preparing them for dead-end careers and being ill-informed voters who can't exercise critical thinking.
And yes, the government is evil, our government. Not all governments are evil, but ours is. The governments in small European countries like Switzerland and Sweden seem like they manage to do a decent job of not being evil, and proving proper governmental services to their populations, but the American government is bloated and evil. If you ask me, the only way to fix it is to break up the country into a bunch of smaller countries. One giant country, with too much power, is simply unable to avoid having a giant government which becomes corrupt and self-serving. Just as giant corporations are generally bad, giant governments are too. Having a giant country like ours with a tiny government simply wouldn't work too well, so the answer is to not have a giant country in the first place, and break it up into smaller countries.
I would disagree with your inclusion of tradesmen in your list.
I worked as an HVAC service tech for about 20 years, and my knowledge of electrical theory was very valuable to me. It made it possible me to easily figure out electrical issues that other guys would spend hours figuring out.
I really struggled with algebra, and didn't take trig, in high school as I couldn't understand what the math was used for, but once I was introduced electrical theory algebra and trig became very easy for I then understood how and why they were useful. Had I not taken the math needed to understand electrical theory I would have been far less skilled in the field. Those math skills helped me visualize a lot of problems that the eye cannot see.
"while democracy seeks equality in liberty, socialism seeks equality in restraint and servitude." de Tocqueville
> nor do they curl up with an algebra book for relaxation
Is it a pun? ...
I think algebra book don't teach vector calculus
I would also re-include differentiation to that list.
Not in the explicit sense of formal differentiation, but in the general sense of the slope of the line tangent to a curve, or the rate of change of some value. People should have the basics of velocity and acceleration before starting physics 101, especially since it's easy to go through the entire education system without taking any physics classes. That sort of understanding lays the groundwork for thinking about interrelated systems, and dependent behaviors that are neither directly nor indirectly related to a parent process, but rather derived from it.
Not, especially given that 5000 cubed is a lot closer to 125,000,000,000 than to 75 billion.
Note, as a useful rule of thumb, that a sphere is about half the volume of the cube of the diameter.
Also, that you can approximate the conversion from cubic miles to cubic km by dividing by four.
"I do not agree with what you say, but I will defend to the death your right to say it"
Depends what you mean by "test-driven". It's a well known fact that the more you give students, the more they retain the knowledge. Testing their recall and reasoning skills under pressure improves the retention of that knowledge and those skills.
Higher Logics: where programming meets science.
i think the problem is math is taught backwards, if at all correctly. I have never once in class found out how or why the formula's and expressions and equations were created. Never. Yet, almost all math I've found has had real-world implications, even in theory to the mathematicians who created it. In my experience, this was even more evident in higher-math courses such as calculus, where proofs were done with the same attitude as simple arithmetic. it got to a point where you didnt ask why, you just did the work and handed it in, knowing the theories and concepts with no real way to think about them. Were it not for my luck in several corresponding courses in calculus, biology, and several string theory and game theory specials courtesy of the Disovery Channel and PBS, I doubt I would ever have thought of the simple beauty of math and it as the ultimate language. Math is the one connecting function of everything, even in say, literature, timing is key to a great story, now how do you express time and its relations to other times? Math is important, theoretical math doubly so: Experimental and theoretical math is the boundary pusher of math and science, the two go hand-in-hand at that level. this is the concept that is lost when math becomes commonplace. all math started as a radical new idea of thinking, of explaining and analyzing. to me theoretical math is the benchmark that shows the boundary of human thought. To me somebody who cannot realize the importance of math, especially theoretical math and its relation to science has no right using a computer, which is above all designed to aide in these respects. we have computers to do math.... i.e. we give them rules and an equation to solve. we are now free to become creative mathematicians because we dont have to do the legwork until we get the right answer from the computer.
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
While I'm not familiar with the pricing of tickets at the globe, at the time there was a much bigger division between first class and third class tickets generally. So pandering to the masses was probably less effective.
A good plumber probably doesn't use much if anything of math higher than a general knowledge of length and pipe diameter.. basic measurements. Very few plumbers are going to spend the time computing the flow volume required to satisfy a toilet drain -- they've got a bunch of "standards" that they know work for the job at hand (whether by experience or from building codes).
That's why you hire engineers to design any sort of complicated structure -- the actual contractors doing the job will know how to read the blueprints and make sure everything is the right size and lines up and whatnot, but they're not going to be sitting there doing load and weight calculations. That's not their job. Their only job is making sure the actual building matches the blueprints and they just trust that the engineer did his calculations correctly. And the further down the line you go right from the foreman of the whole project down to the guy hired off the street to carry lumber and cement, the less math they're going to care about. The flip-side of course is that the engineer can sit back in his office not having to care about things like table saw operation, construction site safety concerns, dealing with the city/etc with respect to road closures or other political junk and so on.
Now whether or not knowing the work required to move a 40lb bag of cement 1 foot is helpful to the guy lugging it around is up for debate.. he's certainly not going to do a worse job because he understands that (unless of course he spends all of his time computing the amount of work needed instead of actually doing the work!)
The article is definitely right -- very few of us are in positions to care about math once we've left school. But I'd go on to say that that applies to EVERY subject in school. Why? Because if you've got say.. 10 subjects and by chance you have 10 occupations, each one (primarily) associated with a subject.. then even with a perfectly uniform distribution, only 1 in 10 people will care about any specific subject after they're out of school (oh wait, I just used math!)
About the only thing that's (nearly) universally required amongst everyone is communication skills. And that's something they don't really teach in school (English class is what most people will claim but really, knowing Shakespeare doesn't really help you much in the real world either. You might get a slightly larger vocabulary but that's only really relevant for large written communication (writing books for example -- things that themselves are generally categorized as professions). The type of communication I'm referring to is more the emails to your boss, phone calls with your customer, etc where the preference is to be as short and concise as possible while still getting your point across.
I think the main reason math gets so much focus is that science has been the biggest driver of progress over the past 100 years or so, and almost all science requires math of some type -- even if its just basic statistics. Producing the next Picasso or Beethoven may well be a blessing, but no amount of paintings or songs and no matter how good they are will ever change the world in the same way as say, the development of computers or the atomic bomb. So we keep pushing people into math and science because if we have to make a choice, we'd rather miss out on the next Michelangelo than the next Einstein (of course defining "we" in that sentence can be a bit of a challenge in itself!)
It's like that guy said of Marketing expenditures,
"50% of what we spend the budget on is wasted, we just don't know which half"
By the way, Germany does push the career decision point down to younger ages (possibly close to 13-14 like you estimate, but seems like I remember it was 16 or so) - to go the technical Engineering or Science route or more manual pursutes like auto mechanic.
I don't know about the deep meta-analysis, but I agree that scientific papers use many of the same skills as literature. Having written more than my fair share of published scientific papers, and having been on the other side as a reviewer quite a few times, I can't stress how important it is that a manuscript needs to tell a damn story. It needs to have a point, and each paragraph needs to sell the reader on that idea. Perhaps it's not Dickens, but a paper that doesn't tell a story that the reader can follow ends up on the scrap heap in a hurry.
Math is a foundation of pretty much everything else in sciences. Moreover, math teaches you how to think about abstract concepts, how to reason logically, how to rigorously prove theorems, and so on. Now, Joe Sixpack doesn't really need math all that much, beyond basic arithmetics. But even Joe could benefit from deeper understanding of it, to avoid getting pwned by banks, real estate agents, car dealers, insurance companies, stock brokers and so on.
Ramanathan is right and wrong. Wrong that we don't need to teach math; right that we're teaching the wrong kind. Calculus, and even trigonometry, are powerful mathematical frameworks that few people will ever use. On the other hand, logical, statistical, and economical reasoning are essential to daily life. Euclidean geometry is a beautiful way to teach logical reasoning, but most schools get caught up in the geometry and fail to recognize the value of teaching people to reason logically _in general_. A course on "statistical fallacies in the newspapers" would be way more valuable than a course on differentiation and integration (and the source material is limitless). Nowadays, given the prevalence on computation in everyone's life, a course on basic programming would also be of greater general value than the math we teach now.
The sun is setting on America, and I have this gloomy feeling that we're going to see a lot more articles like this: we don't need math, Engineering is dying career, college is overrated, it's better to just learn to work with your hands, etc. Maybe I'm jumping at shadows, but this is how I imagine things will go as our youth are converted into low cost portable labor.
It's not that everyone will learn differential equations. You don't finish high school unless you do.
Those who can't do math don't graduate. I expect them to drop out or continue on for another year, though I admit it would be more cool to have them go on stage at the graduation and perform sepuku when their name is called.
fair enough. And no diss meant against tradesmen. I like to tinker with electronics, building tube amps and so forth. I use more math for that than I do for programming. So I do understand what you are saying. And some trades are going to be more scientific than others. Working with anything electrical, for example, would certainly require more theory than say a plumber or a laborer.
Advanced math/theory happened to help you, but the other guys who didn't understand that stuff could still do the job. An electrician may want to know ohm's law and watt's law and a few others like that. But if not that's why standards exist, so a guy who doesn't know ohm's law DOES know to use 12-3 romex for a 20A circuit and not 14-3. Engineers come up with the standards and codes, guys doing the work follow them.
And having troubleshot some HVAC issues myself, I'd say that is a much different skill set than wiring up a a new building or installing all of the plumbing fixtures. With HVAC, you are dealing with interconnected systems, almost like an automobile engine. A crew of guys framing up or wiring up a new office building according to standards is a lot different than the guy I call when my furnace stops working in the dead of winter or when my car starts behaving erratically. Again, having attempted many of these things myself, I understand the skill involved.
Those other jobs, business, sales, trades, etc, are not listed there to degrade those jobs. Those are good jobs to have and require a high degree of skill. But trig and calc, they can in most cases do without. Spoken as a casual observer, I guess. I do have several family members who are union tradesmen, though.
You also hit on another thing: many sciences, specifically physics, are little else than applied mathematics, at least at the high school level. It's always easier to learn a thing when you see how it applies. Maybe that would have helped some of those kids who annoyed me by slowing the rest of the class down.
blah blah blah
"exponents don't seem useful"
Browsing with classic discussion, noscript, at -1 and nested
no hidden comments and I only mod UP
I can't think of a better way to do it
Teach it to them when they do need it.
Or show them what it can be used for, before teaching it.
(ie. Make them need it sooner.)
By giving students interesting problems to solve (that can only be solved using maths) before teaching, their attention will be held that much better.
In my experience this practice is common among good teachers, but uncommon among bad teachers.
Some subjects are harder to teach than others, and require better teaching skills. Such teaching skills can be taught.
A good teacher can even lift a students mental blocks.
This is the difference between the purpose of a public education (ideas established in the later industrial revolution) which is designed to create good workers, and the western university system (approximately 1100 ad) which is designed to create great thinkers.
Modern society doesn't understand the university concept. They think universities are glorified worker-producing schools. Many universities get confused about it themselves.
If someone comes out of the industrial-revolution concept of school as a flat, bland and incapable person, mission accomplished.
If someone comes out of the university system as a flat, bland and incapable person, then there has been a colossal screw-up/waste of money somewhere.
