Discouraging Students from Taking Math

Coryoth writes "Following on from a previous story about UK schools encouraging students to drop mathematics, an article in The Age accuses Australian schools of much the same. The claim is that Australian schools are actively discouraging students from taking upper level math courses to boost their academic results on school league tables. How widespread is this phenomenon? Are schools taking similar measures in the US and Canada?"

Comments

It'll all work out

[SomeJoel]

After a few generations of not taking any math, administrators won't be able to figure out why not taking math increased their average scores in the first place. At that point, they'll re-institute a math program, probably cutting out history, since that's over and done with.

Re:It'll all work out

[donaggie03]

This isn't about each student's ability to gain admission into college. The schools are doing this because when students get good grades, the school gets recognition and money. If more students take harder classes and therefore get lower grades, the school gets less money and less recognition. Therefore, make everyone take classes they will get A's in and all is good.

Re:It'll all work out

[mcmonkey]

Evidently, they've already cut out critical thinking considering that high school grades are only a small part of what universities look at when considering a student, at least in the US. Standardized tests such as the SAT play a far more important role. Get a 1600 on the SAT and it doesn't matter what your grades were, you have your pick of the colleges.

Actually, high school grades are a better predictor for college grades than SAT scores. And most colleges know this. SATs are only a big deal for folks selling SAT prep courses and TV shows that can't come up with anything more original than another 'JR's worried about his SATs' episode.

Someone with a perfect SAT score (which would actually be 2400 now adays, not 1600) and bad grades is likely a smart, lazy high school student who will become a smart, lazy college student. Been there, done that, have t-shirts from several fine institutions of higher learning.

I dropped my math course

[Anonymous Coward]

It was sweet. I went from six classes to four.

Re:I dropped my math course

[Warbothong]

The number of times I've had to remind my fellow University students that 1) we are paying for lectures, 2) we have exams to sit which decide who passes and who doesn't and 3) we are not obligated to attend anything, is frightening. "Yay, cancelled!" is such a stupid ass position to take. Don't want to go to the lectures? Then don't go, nothing's stopping you. Wonder why you spent the exam staring at a page of unintelligible gibberish? Maybe because you didn't go to the lectures.

"Yay, cancelled!" is in the same catagory as "Well nobody else did it either". People who think that is OK will be happy when they are talking about passing their course, which to them means 'getting a high paying job'.

Isn't this a good thing?

[glindsey]

Oh... wait... I thought it read "discouraging students from taking meth."

My mistake.

Re:Isn't this a good thing?

[Larry Lightbulb]

As there's already a thread about Math/Maths, let me say that in the US METH = Methamphetamine, while in the UK METH = Methylated spirit.

in college this would make some sense

[wizardforce]

It would make a little more sense if this was college when you have an idea what you want to do with your life and realize it doesn't make sense to take calculus to finish out an art/language major. But really, a student that is not interested in going into the sciences is unlikely to use calculus or higher mathematics much, but that doesn't mean they should drop it just to boost their GPA.

Re:in college this would make some sense

[happyemoticon]

The mistake you're making is looking at this from the perspective of the student. They're not talking about boosting the students, they're talking about boosting the school's ratings. I don't have the full story on Australian/UK educational policy, but the climate sounds like the US's "No Child Left Behind Act" policy, which diverts teaching resources away from actual teaching and focuses on teaching students to perform well on yearly standardized tests.

The net result is overwhelmingly bad. Just as the article describes, by attempting to make your kids appear better statistically, you make them less educated in actuality.

Re:in college this would make some sense

[R2.0]

Absolutely - I think the NCLB should be unceremoniously dropped, the Department of Education abolished, and the money saved used for debt reduction.

Wait - you want to KEEP the money given to states under NCLB? Just not comply with the terms? I understand now.

Re:in college this would make some sense

[Lockejaw]

Indeed. The NCLB folks need to realize that if you only teach what the least capable students can learn, the class will only be taught what the least capable student can learn.

Re:in college this would make some sense

[Anonymous Coward]

When I took mathematics at A level (That's the hard 6 module version and mostly pure maths for people who care) in the UK, more than 50 people started the course. Many people left of their own accord because they felt it was too difficult and some were 'encouraged' to leave. 12 people finished.

Physics A level started with 10 poeople iirc, and finished with 3, all of whom left of their own free will, as my physics teacher welcomed everyone and believed - correctly in my view - that even if they didn't do well in the exams, it was still time well spent.

She is the most highly educated person, I've ever met incidentally, possessing seven undergrad degrees as well as her postgrad.
I could also tell you the story of the person with two E grades in physics and mathematics, who got in to the University of Cambridge when his contemporary with four A levels, at grade A, didn't.

Fact of the matter is that subjects like physics and maths are valued more highly than many other subjects even when you haven't got such a good grade as you would have done if you'd taken sociology or geography instead.

Re:in college this would make some sense

[Bluesman]

That might be true, but why doesn't the "well rounded education" argument ever come up when math and hard science classes are in jeopardy?

There's no shortage of people willing to defend the liberal arts because a well rounded education is so necessary to being a good person, but they're strangely silent when attendence in technical courses is dropping.

Re:in college this would make some sense

[Gilmoure]

Man, I loved physics, and, once I could see the problem in diagram or demonstration, I was able to get the math part of it. Then I got to college and took basic Algebra 101. Failed it twice. Finally, third time, had a teacher who taught it a different way and I was able to pass it. A few years later, working as a mechanic, figuring cylinder chamber pressures and such, I was using it again. Am one of those people you have to draw a diagram for.

Re:in college this would make some sense

[happyemoticon]

True education has been replaced by the ersatz education of testing and scoring, which is one big, complex game which has little to do with the true advancement of knowledge.

It helps to think about this in economic terms (by the way, feel free to shoot me down here, I'm not that good with economics). With fewer new schools being built and more students wanting to go to college because it is increasingly a factor in one's success, there is a lot of competition to get into college. One would think that more competition would result in brighter kids in college overall. However, colleges are increasingly complaining that incoming freshmen are not prepared for work at the college level.

However, we do not select freshmen based on factors which will lead them to success in college, such as reasoning, curiosity, or perseverance. We select them mostly based on grades and test scores. The tests test the student's ability to solve brain teasers. They are easily subverted, and there are myriad non-cheating ways to game the system in order to inflate your score. Also, classes are increasingly being taught to the tests, because that's what the parents want.

Therefore, there is increased competition, but due to highly imperfect information on the part of the colleges about which kids will perform best, they make worse choices as to who gets in. Furthermore, because the kids are less prepared, and there's nothing to do about it, they must make the courses more remedial. And then, everyone in the educational system gets stupider.

Re:in college this would make some sense

[Stradivarius]

NCLB does not divert resources away from teaching. It influences what is taught. If one happens to think the standardized tests actually test what we want students to learn, then this is a good thing. If one happens to think the standardized tests fail to measure what we want students to learn, then it's a bad thing.

In either case, however, the solution is to make sure the tests are measuring the right things. There are a lot of people who feel the tests aren't doing that - so let's fix the tests.

What we should NOT do is abandon the whole premise of measuring progress just because the tests could be better. (I'm not saying you did or did not advocate this. But a lot of anti-NCLB folks do just that). The only real way to know where a school needs improvement, and whether attempts at improvement are actually working, is to get some sort of empirical evidence, which pretty much boils down to testing.

Re:in college this would make some sense

[digitig]

What we should NOT do is abandon the whole premise of measuring progress just because the tests could be better. Measuring is good. The issue is what you do with the measurements. If they're out of parameter then they should be investigated; there may be good reason, in which perhaps you refine the tests to take that reason into account, or there may not be, in which case you intervene. I don't know about the NCLB situation, but all too often here in the UK the measurement is tied automatically to the measurement, with nobody actually looking at why the measurement is the way it is: management is replaced with administration; it's cheaper and you can always blame somebody else. And the results are disastrous, because the measurements end up rewarding people who are good at manipulating the measurements, and penalising those who focus on the job. Anybody who looks can see it happening, but those who set the targets choose not to look, and the whole performance indicator tied to reward/punishment system doesn't have anybody whose job it is to look.

