Is Algebra Necessary?

[pcfast]

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all


This will cause debate, but I would say for a lot of people NO!

[QIII]

Science is useless. So are Art and History.

We managed to survive the Dark Ages with very few people having any education at all.

We'd save a lot of money getting rid of all of it.

[Smilax]

without Algebra,


how will they give the correct change at MaC D's



oh thats right, the computer will tell them!

down with algebra!

[Grenage]

It would be a sad day if Mathematics was not on the curriculum.

[IncurableHam]

"Making mathematics mandatory prevents us from discovering and developing young talent."

I almost lol'd (and stopped reading). Why would this only be true for math?

[jockyburns]

I think most people miss the point that, tough to grasp subjects, can actually show a persons capacity to learn. Something prospective employers are more interested in. ;-)

[errrn]

Science is useless. So are Art and History.

We managed to survive the Dark Ages with very few people having any education at all.

We'd save a lot of money getting rid of all of it.

glad to see sarcasm isn't a dead art after all

[Earl_Maroon]

Maybe it's not such a bad field. Maybe kids fail it because they are stupid/lazy or are poorly taught.

But that's a crazy thought.

[forrestcupp]

What people don't understand is that even though you may not directly use algebra or trigonometry in your day to day life, it teaches logic and reasoning skills that you do use every day. If you want to become a bunch of mindless sheep, go ahead and do away with mathematics. ;)

[pcfast]

I never understood math and it doesn't reflect on my intelligence or ability.

Most scientists and engineer types I know do not think logically. Hell, they can hardly dress themselves properly or make basic decisions!

[drawkcab]

I think most people miss the point that, tough to grasp subjects, can actually show a persons capacity to learn. Something prospective employers are more interested in. ;-)

True. The reason mathematics and/or logic are core requirements in college has to do with the fact that it shows that you have the intellectual discipline to learn an abstract symbolic system.

[drawkcab]

I never understood math and it doesn't reflect on my intelligence or ability.

In a narrow sense it does. Don't kid yourself.


Most scientists and engineer types I know do not think logically. Hell, they can hardly dress themselves properly or make basic decisions!

I will grant that intelligence is not monolithic which seems to be one of the great fallacies of the 20th century. Aptitude with mathematics or the like does not necessarily imply that one is apt at thinking and reasoning in relation to other spheres of intelligence.

Cultivating intellectual maturity with regard to practical, aesthetic, ethical, emotional and interpersonal judgment is a challenge that is often equal to if not greater than figuring out how to manipulate abstractions.

I still think that there is great value to having learned how to construct a geometric proof and/or work through algebraic conversions. But equally so I think that one learns much from tending bar, studying history, participating in athletics, reading the classics, building friendships, etc.

[madjr]

well it seems some countries want the opposite:

Lords' recipe for great British tech: Make teenagers study maths.

http://www.zdnet.com/make-maths-compulsory-post-16-lords-call-7000001482/


anyway I believe optional is better:
http://www.ehow.com/info_8143121_pros-science-classes-high-school.html

[Bachstelze]

Beyond the trollish title, it is very clear that the author's diatribe is not against mathematics itself, but the way it is taught in US primary and secondary schools. This is hardly a discovery, virtually everyone who knows something about mathematics has been saying that for over a decade. Most eloquently, Paul Lockhart (http://www.maa.org/devlin/LockhartsLament.pdf).

[drawkcab]

I honestly think that part of the problem is that learning math is alienated labor. What I mean is that, even for students that do well, it seems like a bunch of busy work that has no purpose.

If you tethered the teaching of math to its history, the way some universities have, you at least contextualize it. For example, when you learn about coordinate geometry you should first learn who Descartes was, what problems the coordinate system resolved, what its philosophical signficance was. It humanizes the abstractions. Also, the instructor should show what real world problems the technique can address. When I took math and physics together, calculating the volume of a torus suddenly seemed like a good thing to know how to do. Lastly, more effort should be placed in teaching number theory and foundations of math. Godel's proof is cooler than just doing repetitive problems over and over again.

[drawkcab]

Beyond the trollish title, it is very clear that the author's diatribe is not against mathematics itself, but the way it is taught in US primary and secondary schools. This is hardly a discovery, virtually everyone who knows something about mathematics has been saying that for over a decade. Most eloquently, Paul Lockhart (http://www.maa.org/devlin/LockhartsLament.pdf).

^^^ Just read that. Lockhart's got it about right. Thanks for posting.

[neu5eeCh]

My wife is certified to teach Algebra and tutors. What she has told me, and what I have read elsewhere, is that the requirement to teach and study algebra, in the United States, was instigated by the military when they found that prospective soldiers didn't have the mathematical background to operate and target gunnery (and related weaponry). So, the initial impulse to teach algebra was not for the betterment of mankind but a government instigated requirement to more easily enable such grand successes as the Vietnam War. Seriously.

In the meantime, Algebra has become a basic necessity in engineering and all fields of science. At the national level, I would say that Algebra is necessary. We cannot afford to risk the education of any student who could contribute to our nation's economy, well-being, and defense through science and the related fields. That said, there is a strong anti-science strain in the United States that has been (and is) very damaging, in part because science insists on such far-flung and "controversial theories" like Evolution.

At a more day to day level? Basic algebra (Algebra I, I guess) is something that we all use. Algebra II? -- quadratic formulas, conical sections, etc... No. I'm a builder and I still haven't, to this day, had to use *anything* from Algebra II. Trigonometry, on the other hand, remains very useful.

[eddier]

Isnt Algebra the 'Mechanics' of maths. A way of describing a problem without actual numbers?

I thought it hilarious when I came across it in school for the first time--I mean how the hell can x+y=z, x is x and y is y and z is z:confused:

And dont get me going on Logarithms,they cost me a smack around the back of the head.(And that ended up with somebody having flat tyres--and me having detention and someone else getting a smack on the nose-and me getting suspended. OH! Happy Days!)

eddie

[QIII]

Most scientists and engineer types I know do not think logically. Hell, they can hardly dress themselves properly or make basic decisions!

All bears walk in single file. At least the one I saw did.

I think that Classical Logic is overrated and should be eliminated, too. Without Logic, we could make Hasty Generalizations without guilt.

Science is bunk, as I said. Who needs scientists to create the technology that makes computers work or engineers to design the bridges that let us cross rivers in the cars that other engineers design?

We, in the US, have no need for such things. We can let everyone else in the world excel at science and reap the rewards as we wear tunics, sleep with our livestock and roof our homes with straw. Ox carts will get us where we need to go. We can till the soil with iron implements. We can remove cancerous tumors with rusty spoons - or even wave chickens over the patient since we don't need engineers to build the equipment to make spoons.

[QIII]

is that the requirement to teach and study algebra, in the United States, was instigated by the military when they found that prospective soldiers didn't have the mathematical background to operate and target gunnery (and related weaponry). So, the initial impulse to teach algebra was not for the betterment of mankind but a government instigated requirement to more easily enable such grand successes as the Vietnam War. Seriously.

Hmmm...