On October 1st, George M. Phillip, the president of the New York State University at Albany, announced that the French, Russian, Italian, Classics and Theater departments were to be eliminated by 2012.
Humanities and social science programs in the UK face an 80% reduction in government funds for research and teaching. The reduction is interpreted as attempt to steer the UK educational system toward a for-profit model--a move that will force many institutions to close and that will transform all but the elite universities into technical schools.
Could this sustained assault on the public education system and the university itself be a misapplication of mathematics? Now that the development of mathematical methods with the potential to raise the level of political and economic discourse above ideological debate appears within reach, the public education system is faced with massive cutbacks on a global scale. The institution of tenure must defend itself against the adventitious imposition of market based-criteria of faculty productivity. Administrators relentlessly expanding their domain of responsibility and resentful of their support role fantasize "upstreaming" faculty research to themselves. Adherents of the "build to strength" philosophy wreak havoc on their institutions by eliminating departments deemed to be under-performing--typically the humanities and social sciences--as this is the most expedient way to terminate tenured faculty.
But now it appears that mathematics is next.
In my opinion, the greatest value of math is in college preparation. Based on my conversations with students at several college campuses, fear of math seems like the number one reason a lot of people do not go into engineering or science majors in college. It's part of the reason we have so many people going into liberal arts majors like mass communication or political science instead of CS, engineering, or sciences. While one needs just some knowledge of algebra for real life applications, it's really important that as many kids as possible are taught pre-calculus, and even calculus in high school, and that they're taught it well. Just my $0.02.
memorizing vast amounts of crap is hard, but learning lots of new concepts is easy
For you, yes. For me, yes. For everyone else?... no, because we're all different.
I never did learn the times-table. Even now, I work out the answers. I was considered stupid for not being able to memorise. Yet I understand complex concepts very well.
Other people are the opposite. Ever come across someone who says "I don't get it. Just tell me what to do." and then they remember what to do, and do so doggedly for years, without ever putting the thought in to understand that there may be better ways. We might call that stupid, but that doesn't make it any less common.
Some people understand, other people remember. (The lucky ones do both.)
Plenty of people are boring, have limited interests and are very good at what they do.
You can't have someone who's an excellent accountant who never took an English class in their life. They won't be able to communicate well with their peers, no matter how well they can "do the work." The same is true of most positions and math. I was trying to think of something that didn't need math as an example, but I couldn't think of a job. Perhaps something like a janitor, but then you don't even need a high school education for that, so leaving out just math is disingenuous as you could also leave out every other subject. But for general office work, the workers use math daily.
But most people don't need calculus. That includes most people who take it.
I'm a networking guy and I use calculus about once a week. Usually only as a sanity check for something, but taking a derivative (the rate of change of, say, traffic or subscriber numbers) or integrating (total traffic transfered given just a graph of average speeds over time) or such. I guess others could get the same information by looking elsewhere, but being able to take the information given and generate new and useful information from it is essential. Though most people I know in IT got there without a degree in anything, let alone IT (which is weak on math) or computer engineering (which is not weak on math).
Shortcut calculus (decrement the exponent and multiply by that former exponent for derivatives, reverse for integrals) should be taught to everyone. It can be summed up in one sentence, and is useful enough to "force" everyone to understand it. Having them be able to do "real" calculus on complex equations isn't necessary, but they should be able to understand the rate of change of something and how to calculate that rate from the something, or calculate that something from the rate and a starting point. That's basic math and I think should be in elementary school, not held back to select few in high school and treated like cancer in college.
Learn to love Alaska
The question in the title "How much math do we really need?" is really the author, Mr. Ramanathan expressing a low opinion of his students, a low opinion of a textbook he used in his classes and a low valuation of all students.
The pesky word "need" is the pivot point for his sophistry.
If your educational model is to create truly educated men and women, you need at least a quality geometry course and four years of college level mathematics.
(See the curriculum provided by the great books colleges, St. John's College at Santa Fe and Annapolis.)
In my opinion, the two great fields of mathematics are: Calculus (based on limit theorems) and Topology (based on Euler's polyhedron theorem). The calculus has been over emphasized and topology has been seriously neglected.
To be real specific, the high school curriculum could really benefit from a topology course that would cover knot theory (with matrix math), paper folding (with solution of equations), lattices, symbolic logic, network theory (with walks), and surfaces(with klein bottles), and an introduction to fractals. It could be parallel to Algebra I.
Topology has both the beauty of pure math and a wealth of applications. Unlike calculus, in knot theory for instance, after a couple days' study a student can encounter unproven theorems.
Right there: obvious things that nobody has been able to prove in 50 years! Yeah, how does that affect the development of your "educated person"?
I understand that many may not need much math in their day-to-day work, but I think society as a whole would benefit greatly from a better understanding of math(and logic as well). I agree that the higher-level concepts may not be necessary, but perhaps a general class about the application of math to life would be useful?
A lot of people don't know how to budget properly. They don't know how to calculate compound interest rates for retirement, how and where to save in proportion to thir need, how to pay down debt for maximum efficiency. They see big numbers and have no idea how to get those numbers into perspective. They get scared off by numbers and are too afraid to peek at the federal budget and get a real understanding of how much money is "a lot" of money. Statistics can mislead people who don't understand how easily statistics are manipulated. We're all connected in this society in one way or another, and if we lose proficiency in math, our society will suffer in many small but significant ways.
I think that the bigger problem is that, in order to make the math teachable to masses, we often make it repulsive to those who have the potential to become specialists in math. They often reject math as boring, rote memorization with no creativity and insight.
AccountKiller
They've already shown in other research that children are capable of making up lost ground in math if math instruction is delayed until the brain is more developed and ready for it (we currently push basic arithmetic on minds not fully appropriate for such instruction). How much would engineering, physics, and other math-intense fields suffer if students had to do more of the math work later in their education, or even at college? College courses are generally more aggressive than high school courses. What would the implications of delayed math instruction be on these specialized fields, then, and the students who enter them?
Rent? 20 years? WTF?
If you *plan* this, you'll be either paying no rent (parents, siblings, aunts, uncles are the obvious first-level support mechanism here (and obviously you should support them right back... learn to plumb, do electrical work, light contracting, etc.), 11...13 years worth, maybe less (or even a LOT less if you invest), (not 20!) for the 100k example... plus often they'll help financially if you show you're being responsible and they can afford it), or sharing your rent with like-minded roomies.
Also, if you're *in* the house, you'll be paying taxes (and probably a lot of them if its a 100k home on (at least) a normal lot), as well as upkeep and any improvements, as well as house insurance, buying lawn mowers, etc. Being in the house, while relieving you from paying rent, exposes you to quite a raft of other expenses, some of them quite substantial and many of them unanticipated. By the time you budget out for them, the difference between those costs and rent will narrow at an amazing rate.
No... instead, when you're ready to buy, you get right in there, you have NO mortgage payment, no risk of losing the home to the lender and almost none to the taxman, and you have the funds in pocket to deal with whatever comes up. You can also sell it at any time, and *all* of the equity goes right to you - whatever the market will bear. You can insure, or not, as you choose; because the lender is unable to tell you how to handle your affairs. Likewise, your taxes won't be taken in escrow, and as a side bonus, to the bank, instead of "that guy with the big home loan", first you're "that guy with a crapload of relative liquidity, and after that you're "that guy with 100% equity in his home." which, if you're smart, you'll leverage into getting them to hand you a higher interest rate on your money. And soon you'll be "that guy with a crapload of cash. Again. And all before your original 15-year loan would have been up.
No, I'm afraid there is no "get a loan" scenario that can beat simply saving money at approximately the payment rate, if you simply use your wits.
I will grant you that there are many ways to do it wrong, and many people seem to specialize in finding them, but if you do it right... you win, and the lenders never have a chance to get a chunk of you.
Lemme point out a simple number. We've been talking about putting away under a grand a month. That's $12,000 a year. As an IT guy, I'm just going to go ahead and assume that's less than 1/3 of your income. 1/3 would mean you were making 36k. There aren't too many IT folks making less than 36k on here, I hope. And if so, I'm sorry, really. But let's say that you make 36k. You save 12k. That leaves you with 24k a year to live on. Twenty-four thousand dollars.
Would you seriously take the position that you could not live on $24k? I'm not saying it'd be lovely and you'd eat crab every evening, I'm just asking you: Could you live on 24k, about $2000/month, for a decade? While enjoying the knowledge that your WORTH is zipping up towards $100,000.00?
Of course, that's assuming you're not a couple and have multiple incomes... then you should be able to save a LOT more and so the term should be a LOT shorter unless you make the choice of spawning early, and in that case... well. [hollow laughter.]
It *also* assumes you don't light up and work two jobs for a decade, while you're young and full of piss and vinegar. If you can put away $12,000 from your normal job, and another $10,000 from your burger-flipping 2nd job... you'll have your home very quickly indeed. And if you're a couple, and you *both* work two jobs... yeah, you get the idea. Should take about three years.
Another reason to do this when young is because not only are you probably in possession of mo
I've fallen off your lawn, and I can't get up.
The problem is that we don't *know* in 7th or 8th grade who is likely to need more math 5 or 6 years down the line. Most kids, if you tell them in 7th grade that they can stop taking math, they're going to. Then they hit junior or senior year of high school, realize they want to be an engineer, and they have none of the needed mathematical background. Basically we teach 4-5 years of advanced math to every student in the country, so that the 10-15% if them who will actually need it, have it. It's wasteful as Hell, but I can't think of a better way to do it without forcing life altering career choices on 13-14 year olds.
I agree. Considering that Albert Einstein had trouble with Math, I don't think there's any predictor we can use that wouldn't be more wasteful in disallowing brilliant mathematicians from finding their talent. It's just the way the world works. Finding a needle in a haystack requires effort. Once you've found the needle you can't dismiss the effort of looking through the rest of the stack as wasted.
These posts express my own personal views, not those of my employer
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.
Several problems with this:
- Non-specialists teaching math will lead to poor results
- Repetition in different classes for different disciplines
- Mathematical notation and technique would likely fracture even further
If you had separate classes but some synchronization in teaching the technique in math class and applying the technique in other classes, you'd do better. There should be at least one interesting and relavant example given in the math class too.
These posts express my own personal views, not those of my employer
No disrespect taken.
I was a service tech for my entire career. That was made possible by my understanding of the theories involved in electricity, steam, heat transfer, combustion, etc.... I never had to do the grunt work that almost everyone who gets into the trade does, and had a better technical understanding of the systems I worked on than any of my bosses, except for one. He was a retired NASA engineer and one of the two smartest people I've ever met. The other was an Egyptian guy who was working as an engineer for Boeing when I met him.
I'd disagree on the bit about guys who don't understand the theory still getting things done. When you have guys trying to use an ohmmeter or ammeter without the requisite background in electrical theory they have no idea of what the meter is telling them. They're guessing at what the problem is, and acting as parts replacers until they change out the failed part through trial-and-error. I don't know how many times I've watched guys measure the resistance through the windings of a 240v motor, see 20 megohms resistance, declare the motor good because there was connectivity, and want to start replacing controls, or misdiagnose a controller and want to replace an expensive motor. The same goes for almost any electrical component. You don't understand how something is supposed to work, it's extremely difficult to diagnose it.