Re:in college this would make some sense

[thePsychologist]

Mathematics, like reading, exercises the mind, which is never a bad thing.

Re:in college this would make some sense

[CastrTroy]

In Ontario, there's a board that you apply to when you are applying to university/college. They know about all these stupid tricks that highschools try to pull to make their students seem smarter. They know that some schools hand out A's like candy on halloween, and they also know that some schools don't give out a lot of As. My physics teacher told us that he could give us all As, but that wouldn't make much difference for getting into university, because they would look at the class average and conclude that you didn't do much better than anyone else, and you were just average. I think this kind of situation works out a lot better than standardized tests where students can study the test, and learn to pass it without actually learning any applicable knowledge. It also works better than assuming that all schools are following some magical grading standard and assuming that getting an A at one school is the same as getting an A at another school. I think they should take the same approach in this situation. Do a more in depth analysis of what courses the students are taking, as well as how well they do after they leave the school, and you'll get a much better picture of how well the school is actually doing. Basing any metric just on the marks of the students is a very bad way to measure things.

Re:in college this would make some sense

[happyemoticon]

I disagree. Teaching a student so that they perform well in a test and teaching a student so they will eventually perform well in college and life are very different things. I have heard reports of colleges who complain that students are increasingly ill-prepared in terms of reasoning, thinking, researching, and persuasive writing, because these things are hard to test in the standardized testing environment. From what I have heard first-hand from people in teaching credential programs, many kids in charter schools are barely being taught to write. They are being taught to take standardized tests.

I don't mean "Teach this fact, which will be on the test, and not this other fact." I mean teaching only to parrot facts without achieving a depth of understanding. Teaching to bubble in responses rather than write a clear and convincing argument or extracting knowledge from a book unaided.

I know there are a lot of holes in that. I don't have time to really back up my position. However, if you want empirical evidence, testing is not the only way to get it. Testing is just pretty cheap and fast. A far more effective way to get a real sense of the problems in schools would just be to send actually human beings to them to write reports, but it would be very costly and subject to variance and human eccentricity. In fact, I think that our aversion to any type of evidence that doesn't fit in a spreadsheet is part of the problem.

Re:in college this would make some sense

[Sigma 7]

It would make a little more sense if this was college when you have an idea what you want to do with your life and realize it doesn't make sense to take calculus to finish out an art/language major. The problem with that line of reasoning is that it seeped over onto the more technical paths, including Computer Science. Most students (incorrectly) believe that they won't need the advanced math when they go out into the business area, which has resulted in focus being removed on what should be a critical course.

In my opinion, I feel that high-school has suffered from this reasoning as well - especially when combined with the fact that you do not get to keep a permanent reference for future study.

Re:in college this would make some sense

[phulegart]

"NCLB does not divert resources away from teaching. It influences what is taught."
--Wrong.

"In either case, however, the solution is to make sure the tests are measuring the right things. There are a lot of people who feel the tests aren't doing that - so let's fix the tests."

Let me give you some real world perspective. In 2005 I worked for an after-school tutoring company, in Las Vegas. We would tutor high school kids in basic math and English, so that they could pass the state proficiency tests. This was not to boost a school's ratings. This was because just about half of the high school students in Las Vegas were flunking the math portion of those standardized tests. Were the tests too difficult? No. These students could not do math involving fractions. These students could not do math involving decimals. Some of these students could not do math involving division. These were 9th, 10th, 11th, and 12th graders. There was no predominant racial bias to the spread of students. I know that these students could not do these things, because I had to tutor them 2 to 3 times a week for between one to two hours a session. I would tutor up to 5 students per session, and it was a full time (40 hour work week) job.

Do you know what No Child Left Behind means? It means that regardless of whether or not the student can do the work they get promoted to the next grade with their classmates. It also means that at graduation time, if they cannot pass the standardized tests, they are out of school without a diploma. If you find that you cannot believe this, then educate yourself. I was one of the people that had to take a 12th grader who obviously would have been held back much earlier because he did not know algebra, geometry, trigonometry, or even basic fractions, and teach him all of these things so he could actually graduate with a diploma.

The tests don't need to be fixed. The students need to stay in those classes until they learn the information that the tests are testing for.

Re:in college this would make some sense

[hazem]

NCLB does not divert resources away from teaching

Having worked in a school district when NCLB was instituted, I can tell you that it does, indeed, divert resources from teaching.

NCLB requires use of standard tests, which cost a lot of money to administer. In Oregon, those tests are done by computer, and the systems required upgrades to the computer systems and computers. In fact, several schools in the district created computer labs that were only to be used for testing and not for instruction. In addition, new administrative staff have to be hired to handle the workload of ensuring compliance.

In a rural school district with limited resources, the money for all this testing and equipment has to come from somewhere and that somewhere is usually the budget for optional programs, laying off teachers, skimping on resources such as needed new textbooks, and building enhancements.

This is why many school districts claim the NCLB requirements are an unfunded mandate. They have been required by the federal government do to these things yet were not given funds to do it.

On top of that, the testing regime takes about a week of class time out of the year.

So basically NCLB is a big win for companies who sell and administer standard tests. Everyone else pretty much gets screwed. Schools have less money, students get less education, and the country gets dumber.

If you really want to help the US education system, do the following:
* ban sodas and candy and fastfood
* expand the free lunch program to every kid and include breakfast - hungry kids can't learn - and there are too many of them
* go to year-round schooling with longer non-summer seasonal breaks
* make physical education mandatory at every grade level - they need breaks and exercise
* allow merit-based pay/bonuses for teachers who do a good job (using a variety of metrics)
* lower class sizes - a teacher can't manage 38 kids AND teach them
* lower the administrative burden on schools so they can hire more teachers and fewer administrators

Re:in college this would make some sense

[Fulcrum of Evil]

if this was college when you have an idea what you want to do with your life and realize it doesn't make sense to take calculus to finish out an art/language major.

Why not? I took shakespeare and comparative religion to round out my CS degree.

Re:in college this would make some sense

[EggyToast]

Yes, because it makes the difference between watching a movie and saying "by golly, thems some purty pictures" and "oh, that's directly influenced by this classic play, that's neat."

You've got a point on the Monet, though.

Re:in college this would make some sense

[janeil]

Right on, fellow educator.

It's hard for those of us who teach in the public schools to read this sort of thread, people just don't know the reality. For me, the biggest impact of NCLB is like you said, it takes a week out of the school year.

To the tutor above, you bet, most high school students can't do arithmetic with fractions and decimals. This had been a steadily declining skill since the advent of calculator use in the late 80's.

"I have heard reports of colleges who complain that students are increasingly ill-prepared in terms of reasoning, thinking, researching, and persuasive writing,"

No kidding. But tell me slashdotters, did any of you learn to reason or think in school? I'm an old guy, went to school in the 60-70's, crushed the sat's, bfd, but I don't recall any teachers I had that did anything other than just work us hard on old-time school, do 1-90 odd. Teaching reasoning and thinking is just a really hard thing to do.

Bottom line for me is, forcing a teenager to try to do mathematics that is a complete foggy mystery to them is cruel and unnecessary. Everybody has their own level, I thought calculus was easy but fourier series was kind of tough. I couldn't follow the Principia, so does that make me bad at math? Neither does it mean a kid who can't do algebra is bad at math. Give them a break and let them take "Practical Math for the Real World III" and get their math credits.

Re:in college this would make some sense

[Bluesman]

You would absolutely love having a background in EE.

It makes the difference between shopping for a CD player and saying, "Oh, so they put fun inside" and "it's still going to be limited by the sensitivity of the DAC, so I don't need to pay extra for the oversampling."

Re:in college this would make some sense

[mikael]

I'd give you +1 insightful moderation points if I had any.

The best teachers we had were those that had the entire syllabus on glossy workcards (glossy to stop them getting all torn and smudged). In that way every student could more or less work at their own speed. If anyone missed or fell behind a lesson for any reason, they could quickly catch up by working at home. The worst teachers were the ones that made everyone work in lock-step from the blackboard - mainly wordy subjects like history.