Gunnery has been practiced for hundreds of years. Long before the US existed. The Greeks codified Algebra (although they didn't invent it) and the Romans made great practical used of it. The Arabs preserved Algebra (hence al gebra) while the West was mired in the Dark Ages. By the way, the Arabs preserved a lot of the West's science, literature and technology while we systematically forgot it. Irish monks preserved a bunch, too.

Preserving Math and Science was a going operation long before there were black helicopters to make sure it happened.

[jockyburns]

Where I work, we had a 17yr old girl start, and one day, I asked her to fetch me a dozen, of a particular item. She replied, "How many is that?". I told her, "Just the one dozen will do." Again , she asked "How many is that?" I asked her how many she thought it was,, and she just didn't have a clue.... and that's simple numbers, not algebra.

[neu5eeCh]

Hmmm...

Gunnery has been practiced for hundreds of years. Long before the US existed. The Greeks codified Algebra (although they didn't invent it) and the Romans made great practical used of it. The Arabs preserved Algebra (hence al gebra) while the West was mired in the Dark Ages.

Yes, but neither the Romans or Greeks possessed the kind of gunnery that made algebra necessary and useful. I'm not saying that an infantryman needs to know algebra to fire a rifle, but during WW1&2, the big guns needed gunners with a quick and fast knowledge of algebra.

[DoubleClicker]

What people don't understand is that even though you may not directly use algebra or trigonometry in your day to day life, it teaches logic and reasoning skills that you do use every day. If you want to become a bunch of mindless sheep, go ahead and do away with mathematics. ;)

Actually most people DO use algebra in their daily lives. They just don't realize it, because they use words, instead of letter variables and operator symbols.

[QIII]

Yes, but neither the Romans or Greeks possessed the kind of gunnery that made algebra necessary and useful. I'm not saying that an infantryman needs to know algebra to fire a rifle, but during WW1&2, the big guns needed gunners with a quick and fast knowledge of algebra.

Actually, the NCOs in charge of the gun and mortar crews, Lieutenants in charge of gun sections and Captains in charge of Batteries used range and elevation tables during the First War, which someone else developed because pencil whipping an equation would have taken far too long. They also used FOs with land lines to spot the first splash and send instructions back to allow the guns to adjust fire.

By the Second War, they were using "whiz wheels" -- an ingenious circular form of slide rule. The FOs used radios. (My uncle was a Field Artillery Lieutenant who was killed in the Ardennes while observing and directing fire. Got himself a Bronze Star with "V" device, a Purple Heart and a nice peaceful patch of green Belgian grass taking out a pillbox by himself when he was trying to move to a better observation position.)

By the Vietnam war, rudimentary targeting computers were being used.

Half of getting steel on target was the whiz wheel. The other half was someone with a pair of binoculars saying "You didn't quite hit it, adjust your fire so..." Well into the 90s, all Combat Arms Officers were trained in Forward Observation and directing indirect fire. We didn't need algebra. Just a good eye for distance and direction.

Now, of course, sophisticated targeting computers and smart rounds are used.

Nevertheless, someone needed to know the math to fight wars, so in general that part is true.

[Bachstelze]

Have you guys actually read the piece before commenting?

[QIII]

The NYT piece? Yes.

Bunk.

I'd love to discuss that further, but an essay in response is a bit much for a forum.

Removing what one person sees as an impediment in order to achieve "success" by virtue of it's avoidance is no success at all. Do we teach Math poorly? Yes. Do we avoid it because it is "in the way"? No.

"Teaching to the test" and "No child left behind" are exercises in asininity. But as to whether we choose not to teach something just because most people will never use it, I say bunk.

A genuine education results in the long term synthesis of a broad spectrum of learning. It frees us from the tyranny of mere survival. It enlightens and informs the advancement of culture and civilization. It is not a collection of disparate pieces.

Do we not teach Art because most people won't use it? Do we not teach Literature because most people won't use it? Do we not teach History because most people will not use it?

It is precisely the ability to synthesize the parts into a coherent whole that makes us human. The absence of material to use in that synthesis hobbles rather than enables.

Making "What will we use in our likely line of work" the measure of what is necessary reduces us to drones, workers bees and slaves.

[eriktheblu]

I work in a human resources field (career counselor) for the U.S. Army. Algebra is not strictly needed to do my job.

I am frequently tasked with producing reports on personnel based on service dates. Were I to employ simple arithmetic (as I was taught in career counselor school) individually for the hundreds of soldiers I support, such a task would take hours. Instead, I use algebra, create formulas in a database, and I'm done in a couple of minutes.

It doesn't matter if you need it, if your job requires it, or if it is useful. What matters is if you will be able to use it.

[gardnan]

I don't understand. How is algebra the least useful subject taught in school? For me, it was the most important subject to know, period. In fact, I would go as far as to say that the only useful things I was taught in school were entirely based on mathematics, and therefore algebra.

Also, I don't understand how you can say that other mathematics skills are important (trigonometry, statistics), but algebra is not. All useful mathematics skills, at least from my perspective, rely on algebra.

Maybe the articles were discussing abstract algebra. I could agree to not teaching that to high-school students.

[Bachstelze]

The NYT piece? Yes.

Bunk.

I'd love to discuss that further, but an essay in response is a bit much for a forum.

Removing what one person sees as an impediment in order to achieve "success" by virtue of it's avoidance is no success at all. Do we teach Math poorly? Yes. Do we avoid it because it is "in the way"? No.

"Teaching to the test" and "No child left behind" are exercises in asininity. But as to whether we choose not to teach something just because most people will never use it, I say bunk.

A genuine education results in the long term synthesis of a broad spectrum of learning. It frees us from the tyranny of mere survival. It enlightens and informs the advancement of culture and civilization. It is not a collection of disparate pieces.

Do we not teach Art because most people won't use it? Do we not teach Literature because most people won't use it? Do we not teach History because most people will not use it?

It is precisely the ability to synthesize the parts into a coherent whole that makes us human. The absence of material to use in that synthesis hobbles rather than enables.

Making "What will we use in our likely line of work" the measure of what is necessary reduces us to drones, workers bees and slaves.

I agree with everything you said, and I am pretty sure the author of the NYT piece would, too. What you said should not be done is exactly what the current system is doing. As I said, his piece is more a criticism of the current system of mathematics education than of mathematics itself.

The problem is that author, not being a mathematician, has only a vague idea about what mathematics is, and knows nothing about how it is actually done by working mathematicians. This is exactly the problem with the current system: it ensures that most people think of mathematics as dumb memorization of facts given without any kind of context or motivation, and only professional mathematicians know what it actually is. (This is in contrast with, say, music or painting: everyone, not just professional musicians or painters, knows what they are and has some idea of how they are done.) The result is that the author identifies the current US system of mathematics education with mathematics itself, and calls, with reason, for its abandonment.

[thatguruguy]

Most scientists and engineer types I know do not think logically.

Are you trying to imply that you know a bunch of scientists and/or engineers who can't do basic algebra? Because I bet that's not true.


Hell, they can hardly dress themselves properly or make basic decisions!

I bet that they're not good dancers, either. Which is equally indicative of their ability to think logically.