Plus, basically you have to reverse engineer many systems in your head to troubleshoot them as documentation can be non-existent in the field. You end up having to figure out how a system that has components in several locations in, and/or on top of, a building is supposed to work before you can start figuring out why it isn't working. It's a challenging and interesting way to make a living. I enjoyed it.
"while democracy seeks equality in liberty, socialism seeks equality in restraint and servitude." de Tocqueville
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.
No, I meant before grade 7. The article, that I'm thinking of, as crazy as it seems, said that boys could pick it up easily in grade 7, and that they were not really ready for it until then. I know. It sounds crazy. I'm not defending the view. I'm just adding it to the discussion.
As for those who want to do math, I'm very confident in the nerd community's ability to produce a great text book that fits all standards, and that could be licensed to the Creative Commons. I believe that Math is 1 of the few subjects that most people can do via correspondence.
Even learning an instrument is easier these days because of YouTube. Most my music practise is done with a web browser and a PDF viewer [and not while using an actual instrument], and I'm preparing for intermediate-advanced level music that will be played in an actual concert.
testing out my trending skills
What do you mean? You disagree?
testing out my trending skills
Most schools I've heard of require less math than basic calculus for non-technical majors. Some sort of stats or basic algebra is the norm.
I'd also add BASIC statistics, so people can grasp the relevance (or irrelevance) and impact of a basic statistical analysis. There are few things more annoying (to me) than taking a perfectly good (statistic) factoid, and distorting its relevance to support idiocy, whether its sports stadium funding or creationism.
There is no America. There is no democracy. There is only IBM and AT&T and DuPont, Dow, General Electric, and Exxon
I did find that I had to use Calculus once, about 12 years afterward in the real world.
I had to calculate summations; learned in Calculus II.
Either I could do it in Excel, and take 50 pages to calculate it, or I could summarize it into a nice little Calculus formula.
I couldn't figure out how to create the formula at the time, so I went ahead with the brute force method and created 50 pages of Excel to get my answer. Thank heavens for Excel.
Then the following day, I looked at the problem again, and derived my simple formula to solve my problem. A skill which I had once learned 12 years prior in some Calculus class I took in College; while questioning, when the heck was I ever going to use such a knowledge in my life.
Now, I can plug that formula into a program, and it will help me solve more questions that would take me 200 pages of Excel to brute force calculate.
Times like that is when you appreciate the beauty of math.
The median pay for an engineer is above the median pay for a worker. Therefore, we have a shortage of engineers.
That proof is legitimate for any field that doesn't involve bidding wars for superstars and/or a fixed number of positions. It's wrong for things like pro sports, but it works perfectly well for anything normal.
Im sorry, but we are talking about math and you are using those funny units no one understands. Even funnier that you mention Nasa.
Who logs in to gdm? Not I, said the duck.
Not really, the public can't seem to grasp the idea that the benefit to mankind is in the details, and wonders why we need something that has no generalists.
I don't have personal experience to back this up, but it seems that there must be generalists in the math world.
Anyone that applies their knowledge for the purpose of peer review is entering the realm of something resembling a comparative generalization of the math.
It is possible that only specialists attempt this feat, but once they are off and running they are participating in a potential merging of the proposed maths or perspectives with their own.
This process requires reflection and moderation as much as rigorous mental manipulation to establish proof; requires generalization by a specialist.
There is a parade of history detailing centuries of mistaken scientific wisdom and I have noticed that folly seems to follow those that misplace faith in the practice and not the practitioner. When the faith is given to the practice the following hellhounds start licking their chops: the public expectation of continued success, the realities of funding acquisition, the competition of commercialized thought, and the inability to separate oneself from one's accomplishments.
When this happens science fails mightily, ego comes to the fore, and folk start raging debates about the metaphysical properties of aether or some such business.
When the specialists involved demote the tools to the toolbox and keep their vision about them even as their heads are down you get legends. I wasn't there, but I think Bell Labs is a good example this type of success, and I hope more people start aiming for more cross pollination, generalization, peer review, and open processes.
I'm not sure we could know anything without knowing a first thing and extrapolating from there. Generalization is key to this process and maths are not exceptions. Put another way, those that live in interesting times get interesting opportunities - so before and after you are immersed in your science keep your head on a swivel, you might be the next great cross pollinator.
Put yet another way, your science came from somewhere, but much like good encryption and learning to read, you can't easily divine the perspective that formed the system by analyzing the system itself. The most fundamental math is in the fact that math can exist within our purview. Tripping out on this cannot be left to transhumanists, cosmologists, and philosophers if we hope to wield our specialized knowledge with wisdom in an increasingly crowded world without requiring transhuman salvation.
On a stack-based calculator, you should get 100.
When you press "+", you get a stack underflow error. Continuing on as if nothing had happened, you enter the "10". When you press "*" you get another stack underflow error. Continuing on as if nothing had happened, you enter the "100". That just sits there. (you are supposed to do "100 ENTER 10 * 5 +" instead)
Getting 1500 would be really defective. Are such calculators actually sold?
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.
Calculus (and some other advanced math in specialized schools) was included into secondary education course. Students and teachers were moaning, but somehow struggled through. There were no noticeable impact on common workers, but engineering college students were a lot better prepared, and had easier life (advantage they used to drink more). Education ministry of modern democratic Russia decided that advanced math is harmful for working people, Russia don't need many engineers anyway, and advanced math was removed form curriculum.
Thank God for that. I no longer feel ashamed of being horny whenever I see roadkill.
The new right fascists are bilingual. They speak English and Bullshit.
Unlike literature, history, politics and music, math has little relevance to everyday life.
It just seems like lots of people are missing this point. Another point that's getting missed is
That courses such as "Quantitative Reasoning" improve critical thinking is an unsubstantiated myth.
This may or may not be true, but many of the counter-arguments I've read take it as given that math courses improve critical thinking. Personally, I tend to agree with the article, but it doesn't provide enough evidence to truly convince me. That is, I run both inductive and deductive reasoning when considering arguments; my inductive reasoner says "yeah, I think that's right" and my deductive reasoner says "but it's not rigorous enough to really say".
Actually most 1st year micro/macro economics courses are taught with basic high school math, because the students haven't learned calculus yet. Apart for supply-demand curves, which just uses exposure to basic graphing, I remember a lot of it as trivial algebra. There's probably more psychology in there than advanced maths at that level. While that level of econ is certainly simplified, it's enough to make me correctly identify as BS a lot of what I hear demagogues pushing.
Don't get me wrong, I think most people don't get enough exposure or experience in abstract reasoning that maths give you. Heck it's apparent that just some basic logic and critical thinking would go a long way! But if you're going to vote on things which have world-ranging implications, then you should be able to understand enough about the world to see a) the broad strokes of those implications and b) detect when you're getting a snow job. Otherwise, you're just asking for someone to game the system.
Laissez lire, et laissez danser; ces deux amusements ne feront jamais de mal au monde. - Voltaire
I think notion that people don't use math in their lives is very much misguided. Example of compound interest in another post above was an excellent point. We think we don't need and don't use math, but that's only until we go to a bank for a loan, try to check our bill from a vendor, endeavor on a nontrivial household construction project requiring some geometry, or try to understand something about politics and economics around us. Then we remember and apply our math skills, but somehow this doesn't factor in the argument about "uselessness" of math education.
What people mean is not always what they say. If one wants to simply know what they said, anyone can just read it. One may want to conclude that they meant nothing beyond that, and that's fine... but that's not generally the point of literary analysis... it's to search for any deeper meaning beyond the literal words themselves.
File under 'M' for 'Manic ranting'
First of all, probability at an elementary and high school level is generally a matter of motion for nearly all students which take exams on it. If you doubt this, check out the massive number of people gambling online. The fact is, people don't grasp even the slightest concepts of probability in relationship to mathematics. People get excited over statements like "a 500% better chance to win!", but first of all, they don't ask "better than what?" and "what were the original chances". That 500% better chance actually just made it so that they still would have a better chance of getting hit by lightning... in their shower... in a sealed underground bunker... with water provided by an underground storage reserve.
There are many people who use probability for the majority of their decisions all day, every day but couldn't calculate the number of possible outcomes from a roll of a pair of dice. They don't understand probability, but they do survive based on subconscious decisions such as "If I start walking across the street now, the car driving at me will have a chance to see me, then will manage to stop in time to not turn me into roadkill". This is a probability related gamble, but it's based on experience as opposed to pure probability logic.
This is a topic that we often call common sense (or lack-thereof). Even an uneducated coal miner will teach it to his children. It is often something we learn through experience. If we actually took the time to calculate out whether the car will have a chance to stop or not, we could just wait for the car to pass instead... and the 50 cars following it.
I personally prefer that we focus more on boolean logic and discrete math with kids at a young age. Let us force them to learn how to think past a single level. The average person has the ability to identify cause and result at a single level, but can not cope with any complexity introduced by conditions when calculating a second level. For example "If I go to school today, I'll see my friend Jesse" is easy to understand. "If I skip school today AND wait beside the building on 3rd, but NOT between 1pm and 2pm when the principal passes there on his way to and from lunch, the I can see Jesse AND NOT have to take my math exam OR eat a terrible cafeteria lunch" is far more complex.
Demorgan's theorem is one of the most useful topics in solving daily life problems. We often waste a tremendous amount of time waiting for condition A and condition B to be true when we could instead take a moment to verify that either condition A or condition B are not true.
I have personally spent ages waiting to go do something because the person I'd like to go do it with insists on waiting for either two positive or two negative conditions to be true. When you try to explain the simple laws of logic to the person who is forcing you to wait, you might end up losing a friend for making them feel stupid over their flawed logic.
So, forget probability which is hopeless to teach anyone anyway and focus instead on logic which should be taught side by side with addition and subtraction from the time a child can write their names.
Even though we'll never really teach it to the people who never learn it at any age, it will teach them to subconsciously think more intelligently. Beat logic into their heads from a young age and maybe when they're making plans or decisions, they'll actually think things through a bit better without even knowing it.
That being said, as a father of a 7 and an 8 year old, I talk with teachers in schools, teachers who are parents etc... quite often. Some of these are even math teachers and frankly, I find that most teachers are utterly incapable of teaching logic to anyone since they haven't learned it themselves. Such and insanely easy topic is incredibly complex for the majority of people out there.
With out Math? What does it mean?
Math is and has been foremost about solving problems. Real world problems. Get to the moon type problems.
How do you balance you checkbook type problems?
When are we going to get there type problems.
When are we going to get to a society that values Economic and Social competencies as well as cultural awarness?
Certainly not watching TVs Jersey Shore.
Professor is brilliant. Slow news day.
Professor is a blathering idiot! Slashdot front page news! Get it while its hot!
The same goes for whatever subject you sucked at back in highschool.
We should be pushing for everyone to learn Latin by the time they finish high school; how else would you become a doctor?
The point is that most of us won't become doctors. Just like most of us won't ever require anything beyond a basic understanding of math.