The best books were the Lett's study guides for A-levels. They had the entire syllabus for every exam board listed on the front pages, along with each module in a separate chapter. Combined with past exam paper questions, anyone who
wished to learn a subject could simply work from home in this way.

Re:in college this would make some sense

[Nazlfrag]

If you want the state to create you a job move to China.

Re:in college this would make some sense

[aqk]

>>>half-line r = pi/2 has ever made me a more rounded individual or better person.

Huh? trying to square the circle, are you? Rounded you say?
(sigh) Must be a sine of the times...
"Know thyself" - Socrates.

Re:in college this would make some sense

[Chandon Seldon]

Am one of those people you have to draw a diagram for.

The only difference between people like you and the people who are "really good at math" is that they can visualize the diagram by themselves. There are some people who can pass math courses by memorizing formulas and pattern matching them to problems; a lot of math teachers (especially women) learned that way, and so they try to teach to that learning style. Problem is, with that learning style you never really learn the math, you just memorize formulas. It's that teaching style that makes man people who are *innately good at math* hate the subject.

Re:in college this would make some sense

[ShakaUVM]

If you really want to help the US education system, do the following:
* ban sodas and candy and fastfood
* expand the free lunch program to every kid and include breakfast - hungry kids can't learn - and there are too many of them
* go to year-round schooling with longer non-summer seasonal breaks
* make physical education mandatory at every grade level - they need breaks and exercise
* allow merit-based pay/bonuses for teachers who do a good job (using a variety of metrics)
* lower class sizes - a teacher can't manage 38 kids AND teach them
* lower the administrative burden on schools so they can hire more teachers and fewer administrators


I'm an evaluator for around 20 school districts around California, and I have seen all of the above done, and it still doesn't help.

Re:in college this would make some sense

[domatic]

The standardized tests also need to vary tremendously from year to year. A major problem with No Child Left Behind is damn near every school district in the US is "teaching to the test" the state administers. If the test format were highly unpredictable from year to year then designing curricula around it would be of little help and the tests might then actually measure something.

Re:in college this would make some sense

[hey!]

The same argument could be made against honors math classes.

When I was an MIT freshman, many, many moons ago, the European students were from the elite. They had tons more calculus than the Americans. This was a big advantage -- for about half a semester. By the end of freshman year, there was no difference in mathematical skills between European and American students.

In the end what matters is the ability to reason mathematically, not having a checkmark on your transcript, or a high grade on a test.

Here's a story I often tell. In one of my jobs after school, I was the company geek. People came to me when they needed their newfangled digital watches set (this dates me pretty well). I once had a guy come to me with a problem: he had a friend who made penny whistles, and that friend knew the correct length to make a B flat whistle, and he had a formula that, given a properly sized whistle, yielded the correct length for a whistle a half note higher. But he wanted to make an A whistle, and couldn't figure out how to do it. He went to his friend, who went to me.

After rearranging the formula, I calculated the correct length, and then plugged it back in to the original formula to show it was right. I then asked this guy whether he had taken Algebra in high school. He said he had, and he had done well in it. In fact, he was perfectly capable of doing the operations I did, but it didn't even occur to him to use anything he'd learned. He actually seemed surprised that I had found a practical application for Algebra..

So -- I don't think it matters that much. A lot of people graduate with what I call a "cargo cult" math education: they can go through the motions, but they don't know what it all means. I'd rather have people entering college with strong math reasoning skills and solid math through algebra and trigonometry, than entering with the ability to manipulate symbols in a Calculus-y sort of way without grasping the significance of what they are doing.

There's nothing intrinsically wrong with testing, as there is nothing intrinsically wrong with honors math courses. The problem with testing is how much harder it is to create a good test than a hard test, and how few people realize the distinction between the two. Tests that are inordinately hard generate a flurry of action; they make things happen. Unfortunately, it's pure luck whether those things are really useful things. A good test tells you things you really need to know. It is neither so hard that most people fail it, nor so easy that everybody passes. Difficulty is the least important aspect of a test; you simply calibrate the difficulty to yield the most information. Difficulty is almost not a policy issue at all, or shouldn't be. The test difficulty is simply calibrated to yield the highest entropy in score distribution. It is the nature of the challenge that is critical. Does it really require the student to engage in mathematical thought, as opposed to procedure?

A retreat from offering advanced math courses is not necessarily good, or bad. If you are doing less advanced math, the question is what are you doing in its place. If you are concentrating on bringing your school's pass rate up, it is a sign that the tests you are teaching to are (a) too difficult and (b) bad.

Here in the States, we have a law called "no child left behind", which is basically a "states rights" version of ed reform. States are free to create their own tests, so everything depends on what state you're in. I've looked at some of the questions in my state, and I actually think the questions are pretty good. Much of the emphasis is in converting problems into mathematical representation -- precisely what my post-Sputnik generation needed most. As a result, my children got intensive practice in reasoning with mathematics from the first grade. As soon as t

In soviet Russia...

[frieza79]

Math discourages you!

Shhhhhh

[RealityMogul]

The US doesn't do that, we just hide our heads in the sand and ignore the problem: http://www.msnbc.msn.com/id/20205125/site/newsweek /

Re:Shhhhhh

[jc42]

Well, in my high school (a couple decades ago now), they went past ignoring the problem. In my sophomore year, I decided that math was interesting, so in the first month, I read through the entire textbook. Then I started borrowing books from the math teachers. By the end of the year, I'd made it through their college calculus books.

Their response? They finally woke up to what I was up to, and let me know that they wouldn't be loaning me any more math books. I was supposed to learn it in classes, not on my own time. They were all in agreement, and I didn't get another math textbook from them.

However, I did have some good friends at a nearby college. I borrowed math books from them. The high-school teachers didn't learn about it until the next year, when I didn't enrole in any more math classes, and explained why.

What was especially bizarre was that when I finally graduated and went off to college, I passed all their entrance math tests and got the most "advanced placement" that they gave bright students: They let me enroll in second-year calculus. I knew the subject better than the instructor did, which didn't exactly endear me with the instructor. But "That's the rules", and there were no exceptions; I had to have that class to be allowed into more advanced classes.

(Note that I've carefully said nothing that would identify the schools. This is intentional, so you might suspect that it might be schools in your area. ;-)

Re:Shhhhhh

[sqrt(2)]

I read that same article earlier today. Did you notice the part where Germany and several other countries dropped out too? And the price tag? We could throw that money somewhere else, maybe...hire a few more math and science teachers?

Re:Shhhhhh

[tftp]

Graduate math students or full professors taught all the math courses at my university

In my university years I had to have a full year course of Technical Electrodynamics. It was super-heavy on math (we started on Maxwell's Equations about five minutes into the course.) It was taught to us by a TA. I am still amazed at his memory - he was really good with the stuff, and you need to literally remember whole books (or to be a genius of Heaviside class who would do that from scratch as needed.) He was not a professor yet, but he wasn't far away from that.

Re:Shhhhhh

[Moridineas]

(Note that I've carefully said nothing that would identify the schools. This is intentional, so you might suspect that it might be schools in your area. ;-) Let me guess.. Washington State and Wisconsin?? ;-)

But seriously, that's pretty pathetic. At my highschool, there were a handful (out of a graduating class of ~300, maybe ... 4-5?) kids who were above AP Calc BC level and were going to a local university to take math classes. I kinda feel like in a situation where teachers are hostile and unhelpful, parents really need to get involved if the teachers are too lazy to do anything on their own!

With regards to prerequisites... they are about knowledge yes, but they are also about work. Plenty of people can score well on tests, but a lot of those people then don't have the willpower to work. Whether it's laziness, getting distracted by parties, social life, video games, whatever. The education system is basically about weeding people out, and prereqs are just one way of doing that.