[Bachstelze]

Specifically



Making "What will we use in our likely line of work" the measure of what is necessary reduces us to drones, workers bees and slaves.

Again, this is exactly what the current system is doing. It force-feeds students with an enormous amount of facts, some important and profound and some mundane and trivial (without distinction), but always without any kind of context or motivation. And this is justified by "you will use it in life". Saying that no, you will not use it in life, is not an argument against it, it is a rebuttal of the only argument for it. The real mathematics that should be done instead are also things one will never use in life, but infinitely more fascinating and intellectually stimulating.

[QIII]

But the tenor of the article is "we are doing it wrong and most won't use it, so stop doing it". I say fix it and keep teaching it.

We need to teach people beyond boxes, not trap them within.

It is not "teaching more than is needed" that damps creativity and productivity. It is not struggle. It is precisely the opposite of the author's premise. NOT teaching "more than is needed" is the trap. Not sweating through the difficult things diminishes achievement.

As I said before, we do not teach Math well. We teach to standardized tests and regulations. We do not teach to understanding and mastery. But saying we should just stop damns us all.

[Bachstelze]

But the tenor of the article is "we are doing it wrong and most won't use it, so stop doing it". I say fix it and keep teaching it.

We need to teach people beyond boxes, not trap them within.

This is true; I suggest you read the piece by Lockhart I linked earlier (if you have time, it is quite lengthy), I think you would like it.

[vexorian]

http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all


This will cause debate, but I would say for a lot of people NO!
I've read this somewhere.

The article is just so full of lameness.

First of all, removing algebra to improve scores is basically the same logic same as legalizing murder to reduce the rate of illegal homicide. It mistakens stats as the final objective.

Second, asking engineers if they use school level algebra is misleading. Because such a question does not answer the key question: Are engineers using the skills they gained while learning algebra as kids? Algebra takes you to a wide array of skills called Abstraction. And abstraction is difficult for the human being. It is precisely because it is difficult that we must begin teaching it early. Abstraction is a skill that will make you a better engineer, even if you don't solve trigonometric identities yourself.

Third, it assumes that schooling is to teach you useful stuff. It really is not. It is so you can learn how to learn. And also so you can learn what is it that you like. Math is used heavily on Sciences. I am a computer scientist and I am locked into it. You will need computer scientists and phycisists in your future and you better make sure they get to know they like to learn that stuff when they are kids. Just like your artists and writers will find out they like that stuff through art and literature subjects. And just like people who are good with their hands will find out in those classes in which you build stuff.


Fourth, it proposes to teach "numerical literacy" INSTEAD of algebra? May I ask how can it be done?


Numbers as we know in this era are polynomials. 26281 is a polynomial 2*10^4+6*10^3+2*10^2+8*10+1. It is thanks to algebra that we can do long multiplications. The cute algorithms for long multiplication, long addition and long division are all algorithms. Cute algorithms completely based off algebraic rules. In this regard, anyone who has used those algorithms in their lives has to apply algebra.

Algebra is right there in the foundation of all our phycics discoveries of the 20-th century. Algebra is also the basis for our computer circuits. Software is basically a ton of algebraic operations too. Try writing a video game graphics enginer without some algebra. This world is running on algebra. And then we have abstraction, which I already mentioned. Abstraction is a skill that will help you in life no matter where you go.

And then we got proofs. The difference between knowing just how to use an algorithm (formula) and knowing how to prove the algorithm. Is like the difference between knowing how to read a novel and knowing how to write one. We teach reading AND writing, even though most kids will not write books when they grow up. We gotta teach proofs, just in case some of your kids are the sort that will come up with new algorithms and need to prove them.

---
If everyone is failing algebra. It is not Algebra's fault. The subject needs to be updated and it would be awesome if kids learned algebra, may as suggest, in conjunction with something like Turtle Art (http://en.wikipedia.org/wiki/Turtle_graphics)* or Scratch (Just a mere example). I see in general that there is excessive focus on grades, when there should be a better focus on methods.


*I happen to have had the incredible luck of being at a class that was taught LOGO when I was 7 years old. I have come to realize that I owe my whole life to the geniuses behind that idea.

[lisati]

IMO we should skip worrying about algebra and maths, when a grasp of basic arithmetic would be a useful foundation for many tasks.

[freakycheeseman]

I'd go with yes, absolutely, yes. Mathematics isn't just the study of numbers; it's the formalization of rational thought. Even if the specific methods taught in Algebra weren't commonly used- which they are - the basic language and toolset of finding unknowns, judging "actual" logic/proofs from things that just look like such, is an invaluable toolset.

I agree that a lot of the time it's poorly taught- the people drawn to mathematics are often not the ones drawn to early education. However, that doesn't change the fact that mathematics is the most fundamental field of human study.

If anything, I would argue for more required mathematics - in particular, Bayesian Statistics. For those unfamiliar, Bayesian Statistics covers the hard math behind how particular evidence supports or refutes a given hypothesis- a skill needed for *any* significant decision making.

[vexorian]

IMO we should skip worrying about algebra and maths, when a grasp of basic arithmetic would be a useful foundation for many tasks.
Arithmetic, the one part of math that computers can already do completely well without any help from us. Sounds like a great idea.

[Bachstelze]

Arithmetic, the one part of math that computers can already do completely well without any help from us. Sounds like a great idea.

If someone tells you "Give me this $100 bill and I will give you four $20 bills", will you use your computer to check that he's not tricking you?

[QIII]

This is true; I suggest you read the piece by Lockhart I linked earlier (if you have time, it is quite lengthy), I think you would like it.

Probably. If I get the chance.

I worked with my kids in High School and College so that they would understand rather than regurgitate. They both excelled at Math and Science. They both loved Literature and the Arts.

The greater fault in all of this, in my humble opinion, is parents who don't care or see schools as a daycare. They want their kids to get a gold star for nothing and they rail against the institution. The institution responds by making the process mechanical and the thing spirals down one more notch. Facts come from the classroom. A sense of curiosity, wonderment and inter-relatedness of things comes from parents and family.

[vexorian]

If someone tells you "Give me this $100 bill and I will give you four $20 bills", will you use your computer to check that he's not tricking you?
Just saying that focusing on only teaching the easiest part of Math would be very lame. Of course, it has to be taught. Also Algebra, and trignometry and proofs, obviously.

But you know, I happen to live in a country full of number illiteracy. I've noted people that obviously didn't go to school can still use simple arithmetic. They just memorized it. "4 20s is 80" is as trivial as it gets. I also noticed that people who have learned it in school are still very bad at it. 20 * 4 = 80 is easy for them, 21 * 11 not so much...

[Bachstelze]

Just saying that focusing on only teaching the easiest part of Math would be very lame. Of course, it has to be taught. Also Algebra, and trignometry and proofs, obviously.

There is some disagreement here apparently about what "algebra" even is, so I'll not speak of that.

Trigonometry, really? The only trigonometry you need is x = r.cos(t) and y = r.sin(t). When I see the kind of trigonometric equations that US high-school students have to solve (especially those involving obsolete functions like sec or csc), it makes me cringe. No one, absolutely no one, not even scientists or engineers, will need to do that. And if you think it serves any other purpose such as broadening the mind or whatnot, well, I disagree.