Slashdot social media options: AIM, ICQ, Yahoo, Jabber and Mobile Text. Why no MySpace?
There was a need for me to examine the spreadsheets at work that the middle managers were using. There wasn't a single one that didn't have an error. There were some with massive errors. I guess the argument is that they don't need math if no one cares if they can't do it. But the the difference between being able to muddle through and the ability to do a correct job may just depend on math. Even for middle managers without a degree in anything that emphasized math.
Learn to love Alaska
Actually, it is widely human to have small memories. The typical person can hold 7 numbers in their short term memory at a time. A phone number. However, I know I can take at least 10 hours of advanced college lecturing before my brain starts to hurt. I have no doubt the average person could take at least 2 or 3 hours of solid lecture a day if it was done well.
The only time I have seen people struggle with complex concepts is when certain important steps are left out. Nationalization of education and utilization of things like Khan Academy could really help this along.
Those who only rely on memorization have to put in a good 10 hours of studying a day on top of school to get through a regular high school program. You can do it, but it is a lot more work. I know sitting along side fellows in high school, I owned them in terms of understanding for only a small fraction of the effort. It just depends on how well those concepts were presented.
Where is the mod rating for "scary"? Also,
Teaching math isn't about teaching a specific skill that everyone will use, it's about teaching how to approach problems quantitatively. ... 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.
I agree with your post. However I believe it goes beyond only the actual math skills. Math and physics force us to think beyond the obvious, and help develop the growing brain of a teenager, precisely when it is needed. Studies show that although no more neurons are grown during the teenage years, connections are still being made, and a pruning process takes place, which removes those skills not being used. Math exercises those connections and creates new ones, helping the person acquire capacities which may be more difficult to get afterward.
"On a long enough timeline. The survival rate for everyone drops to zero." - Chuck Palahniuk, Fight Club
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.
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.
But what happens if you had gotten the 20 year loan at 6%? With the 30 year loan paying $103.50 a month over coupon rate at 6.5%, if you could pay it off in 20 and get a 6% interest for that, you'd have payments of $716.43 rather than $735.57. You waste money just to prove yourself a jackass on slashdot.
If you make the term for exactly what you can pay off, then you are making the best choice. To purposefully get a longer term than you could and pay it off early to feel better is a very poor financial decision. The only time to make that decision is if you want the flexibility to not pay the extra if your circumstances change.
Learn to love Alaska
Most kids, if you tell them in 7th grade that they can stop taking math, they're going to. Then they hit junior or senior year of high school, realize they want to be an engineer
So the minute people have real educational choices within sight, they start thinking about them. I say give people real choices in education much earlier.
It's wasteful as Hell, but I can't think of a better way to do it without forcing life altering career choices on 13-14 year olds.
Good sense comes from experience*, not age. The reason I agree that it would be unresponsible to ask 13-14 year olds to make career decisions is that they have no real idea about what various careers are like, because they are forced to spend all their days in school, which only teaches them about two careers (teacher and administrator) and only from the consumer side, not the producer side.
It might be a good idea to let kids intern where applicable, or just sit by and watch if nothing else is going to work, such that they have first hand experience in various trades and can make informed choices at age thirteen.
(* experince comes from bad sense)
If you stop infantilizing teens, you'll see them as adults wanting to have real responsibility along with some freedom to choose it and to manage it.
the style of critical thinking that is exercised in literary analysis
"Agree with teacher" is a kind of critical thinking?
Then maybe I didn't get the message. I would be happy if you would explain to me the point and purpose of literary analysis, or some of the take-away messages that can be applied in my life.
For comparison, history is "a video running in a loop, in which a small group of people try to dominate and extract resources from a much larger group of people" (paraphrasing Brett Veinotte of schoolsucks.podomatic.com). The point of studying history is to learn how to affect societal change and how people might try to extract resources from you.
Advanced math in school useful in support for education of big number of engineers. Otherwise it has no impact.
No, I'm afraid there is no "get a loan" scenario that can beat simply saving money at approximately the payment rate, if you simply use your wits.
This didn't work when house price inflation was rampant. Despite my salary increasing by substantially more than inflation (compounded) it's only been in the last four years or so I would have been able to buy with a mortgage the properties I own outright because house prices rose so much faster than inflation.
I, of course, used my above inflation salary increases over the years to pay off my mortgages.
Borrowing money to buy my second car was also a good move. The reduction in fuel and maintenance charges more than paid the interest on the loan (in fact the reduction paid the interest plus the repayments so for three years I saw no net cash flow change and then on year four I had an extra 190GBP/month). At that time in my life there is no way I could have saved enough money to buy the car outright when I needed it. I was never desperately short of money but for the first three or four years of working life I was definitely not flush with cash.
Tim.
God said, "div D = rho, div B = 0, curl E = -@B/@t, curl H = J + @D/@t," and there was light.
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?
>>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.
The cells in spreadsheets are essentially variables, and so all the stuff you do inside of a spreadsheet is essentially algebra, even just very basic stuff like averaging a bunch of data and projecting it out for the next five years will be very error prone if you're trying to do it by rote without having even an inkling of algebra backing you up. Sure, you may never use the binomial theorem, but I'd honestly say that algebra is amazingly more useful than people give it credit for. Less so with trig and geometry, certainly. Calculus is more useful than trig and geometry, though in order to study calculus you have to know trig, I guess, and trig relies on a foundation of geometry and algebra.
So really, the order we teach math makes sense, but ignoring probability and statistics seems criminal to me, since they're much more applicable in real life, and are very useful for logical thinking and bullshit-sorting.
"Right, because high school students make such good choices about their futures."
Did you read my comment?
"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!
People should have the basics of velocity and acceleration before starting physics 101
which is great for the kids who might ever or will ever do physics 101.
there's no shortage of kids who know damn well what they want to do and it's not physics 101.
We should also be pushing for everyone to learn ancient greek and hebrew.
Sure it's utterly useless in just about everyone's lives but damnit everyone should be interested in my hobbies!
The problem is that people are afraid of ancient dead languages, not that they really can't do it.
none of which requires anything like the kind of stuff which you'll find on most HS math courses.
most people need the basics and a few applications of the basics far more than they need linear algebra or differentiation.
I'm pretty sure I've related this story on here before, but here goes again.
I used to work for West Australian Police (as a civilian) and one of the things I used to do was look after juvenile delinquents. I had a high school kid with me one day who tried telling me that maths was crap and he didn't need to learn it etc.
I asked him, 'If you were offered a job for $400 a week or one that paid $50 an hour for 40 hours work a week, which would you take?'
He insisted the $400 a week job was worth more than the $50 an hour x 40 hours job. I had to explain to him that the $50 an hour x 40 hours a week was $2000 a week. He still insisted for a while that the $400 a week job was more. It was hell trying to get him to think it through.
But, the main point is, how relevant is the maths we are teaching now a days to what they will use. Many will need at least basic skills and they will need those skills re-inforced as they go through school. If an average kid in High School can't tell the difference in pay between a $400 a week job and a $2000 a week job, then society has failed. Good skills in the areas that they will use in every day situations (like not getting ripped off for change or bank interest etc) is important. Learning how to calculate the area under a curve using calculus, less so for the average student.
Sure enough, the cow costume was hanging up next to the superhero outfit and sailors uniform. (S,Spud)
When I asked my third grade teacher what use I could possibly make of Venn diagrams in everyday life, she told me "when it happens, you'll be happy that you know them." It's been almost thirty years and I'm still waiting for that day when I face a problem on the street or at work that can ONLY be resolved by a Venn diagram...
I think it's a bad strategy to say things like "kids who have no talent for math." It's this rather antiquated view of education that's contributing to the problems.
I'm of the opinion that geniuses aren't born, they're made. Everyone - some specific, diagnosable medical problems notwithstanding - has the potential to excel at any discipline if they put the effort into it. The real difficulty, which was expressed by an earlier poster, is getting people to care enough to put in that effort.
Basically you're giving up on these kids rather than giving them the opportunity and motivation, which is a great disservice to their potential.
The world really doesn't need more ditch-diggers... we have machines for that. Machines that were designed by people who had the motivation to learn mathematics.
=Smidge=
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=
Seconded. I picked up a math minor in college so that I could understand what was going on in my quantum mechanics classes. The semester after I graduated, the university created a "Math For Chemists" course that condensed the necessary maths into a single semester. Had that course been created earlier I could have saved a lot in tuition money and still gotten the neccesary information I needed to pass the rest of my courses. Yes, studying math for math's sake yields useful results, but not everyone has the inclination or the time to do so.
Only two things are infinite, the universe and human stupidity, and I'm not entirely sure about the universe - Einstein
I think you're right:
Acoording to Wikipedia (http://en.wikipedia.org/wiki/Tinplate), tin-plated iron was used for cheap pots, pans and other holloware. From the term "tinware" it is not far to "tin pan", which is probably what the Fermis used.
C - the footgun of programming languages
I hate to tell you this, but your core premises are wrong. Continuing to argue with you would be like trying to convince a creationist that evolution is correct; you're so whacked that it won't do any good.
The real shame of it is that it's people like you who are doing real damage to the country, always criticizing with no productive ideas, trying to tear down the very institutions that DO work well and that made it great.
It would be nice if all the people exposed to political ads and then voting would have a basic understanding of statistics.
no, your attitude is the one doing these kids a disservice.
I've seen people destined to be fantastic linguists waste huge amounts of their time trying to cope with imaginary numbers and similar useless crap?
Similarly kids with a knack for math forced to sit through the musings of some failed author about the meaning of flowers in the writings of a dead poet.
why?
because people like you who think that kids are all to stupid to know what the hell they like or want.
Some of them are. pleanty of them know damn well what they want to do and shouldn't be help back for the sake of the indecisive.
tallent, interest, personal liking.
call it what you like but some kids click with certain subjects and have the potential to be great at them.
Then someone like you comes along and insists that no, *insert their favority pet subject* is far more important than *whatever the kid is good at or loves doing* and insists that the kids waste their time on things they don't need, never will need, don't like and are not good at rather than what they have a tallent for.
I learned Latin at school from being 10 up to 17 years old. That's quite common in Germany on public schools and the idea is that it makes you learn other roman languages more easily, trains your sense of logic and educates you to learn stuff you can not directly apply anything.
And being capable of translating roman inscriptions impresses friends who are not from old Europe :)
The point I'm trying to make is that a child's brain needs challenges, math, languages and history are good, complex challenges and learning them not only trains your brain but knowing them gives a common cultural base.
I've long felt that math teaching would be much more successful if there was more context ie what could I use matricies /for/
I recall the many happy hours I spent optimising ship/mecha/whatever design and that started me toying with the idea for a game (computer or board) that could put maths into some sort of context (for boys at least :-)
The main element of the MathFleet Battles would be and intentionally complex the ship design system set up in such a way as to allow many optimal ship designs and many many more non optimal ones. The rules would imply (but not state) questions like:-
The optimal battleship shape is a sphere, but the Meson Cannon is a long spinal mount weapon which increaces power with length what is the optimal shape for the ship.