One of my friends since middleschool (say age 11/12 or so) is an absolutely brilliant guy. In school he was excellent at math and physics and a supremely talented musician. ~8 years after we started college, he still hasn't completed his undergrad, and works at a waffle house. Kinda makes me sad because he would be absolutely brilliant at whatever he did, but he just can't pull it together. He's pretty happy though--he spends most of his time as a moderator on a gaming board, gaming, and ranting about corporations and the system. He's smarter than me, so maybe he knows something I don't :-)

What upper-level math courses?

[jcorno]

In my high school (it was a Georgia public school), you had to have skipped 6th grade math to get to super-basic (no AP) calculus in high school. Otherwise, you topped out at trig. On top of that, trig was optional even for what they called "college prep" diplomas. Guess how many people were in that class. That was going on 15 years ago, though.

Worrying

[Midnight Thunder]

This is what you get when schools do what it takes to look good. While they are too blame, the blame also lies on governments and parents who are looking for schools which turn out the most graduates.

Ideally a rating system should be based on the "quality" of those grades. What I mean by this is that the maths levels would be broken down into categories from easy to advanced. A school should be given higher marks if they manage to turn out a few good maths students as opposed to many low level maths students. I am not sure how this could be made to work in reality though.

Re:Worrying

[Pecisk]

This "tweaking" of performance is one of the reasons WHY I hate ratings of schools. I mean, wtf, we already have competitions between students themselves at country, world level. So let's stay it that way.

Ok, maybe it is fun to have such competition between schools once in ten or five years, but in long term it is hurtful. Education is NOT competition, when you learn, you just start to understand what to do with your power of knowledge and wisdom. Competition at such level crushes pupils which are emotionally weaker in time when they are not ready yet to stand on their own feet. It also popularizes more cynical point of view (versa friendlier, knowledge sharing like) to the world and can harm also motivation of smarter students.

When competition takes main role in the school, lot of students rushes trough material without trying really to understand it. Hapily, I spent my last secondary school's years in class which was full of "common man geniuses" (seven people tried to enter Med Academy, only two didn't succeded), I never felt to be in competition with them, because it was never forced. Yes, in the end, they dug material better, but I got my share of knowledge. And lot of very good friends.

In the end, it is not only knowledge that matters.

The obligatory...

[Kerrit]

I, for one, welcome our new woefully innumerate overlords.

True story:

[Anonymous Crowhead]

I worked in a lumber yard one summer when I was in college. I worked on the end of line that spit out two by fours cut from logs. The pallets were always of different height, but always the same width - 10 units. At the end, you had to paint the total on the side. So if it was 14 units high, you'd have 140 pieces. Me being "just a kid" wasn't trusted to paint the number. The "senior" person busted out a calculator every fucking time. To multiply a number under 20 (the max) by 10.

Re:True story:

[hajus]

Those kinds of people make me feel like rainman sometimes.

Re:True story:

[Garabito]

I bet posting twice the same comment really makes you feel like rainman.

I am fine with this

[thesupermikey]

There is little reason for most students to take upper level math. As a historian and a writer, i never EVER use anything more than arithmetic or geometry. Not being able to do calculus has never ones been a problem in my education or work.

In fact, when i was applying for grad schools a year ago, i asked the head of the department that i am in now if my VERY low GRE math score would be a problem. The answer was very clearly "no"

at any rate...American schools need to give kids the option of doing a calculus track in math or a statistics track in math.

Not really a new thing

[rsavela]

At my high school 10 years ago, I was not allowed to take Calculus senior year. An A or B+ average was required in trigonometry to take the calculus course. Other than pushing up the schools average on the AP exams, I didn't understand why I was not allowed to take the course. Trig is a small part of differential and integral calculus. Memorizing double and half angle formulas turned out to be a waste of time anyway (my professors later in life insisted that we be able to derive them ourselves, rather than memorize...) Besides, I had passed trig anyway. Why take trig again for a better grade? I calculus needed it for the university I ended up going to. I ended up paying out of my own pocket to take the course at a local university after school. Kind of a waste for me to be sitting in a study hall, while the class was already being taught at my high school. In the end, it worked out for the best. A university mathematics professor is a far better qualified to teach calculus than a high school teacher. I knew plenty of teaching majors that went on to teach high school math. Compared to engineering majors, they understood very little about mathematics.

I taught 8th grade science

[EMB Numbers]

I taught 8th grade science, and we were always encouraging students to take as much math as possible.

Unfortunately, students make short sighted decisions in 8th grade that determine whether they are on the calculus track or not. You must start on the path that leads to calculus in 8th grade or it is unlikely you can catch up by 12th grade.

We held an annual pep-rally for 7th graders encouraging them to enroll in math and science courses in 8th grade. If they don't, they are closing doors for future opportunity. Without calculus in high school, it is difficult to be accepted directly into technical/science degree programs in universities. At a minimum, some remedial college math is likely to be required. If you think you might want to be an engineer, scientist, doctor, mathematician, actuarial, astronaut, architect, etc. you should take the most advanced math offered by your school.

In fact, with few exceptions, if you want a high paying job that doesn't require graduate school, you are well served to take advanced math in high school.

Re:I taught 8th grade science

[fermion]

Here is my experience. Everyone is encouraged to take four years of math, science, english, and social studies. If one does this, then one can have full schedules for all four years of high school. Practically, however, students often skimp on the free, albeit not neccesirily relevant, education and try to minimize classes in the senior year.

Given that students do not want to take 4 years of math, and in many cases are not required to take four years of math, and there is often not a fourth year of math at the suitable level, in many cases it make sense for the student not to take a fourth year of math, which in many cases would be considered advanced.

Here is what I see happening often. A student manages to squeak through to calculus. Unlike other math classes with can be taught at various levels, Calculus is a college prep course that must be taught with some degree of rigor. However, if one encourages every student to take the class, it cannot be taught with rigor as half the students will be ill prepared, and it will become a review class. Therefore, it might be that some students don't take advanced math. Even if the correct decisions are made in middle school, and even if work is done in high school, not every student will learn what is needed for calculus, and that just hurts those that do. Remember, the teacher will be penalized if too many students fail.

Here is what I have seen. The latest indication that math is important is a study in Science that indicates there is little cross pollination among the high school science courses, but more HS math does improve college science work. Also, and i don't recall where I saw this, there is an indication that the number of years of math is not as important as the rigor of math when it comes to college readiness. This is critical because in the educational debate the number of years and level of course are often used interchangeable, which is invalid. With respect to college, one needs four years of increasingly rigorous courses. When it comes to just educating the masses to maximize their ability, exposure is often the most important thing, and for that we may just need a capstone survey math course.

Weight scores.

[Etherwalk]

That's ridiculous--the moment there's even a shadow of that problem, you weight upper-level classes with a 1.1 or so. The idea is not to punish someone for taking a harder class, after all. (High school math was probably trivial for all of us, but it isn't for everyone.) My high school weighted honors classes at 1.05 when they averaged them into your GPA, and AP classes at 1.10; a similar technique would work here.

Re:Math?

[dosius]

In the US it's "math". In the UK (and also Australia, at least) it's "maths". Like elevator/lift or color/colour, prolly.

-uso.

Maybe...

[RichPowers]

Maybe not intentionally. But the way math courses are setup discourages many otherwise capable students from being successful in the subject. My middle school district did a poor job of coordinating math courses with the high school district. As such, I was behind by the time I reached high school and struggled the whole way.

Couple this with the ridiculous "integrated math" fad that plagued countless districts (at least in California). We barely covered trig functions, factoring, and other critical topics. (Anyone else have a thought about integrated math?) High school physical science courses did a poor job of incorporating math.

In college, I changed to a geology major that required calculus courses. Having struggled with math in high school, I had to start from intermediate algebra and work my way up. At least college math curriculums were organized in a logical and relevant fashion. It helped when the professor said, "Yeah, pay attention to this because you might have to derive the formula for centripetal acceleration in a physics course." Connections are important, especially when dealing with abstract math concepts.

My friends had similar experiences and, not wanting to blow a year taking bonehead math like me, decided not to explore their interests in astronomy, physics, chemistry, and other math-intensive subjects. It's a shame, really.