Proofs, definitely. Proof-based classes are generally where students who were always told that they were "good at math" and chose to major in it discover that they actually have no mathematical talent at all. I remember a class I took last year (Galois theory) where you could see very clearly who had the kind of insight and creativity it takes to do math, and who didn't.

More about proofs, though. The current US high-school curriculum does feature a proof-based class: geometry. However, the "proofs" there are presented in an absolutely impalatable way, which would make any mathematician cringe a lot.

[CharlesA]

Beyond the trollish title, it is very clear that the author's diatribe is not against mathematics itself, but the way it is taught in US primary and secondary schools. This is hardly a discovery, virtually everyone who knows something about mathematics has been saying that for over a decade. Most eloquently, Paul Lockhart (http://www.maa.org/devlin/LockhartsLament.pdf).
Nice link.

I had to work with some finanical numbers the other day and I don't think I could have done them on paper because the numbers were rather large.

Calculators are a godsend for stuff like that, but for normal people, doing math shouldn't be too difficult.

Also this (http://what-if.xkcd.com/4/).

[vexorian]

I read Lockhart's lament years ago. To compare it with the NY times article is blasphemy to me. Whilst Lockhart's lament asks us to fix maths and proposes how. The NY times article proposes to get rid of Algebra. And that's just wrong.


There is some disagreement here apparently about what "algebra" even is, so I'll not speak of that.

Trigonometry, really? The only trigonometry you need is x = r.cos(t) and y = r.sin(t).
The only trigonometry you need. I have used a lot more stuff in my fun programmatic rollercoaster that my life has been.

Why exactly are we supposed to judge things by whether we are going to need them or not? I do not get to use 95% of the subjects I used in school. Is that a reason to stop having them?




When I see the kind of trigonometric equations that US high-school students have to solve (especially those involving obsolete functions like sec or csc), it makes me cringe. No one, absolutely no one, not even scientists or engineers, will need to do that.
You are leaping though. From saying that sec is useless (and it is, but it is also a function that defines a shortcut for another function. A very programmatic concept that is a basic skill for programmers). Sure, sec is useless, does that mean that really x = sin(r) and y = cos(r) is the only thing you'll ever need? That's a false equivalency.




Proofs, definitely. Proof-based classes are generally where students who were always told that they were "good at math" and chose to major in it discover that they actually have no mathematical talent at all.

But do you know what is needed to learn proofs? Material that has to be proved. In this way, a trigonometric identity is as good to teach you proving skills as just about anything else. And the more different topics at which you are forced to proove stuff, the better for you. Because, if you grow up to be that sort of Mathematician, you will find yourself proving stuff in topics that were unknown to you.



More about proofs, though. The current US high-school curriculum does feature a proof-based class: geometry. However, the "proofs" there are presented in an absolutely impalatable way, which would make any mathematician cringe a lot.

That's the reason all math-related topics should include proofs.

And I mean all of them. Each area of mathematics should be a small step towards a grand objective, to learn how to prove stuff. That's basically how I learned math in my school (bless it) and the good parts of my college. Every theorem used would include a proof before using it.


It is way too common to find people who don't know that base 10 multiplication can be proven.

[Bachstelze]

The only trigonometry you need. I have used a lot more stuff in my fun programmatic rollercoaster that my life has been.

Specifics, please.


Why exactly are we supposed to judge things by whether we are going to need them or not? I do not get to use 95% of the subjects I used in school. Is that a reason to stop having them?

I have already answered that (here (http://ubuntuforums.org/showthread.php?t=2035814&page=4#31)).



But do you know what is needed to learn proofs? Material that has to be proved. In this way, a trigonometric identity is as good to teach you proving skills as just about anything else.

No, it is not. Proving a trigonometric identity (or any other identity) goes like this: start from one side of the equality and apply some computational rules until you end up with the other. It's the most trivial form of proof, and thus the most uninteresting one.

[KiwiNZ]

http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html?pagewanted=all


This will cause debate, but I would say for a lot of people NO!

We should stop teaching English, Geography, Biology, Physics, History ............ as people may fail. While we are at it lets all save thousands and close all the schools.

Is algebra necessary..... yes. Are Journalist necessary?.....No

[pissedoffdude]

It is necessary. We must prevent this from happening: http://www.youtube.com/watch?v=omyUncKI7oU
http://www.youtube.com/watch?v=f7pMYHn-1yA&feature=related

In all seriousness though, the problem lies with the way it's taught. The way math is taught in school is incredibly unmotivated and it stresses memorization and computational tricks so that everyone student can pass.

We do need an entirely different curriculum that teaches students what's going on behind the scenes and why they're learning what they learn.

A lot of fault also lies with the teachers. When I was in high school, a lot of math teachers were also coaches, and many had no degrees related to math

[Bachstelze]

I read Lockhart's lament years ago. To compare it with the NY times article is blasphemy to me.

What exactly do you mean by "compare"? If you can't see that the two pieces stem from the exact same observation, you have not understood either, and should reread both. Also the word "blasphemy" has no place here. Math is not religion, nothing is sacred. Not even Lockhart's piece.

[KiwiNZ]

nothing is sacred.

Except the Darkside

[CharlesA]

except the darkside
+1

[madjr]

It is necessary. We must prevent this from happening: http://www.youtube.com/watch?v=omyUncKI7oU
http://www.youtube.com/watch?v=f7pMYHn-1yA&feature=related



why prevent that ?

most people only learn the hard way :D

[KiwiNZ]

73, is the 21st prime number, its mirror 37 is the 12th and its mirror 21 is the product of multiplying, 7 and 3.In binary, 73 is a palindrome, 1001001, which backwards is 1001001, exactly the same.

[CharlesA]

73, is the 21st prime number, its mirror 37 is the 12th and its mirror 21 is the product of multiplying, 7 and 3.In binary, 73 is a palindrome, 1001001, which backwards is 1001001, exactly the same.
*mindblown*

[Bachstelze]

About the link between Lockhart's and Hacker's pieces, here's what I wrote on Tumblr:


Okay so the latest hot thing in the math tag is not some lousy joke or picture with a yellow background, but Andrew Hacker's piece in the NYT. Those who have read Lockhart's lament (and actually paid attention) will have noticed that Hacker's and Lockhart's griefs with US mathematical education are the same: it consists in force-feeding students with an enormous amount of facts, some important and profound and some mundane, without distinction, and always without context or motivation. The result being that most students are not motivated, find the classes boring and stupid, and ultimately fail.

The difference between Lockhart and Hacker, though, is that Lockhart is a mathematician, and Hacker is not. In particular, Lockhart knows that mathematics as it is practiced by mathematicians has nothing to do with the mockery that passes for mathematical education in the US. Lockhart also notes, and this is the important point, that the US mathematics curriculum is (or at least seems to be) designed so that only mathematicians will know what mathematics is and how it is done, while other people will think the curriculum they have had to go through is all there is to mathematics, and will identify the two. (A US high-school student once asked me how one could major in mathematics: "There can't be that much calculus around!") Hacker is (or at least seems to be) one of those people, and thus in my mind all the flaming he got is misdirected. It should be directed at the system who creates this confusion between rote memorization of random facts and the beautiful art of mathematics. I am pretty certain that if mathematics were taught as Lockhart describes it, Hacker would not have written his piece.