The probability drive has a 2/3 chance of hoping the ship in a random direction forward and a 1/3 chance Drives come in a number of models with different jump lengths, jump frequency's and power consumption. Which is the best one for your particular ship.
How many mine dispensers do you need to have a reasonable chance of hitting a following ship if each mine has a 1% chance of hitting.
The object of the game would for groups to design be best ship they can and the try and blow up the opposition.
A group that had worked out that if they could would out that if they had X mine dispensers would give them a 65% hit chance and still leave enough room to pack a dozen extra medium lasers, which, between the systems would give a 95% hit chance
During the 1770s 1780s, common practice was for college bound 13-15 year olds to just attend college. I'm not sure what the supposed need for high school is, other than to give people 4 more years to learn what they ought to have learned in middle school / grammar school.
...
If you help me find the Time Masheen, I'll pay you like 4 billion dollars.
...
The "Mechanical Universe" includes an animation of rocket with velocity and acceleration graphs: http://www.learner.org/resources/series42.html
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Methinks the troll tag on this article is most appropriate. I almost spit my Cheerios on the floor yesterday when I read Dr. Ramanathan's article in my local fish wrap. I'm guessing his intent was to proffer the most basic straw man so as to spur discussion as to how to make math education more effective in modern society. I offer this forum as my first point of evidence.
US2B
You're right!
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Good catch. You're right, that is an error in my math of cubing 5 as an incorrect 75 and not the correct 125.
Still close though. :-)
Maybe we should mostly teach kids how to use the free equivalent (someday) of Wolfram Alpha?
http://www.wolframalpha.com/
http://www.wolframalpha.com/input/?i=5+*+5+*+5
http://www.wolframalpha.com/input/?i=5+cubed
Of course, that might make it too easy to take things completely on faith: :-)
http://www.wolframalpha.com/input/?i=weight+of+the+earth
"5.9742×10^24 kg"
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
except I would change it to read: unlike math, literature, history, politics and music have little relevance to everybody's daily life.
If you are not allowed to question your government then the government has answered your question.
No, the point is that it will better prepare those who do choose to become doctors, ultimately enabling more American students to choose better degree paths than "fry cook."
When you're afraid to download music illegally in your own home, then the terrorists have won!
The weight of the Earth comes in useful in calculating how many space habitats you could build from it. :-)
Let's see:
http://en.wikipedia.org/wiki/O'Neill_cylinder
http://www.newworldencyclopedia.org/entry/Space_habitat
http://ramblingsonthefutureofhumanity.blogspot.com/2009/10/designing-space-habitat.html
You can support 15 million people with a habitat requiring 3000 million metric tons of mass (if I got that right), or about
3 billion tons. (One could also ballpark that mass calculation, but I won't right now, just by thinking about a shell of six feet deep material with some surface area.)
The Earth weighs, as above, about 5 billion trillion imperial tons (close enough to metric tons). So, if we vandalized and vaporized the Earth to build space habitats (not that we know how yet), we could build a trillion space habitats that each support 15 million people. Or, that would be about 15 billion billion people, or about a billion times more people than the Earth supports now. I have not double checked that, but it sounds more or less right within a thousand or so. :-)
Anyway, while I don't recommend disassembling the Earth to make way for a space habitat(or hyperspace) bypass, as there are plenty of asteroids and moons in the solar system that are easier to use for mass, and it makes sense to preserve Earth as a historical landmark to our past, this points out that people like William Catton who are spouting imminent danger from "overpopulation" are more just lacking basic math skills and some imagination. :-)
"[p2p-research] Earth's carrying capacity and Catton"
http://listcultures.org/pipermail/p2presearch_listcultures.org/2009-August/004123.html
"Bottleneck: Humanity's Impending Impasse, by William R. Catton, Jr."
http://www.theoildrum.com/node/5954
Contrast with someone who though the empowered human imagination was the ultimate resource:
http://www.juliansimon.com/writings/Ultimate_Resource/
These calculations have life-and-death consequences as relate to human wars and decisions about having children or abortions. Seriously. Whether someone is stockpiling ammo for the "overpopulation die-off" or trying to get a job at NASA or private or volunteer efforts to build space habitats or even just design better solar panels hinges on this sort of basic math.
The consequences that flow from this simple calculation about the weight of the Earth and the weight of a space habitat in comparison are politically profound. They suggest we should not be fighting over oil as a form of dogma-driven collective "suicide" but instead should be putting a lot of time and effort in developing a serious space program and other advanced technology, but from an abundance paradigm where the wealth is widely shared, not a scarcity paradigm where wealth is tightly hoarded. See also my essay:
http://www.pdfernhout.net/recognizing-irony-is-a-key-to-transcending-militarism.html
"There is a fundamental mismatch between 21st century reality and 20th century security thinking. Those "security" agencies are using those tools of abundance, cooperation, and sharing mainly from a mindset of scarcity, competition, and secrecy. Given the power of 21st century technology as an amplifier (including as weapons of mass destruction), a scarcity-based ap
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Ancient Greece and Ancient Rome did not have compulsory education, were they not "advanced" for their time?
The Haudenosaunee (Iroquois) had no compulsory schooling as we know it hundreds of years ago, but the USA borrowed ideas from their society for its constitution.
The USA did not have compulsory education for most of the 1700s and 1800s. Was US American not advanced for its time? Was it perhaps in some ways more advanced back then, as Gatto suggests, with more independent self-educated people with a higher degree of literacy?
Anyway, another reply by someone else (who you may have confused with me?) makes a related point.
There are lots of better educational alternatives than compulsory mainstream public schooling listed here:
http://www.educationrevolution.org/
Why not just give the money that now goes to compulsory schools directly to the parents to let them decide how to spend it on their children's behalf? A related specific proposal:
http://www.pdfernhout.net/towards-a-post-scarcity-new-york-state-of-mind.html
And if you say, you can't trust the parents to look out for their own children's interests, then what does that say about the value of thirteen years of compulsory schooling?
Anyway, there are lots of alternative ideas out there if you look around with an open mind. But the whole point of compulsory schooling is to close people's minds and distract them. That may not be the intentional purpose of most schoolteachers, but it is the end result of the systemic process, and as Gatto suggests, that process is doing exactly what it was designed to do, so if you give it more resources, it will only dumb people down faster and more comprehensively.
See also from a previous vice-provost of Caltech and a previous editor of Physics today that say related things:
http://www.its.caltech.edu/~dg/crunch_art.html
http://www.disciplined-minds.com/
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
G.V. Ramanathan expresses a common ethnocentric egotistical point of view of Academics. Math is more than equations and numbers it leverages brain power by giving the possessor the power to think and make decisions in quantitative rather than qualitative terms. Second those gifted with math abilities do make it through a educational system that teaches math so poorly that it creates mental illness. Everyone has the ability to learn math, which is after all merely a language. The problem is that the ability to learn languages must be exercised before it atrophies. I do agree that the approach to encouraging math is flawed, Kindergartners should be graphing lines instead of learning to do calculations. The need is for math is much greater in today's information age than in the industrial age. In fact math is as important in the information age as reading literacy was to the industrial age. Math ignorance leads to science ignorance which today is seen in the climate debate. This debate is not scientific but political and only exists because of math illiteracy of the American public..
And who decides what knowledge or skills (including unquestioned immediate obedience to authority as exemplified in classrooms?) are important to a child's present or future, or the present or future of the culture they live in?
Who picks the hoops a person is forced to jump through (in a democracy)? The person? His or her parents? Neighbors? Elected officials in the community? Big foundations? How should these different voices be balanced in a democracy? What are we trying to achieve as a culture? Do some of these voices (business concerns?) have a stronger influence than others (like Gatto suggest)?
What different views are there on this?
http://www.mindfully.org/Reform/2003/Compulsory-Schooling-AnarchistMar03.htm
"The history of the development of Western schooling is a complex and meandering thing, but I think it is worth looking at in a very abbreviated form here. A little insight into the logics and basis for contemporary compulsory schooling might be useful to social ecologists."
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Nice strawman there.
You're the one that is advocating burning bridges but cutting back programs, not me. It's not that "my favorite pet subject" is more important, it's that "your least favorite subject" is not less important. Your hypocrisy is almost palpable.
We should not be cutting back programs like math just because you (or the article) feels it's a waste. We should not cut back on any subject, and we should work to make all subjects more appealing and encourage students to put their efforts into them.
Furthermore, being good at math and good at linguistics (to use your example) are not mutually exclusive. Shame on you for implying they are and shame on you for perpetuating the mythical idea that people are born/destined to be anything in particular. That very concept is self-defeating.
=Smidge=
The question of what to learn, or who decides it, is irrelevant. The point is simply that testing has been proven to improve retention. You can argue social policies all you like, but it won't change this basic fact.
Higher Logics: where programming meets science.
WTF? I just gave you a productive idea in my previous post: break up the country.
And exactly what institution that works well did I tear down? Our education system in the USA is an utter disaster. The only governmental institution that really works well in the USA (I know the libertarians will disagree) is the USPS. They deliver my small packages across the country in 2 days for far less money than UPS and Fedex want, and they don't break them like UPS does to everything.
If you think our pre-college education system works well, then you are an idiot. Your idiotic post definitely deserves the Flamebait mod it got.
I suppose this is a strong argument for teaching a lot more "practical" math and a lot less theoretical math. I actually enjoyed things like calculus and advanced geometry, but I can readily see most people don't need it. What I never got, and what I think everyone needs, is some basic discussion of practical things like interest, taxes, investing, etc.
The Quirkz Handbook of Self-Improvement for People Who Are Already Pretty Okay
Luckily, you didn't catch my own math error... Cubic miles to cubic km requires multiplying by four, NOT dividing by same. ;)
Oddly, enough, my own off-the-cuff estimate (using my approximations), gave me 6x 10^24 kg. Largely as a result of me rounding up on density, rather than down, since I knew my approximations tended to understate volume somewhat.
Note that in general, I agree with you conceptually. I just disagree on just how/what to simplify....
"I do not agree with what you say, but I will defend to the death your right to say it"
I feel that music and literature is important
But which literature? The high school that I attended forces six tragedies by one British playwright on all students. It also forces students to read love-drama novels when their brains are not yet formed enough to understand the motivations of the characters. Under what criteria do those who set the required reading list decide which works are The Classics(tm)?
There are lots of areas we need more math in, but probably not what you think. Logic would be the first one, yes probability and statistics (80% of all statistics are made up) ... not all math is about numbers after all. Oh yeah, I'm always surprised by how little people seem to understand of geometry. No, I don't mean proofs, I mean shapes, filling spaces, general concepts like that.
Yes, I am one of those who likes to curl up with a good Algebra book. But it is amazing how much of this stuff could be used every day if people knew it.
We all use literary analysis every time we read a news site, watch a movie, or myriad other situations every day
Then why do literature teachers teach literary analysis on novels, short stories, and poems, rather than on news sites, movies, or other situations?
apparently even if the director/author/poet personally says straight out that no, their use of some church bells is not a symbol for neo-colonialism or whatever else you've dreamed up that doesn't count because everyone makes their own meaning.