There needs to better curriculum coordination at the middle- and high-school levels so kids understand the importance of math and have a foundation that preps them for college. I understand how easy it is for a student's math foundation to get ruined. Such foundations, at least in my case, take years to build. Oh yeah, and (excessive) testing doesn't help -- but that's a whole other rant! If you want to encourage kids to take math, do a good job of setting up the courses in the first place...and tell them how important it is!

Math in Canada

[umStefa]

As a former mathematics teacher in Canada (Winnipeg, Manitoba if it matters) I can say that there is a worse scenario, it is not uncommon for school principals to put pressure on math teachers to give all students good grades. The logic being that since math courses are mandatory for graduation, failing a student will socially stigmatize them.

As a specific example, I personally had 3 students who did not attempt a single assignment and all of them had attendance rates below 50%. I was told by the principle that if I wanted to be hired on next year I would need to give these students an extra assignment for 'Bonus' marks so that they would pass. I refused and hence am a former math teacher.

Re:Math in Canada

[jeko]

No, you're not a former Math teacher. You're still a Math teacher, only now you're a math teacher with integrity. That's a former school. You're still a Keeper of the Flame of Knowledge. That building used to be a place where Knowledge was passed on. Now, like me, you're probably making the money you should have made as a teacher doing something else. And, yes, our world is poorer for it.

Even in Art, Math has its place

[Cassini2]

Math still has its place. If you want to go to graduate school in humanities, then you may still need some advanced math. In particular, many students from medicine, political science, humanities, and the arts, do advanced multi-variate statistical studies as part of their post-graduate studies. Understanding the tools used in these advanced statistical studies typically requires first or second year statistics skills. If you want your Master's degree, you need your undergraduate math.

As such, a significant number of undergraduate degrees require "Math for Humanities" or "Statistics for Non-stats Major" courses. It is a good idea to keep math throughout high school. It gives you many more options when you reach university.

Re:Even in Art, Math has its place

[digitig]

Math still has its place. If you want to go to graduate school in humanities, then you may still need some advanced math. In particular, many students from medicine, political science, humanities, and the arts, do advanced multi-variate statistical studies as part of their post-graduate studies. As an example, I'm doing an English language degree for fun (already having degrees in Electronics and Computing, for my career). One aspect of my (undergraduate) course is corpus linguistics, which involves multivariate statistical analysis. Another area is trend analysis in type-token ratios to identify critical points in texts. I've rather enjoyed seeing how maths applies to linguistics (and my tutors are bewildered by how quickly I can whip up a Python script to do some esoteric analysis :-)

How do you know?

[WrongMonkey]

If you never learned calculus or any higher maths, how do you know that you would have never used them? Math is used for all kinds of research in history: population extrapolations, statistical correlations, dynamic modeling, hypothesis testing, etc.
You're like a blind person who has found ways to cope with what you're missing, but that doesn't mean that you wouldn't benefit from sight.

Re:How do you know?

[AccioBrain]

This reminds me of the quote:

"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe and not make messes in the house." -Lazarus Long, "Time Enough for Love", Robert A. Heinlein

Thank you for your insightful comment!

Re:How do you know?

[lawpoop]

If you never learned calculus or any higher maths, how do you know that you would have never used them? Math is used for all kinds of research in history: population extrapolations, statistical correlations, dynamic modeling, hypothesis testing, etc. This may be a red herring argument. He didn't say that he didn't use math; all he said was that he's gotten what he's needed: arithmetic and geometry ( and I would bet he also uses some statistics ). Can you think of some examples where you would need trig or calculus to understand some historical phenomenon?

Can you tell whether you understand something or not? If he's grasped every graph or math-based explanation he's needed to, and knows only arithmetic and geometry, that means that he's never needed trig or calculus.

Re:How do you know?

[tftp]

Can you think of some examples where you would need trig or calculus to understand some historical phenomenon?

Between 1400 and 1500 the population of Languedoc doubled, but the war in 1450 reduced it to 88% of what it was in 1400. During this time the average profits per household tripled, except the 40% dip in the drought of 1470. Can you estimate the taxes that kings collected over this period of time if records give you some absolute numbers to fit the curves to?

Re:Tinfoil

[Gilmoure]

Stick it to da' man: factor a polynomial!

Re:Why is this a bad thing?

[Bluesman]

Great. While we're at it, let's also drop the "core" classes in English, diversity, and art history that engineers have to take.

Re:Math?

[Spazmania]

Math and maths both being short for mathematics. I guess it depends on whether you consider mathematics to be a science (ergo singular) or a group of sciences (ergo plural).

Re:Heh.

[tthomas48]

Teaching people to learn to think is a worthwhile endeavor. Especially in the age of Wikipedia teaching people facts is somewhat useless. I can lookup almost anything I want to know on the Internet, but I can't necessarily interpret what I've read or tell if there's any value to it.

Teaching a vocational education sounds good in theory, but what happens when your job gets moved over to a cheaper country? You have been left with no skills to learn a new trade.

Not to mention the fact that I use a large amount of what I learned in high school. When my wife got pregnant my Biology came in handy, as it does when planting a garden and deciding the best types of plants and where to plant them. I needed my Geometry and calculus to build a non-rectangular deck behind my house. I use English when writing programming documentation and to communicate with other people. I use German and Latin in deciphering words I come across as well as some low-level communication. I use Chemistry in cooking. I use History, Government, and Economics to analyze the world I live in and truly understand the news. I use theater with my theater company. I use musical concepts I learned in band to understand my musician friends. I'll be honest, I haven't really used by health education much, but I think that was probably just because it was covered better in my two years of biology. Frankly, I've found my high school education immensely helpful.

There are people who don't seem to have needed their high school education, but is it the fault of the education that the recipient doesn't want to use it?

who needs math

[nurb432]

When you are being bred to be a bunch of mindless controllable sheep?

A country of dishwashers and burger flippers dont really need an advanced education.

Eventually it will backfire of course, when the country slips into place as a 3rd world nation that cant even support itself. But until then, it keeps the ones in power, in power.

Re:Bath?

[P00rSpy]

As long as they do not try to discourage them from taking Bath...

Don't need more math, more common sense

[Bengie]

Screw math, we need a class on general problem solving and trouble shooting. In IT we have to understand *everything* in order to help someone. My CIS teacher told me "The client doesn't know what he wants or needs, you need to find this for him" and the client being the owner/CEO/whatever. "my speakers stopped working" = the *green* plug is plugged into the *blue* port next to the *green* port.. WTF?! This is your average person. How can the speakers stop working if they couldn't have worked in the first place. We need people capable of figuring out stuff on their own and researching. Once we can start getting this down, math will come naturally. The only thing I've learned as IT is "Never underestimate the stupidity of average intelligence." I love working with and helping people... but wow.. it's never ending

Re:Why is this a bad thing?

[swokm]

It's easy for us to knee-jerk and say this is bad, but why? Most people don't need mathematics beyond basic arithmetic and fractions. Outside of a classroom, the concepts taught in algebra and above are rarely, if ever, encountered by the day to day people.

"Most people" don't really use more that a set vocabulary of less than 1,000 words. Me think you true say -- why need us later days think of?!

A normal student in public schools in America will take at least two to three years of algebra, sometimes more, plus a year of trig or geometry. The ones who are interested in such things will take more advanced stuff yet...

You are completely missing the point. Why would you discourage students from taking anything in high school? And whole point of public education is to expose students to everything, not just what they would have found on their own! I took trig in 9th grade. Should that be my only exposure to math? Well, that'd be great if we all still worked back on the farm. Actually, not even that, as Agriculture programs have requirements for calculus at least.

So we're looking at three to four years of mandatory math classes. For someone not strong in math, isn't that enough?