[standingwave]

73, is the 21st prime number, its mirror 37 is the 12th and its mirror 21 is the product of multiplying, 7 and 3.In binary, 73 is a palindrome, 1001001, which backwards is 1001001, exactly the same.

Bazinga!

[mips]

We should stop teaching English, Geography, Biology, Physics, History ............ as people may fail. While we are at it lets all save thousands and close all the schools.


That will actually go down well with some people I reckon, like the author of the article.

[mips]

You actually get 'taught' algebra if I could call it that very early on in school, first 3 yrs or so people just don't realise it.

When the teacher writes 3+◻=7 on the board and you have to figure out ◻ it's no difference than figuring out 3+x=7 except you don't go through all the motions on paper.

[QIII]

What's the point of being a Mathematician when one is a software developer?

Shouldn't one just have to learn programming?

Boy, do I feel like a schmuck. I didn't have to spend all that money and 12 years at three Universities. I could just have gone to a Community College for a couple of years.

[WinterMadness]

What's the point of being a Mathematician when one is a software developer?

Shouldn't one just have to learn programming?

Boy, do I feel like a schmuck. I didn't have to spend all that money and 12 years at three Universities. I could just have gone to a Community College for a couple of years.

Even community colleges require calculus and discreet math for cs degrees.

at least the community college in my town does. you have to take calc 1-3, discreet math and linear algebra

[CharlesA]

Hrm, I only had to do algebra and discrete mathematics. I'm sure I would have fun in calc...

[diesch]

Gunnery has been practiced for hundreds of years. Long before the US existed. The Greeks codified Algebra (although they didn't invent it) and the Romans made great practical used of it. The Arabs preserved Algebra (hence al gebra) while the West was mired in the Dark Ages.

Usually the Greek Diophantus of Alexandria or the Persian Muḥammad ibn Mūsā al-Khwārizmī are said to have invented algebra.There have been important contributions from India, too, especially from Aryabhata.




By the way, the Arabs preserved a lot of the West's science, literature and technology while we systematically forgot it.

They actually invented a lot of it, and brought ideas, science and technology from India to Europe.

[QIII]

Usually the Greek Diophantus of Alexandria or the Persian Muḥammad ibn Mūsā al-Khwārizmī are said to have invented algebra.There have been important contributions from India, too, especially from Aryabhata.

Ah! Math History. Good stuff! Took several courses. Always fascinated me. Diophantus' Arithmetica built on Egyptian and Bablylonian understanding of things like linear and quadratic equations. That understanding is actually pretty ancient. Arithmetica codified it and took it to the next level, of course.

al-Khwarizmi actually wrote his works during the Dark Ages in Europe. His algebra was a significant improvement (and gave us the name, which is derived from one of the operations he used. His name, incidentally, was transliterated in Latin as "Algoritmi", from which we get "algorithm"). Very bright guy. The Moslems were particularly fond of equations, or "balancing". I don't know if that was something that came about after the advent of Islam or if it was simply a part of the Arabic psyche (or Persian in the case of al-Khwarizmi) . Fibonacci was particularly influenced by his travels to Islamic countries.


They actually invented a lot of it, and brought ideas, science and technology from India to Europe.Don't forget the Chinese, who had a lot of very sophisticated knowledge. Some of it drifted west by way of the Arabs long before Polo.

But who cares about all this hooey anyway? Algebra holds us back, if you agree with the NYT article.

[mips]

Boy, do I feel like a schmuck. I didn't have to spend all that money and 12 years at three Universities. I could just have gone to a Community College for a couple of years.

You could have achieved the same thing sitting on the couch playing playstation.

[pcfast]

Schools say the issue is how math is taught, but the majority of math teachers and institutions have not really made any efforts to change teaching methods.

[QIII]

Schools say the issue is how math is taught, but the majority of math teachers and institutions have not really made any efforts to change teaching methods.

Most US K-12 teachers, during the time when a student's interest can either be piqued or destroyed, are not given the opportunity to make changes. Institutions buy shoddy, inadequate instructional materials at cut rates to meet budgetary requirements and teachers make due with them as part of dictated curricula and syllabi.

My kids were fortunate to have a Mathematician for a dad. I taught them to understand Math, not regurgitate by rote.

Teach them what and they struggle to remember. Teach them why and they understand.

[phrak]

What people don't understand is that even though you may not directly use algebra or trigonometry in your day to day life, it teaches logic and reasoning skills that you do use every day. If you want to become a bunch of mindless sheep, go ahead and do away with mathematics. ;)

This, while most people will use very little algebra it teaches a lot of critical thinking skills. The day math became easy for me was when I figured out that it's just a logic problem. On a basic level all math boils down to add, subtract, multiply, and divide. The fun part is putting the puzzle together so you can do one of those four things.

I may never use my trig course from college in real life, but I'm very happy to have taken it.

[georgelappies]

The NYT piece? Yes.

Bunk.

I'd love to discuss that further, but an essay in response is a bit much for a forum.

Removing what one person sees as an impediment in order to achieve "success" by virtue of it's avoidance is no success at all. Do we teach Math poorly? Yes. Do we avoid it because it is "in the way"? No.

"Teaching to the test" and "No child left behind" are exercises in asininity. But as to whether we choose not to teach something just because most people will never use it, I say bunk.

A genuine education results in the long term synthesis of a broad spectrum of learning. It frees us from the tyranny of mere survival. It enlightens and informs the advancement of culture and civilization. It is not a collection of disparate pieces.

Do we not teach Art because most people won't use it? Do we not teach Literature because most people won't use it? Do we not teach History because most people will not use it?

It is precisely the ability to synthesize the parts into a coherent whole that makes us human. The absence of material to use in that synthesis hobbles rather than enables.

Making "What will we use in our likely line of work" the measure of what is necessary reduces us to drones, workers bees and slaves.

+1 Brilliant, I could not agree more.

[Warpnow]

The real question in my mind is how does such an obviously idiotic person get their story posted on the new york times website?

[gardnan]

On a basic level all math boils down to add, subtract, multiply, and divide. The fun part is putting the puzzle together so you can do one of those four things.

You may want to rethink that. Not all math boils down to fundamental arithmetic operations. Math can be done with things other than numbers, with operations other than those you listed.

[IWantFroyo]

I use algebra enough in my daily life that I can't imagine living without it.

Then again, I use calculus too, so I'm likely biased.

Without algebra, managing money and basic skills would be a lot harder, and you would be reliant purely on computer tools that take about as much skill to master as algebra does. And you would have to learn a new program and whatnot for every new job.

I think learning algebra would be easier.

[zombifier25]

The real question in my mind is how does such an obviously idiotic person get their story posted on the new york times website?
.