In other words, death of the author. But in the real world, it's difficult to apply death of the author in the literary criticism sense until 70 years after the death of the author in the legal sense because the author or the author's estate still has the exclusive right against certain reinterpretations.
Does anyone NEED math in their life? I'm sure you could get by without it and survive...but you're guaranteed to live a lot worse! Probability, basic accounting practices, decimal/fractional math, and other basic stuff we learned early on may seem simple and basic enough, but few people understand it well enough to use it to their advantage in life! Taking out a mortgage? You'll be in bad shape if you don't understand all the types of loans out there, the benefits of each, and be able to determine which is the best deal for your house. Our mortgage crisis wasn't caused by well-educated Americans making careful and thoughtful decisions! Out shopping? Being able to compare prices and quickly do that basic decimal math in your head (and add or subtract percentages) can save a lot of money in the long run! Beyond all the simple economic examples, I like being able to read the news, whether it's politics, science, or economics, and have a clue what's really going on. Math isn't just for test scores and educational grants, it's so people can understand the world. Understanding math allows people to solve problems better and to apply analytical skills to the world around them instead of judging based on biases, rumor, or the opinions of others. It's lack of science and math knowledge that's allowing people to hold ignorant beliefs and make poor decisions, whether on a mortgage, or on who to vote for in an upcoming election. Will the average guy need Calculus for anything...nope. Will they need alot of other math skills in order to live their lives the best they can? Most definitely!
I had citations everywhere, and everything was either a direct quote or a paraphrase. The extent to which I injected original thought or analysis into this work consisted of conjunctions, articles, and perhaps a two- or three-word connecting phrase in a couple of places.
So in other words, you made it look like a Wikipedia featured article.
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.
I think it might have helped if they increased the pace of your logic instruction.
The Daddy casts sleep on the Baby. The Baby resists!
This is a horrible way of thinking about it. A friend of my father's is a EE Professor at USC, who has studied all sorts of high level mathematics. He freely admits he's probably never going to use 90% of them, but what's important in life is improving your toolbox so that you can solve the broadest range of problems possible. This doesn't just mean math, either - he passed the bar not too long ago because he found that not having a background in law had screwed him over pretty badly. So he worked to improve himself.
The key point here is that as a high school student, you're not going to know where you're going to end up, or what opportunities will be opened/missed by having/not-having certain skills.
It looked to me like the key point was that if you want to improve yourself, it's up to you to make it happen.
I agree fully with your assessment of missing elements of schooling, and I'm glad to see history gets a mention. It's very important not only for politics and business but also for pedagogy and the sciences. Understanding "the shape of things" often gives clever minds insight into how to (or how not to) improve them. The only reason this article exists is because we have all but abandoned the collective experience of teachers gathered since the 18th century in favor of "modern" practices dictated by bureaucrats...
Your brain is not a computer.
As long as we teach what's really going on the the place value system, not stupid tricks like long division and lining up columns for multiplication.
Considering that Albert Einstein had trouble with Math
That's not true.
In fact, he actually excelled at mathematics throughout his schooling and even considered becoming a mathematician for a time.
Some years ago, I helped a colleague at work, who was attending a night-school accounting course, who had no idea how to calculate a simple proportion sum.
(If 5 apples cost $4.00, how much do 12 apples cost? 12 apples cost more than 5, so it's 12 / 5 x 4.00 / 1 = 48.00 / 5 = where's my calculator? ummm $9.60)
He'd passed senior high-school and been accepted into the course on his results.
I don't think things that "simple" are taught any more, as a simple stand-alone arithmetic tool ... something I learnt in primary school (elementary school).
So maybe, to keep it useful and relevant to daily life, more Arithmetic to a higher level needs to be taught (possibly in the simplistic repetitive rote manner it always was taught) and perhaps a greater level of interest in higher Mathematics will result.
Don't blame me, it's usually 2 in the morning when I post
Completely agree.
Some "eternal truths" I'm been relentlessly drilling into my kids:
.
"I don't know, therefore Aliens" Wafflebox1
The weight of the Earth comes in useful in calculating how many space habitats you could build from it.
No it does not. The mass of the Earth might be useful to know though. Since imperial units like pounds and tons measure weight, not mass, you cannot use the normal conversion of one metric ton (mass) to imperial ton (weight) for this because it assumes a constant gravitational field of 9.81m/s^2 which is clearly not the case when dealing with space habitats.
When it comes to constructing real-world things maths alone is not enough and you do actually need some basic physics as well.
What gave you the idea that i didn't like math?
it was my favorite subject, I'm just not so full of myself as to assume that what I like is the be all and end all of learning.
Where did I say I wanted to cut back anything other than wastes of time?
Choice is what I'm talking about.
being good at math and good at linguistics are not mutually exclusive and I did not imply as such (nice strawman BTW).
But if someone is not good at math and is good at something else forcing them to waste their time on a subject they don't like and they're not good at is pointless.
"Shame on you for implying they are and shame on you for perpetuating the mythical idea that people are born/destined to be anything in particular. That very concept is self-defeating."
Sure.
And I also perpetuate the mythical idea that people are born/destined to be tall or short.
If they're not tall enough back on the rack for another hour!
Every child has the potential to be a giant!
Children are different.
Some are tall, some are short, some are good at math, some are not, some are good at languages, some are not, some have fantastic spacial ability, some do not, some have a knack for working with their hands, some do not.
but that doesn't fit with certain naive and deluded views of the universe.
If we could do that in the U.S., you can bet our scores would be a LOT higher too. Just look at the spread in the average city between the good schools and Gangbanger High. Anytime you provide a way for a school to consciously limit its enrollment, that school is going to do a lot better than one that has to take in everyone.
SJW: Someone who has run out of real oppression, and has to fake it.
Education can have several goals in this descending order:
* To help a person grow as a person
* To help a person be a good citizen
* To shape a person into someone elses' vision of a good consumer and good worker and, for a few, a good obedient professional with the "right" politics
I don't find these categories helpful. The third simply informs the first and second.
The Daddy casts sleep on the Baby. The Baby resists!
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.
The argument isn't that most people don't need math, it's that they don't need any more than the basics (arithmetic, probability, basic statistics). Certainly not calculus. Off the top of my head, my friends are: electrical engineer, physical therapist, librarian, restaurant manager, architect, corporate internal relations manager, runs her own daycare out of her house, business analyst for a health care practice, nurse, genetics researcher, state disabilities claim evaluator, lawyer, editor for local news outfit and graphic designer. Out of these 14 occupations, I see electrical engineer, architect, business analyst as the only 3 that would probably require more than basic math (the genetics researcher doesn't; I was quite surprised when I had that conversation with him). Why would any of the others ever need calculus?
...sometimes, in order to hurt someone very badly, you have to tell that person terrible lies. - PA
See what I mean about arguing with "government is evil" pricks? Pointless. No matter what I say, you've already zealously started with a false premise, and nothing anyone says will change your mind.
I do indeed think that our pre-college education system works very well. It has--and continues to--turn out some of the most brilliant minds that the world has ever known. But because it's not perfect, in your demented little world, it's "an utter disaster." Yes, there's definitely idiocy going on, but it's not on my part.
Personally, I've had experience with both public and private school. Both had upsides and downsides. In the end, I chose to leave the private school I was attending because I realized the simple notion that which school you attend has little to do with success and happiness in life. It mostly depends on how well your parents train you for dealing with the real world, and how much you take personal responsibility for your own education, both book-wise and common sense-wise.
I can't speak to the former in your case because I don't know you, but based on your posts, I can definitely speak to the latter. You have very little common sense.
So tell me, in your educational utopia, what happens after we've dismantled the public education system? I can tell you, because we've been there. You pretty much took over whatever job your parents were doing because there was little to no opportunity to do anything else. Only the rich people could afford to send their kids to school or pay for private tutors. Will you be the one to explain to poor people how in this land of so-called "opportunity," you're looking to take away the one great opportunity equalizer among different social classes we have away from them?
"I'm sorry, Timmy. You used to be able to learn calculus in high school for free so that you could become the engineer you wanted to be. But in 2010, Grishnakh declared that the government was evil, your parents who work at the local 7-11 can't even teach you basic math, let alone calculus, and of course your family is too poor to pay for you to have a private tutor. Oh well, c'est la vie! Oops, sorry, I forgot that you've never learned French, either. That means, 'That's life.' Oh, no, I didn't mean that no one can be an engineer, that privilege is reserved only for kids of families of means. C'est ta vie--that's your life!"
Yes, we tried it that way, and it didn't work very well. Thus, we tried it another way, and we became one of the most well-educated and universally-educated countries on the planet in a very short time. Now because of some irrational hatred or paranoia, you want to tear it all down. The result is predictable, because again, we've been there: most kids will not get an education, and the general level of intelligence of the population as a whole will dramatically go down. If you think this is a good thing, you're either so rich that it wouldn't matter to you or you're so stupid for listening to rich people pushing that agenda that you don't know better. Either way, you clearly do not have the best interest of our country at heart, and thus your opinion holds no weight to me.
Only idiots buy into the whole "government is evil" pablum that is being foisted by and upon people like you. Only a total tool actually tries to tear down an institution that has provided immeasurable opportunity to countless people.
Tell you what, if government is so evil, how about putting your damned money where your mouth is? Stop driving on those cushy government-provided roads and interstates. Go mix some arsenic in your water and take some drags off your tailpipe, since the government is what sets environmental standards for how clean our water and air must be. If your house catches on fire, don't bother calling that socialist bastion of evil fire department. Let me know where you live so I can come rob you, secure in knowing that you'd never dream of calling those evil police on me. Mix some poison i
I have an education in electrical engineering. Yet I can think of only one time in my professional life I ever had to solve a differential equation, and by that time I had to look up how to do it since I mainly forgot the the details. But differential equations can help you understand transistor physics.
My experience with vector calculus enabled me to understand important concepts such a coaxial cable and antenna design. I also learned a great deal of applied Real and Complex analysis in terms of Laplace and Fourier transforms, but I never had an actual "analysis" math course. I don't typically solve transforms any more, but my knowledge that they exist inform my understanding of video and audio compression and signal equalization techniques.
In high school, I had an awesome combo of synchronized calculus with physics, which truly helps you understand both.
So I think often math is a tool to understand technology, even if you are more of a technology user than developer.
On the other hand, I think everyone could use more probability and statistics knowledge, as we do have to deal with understanding financial, economic, and political statistics on a regular basis.
You, sir, have a good question. Literary analysis is, by definition, the analysis of literature, so it's taught on literature. I was unclear in saying that it's used all over. The skills used in literary analysis are used all the time. It's our ability to interpret, analogize, and make inferences about meaning that make communication richer than simple communication of action. Listen to or read Carl Sagan's works for a great example of how very intricate and exciting scientific ideas can be communicated in a rich and interesting way that would not be possible without skills which are often described as "interdisciplinary". My overarching message was just that all studies are important; yes, to varying degrees to different people due to both their work and aptitude. But if we completely ignore any subject we do so at our own peril.
I never said government is evil, only OUR government. There's plenty of governments that work quite decently, but they happen to be in smaller countries.