What the hell is the point of education? If you are not strong in math, perhaps more classes are required. If it isn't required, you aren't really "exposing" the student to it. Last time I checked, there was no prediction of huge demand for Master Basket Weavers in the future. I really don't understand why everyone seems to think that it is noble and good to train for requirements 25 years in the past instead of the future. That is certainly the direction of my old school district. Things were great when I was there. They expected each student to perform to their abilities. No more, no less. The heavy yoke of NCLB standardized testing, and officials looking the other way when high schools flush poorly performing students out before 12th grade to improve their graduate statistics has certainly ruined that. And, by the way, not having a diploma is really awesome for those students, let me tell you. The students that remain in school are taught to a banal national test. Period. Who cares what their individual capabilities are?

I am not saying that exposing the students to the classes is a bad idea. But by high school age, it is usually fairly apparent whether or not the student has an aptitude for math or not. If he doesn't, there is no point in making endure a forced march through a bunch of crap he'll never internalize, fully understand, or find any use for.

It sure sounded like that is what you said. In 9th grade, I had no idea what I wanted to do in the future. Well, actually I know what I wanted to do but things turned out completely differently (to date, no one has paid my to play video games on my lear jet while flying to my NBA finals box party). The student might have some idea of their interests, but they will probably have no realistic idea of the future, or what might possibly be required of them later in life. That is what the schools are for! I sure as hell needed better math skills than my father, why this trend be different for my son? Time happens.

I, for example, am hopeless when it comes to math, but was always strong in English and decent at visual arts. I'd have been ecstatic had an administrator said to me, "Your scores are consistently low in math but high in these areas. Would you like to shift your credit focus to reflect the subjects in which you excel?"

Did you really need permission? It doesn't sound like you were forced to do anything. Maybe your administrator had a Masters in Comparative Literature and did replica oil painting on side... maybe they realized that maxing out at $22,000/yr and unhappy as a high school counselor with these skills was something you might want to avoid.

I'm sorry you resent the math you had to lear

It make me sad to see...

[AccioBrain]

It makes me sad to see that there are actually comments here that claim most people only need arithmetic and fractions. Well, first of all, the majority of people I know have trouble even doing that. I'm convinced that it's because elementary school teachers (at least here in the US) are *education* majors and can get through college without taking even a basic college level math class (the remedial courses are *not* college level).

But, since one of my majors in college was math, I have seen the valuable skills math gives you to go into any science or tech field, most business fields (in fact if more business majors did *real* statistics in college, they'd be much more valuable to the companies that hire them), and even law.

Proof, logic, and statistics (which requires calculus if you do it right) teaches people to think.

But perhaps by "upper level" people are thinking abstract? It's true that abstract math is mostly a play field for us mathies, but even some extremely abstract stuff has proven to be very important in computer science hundreds of years after it was merely played with. (See:cryptography, error checking codes/coding theory, Galois theory.)

I was also a computer science major and continue in that vein for work; some of the best computer scientists and programmers I have met were also originally math majors.

My Experience

[eepok]

In high school, they took the me and other 49 or so kids that were taking more than 2 AP classes aside for an entire day of testing in the school library. We had snacks and were able to take breaks. They did this so that we would have a calm, cool, environment to do the best we could and thus bring the school scores up. Far from ethical, but better than denying others the same test.

Working now in education and having worked with a very large school district, I've seen a similar system practiced.

Re:Why is this a bad thing?

[jd]

That's not entirely true. Recent studies show that taking maths in high school is worth a twenty percent increase in ANY science-based subject at University, whereas taking one science at school and another at University conveys no benefit whatsoever. In fact, Classical Education demonstrates that learning maths well enables you to learn many subjects that appear totally unrelated to a degree unparalleled by modern schools.

(Also note that 99.9% of the time, if someone is "bad" at maths, it's because the instructor is incapable of teaching them, it has almost nothing to do with actual ability at all. A different instructor, working at a different pace, can turn a person with consistent scores of zero into a mega-star grade-A+ student - or turn a grade-A+ student into one with a score of zero.)

Then you get into the "real world". Those involved in computing do an extraordinary amount of maths - whether for 3D graphics, figuring out how to optimize the normalization of the databases, maximizing network performance, or performing non-trivial QA functions. Those in any research field also use extensive amounts of maths. Geological work? Maths - and bloody complicated wave functions through multiple boundary layers it is, too. This isn't the stuff of amateurs, this is seriously hard work.

What else. Engineering. Those who lack maths are doomed to rebuild roughly 14,000 incompetently-designed, incompetently-maintained bridges because those before them never applied the maths to spot design defects or prevent potentially catastrophic deterioration. Those who have maths are likely the ones to actually do the architectural redesigns and make bucketloads of money. Those who lack maths might weld, glue or rivet bits of aircraft together, but the designers - the ones doing the real work - are the ones with top-notch maths. Which is just as well, because those are the people who matter. The person gluing could be replaced by a robot - if they haven't been already - and you'd never notice or care.

Even at the cash register, you can spot the ones with strong maths skills. They're the ones telling you the total BEFORE the machine, who can get the change right by touch alone, who can process more customers than the rest of the lines put together. Yes, I've seen plenty of people that good, and I've seen plenty of morons who can add and subtract but that's it.

What about salespeople, cable runners and other high-travel folk? If you don't understand optimization, you will never minimize travel times. There is no computable solution, so you have to do the maths in real-time in your head.

Manufacturing? There's no high school I know of that teaches Operational Research and SIMPLEX. There's also not the remotest possibility of maintaining high profits and high quality without such techniques.

Journalism! Journalism can't need maths, can it? It's just writing skills. Uh, no. Packing the maximum number of key points into the least space is the packing problem. Anyone can write, anyone can (with practice) write something readable. But only those with a good understanding of the packing problem can write efficiently and effectively. That is why so few journalists are truly excellent and why so many are merely OK.

What about creative writing? That's an even clearer one. Look at the ground-breaking writers - Arthur C Clarke, Isaac Asimov, JRR Tolkien, C. S. Lewis. What do they have in common? They're ALL scientists, which means they're ALL maths-oriented. There's no point trying to say that the Lord of the Rings is science fiction and therefore needs science skills, because it isn't. It needs science skills because coherent, structured, self-consistent, efficient, disciplined stories cannot be written by anyone other than someone with a mathematical mind. It can't be done. Those who try will almost invariably be sloppier, produce formulaic work (or steal it outright), be inconsistent and/or be wholly lazy about the whole thing. It may be perfect by English class standards, it may eve

Re:Why is this a bad thing?

[rantingkitten]

I just don't think that's the case. I took the four years of math (two of algebra, one of statistics, one of geometry). plus another in college (having deliberately chosen a major that would let me avoid as much math as possible). That's five years of math, plus the algebra class in eigth grade, which could count as a sixth year of math even though it was, obviously, not very advanced.

To this day I have absolutely no idea what a quadratic equation is beyond a vague "something to do with parabolas". I still remember the formula thanks to a silly mneumonic, and if forced I could probably still crunch through one. But that was ten years ago, and that is all I can do today.

Even then, being exposed to it every single day, I didn't understand it. I had no idea what it was used for, and I had no idea whatsoever how it worked. At all. And I still don't.

To say I -- or anyone like me who is not inclined towards math -- is "learning" it is somewhat disingenuous. I learned nothing about math in high school. I did what most non-math types did, which was memorize the formulas long enough to plug the numbers in and pass the test. I had no idea what I was doing -- just steps in a dance I was forced to go through like a trained monkey.

And today I still suck at it.

See, the reason I don't like your analogy is because, unlike math, English (or whatever your native language may be) is something you are constantly exposed to, and you will use it every single day of your life, regardless of your profession, interests, social status, etc. And because of that, it is useful to everyone, from every walk of life, in every professional or personal communication they have with anybody. Ensuring that people are better at this is a good thing for everyone, and moreover, it doesn't take much, because everyone is exposed to it all the time.

You cannot make the same argument for math. It is rarely used by anyone; only a small subset of people use it for their professions, and another small percentage find it of personal interest. But the majority of people never encounter math beyond arithmetic outside the classroom -- and because of that, they forget what they allegedly learned.

Learning English may have helped you be somewhat better at it, but then, you have plenty of opportunity for practice. Learning math won't help most people, who will never find a chance to use it, and after only a year or two away from the classroom, will have forgotten most of it.