[georgelappies]

Mathematics may just safe you some money as well...

http://farm9.staticflickr.com/8023/7709500562_73fc4a4892.jpg (http://www.flickr.com/photos/79382089@N03/7709500562/)
math for dummies (http://www.flickr.com/photos/79382089@N03/7709500562/) by georgelappies (http://www.flickr.com/people/79382089@N03/), on Flickr

[thatguruguy]

I'm still looking forward to the OP providing a list of all of the scientists and engineers he knows who can't do algebra.

[Morbius1]

There are 2 kinds of people in the world: those who can and those who cannot.

Those who can include people such as surgeons, carpenters, electricians, pipe fitters, software developers, engineers, you get the idea.

Those who cannot include politicians, lobbyists, managers, corporate vice presidents and beyond.

Those who can always have been, are now, and always will be under the control of someone who cannot.

So if your goal is to be someone who cannot then you do not need to bother with Algebra.

[3Miro]

There are three levels of math.

Level 1: see the cartoon above. This is very basic you need to live in a modern society. I wonder about the people that take loans that they cannot replay, how many of them do you think can work out a problem with percentages or even know what APR means.

Level 2: you may never have to use trig or basic Euclidean geometry, but it does train your brain. Football players practice for a game on a flat field by running up and down the stairs of the stadium. Basketball players practice lifting a basketball, by using much heavier weights. The brain is trained in the same way like any other part of the body. Math trains you how to use logic to solve a problem.

Level 3: in science and engineering there is no such thing as too much math. The only way a person can get a degree in engineering without knowing math is if they payed for it. Then of course, the degree is useless as nobody would keep such person working for them.

Currently math education in USA is garbage. Kids learn nothing but basic mechanical skill of plugging in numbers into learned formulas, any alight variation kills them. However, the solution to this problem is not to stop teaching even the little they get thought.

[mips]

You have to ask yourself if maths was so difficult then surely the failure rate would be the same around the world. Yet other countries excel with a lower cost input (and I'm talking about 1st world countries).

Accepting the authors stance then to me it implies that people from certain countries are 'stupid' or 'lazy' and I simply don't buy that. If people from Finland or S.Korea can do it then people from the US can do it. The problem is a broken system that needs fixing.

Would it really be that hard to go and look at what they do in countries where kids do well in these subjects and them implement the same system at home instead of throwing the baby out with the bath water?

[Ubun2to]

Algebra is a part of our lives whether we realize it or not.
You want to make twice as many cookies than the recipe calls for. So, you double the ingredients.
This can be represented in the equation y=2x, where y is the final amount of ingredients you need, and x is the number of ingredients for 1 batch, which you multiply by 2 to find the total amount of ingredients you need (Y).
The day they stop teaching math is the day we fall into the dark ages. If we can't figure out what 2+2 is, how will we survive in this world?

[Kreaninw]

In my opinion, every knowledge in this world cannot be useless. But the fact that we ignore what children interest, even the every same knowledge we're talking about are bound to be useless in someone life.

[Bachstelze]

Level 3: in science and engineering there is no such thing as too much math. The only way a person can get a degree in engineering without knowing math is if they payed for it. Then of course, the degree is useless as nobody would keep such person working for them.


This made me laugh. The kind of math that is required for engineering is no different than high school math: plug this number into that formula. Of course there is such a thing as "too much math" for a scientist or an engineer: any kind of pure mathematics (i.e. mathematics that are not relevant to their field of application--or any field of application, for that matter, except perhaps cryptography), which is the same as saying "any kind of real mathematics". The only exceptions are theoretical physics or computer science.

Do you know why most math professors in college hate teaching calculus courses and leave that burden to grad students when they can? It's because those courses are filled with science/engineering majors who don't give a damn about math.

[vexorian]

Engineering is not the epitome of math usage . In reality all you get to use most of the time is already-made formulas and methods.

Science is another level and there you really need that sort of stuff. Algebra is very basic to deduce new stuff from other stuff.

I think the US (and just about all countries) need a lot of science more than they need engineering. Changing math curriculum to better suit engineering as opposed to science sounds very lame.

Engineering is great and very useful, but it is applied science. Without innovation from science, engineering will stay the same and not move forward.

[Paqman]

Level 3: in science and engineering there is no such thing as too much math.

As an engineer I'd like to say: yes there is!

Maths is a tool, just like a spanner or an ammeter. It's usefulness is defined by the results it can achieve. After using the maths you need to solve your problem, it goes back in the box. Engineers don't have any interest in pure maths or complex proofs, they want to get things done.

[Bachstelze]

http://www.smbc-comics.com/index.php?db=comics&id=2647#comic

[Greenborn]

There are 2 kinds of people in the world: those who can and those who cannot.

Those who can include people such as surgeons, carpenters, electricians, pipe fitters, software developers, engineers, you get the idea.

Those who cannot include politicians, lobbyists, managers, corporate vice presidents and beyond.

Those who can always have been, are now, and always will be under the control of someone who cannot.

So if your goal is to be someone who cannot then you do not need to bother with Algebra.

Perfectly stated IMO.

If I was not forced to take a foreign language in high school I never would have realized I had an aptitude for learning languages. Realization of my new found skill led me to take Japanese in college then taking a job in Japan where I met my wife who is Japanese.


The same could be said for a high school student who dreads taking algebra, who after taking the algebra class, falls in love with algebra and becomes an engineer- a profession we sorely need American kids to aspire to be.


Thinking back to my high school and college days, the courses I did the best in were the ones the professors were the most passionate about teaching.

[3Miro]

As a Mathematician I know many people that do Math and don't care whether or not it has any applications. However, I have yet to see Math that doesn't have at least some kind of practical value.

Complex proofs are not simply mental gymnastics, they are a path to making things better. Not all engineering applications are the same and I cannot do the job of an engineer, but engineers come to me when they need math (i.e. this is my job).

Engineers need proofs that drive new algorithms. Engineers may rarely go into making those proofs themselves, but if you think that an engineer can go with just high school math, then you are clueless about the subject.

If you want to go back to my model and split level 3 into direct application (engineers) and level 4: theoretical derivation, this is fine by me. I lumped things together simply because the discussion is about high school algebra and I simply combined everything above that level into one.

[Bachstelze]

Engineers need proofs that drive new algorithms. Engineers may rarely go into making those proofs themselves, but if you think that an engineer can go with just high school math, then you are clueless about the subject.

If you want to go back to my model and split level 3 into direct application (engineers) and level 4: theoretical derivation, this is fine by me. I lumped things together simply because the discussion is about high school algebra and I simply combined everything above that level into one.

For lumping together two things so fundamentally different, I would say it's you who's "clueless about the subject". Are you really a Mathematician (with a capital, no less)? I doubt it.

[thatguruguy]

There are 2 kinds of people in the world: those who can and those who cannot.

Those who can include people such as surgeons, carpenters, electricians, pipe fitters, software developers, engineers, you get the idea.

Those who cannot include politicians, lobbyists, managers, corporate vice presidents and beyond.

Those who can always have been, are now, and always will be under the control of someone who cannot.