I do indeed think that our pre-college education system works very well. It has--and continues to--turn out some of the most brilliant minds that the world has ever known. But because it's not perfect, in your demented little world, it's "an utter disaster." Yes, there's definitely idiocy going on, but it's not on my part.
No, you're an idiot, and I don't think many people will disagree with me on this. The American education system is consistently ranked at the very bottom of industrialized countries'. The brilliant minds coming out of it are coming out in spite of the education system. Moreover, many of the "brilliant minds" in America are coming from PRIVATE schools, not the government-run public schools.
In the end, I chose to leave the private school I was attending because I realized the simple notion that which school you attend has little to do with success and happiness in life. It mostly depends on how well your parents train you for dealing with the real world, and how much you take personal responsibility for your own education, both book-wise and common sense-wise.
According to your logic, then, we don't need schools at all! Or at least we shouldn't worry about making them any good, because it's all up to the kids and parents. I'm glad more enlightened countries don't take your laissez-faire attitude.
So tell me, in your educational utopia, what happens after we've dismantled the public education system?
And this here is the proof that you are an idiot. I never said anything about dismantling the public education system, and I actually said that a good public education system is necessary for an advanced society. Do you even bother to read the things you reply to? Or do you just read one line and assume someone is another stereotypical right-winger?
My proposal is to break up the country into smaller countries, and let them rebuild their school systems, hopefully along the lines of the successful schools in countries like Germany and other European countries. It can't be done in America as it is now, because the country and government are too big and too corrupt, and that can only be fixed by downsizing. Just like you can't fix a monopoly by any method other than breaking it up, so it is with nations.
Tell you what, if government is so evil, how about putting your damned money where your mouth is? Stop driving on those cushy government-provided roads and interstates.
Here I am, advocating that we copy the socialist Europeans, and you're calling me an anti-government right-winger. Are you beginning to see why you're an idiot yet?
Jesus, you really are stupid, as is anyone who modded you "Insightful."
Sorry, but you're the stupid one here. You can't even coherently reply to anything I've said, and instead put words in my mouth. Moron.
Literary analysis is, by definition, the analysis of literature, so it's taught on literature. I was unclear in saying that it's used all over. The skills used in literary analysis are used all the time.
Then why is only literary analysis taught in K-12 school, not news analysis, film analysis, or the over 9000 other fields you implied? I imagine that students will be more eager to learn if they can see more immediate applications.
LOL. I remember this argument in college. And you are correct, everybody makes their own meaning (more so on post modern and later literature, but that's the point of that genre, no?). So? Did you have a bad experience with a professor who got upset that you didn't see the same meaning?
I was actually part of the very experiment you described (again, in college). We found that interpretations varied widely. It was both frustrating and fun. It taught most of us that even when given the same input, people would come to hugely different (and often equally logically valid) conclusions. One reason for this is past experiences. Knowing all this helps me all the time; how else can you explain logical, reasoned analysis of the same input leading to both Smart Conservatives and Smart Liberals? Both have equally defensible points logically, but their starting interpretations of the data are so divergent that they're unlikely to agree. If you can find the divergences, one can better figure out how to re-frame the starting arguments to bring them both to a more agreeable position.
Example: Randall Munroe. I interpret that comic as a dig against literary analysis, but not a definitive one. Randall appears to see everything in life through the lens of mathematics, making Deconstructionism, a highly interpretive practice which is heavily influenced by Philosophy, as unintelligible to him as mathematics above 7 dimensions was to me. However, I can appreciate both his frustration and see how he can be just like the nincompoops who think that since they don't understand the equations behind how quantum foam behaves near an event horizon that it's both useless and meaningless (just in reverse). We all do it sometimes, and it doesn't make me dislike XKCD (it is the only comic I read religiously), but it seems we have different takes on this strip.
I'd like to give you an answer, but I haven't had enough math to figure it out.
If you make the term for exactly what you can pay off, then you are making the best choice. To purposefully get a longer term than you could and pay it off early to feel better is a very poor financial decision.
Getting a longer term loan is like self-insuring. You take a very modest hit in interest for the outstanding duration of the loan, and you get payments that are about 1/3rd the size. I paid off my 30-year loan in ten years, and I wouldn't have done it differently. I guess I just lean fiscally conservative. In some cases there are no benefits to setting a higher minimum schedule, such as HELOCs. Better to take out a loan against it with interest-only payments, and then pay them off as fast as you can.
I'd probably draw a distinction between evaluating a formula (x=a+b/c, provide a,b,c, find x), and solving an equation (a=bx+c, give me a general expression for x). Spreadsheets are almost always used for the former and rarely used for the latter. Sure, Excel has a "goal-seeker" function that will use some kind of iterative solver to do the equivalent of solving equations (numerous ways of doing this - all fallible and they don't deal with multiple roots).
No dispute there. However, if they can get paid more than you for their entire life doing their job wrong, it is hard to argue that math is all that important to their employment. Their success is based on the ability of their corporation to ensure that new companies that are competently managed are barred from competing effectively via legal measures. :)
Your argument basically amounts that if you do without you'll have more money than if you spend it. Well, clearly that is correct.
However, my point was that if you for whatever reason want to live in your own home, then mortgages are not a bad way to accomplish that.
Sure, if you can live with your parents until you're 30, or whatever, and not spend all that cash on other things, then you'll have more money.
In fact, if you live on ramen in your parent's basement until they die, you'll probably be a millionaire. If you maintain a similar lifestyle until your die, then whoever you leave your money to with be even better off.
If, however, you feel that money is earned for the purpose of being spent, then what matters is getting the most for your money. Perhaps living at a house at the age of 25 is worth enough that somebody would be willing to forego being able to afford a plane at the age of 55.
Well said! I think one of the foundational basics of math is teaching people logic and causal relationships. It seems like so many people don't understand simple if/then relationships.
To be honest, there is no reason whatsoever we can't have taught kids basic differential equations by the time they hit 8th grade.
We tried that -- it was called New Math. The problem is that students came away with great conceptual understanding, but few practical skills. They knew "Subtraction means I'll have fewer items," but they couldn't solve 83917.532 - 27838.93925. (An oversimplification, but not by much).
I do however agree that calculus should be split up (and renamed as a consequence/benefit) and taught in conjunction with the relevant algebraic and geometric tools. As a side effect, more students might find mathematics more compelling when they realize the breadth of problems that can be solved mathematically.
On a related note, we really need a class specifically about managing personal finances.
https://www.eff.org/https-everywhere
I think I agree with your distinction of "university education" versus "industrial education"; but I don't think it's accurate to conflate public education with "industrial education". The idea of public education predates the industrial revolution -- Thomas Jefferson was an advocate of public education, for example.
It certainly may be the case that public education has been twisted and perverted to be more of a system for producing workers than citizens -- though that was not my experience in the Baltimore County Public Schools of the 1970s and 80s. Indeed, I think that the public education I received was more geared towards developing independent critical thought, than the education I would have received in the private alternatives -- which were Catholic schools, military-style academies, or boarding schools.
But then, I was in a lot of "gifted and talented" classes, in the very early days of BCPS's GT program, so my experience might not be representative. Plus, it was the touchy-feely 1970s.
Tom Swiss | the infamous tms | my blog
You cannot wash away blood with blood
If the physical therapist doesn't understand physics (mechanical advantage) and the ability to apply it (calculus), then they suck at their job. If a business analyst is unable to spot the rate of change of sales (calculus), then they suck at their job. Without knowing specifics about what people do, I can't comment on the others, but after a stint with physical therapy and a business degree, I can speak some to those two.
Learn to love Alaska
Math applies to every single aspect of not just your life, but your entire existence.. People just prefer the path of least resistance (to guess) instead of actually trying to figure out the truth of things.
BeauHD. Worst editor since kdawson.
Did you have a bad experience with a professor who got upset that you didn't see the same meaning?
Nope, I just recognise it as about as useful as a glass hammer.
Actual psychology would be far more useful for simply understanding people and their points of view.
It taught most of us that even when given the same input, people would come to hugely different (and often equally logically valid) conclusions.
in other news water is wet and ducks go quack.
did you doubt this or something?
how else can you explain logical, reasoned analysis of the same input leading to both Smart Conservatives and Smart Liberals?
You get the same divergence between people with even mildly different precepts.
Again.
water, wet, ducks, quack.
The view tends to be quite common amongst people who actually deal with genuinely understanding the nuts and bolts of the universe.
Try reading "A map of the cat" by feynman and his brush with philosophy.
In the Graduate College dining room at Princeton everybody used to sit with his own group. I sat with the physicists, but after a bit I thought: It would be nice to see what the rest of the world is doing, so I'll sit for a week or two in each of the other groups.
When I sat with the philosophers I listened to them discuss very seriously a book called Process and Reality by Whitehead. They were using words in a funny way, and I couldn't quite understand what they were saying. Now I didn't want to interrupt them in their own conversation and keep asking them to explain something, and on the few occasions that I did, they'd try to explain it to me, but I still didn't get it. Finally they invited me to come to their seminar.
They had a seminar that was like, a class. It had been meeting once a week to discuss a new chapter out of Process and Reality - some guy would give a report on it and then there would be a discussion. I went to this seminar promising myself to keep my mouth shut, reminding myself that I didn't know anything about the subject, and I was going there just to watch.
What happened there was typical - so typical that it was unbelievable, but true. First of all, I sat there without saying anything, which is almost unbelievable, but also true. A student gave a report on the chapter to be studied that week. In it Whitehead kept using the words "essential object" in a particular technical way that presumably he had defined, but that I didn't understand.
After some discussion as to what "essential object" meant, the professor leading the seminar said something meant to clarify things and drew something that looked like lightning bolts on the blackboard. "Mr. Feynman," he said, "would you say an electron is an 'essential object'?"
Well, now I was in trouble. I admitted that I hadn't read the book, so I had no idea of what Whitehead meant by the phrase; I had only come to watch. "But," I said, "I'll try to answer the professor's question if you will first answer a question from me, so I can have a better idea of what 'essential object' means.
What I had intended to do was to find out whether they thought theoretical constructs were essential objects. The electron is a theory that we use; it is so useful in understanding the way nature works that we can almost call it real. I wanted to make the idea of a theory clear by analogy. In the case of the brick, my next question was going to be, "What about the inside of the brick?" - and I would then point out that no one has ever seen the inside of a brick. Every time you break the brick, you only see the surface. That the brick has an inside is a simple theory which helps us understand things better. The theory of electrons is analogous. So I began by asking, "Is a brick an essential object?"
Th
Wow, there is not what I was talking about. I mean actual teaching of actual math and how to do it. I just mean that instead of being told to memorize the quadratic forumla, and spending weeks teaching it, simply derive it, put it on a reference sheet and move on. After all, if you don't know how to apply it you are screwed no matter what, but there are tons of kids that know the formula and have no clue what to do with it. However, it would become second nature as you move to higher math and get experience using it in.
The backing off from facts entirely to look at theory goes too far towards not understanding how they work in a practical setting. I am simply saying that if we rework mathematical education so that everything is learned in context, and concepts are taught as needed and by concept with reference sheets, then once they reach the highest math they take just practicing a lot of problems until all of it is really cemented in and the reference sheets are no longer needed.