I'm not denying that math is important -- the fact that we're talking about it using computers which require an intimate understanding of silicon semiconductor physics demonstrates that. But Joe Average didn't design the computer. But can you really, with a straight face, tell me that most people have any use for math beyond basic arithmetic?

Other possible systems.

[jd]

At the moment, students are graded in absolute terms at the end of the year, which means schools who bring in only people who are superb already at the subjects will get good grades. Schools working with less-able students can do a brilliant job but get lower grades than the lazy schools who merely tread water. So, how would you test this?

The expected change in ability will roughly follow an S-curve. Those who know very little will need to learn a lot to advance just a little. Those who know a lot must learn a lot more for it to make any difference. Those in the middle have the tools to learn rapidly and will do so.

All you need to do is have a test at the start of the year, extrapolate from prior years the constants needed to define the curve, then use that to determine where the student can be expected to be at the end of the year. The end of year exam is then normalized the same way. Your actual grade would then be equal to ((normalized end of year) - (normalized start of year) + (mid-point score)) * (multiplier needed to stretch/shrink scores over traditional range).

If you do this, any student who works consistently will score consistently. Any student who achieves better than they could have been expected to will always score well, no matter what their abilities are like compared to others of their own age. Likewise, someone who learned a lot once upon a time and is now sleeping through lessons will automatically fail, no matter how good their knowledge.

To make this system fair and easy to apply, you've also got to stream classes. Mixed-ability classes would not work well with a relativistic rating system. Ideally, each subject would be broken into 5 or 7 streams, giving you 2 or 3 subdivisions from neurotypical ability on either side of the bell curve. For large enough schools, I'd expect such a system to use standard deviations from average. With smaller numbers, you'd need to narrow the bands more. You'd also have multiple classes of the same ability, as needed. You need an age-appropriate number of instructors per student in each class, but no class of any age should exceed about 15-18 students.

The multiple classes would allow you to cover different styles and methods of covering the same material, so students who did poorly with one style/method could find one that worked better for them, as learning - not ability - is the part that is truly individual. Ability places demands on learning, but has no direct impact at all.

Re:Why is this a bad thing?

[rantingkitten]

Look, I understand what you're trying to say here, but I can't really see where you're coming from. You're trying to show me how useful math is for everyone, with these examples culled from real life, but that just isn't how it works.

Almost every example you give is intuitive, not mathematical. Ask the reporter how they write, and they aren't going to start talking about complex algos and maximizing space potential. It just comes to them. Yes, math can be used to describe what they are doing, but the reporter is certainly not sitting down with paper and calculator and crunching the numbers.

Neither is the salesperson and cablerunner you describe. They just do it. Again, math can be used to describe what they are doing but they are not performing any actual calculations in their head the way you might perform them with pencil and paper.

Consider a baseball player trying to catch a pop fly. Even a Little League player can look at the ball, watch it for a split second, and run to where the ball will be. He sticks out his hand, makes a few minor adjustments, and catches it.

Did that kid "compute" the quadratic equation for the ball's parabola in his head? No, of course not. He just innately knew how to do it, from a life of experience.

Don't confuse "can be described by math" with "was done by using math".

Re:Why is this a bad thing?

[1729]

See, the reason I don't like your analogy is because, unlike math, English (or whatever your native language may be) is something you are constantly exposed to, and you will use it every single day of your life, regardless of your profession, interests, social status, etc. And because of that, it is useful to everyone, from every walk of life, in every professional or personal communication they have with anybody. Ensuring that people are better at this is a good thing for everyone, and moreover, it doesn't take much, because everyone is exposed to it all the time.

You cannot make the same argument for math. It is rarely used by anyone; only a small subset of people use it for their professions, and another small percentage find it of personal interest. But the majority of people never encounter math beyond arithmetic outside the classroom -- and because of that, they forget what they allegedly learned.

The value of the math content in a curriculum is more than just "useful math", in the same way that composition, literature, art, science, and history courses have value far beyond the explicit content. It's true that the specific mathematical skills that are taught in high school and college math are not necessary for most people. However, the rigorous logical analysis and problem solving skills necessary in mathematics are absolutely essential to an educated person.

I've forgotten most of the specific content of my literature courses, but they were part of how I learned how to read critically. I don't remember much from my college chemistry courses, but they helped me to think scientifically. I've forgotten many of the details from my history, art, and social science courses, but along the way I learned to analyze and appreciate the world around me.

The purpose of an education is to learn to think, and mathematics is a crucial part of that process.

Re:Why is this a bad thing?

[jd]

You're assuming that intuition actually exists as an independent thing. I would argue that intuition does not exist at all, that what is called intuition is merely a very effective computation process performed by the brain at a low enough level that there is minimal or no conscious involvement. You've seen martial arts experts - do you think they consciously think about their every move? No, of course not! But did they need to learn those moves consciously and understand the mechanisms involved? Yes, very much so.

The same is true of catching a ball. Anyone can catch a ball without thinking, some of the time. Anyone can practice, consciously, to catch a ball and improve their success rate considerably. Anyone can learn the principles of dynamics so deeply and so thoroughly that it becomes what is called "second nature" or "intuition" even though it's nothing of the sort. It is merely exactly the same process as doing the whole calculation with pen and paper, but using extremely fast, dedicated circuitry deep within the brain.

"Intuition" is the word of mystics to describe a brain that is nothing more than a fancy protein-based computer because they cannot and will not accept the fact that the brain can do precisely nothing that a computer cannot.

Re:Tinfoil

[Original Replica]

Stick it to da' man: factor a polynomial!

Funny but also kinda true. Math is a gateway to Critical Thinking or Logic. The kind of accuracy and clarity you get with math isn't something that most modern governments really want to encourage in the populace. Not the math itself, but the kinds of thinking you learn by way of math. It's much easier to sway them with a convincing soundbite than to actually have to have a through and logical understanding of an issue. Factoring a polynomial teaches you break things down into clear components in a much different way than you will get if you are only ever exposed to literature,history,and civics. A well educated thinking man is going to be a politicians toughest constituent.

Re:Tinfoil

[TheRaven64]

When I was doing A-level physics, I discovered just how dumbed-down the course had become. The pre-requisite for the course is only a C at GCSE in maths. It's possible to get a C (the lowest passing grade, below B, A and A*) by taking a simplified paper, which caps your mark at a B (I think; it may be a C). This simplified paper does not include solving quadratic equations. As such, the A-level physics course could not require them. Similarly, it could not rely on any knowledge of calculus (taught in A-level maths). This meant that you were expected to remember a load of equations for motion, rather than just a couple and how to integrate / differentiate the rest. Worse, you would not get all of the marks for showing your working if you used calculus to solve the problems. That was when I stopped regarding the course as worth anything, and gave up doing any work.

I was glad when I got to university to discover that the dumbing down hadn't reached quite that far, but I discovered that universities were having a problem selecting from applicants, because A-level performance was not any kind of indication of ability at degree level.

Re:Math?

[ricree]

In general, community colleges in the US only offer two year degrees, whereas universities generally offer four year degrees. However, the courses at many community colleges are transferable, so it is very common for people to spend a year or two at a community college to save money before transferring to a university to get a four year degree. So employers in the United States will obviously care which you graduated from simply because they are different degrees. However, there is generally no distinction made between someone who spent part of the time at a community college versus someone who spent the whole time at a university. However, you also need to keep in mind that colleges and community colleges are not synonymous in the US. In general, universities tend to be larger institutions with many areas of study (often divided into smaller units called colleges), while there are many smaller institutions called colleges that have a much narrower academic focus. These sorts of colleges usually offer four year degrees as well as advanced degrees, so they are generally comparable to universities in terms of prestige and value of the degree.

Re:Why is this a bad thing?