So if your goal is to be someone who cannot then you do not need to bother with Algebra.

Setting aside for the moment the Ayn Randian nonsense of this statement, I'm willing to bet that there are a number of managers and corporate vice presidents who have MBAs. I'm also willing to bet that most people who have an MBA are capable of doing algebra.

[Paqman]

Engineers need proofs that drive new algorithms. Engineers may rarely go into making those proofs themselves, but if you think that an engineer can go with just high school math, then you are clueless about the subject.


Depends, engineering is such an incredibly broad subject that its difficult to generalise. You could quite happily design a simple truss bridge or a pressure vessel with high school maths, but you couldn't design the software to model the flow of hypersonic gases in a rocket engine.

In practice most people don't do hard sums by hand, they use tools that have been built to automate the process of common computations. The tools are built by a minority who find it interesting, and everybody is happy.

I'd also be interested to hear what people defined as "high school math". The article singles out algebra, but the kind of examples it gives are about what I remember doing about age 14-15, I'd expect an 18-year old to be capable of much harder stuff.

[3Miro]

For lumping together two things so fundamentally different, I would say it's you who's "clueless about the subject". Are you really a Mathematician (with a capital, no less)? I doubt it.

The topic here was about high-school algebra and everything that I lumped together is well above that and hence all the same as far as the original point goes. I do have a ph.d. in math and I am a mathematician working in the largest science lab in the USA, although you do have a point that I should work on my spelling as far as capitalizing words goes.

[3Miro]

Depends, engineering is such an incredibly broad subject that its difficult to generalise. You could quite happily design a simple truss bridge or a pressure vessel with high school maths, but you couldn't design the software to model the flow of hypersonic gases in a rocket engine.

In practice most people don't do hard sums by hand, they use tools that have been built to automate the process of common computations. The tools are built by a minority who find it interesting, and everybody is happy.

Fine, split it into two more levels, I have no problem with that. Check the post above on why I lumped things together.




I'd also be interested to hear what people defined as "high school math". The article singles out algebra, but the kind of examples it gives are about what I remember doing about age 14-15, I'd expect an 18-year old to be capable of much harder stuff.

USA high school math covers Algebra, Trigonometry and sometimes basic Calculus. They also have things like pre-Calc which is more or less advanced algebra and/or trig and also some students take Euclidean geometry.

I have seen high-school students taking college senior level Real Analysis, which is very advanced, but is a rare exception. The overwhelming majority of students don't even take Calculus.

[JDShu]

Engineering is not the epitome of math usage . In reality all you get to use most of the time is already-made formulas and methods.

Science is another level and there you really need that sort of stuff. Algebra is very basic to deduce new stuff from other stuff.

I think the US (and just about all countries) need a lot of science more than they need engineering. Changing math curriculum to better suit engineering as opposed to science sounds very lame.

Engineering is great and very useful, but it is applied science. Without innovation from science, engineering will stay the same and not move forward.

To be fair, scientists have trouble getting jobs and engineers don't (generally speaking). That would imply that we need engineers more than we need scientists.

[Paqman]

That would imply that we need engineers more than we need scientists.

Two sides of the same coin, and neither is much use without the other. It's just easier to monetise the realisation of products than the ideas they depend on.

[JDShu]

Two sides of the same coin, and neither is much use without the other. It's just easier to monetise the realisation of products than the ideas they depend on.

If we were to believe that the market efficiently signals our preferences as a society, then I think it's a good indicator of what kind of people we "need" to train.

[KiwiNZ]

No more derogatory statements or this thread will be closed.
Refer Code of conduct

"Trolling, Attacks and Flaming: These are always forbidden.
Trolling is posting in a way that provokes emotional responses.
Attacks and derogatory terms of any kind are not welcome......"

[mips]

I'd also be interested to hear what people defined as "high school math". The article singles out algebra, but the kind of examples it gives are about what I remember doing about age 14-15, I'd expect an 18-year old to be capable of much harder stuff.

Over here when I was in school we did trigonometry, geometry, algebra, calculus and a few other things.

For algebra I recall things like polynomials,quadratic equations, matrices, linear equations.

For calculus I recall limits, differentiation & leibniz notation.

The stuff mentioned in the article you would have been doing very early on in high school. High school here was from age 13-18 (grades 8-12) and you could only drop mathematics as a subject at the end of grade 10.

Thing is a lot of kids only figure out later what they want to study after school and many of them do not meet university entry requirements as they did not do math (or maybe science). We don't have an open admissions policy here unless you are over a certain age.

[Paqman]

If we were to believe that the market efficiently signals our preferences as a society, then I think it's a good indicator of what kind of people we "need" to train.

Training one without the other would be pointless though. They're mutually dependent.

[Morbius1]

I'm willing to bet that there are a number of managers and corporate vice presidents who have MBAs. I'm also willing to bet that most people who have an MBA are capable of doing algebra.
You've never made an executive presentation to any of those people have you? I was having a perplexing time getting the message across to these folks until I discovered the miracle of stoplight charts. Big bright colorful circles - Green ( good ), Yellow ( Roh - Roh ), and Red ( somebody's going to get it - I pray it's not me ).

They only had to know 3 states and it was best if there were as few words as possible on the chart - unless it was Red in which case I would try to divert attention to someone or something other than me. Out of an instinctual sense of self survival I rarely had Red charts and if I did it was never for things for which I was directly responsible. I made sure of it since I was one of those who can. :p

[thatguruguy]

You've never made an executive presentation to any of those people have you? I was having a perplexing time getting the message across to these folks until I discovered the miracle of stoplight charts. Big bright colorful circles - Green ( good ), Yellow ( Roh - Roh ), and Red ( somebody's going to get it - I pray it's not me ).

They only had to know 3 states and it was best if there were as few words as possible on the chart - unless it was Red in which case I would try to divert attention to someone or something other than me. Out of an instinctual sense of self survival I rarely had Red charts and if I did it was never for things for which I was directly responsible. I made sure of it since I was one of those who can. :p

I've recently had a similar experience. I had a client who's an engineer who was buying into a an LLC and taking a management interest. Prior to my involvement, all of the relevant documents (inter alia, various agreements, as well as the documents relating to the management of the company) had been drafted by non-attorneys; in fact, they had been drafted by the guy who started the company, who is also an engineer and a software guy. It was clear that these non-attorneys didn't understand how to properly preserve the corporate veil, nor did they understand the basics of fiduciary duties (the ones which run from the managers to the LLC, the ones that run from managers to the members, nor the ones that run from the members to the other members). Just about every document had to be significantly revised in order to be legally enforceable.

It is possible to derive one or more inferences from my experience:


everyone who is not an attorney is a simpleton, or
smart people tend to understand those things that they deal with on a regular basis, but don't necessarily understand things that are outside of their expertise.

I'll leave it to you to decide which of the above inferences is true.

[vexorian]

To be fair, scientists have trouble getting jobs and engineers don't (generally speaking). That would imply that we need engineers more than we need scientists.
It could imply the perfect opposite. That we are doing too much engineering and too little science.

Science has to be competitive though and it has to be difficult to get in. We need elites.