Really, calculus is just a tool, I think math education would work much better if students were introduced to the concept of a differential unit, a sumation, the integral and derivative with the rest of math. It really changes things from this math is totally useless to I can do anything with this math.
Not only do we need a class on managing personal finances, but we need a class on basic logic and reasoning skills. I see far to many people graduate high school with factual knowledge that are totally incapable of thinking anything beyond the most rudimentary and straightforward emotions. And then we got the tea party.
Where is the mod rating for "scary"? Also,
Sorry, old episode, out of date, so are you.
You're welcome.
Well, if you liked those, here are some other links accumulated from some years of homeschooling/unschooling... :-)
At a somewhat older age, this site on learning to read is interesting:
http://www.starfall.com/
We also like the original Electric Company with some episodes available on DVD:
http://en.wikipedia.org/wiki/The_Electric_Company_(1971_TV_series)
And it looks like there is a new version but I don't know how good it is:
http://today.msnbc.msn.com/id/28675624
But don't sweat "early reading". A kid is learning all the time. If they learn to read nature and computers and blocks and people and social situations and sand and water and pets and so on for seven to ten years (while listening to you read stories and other information aloud), they are learning in general a lot more than they would by trying to learn such things from books and other print media on the computer. If a kid wants to learn to read early (age two to four), fine. And of course, all kids should probably be exposed to reading material and the power of the written word (like adding things to shopping lists, or making signs). But if you go back two hundred years, learning to read at a later age was quite common, and kids catch up very fast. Don't let a stupid schooling lockstep age-focused paradigm harm your kid. Some kids also learn best to read by writing first (John Holt talks about this -- and how if you kid expresses an interest in writing, even just by scribbling stuff with no relation to regular letters, build on that). Note also that late reading in a homechooling/unschooling situation (where kids make their own choices) is different than late reading in a school-based print-based academic environment (where late reading is often a sign of some underlying health issue or just a broad, often justified, rejection of the authoritarian school paradigm, and problem piles upon problem if you can't read).
Contrast the probably true as far as it goes for compelled schooled children:
"Waiting Rarely Works: Late Bloomers Usually Just Wilt"
http://www.readingrockets.org/article/11360
"In the simplest terms, these studies ask: Do struggling readers catch up? The data from the studies are clear: Late bloomers are rare; skill deficits are almost always what prevent children from blooming as readers. This research may be counter-intuitive to elementary teachers who have seen late-bloomers in their own classes or heard about them from colleagues. But statistically speaking, such students are rare. (Actually, as we'll see, there is nearly a 90 percent chance that a poor reader in first grade will remain a poor reader.)"
with what happen when early reading is not emphasized because the environment is more flexible:
"Children Teach Themselves to Read"
http://www.psychologytoday.com/blog/freedom-learn/201002/children-teach-themselves-read
"In marked contrast to all this frenzy about teaching reading stands the view of people involved in the "unschooling" movement and the Sudbury "non-school" school movement, who claim that reading need not be taught at all! As long as kids grow up in a literate society, surrounded by people who read, they will learn to read. They may ask some questions along the way and get a few pointers from others who already know how to read, but they will take the initiative in all of this and orchestrate the entire process themselves. This is individualized learning, but it does not require brain imaging or cognitive scientists, and it requires little effort on the part of anyone other than the child who is l
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
What's interesting about these sorts of discussions is that they are much more approachable for everyone than if we were arguing over calculus type things. And, these sorts of calculation are sometimes much more amenable to reasonable discussions and amendments and improvements related to bounds than overly precise ones about exact outcomes.
As Freeman Dyson said:
http://www.edge.org/3rd_culture/dysonf07/dysonf07_index.html
"As a scientist I do not have much faith in predictions. Science is organized unpredictability. The best scientists like to arrange things in an experiment to be as unpredictable as possible, and then they do the experiment to see what will happen. You might say that if something is predictable then it is not science. When I make predictions, I am not speaking as a scientist. I am speaking as a story-teller, and my predictions are science-fiction rather than science. The predictions of science-fiction writers are notoriously inaccurate. Their purpose is to imagine what might happen rather than to describe what will happen. I will be telling stories that challenge the prevailing dogmas of today. The prevailing dogmas may be right, but they still need to be challenged. I am proud to be a heretic. The world always needs heretics to challenge the prevailing orthodoxies. Since I am heretic, I am accustomed to being in the minority. If I could persuade everyone to agree with me, I would not be a heretic. We are lucky that we can be heretics today without any danger of being burned at the stake. But unfortunately I am an old heretic. Old heretics do not cut much ice. When you hear an old heretic talking, you can always say, "Too bad he has lost his marbles", and pass on. What the world needs is young heretics. I am hoping that one or two of the people who read this piece may fill that role."
Back of the envelope calculations can give us a better idea of the range and scale of possibility, even if someone probably needs to do more detailed calculations to really make things work. So, we can answer "Might it fly?" with ballpark figures, whereas, "What is the best way to make it fly, given certain constraints and goals?" might take calculus or something else (evolutionary annealing algorithms or whatever).
It's been said (Knuth) that "premature optimization is the root of all evil": :-)
http://en.wikipedia.org/wiki/Program_optimization
but related to that may be the notion that teaching people optimization techniques and high precision math (like calculus or even the full times table) as opposed to basic approximation (like working with only one degree of precision or round numbers) may be the root of all extreme dumbness and math illiteracy?
By the way, related to general errors in assumptions (or calculations), especially in relation to the LHC at CERN:
http://reason.com/archives/2008/09/02/a-1-in-1000-chance-of-gotterda
"At the Global Catastrophic Risk conference, Future of Humanity Institute research associate Toby Ord asked an interesting question: How certain should we be about safety when there could be a risk to the survival of the human species? As Ord argued, "When an expert provides a calculation of the probability of an outcome, they are really providing the probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in their modeling of the problem, or a mistake in their calculations.""
There is also the risk of "social group think" perhaps leading to this:
"The CERN black hole"
http://www.youtube.com/watch?v=BXzugu39pKM
Seriously, the LHC cost billi
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Sure, you got me there. :-) Thanks.
And also a lot of great math comes from great physics, and is easier to understand that way. My young kid really liked the "derivative machine" cartoon in this series, as well as other animations connecting physics with the math (especially calculus) it inspired:
"The Mechanical Universe... and Beyond"
http://www.learner.org/resources/series42.html
With so many great resources, learning both math and physics can be a lot more fun at an early age than slogging through a lot of paperwork:
http://www.fun-motion.com/list-of-physics-games/
Other sciences are part of that too, from chemistry through psychology and zoology, etc.
A great resource on chemistry, and how it connects with various logical and practical challenges:
"The World of Chemistry"
http://www.learner.org/resources/series61.html
Even if at the end, Nobel Laurette Roald Hoffman extols the wonders of Bisphenol-A. :-)
http://www.chemicalsubstanceschimiques.gc.ca/challenge-defi/batch-lot-2/bisphenol-a/index-eng.php
"Canada is the first country in the world to take action on bisphenol A, thanks to our Chemicals Management Plan. This Plan was introduced in 2006 to review the safety of widely-used chemicals that have been in the marketplace for many years, and to update our knowledge and understanding of these chemicals."
I made something like this poem up once before (maybe I heard it before, too?). Here is another try at it:
The circle of knowledge, a poem by Paul D. Fernhout
All philosophy is anthropology; :-)
All anthropology is psychology;
All psychology is biology;
All biology is chemistry;
All chemistry is physics;
All physics is math;
All math is philosophy.
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
The difference comes down to the fact that how a person chooses to grow as an individual, or what a person should do to be a good friend, neighbor and citizen, may both have very little to do with how someone else wants to enslave that person to do work for them.
Of course, one person's view of being enslaved (say, to rabid nationalism or even just professional ethics that involve not taking a political position for a personal view of social justice) may be another person's view of progress and social uplift. And work as in "doing productive stuff" and "hard fun" and "making things happen" and "helping others" may well have many good qualities which are irrespective of who is defining the work (and the workplace) and who is getting the fruits of the work.
Still, ask yourself, what would be the "perfect" education for a slave these days? How far away are we from that with our public school system?
http://www.thewaronkids.com/
This is a typical example of the intent behind it connected to the "marketplace" and not personal growth (or even just citizenship):
"To fix US schools, panel says, start over"
http://www.csmonitor.com/2006/1215/p01s01-ussc.html
"What if the solution to American students' stagnant performance levels and the wide achievement gap between white and minority students wasn't more money, smaller schools, or any of the reforms proposed in recent years, but rather a new education system altogether? That's the conclusion of a bipartisan group of scholars and business leaders, school chancellors and education commissioners, and former cabinet secretaries and governors. They declare that America's public education system, designed to meet the needs of 100 years ago when the workplace revolved around an assembly line, is unsuited to today's global marketplace. Already, they warn, many Americans are in danger of falling behind and seeing their standard of living plummet."
While I completely agree with the title of the article that we should start over with our education system, I disagree with the approach as well as "the marketplace" as a primary aspiration. See my other posts on this article for unschooling alternatives).
http://slashdot.org/comments.pl?sid=1847578&cid=34099866
And see this for other real solutions to the jobs crisis transcending marketplace problems resulting from a combination of limited demand through saturation and the falling value of most paid humor labor due to robotics and other automation, better design, and voluntary social networks:
http://knol.google.com/k/paul-d-fernhout/beyond-a-jobless-recovery#Four_long(2D)term_heterodox_alternatives
It's true that eventually black slaves in the USA were kept from learning how to read (though that was not the case at first, only when they were getting uppity). But, what would you want a personal slave in the 21st century be able to do for you, and would reading, writing, and arithmetic be part of it? Sort your emails according to written criterion you supply? Drive your car while reading all the road signs and navigating efficiently? Be good in bed just the way you like it through extensive study of writings on the topic? Have brilliant engaging conversations about whatever you wanted to talk about based on being informed about current events? Build for you a comfortable house without a leaky roof by being able to follow blueprints precisely?
Remember, the Egyptians must have had many very technically skilled slaves (for the time) to build the pyramids. Slavery is not incompatible with some forms of learning. Even if eventually the slaves might choose to revolt in some way:
A 21st century issue: the irony of technologies of abundance in the hands of those still thinking in terms of scarcity.
Why would the physical therapist need to know calculus in order to apply force? Sure, calculus describes what she is doing, but she doesn't have any need to understand the underlying mathematical model. She just does it, based on her physical experience of the situation. Same with the physics. I'm sure she has a basic grasp of the concept of mechanical advantage; why would she need to be able to identify the formulas that describe why leverage increases applied force?
...sometimes, in order to hurt someone very badly, you have to tell that person terrible lies. - PA
I never said they needed it. I said they'd suck without it. They don't test physics to drive a car. So people suck at driving. Flying a plane is no different. You could train someone to fly a plane without any teaching of physics at all. However, every major licensing structure on the planet requires physics on their pilots tests.
Sure, a pilot could fly a plane with no knowledge of physics/math at all. But would you want to be on that plane?
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