[sqrt(2)]

the rigorous logical analysis and problem solving skills necessary in mathematics are absolutely essential to an educated person A resounding and absolute "Yes!" on this. No question about it. Eloquently summarized by your final sentence on the underlying goal of all education, "...to learn to think" . On all this we agree, but where we begin to diverge is at the idea that math is a proper and necessary tool to accomplish this for everyone. I simply don't agree with that statement. I, like many others, slogged through four difficult, agonizing years of math education in high school. Those classes, at least as they were taught at my school and when I was being taught there, did no more to teach me "rigorous logical analysis and problem solving skills" than any other classes. I was simply memorizing and regurgitating equations and formulas--and very poorly I might add. I believe the highest grade I ever received in one of my math classes was a merciful C-.

The class that came closest to your ideal was my AP Physics course (that did not use calc). This was largely because we had the benefit of a brilliant and qualified instructor who was amazing at taking complex ideas and explaining them in simple and easy to understand ways (and all without us feeling like he was "talking down" to us). He was constantly stepping back from the actual work at hand and showing us how it fit into the logical, natural world at large. His lectures weren't just about learning what we needed to make the school look good on tests, he constantly reaffirmed that it was the process of discovery that was important. He wanted to teach students how to be good scientists, not good test takers.

My point with all this is that "rigorous logical analysis and problem solving skills" ARE NOT the exclusive domain of mathematics. If you look, and have the correct approach to teaching the subject, you can find this just about anywhere.

Selection criteria.

[TapeCutter]

"I think they should take the same approach in this situation."

I'm an Aussie with two grown kids and a partner who selects students for a university degree in the state of Victoria. I can attest to the fact that your post describes the way the system works in Australia fairly accurately, the math to determine the final "score" is quite complex and the "score" cannot be determined before all year 12 students in the state have taken the test.

Truth is some people can't do math just like some people can't kick a football or paint a picture. To be able to do the "hard math" in the final year (year 12) the student must do the preparatory "hard math" in the preceding two years, if (as many do) they can't cope with the year 10-11 "hard math" I can understand why teachers suggest a less demanding course. It's the same as a kid who never practiced football but suddenly wants to be picked for the school's senior team, it's simply not going to happen that quickly.

Personally I dropped out of high school at 16 and ended up going to uni at about age 30, however having dropped out of HS I could not just waltz in as a mature age student, I had to do a year 12 math course by correspondence and sit the HS "hard math" test to meet the selection criteria (also it was a good way for the uni to see if I was serious).

A good high school "score" is important when you are young because it gives you an advantage over others entering the workforce/uni. It's basically societies reward for your efforts to complete the "grasshopper" stage. It's not a guide to "intelligence" or "wisdom" any more than a fat wallet is, and it's most definitely not a "make or break" moment that follows you around society for the rest of your life.

Re:Math?

[aqk]

Hey, lissen, assolle!

I have studied Mathematic! And Physic too.

You haven't. So shut ups.

Re:Math?

[Your.Master]

Community college has a negative connotation here in the US, same as in Canada. I think you misread the person you were responding to. Community college just does not have the same negative connotation in Canada as it has in the US, in my experience -- and that's because these are only rough equivalents to your Community Colleges. The education system is different even though we share a lot of terminology. However, the terms University and College are delineated much more carefully in casual speech, and precisely what they mean is not quite identical, although the 2-year diploma vs. 4-year degree thing is a facet of it (as is University's academic approach to education vs. College's practical approach, and others). Just to explain some differences in terminology -- and I know not all of the US or Canada is the same in this -- I go to University, I do not go to College, I do not have the British accent. I went from grade 1 in elementary or public school, 1st Grade in grade school (note that even a private school can be called public school as a synonym for elementary school), and high school went from grade 9 through grade 12. In high school, Junior meant grades 9 and 10 while Senior meant 11 and 12. In elementary school, similarly, Junior was Kindergarten through Grade 4 and Senior was Grade 5 through Grade 8. There was no Freshman or Sophomore. I get good marks, not good grades. In University, my 1st year there was called 1st year. My second year there was called 2nd year. That much was pretty straightforward. We did also call 1st year students "Frosh", which is apparently a contraction of Freshman. Frosh was also slang for the first week of school, and the parties and events that went on during that time.

Adsvert too

[MarkByers]

Yes. In the same way 'ads' is short for 'adsvert' and 'abs' is short for 'absdominal muscle'.

Funny.

[TheLink]

A lot of students here in Malaysia like math at the high school levels because it's easier to get high grades.

With high school math it's pretty clear when you're right or not.

Whereas stuff like art is subjective, and same with stuff where you have to write essays/papers - where it can be a matter of taste whether you get an A or not.

Re:Tinfoil

[mabhatter654]

you hit on something that nobody is teaching stuff to know it and love it, merely to have the mark on their records that they took the class and the school offered it. Mastery of material is not really something taught anymore. It doesn't fit in the neat little 13 week class to learn 500 pages of math concepts. Nothing about how to use them, what you might do with them, or how to pursue the field I have the typical "technical" round of 4-5 semesters of math in college and while I like it, none of it means anything. The really cool stuff is reserved for "math majors" and hobbyists aren't really welcome or encouraged. It's quite dismal really.

Re:Math?

[ardle]

This is what happens when a target is allowed to be more important than a purpose; school staff may have to choose between their families' welfare and that of the people they are paid to help.
It's ironic that Mathematics is the subject to suffer, since it was used to create the situation.

Incentives

[Anonymous Coward]

In *general* (not in *all* cases but in the majority of them) people tend to do whatever they have been given incentive to do. When you judge the success of a school by how many A's they give to their own students, you have given them just as much incentive to exercise statistical manipulation and practice grade inflation as you have to provide an education.

I believe that the people who test students, and the people who educate students, should be different people. The educators should not be able to rate their own success by giving whatever grades they please to their own students. Instead, the public school should only provide the education. Then, at the end of the year, the students are sent off to take some standardized tests which are graded by people who do not work for the school board, and who focus primarily on objective criteria.

Since the educators will no longer be able to determine the grades, and since the grades will still be used as a determination of the success of the educators, they now have to focus their efforts on the providence of a good education (rather than the grade inflation and what have you).

I think it would help. It would create its own set of problems (schools trying to expel special-needs students rather than help them, for example), so it is not a perfect solution. But I do think it would help.

Re:Tinfoil

[p0tat03]

IMHO that's just wishful thinking. How strong are Chinese students in math? I'm one, and I consider myself quite strong mathematically, though most of my Asian peers are even more insane. Of course, I am probably *the* only critical thinker out of the bunch. It's entirely possible to create a bunch of math geniuses without risking exposure to democratic ideas.

Slightly off topic, but what I find most interesting about my Chinese peers is that they haven't been indoctrinated to worship Mao, or any such nonsense. Rather, they've been indoctrinated not to care. Most have a very mild contempt for Mao, and aren't writing rave reviews about their government, but at the same time they fail to see what the fuss is about with democracy, freedom of the press/religion, etc, having been totally trained to believe that politics simply aren't important in a proper person's life. I find it altogether much scarier than a bunch of Mao worshippers, and infinitely more depressing.

Re:in college this would . . . Empirical evidence?

[JohnFluxx]

Then you set up a moral hazard. ( http://en.wikipedia.org/wiki/Moral_hazard ). A school would have the incentive to not improve, because improving would mean being punished with their funding being cut.

Fun fun.

Re:Tinfoil

[mstahl]

This has been a problem in the US for a few years now and I fear that with No Child Left Behind we're going to start seeing more of it here. The valedictorian at my high school had a perfect 100% average all throughout, and he did it by never taking any advanced courses even though he was smart enough to take them, because they might've messed up his grades. (He went to Yale; he was an asshole; that's a story for elsewhere.)

With physics especially, calculus was *meant* for physics. The two belong together, and taking calculus out of physics makes physics a very, very, very dull pursuit. I think that more and more colleges are seeing that their applicants with high marks from high school just don't match up to what's expected of them in college. I got by through my own studies, by myself, in high school, because I was at a vocational high school anyway and the math programs just weren't challenging enough.

It just depresses me that the solution to low test scores seems to always be to set the bar lower and lower each year. Soon enough we'll have kids who scored perfect in high school but really are as smart as a box of rocks. I've written a lot of stuff on my blog about this, actually, as it makes me really sad a lot.