A lot of people have the idea that school is supposed to teach you useful stuff. I say nay. A lot of the good school does is to teach you not things you are going to use in the future, but to teach you what you are good at. If we remove true math and leave the "do this" math, those few potential scientists may never know that they could be good at.

Just like we teach literature even though most people will never write a novel.

[thatguruguy]

It could imply the perfect opposite. That we are doing too much engineering and too little science.

Science has to be competitive though and it has to be difficult to get in. We need elites.

A lot of people have the idea that school is supposed to teach you useful stuff. I say nay. A lot of the good school does is to teach you not things you are going to use in the future, but to teach you what you are good at. If we remove true math and leave the "do this" math, those few potential scientists may never know that they could be good at.

Just like we teach literature even though most people will never write a novel.

Likewise, it's fairly easy to get a job as a garbage collector. That doesn't mean we need to gear the entire educational system to produce garbage collectors.

[JDShu]

Training one without the other would be pointless though. They're mutually dependent.

Nobody is saying that we don't need scientists at all. It just seems to me that we just need more engineers than scientists.

[JDShu]

Science has to be competitive though and it has to be difficult to get in. We need elites.


Well what we're seeing right now is people graduating with PhDs from top universities having a lot of trouble getting jobs. They are, arguably, the elites which we supposedly need. And evidently, we don't need them enough to pay them.

[Lightstar]

Definitely needed.
It helps a lot in passive ways.

[Old_Grey_Wolf]

Algebra is a part of our lives whether we realize it or not.
You want to make twice as many cookies ....

I was thinking the same thing. People use algebra all the time and don't realize it. Converting currency is the one that I was thinking about; such as, e=1.24d or d=0.81e, where e is EUR and d is USD. Carpenters use what they call the 3-4-5 rule, which is actually the Pythagorean Theorem (A^2+B^2=C^2).

Maybe algebra seems hard because of the way it is taught.

[mips]

I was thinking the same thing. People use algebra all the time and don't realize it. Converting currency is the one that I was thinking about; such as, e=1.24d or d=0.81e, where e is EUR and d is USD. Carpenters use what they call the 3-4-5 rule, which is actually the Pythagorean Theorem (A^2+B^2=C^2).

Maybe algebra seems hard because of the way it is taught.

When someone throws a ball towards you your brain is actually doing some mean integral calculus in order for you to be in the right spot to catch said ball at the right time.
https://docs.google.com/viewer?a=v&q=cache:plhrZDked5kJ:math.msu.edu/users/gnagy/teaching/11-fall/mth234/L10-234.pdf+&hl=en&gl=za&pid=bl&srcid=ADGEESiHNS6CfBJTlLl7qF2rWQbxwn2WG-OSXNulG9kLzVLC8Ae8ZtQvSx1ARAHJfHLxcJdTkLWGq4fS04ze cd_YBTm2BTZdjTrUNxkaGINe60mJYW_8MlDhY59Q1Y435li3VH R_ZNkr&sig=AHIEtbT-DckzeG_JtEdOCYcNFA3BWSjrlg

[ZarathustraDK]

Pfff... yeah...good luck with that nature-scientific-related education at the university if you first start learning "difficult" math in highschool/college.

I learned trigonometry, algebra and arithmetic in elementary school, which I found tasking (I didn't particularly like math). Then I learned differential- and integral-calculus in highschool/college (we call it "gymnasium" in Denmark, 3 years, usually from 17-19 years of age). That was pretty hard in itself.
THEN I went to university and had classes in OMGWTFLOL-math, because I wanted to study biology. It was simply too hard for me so I gave up.

Point is, that last OMGWTFLOL-math was NECESSARY in order to study ANY of the scientific fields. It doesn't get any easier if you postpone the basics, it just makes the hill steeper.

I'd much rather substitute religion-class (yeah, we had those in elementary-school) with philosophy, logic and argumentation-theory, much more useful.

[pcfast]

I guess Colleges are realizing if they want to attract students, dropping math requirements is a good idea! :)

http://dyscalculiaforum.com/forum/viewthread.php?thread_id=1750&rowstart=0

[whatthefunk]

I guess Colleges are realizing if they want to attract students, dropping math requirements is a good idea! :)

http://dyscalculiaforum.com/forum/viewthread.php?thread_id=1750&rowstart=0

Ehh.....that is a list of colleges that will wave the math requirement if a person has dyscalculia, a learning disability. I had a friend in college who had that. He simply could not understand math. He had to start with remedial geometry which most people take either in junior high school or early in high school. In order to graduate, he had to pass basic algebra and an accounting class, which he did after three times and with a D-.

[eddier]

Where I work, we had a 17yr old girl start, and one day, I asked her to fetch me a dozen, of a particular item. She replied, "How many is that?". I told her, "Just the one dozen will do." Again , she asked "How many is that?" I asked her how many she thought it was,, and she just didn't have a clue.... and that's simple numbers, not algebra.

Aha! the wonders of Metrication--no such thing as a dozen?

eddie

[lindsay7]

The dumbing down of America continues. Let the Chinese and Indian school kids study the hard subjects, we will be the third world countries in a few short years. Ever wonder why all the engineers and high tech people are not Americans?

[mips]

Aha! the wonders of Metrication--no such thing as a dozen?


He should have asked for a bakers dozen, imagine the confusion then :biggrin:



The dumbing down of America continues. Let the Chinese and Indian school kids study the hard subjects, we will be the third world countries in a few short years. Ever wonder why all the engineers and high tech people are not Americans?

Maybe it's easier/cheaper to hand out green cards/visas than to invest in local education. You guys import a lot of skill and it's a fairly easy process. I went for a interview once with a company from Boca and they had a contract ready for me to sign at the end of the interview, visas, plane tickets and other stuff they would courier to me within 4-6 weeks and when you arrive there make sure you have accommodation (on their tab). There are agencies that do aggressive recruitment overseas all the time for the US market.

I always find it hard to believe that someone in the US with a science/engineering background can't find work while lots of skill is being imported.

[lisati]

Aha! the wonders of Metrication--no such thing as a dozen?

eddie

*mildly nostalgic rant begins*

When I started school, the New Zealand currency was pounds, shillings and pence. A year or two later, it changed to the $NZ and cents, with $0.10 being equivalent to 1 shilling. Metrication/decimalisation of weights and measures came a few years later. Mrs Lisati, being a few years younger, missed out on some of the fun of learning the "odd" conversion rates.

I'm still a bit baffled, however, about this newfangled weight based on the mysterious cagey! :D (Yes, I know, they mean kg but can't be bothered working out that it's pronounced "kilogram"....)

*mildly nostalgic rant ends*

[zombifier25]

Aha! the wonders of Metrication--no such thing as a dozen?

eddie

I use metric and I know what dozen is. It's a word, some knows it, some don't, metric or not.
On a related rant, Americans might do better at math if they adopted the Système international d'unités :P

[WinterMadness]

I use metric and I know what dozen is. It's a word, some knows it, some don't, metric or not.
On a related rant, Americans might do better at math if they adopted the Système international d'unités :P

this american agrees