Slashdot Mirror
Have Mathematics Exams Become Easier?
Coryoth writes "The BBC is reporting on a recent study in the UK that found that the difficulty of high school level math exams has declined. The study looked at mathematics from 1951 through to the present and found that, after remaining roughly constant through the 1970s and 1980s, the difficulty of high school math exams dropped precipitously starting in the early 1990s. A comparison of exams is provided in the appendix of the study. Are other countries, such as the US, noticing a similar decline in mathematics standards?" Readers with kids in school right now may have the best perspective on changes in both teaching and testing methods -- what have you noticed?
Clearly this is happening ... in the western world anyway. It's the only way that schools can keep up with the shear numbers of parent classified geniuses.
We've noticed this 'dumbing down' (thanks Idiocracy) for a while now at Uni. The newer mathematics students enrolling in first year are lacking some of the basic skills. Example: a couple of years ago, trigonometric functions and identities were completely removed from the high school syllabus. It goes back all the way to year one at school.
I don't think teachers are being paid enough and they are certainly not valued enough by the community. Once upon a time, the best and brightest minds went into the teaching profession; it had respect and was highly valued. Now, it's whoever wants to become one, winner by default. The best and brightest need to be attracted back. Why would somebody who has the ability to earn more than four times the national average wage go into a job that earns less than the average wage?
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we don't want to upset the poor children or make their lives too difficult. their parents might sue.
The reason girls and Windows users don't understand UNIX is because all the documentation is in Man files.
The grade I received on my most recent calculus test says differently.
They had to lower the standards because the kids today can't handle simple math.
I'm glad somebody finally pointed this out in black and white. I remember lining up A-level (UK age 18 exams) maths papers from the 80s and 90s, you could see the questions get easier almost year-by-year.
Yet every year the exam results get better and the government congratulates itself on improving standards while denying the exams are getting easier.
There is strong pressure on the education system to "improve"; and these improvements are measured by tests. Students are generally not going to get smarter, so why not make the tests easier to make it seem like you are doing your job?
back in the 50s, 60s, 70s, and 80s kids got a slide rule, protractor, compass, and graphing pad. Now it's ti-83+ for algebra class and the ti-89 has more computing power than the original Macintosh.
doing the math is going to be easier, even if they didn't ask harder questions. However, the amount of automation these days means that most people aren't ever going to have to do the harder math in their daily lives.
Slashdotters are an anomaly because our careers and interests require us to do maths all the time. If the future historians are allowed to slack off on their trig tests, so what? They weren't going to be engineers anyway.
They probably should track out classes more than just "regular" and "honors/AP" though. That way the future nobel prize winning poet who is an over acheiver and the future NASA scientist don't have to compete for the teacher's attention to detail in Calculus.
Just a suggestion.
Did they get all the logic right in the story?
My first Journal Entry ever, in 8 years! http://slashdot.org/journal/365947/aphelion-scifi-fantasy-horror-poetry-webzine
I failed more maths A'Levels than most people have sat, but still know how to count the pennies in my wallet.
Pro Coffee Drinker
So I have my A level maths exam (core 3) in two days, taking it a year early, and I'm still finding it trivial, and thats because I'm working from '90s papers and they're so much harder. So basically yes, the exam I am taking has gotten easier over the past years. It's not that the questions are easier though, it's because year by year subjects get dropped so you can focus so much more time on one subject so you can quite easily perfect your understangin of it.
This is trotted out every single year
pass rates go up - exams are getting easier. education system in decline
pass rates go down - teachers not able to communicate with students. education system in decline
If Sally has a 3 gallon bucket, and Joe has a 2 gallon bucket, how many buckets are there?
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Pencils down!
"Quote me as saying I was mis-quoted." -Groucho Marx
I'm a licensed teacher - Social Studies, not Math - and I've seen many district personnel changing how tests are delivered or graded, simply to make sure that the school is meeting the NCLB standards. As a Social Studies department, we were asked to make certain questions easier to understand, or to eliminate hard to study areas all together in order to make sure that the results would be up to where they need to be. Math teachers in my district have complained a LOT that the district is forcing them to dumb down the tests simply to make sure that scores are where they need to be.
Kids aren't dumber, they just aren't given the opportunity to fail. If they aren't given the chance to make mistakes, they don't learn from them, and unfortunately, that is where the NCLB is leading us.
Well, my US university insists on making the math exams all multiple choice--to make grading easier, I presume. However, they convolute the problems so much, and require you to "add both solutions, if any, together after multiplying them by the phase of the moon on July 18th, 1993, and divide by 2.5503342134 to get the answer," or something similar that it makes it extremely annoying. Good thing I'm done with my math requirements.
My last calculus class was in the early 1990s. Now, I'm not sure if I should be grateful or pissed.
My Dad was in high school in the late 1950's, he took and passed Calculus, and he told me his high school offered Differential Equations to the top students in math, and if he had tried harder, he could have taken it in high school instead of his freshman year in college.
My wife and I both took Calculus in HS, and Differential Equations in our freshman years of College (mid-90's). Neither of us were offered a chance to take Differential Equations in HS, though.
Are there schools, or does anyone know if High School used to offer math up to Differential Equations?
Kids these days. Why, back in my day, we had to calculate pi to 5,000 decimal places in our heads.
Oh wait. I'm only 28. And I nearly failed geometry.
The problem is, our current bottom-to-top emphasis on mathematics and the sciences effectively ensures that all but the brightest, most driven students will be alienated from these core disciplines because of the minutae they are forced to memorize. The prevailing logic would seem to be that this creates a detailed knowledge base for higher learning.
While this is true, very few actually pursue higher learning in these fields because all of the emotion and excitement is gone when math and science are taught in this way. The wonderment that inspired so many young engineers during the space race is gone. Teachers need to address and emphasize the larger concepts to get children excited about math and science.
I think the exams have become easier. I took GCSE maths in 1991, and I had a chance to compare the papers of those days with the O-levels (the equivalent exam) of a few decades before. I got an easy A grade at GCSE, but the O-levels were way beyond me at the time.
A couple of years ago, I took a look at the latest syllabus, and it appeared that the exams had got even easier.
It's not a good situation for those that go on to take A-level and university courses in maths or science subjects. There is a lot of catching up to do later.
Cynical Idealist
Maths, and other subjects, becoming easier actually makes it harder for students. Back then, you can do 8 or 9 O-levels, 3 A-levels and that would be enough to get you in a top university like Oxford, Cambridge and Imperial. Now-a-days, students need at least 11 GCSE's (new name for O=levels to those not educated in the UK) and 4/5 A-levels to get in the same universities, avoiding less academic subject like Business Studies, on top of entrance exams because the public and universities have lost faith in the public education. It is time to make the exams harder so that at least with the harder questions, it tests your inert ability that has been developed over time rather than overloading student with so much knowledge to prove themselves. This is a classical case of quantity over quality, if one is to look at it that way.
Our local school district has unfortunately adopted a math curriculum called "CPM" which is supposed to stand for "College Preparatory Mathematics" - an oxymoron if there ever was one. My wife is a licensed secondary-level math teacher, and does tutoring locally although she wouldn't be able to ethically work in the district if she was forced to use this horrible curriculum that amounts to educational malpractice.
Because the government education establishment in many places has given up on any attempt to maintain the tried-and-true approach to math education that has been employed in the past - building skills step-by-step in such a way that the student's "toolkit" grows in a logical fashion through the different skills, now they are left with a very fuzzy approach that doesn't really build anything on anything, and mostly is concerned with keeping busy doing something that they can pretend is math and pretend that some sort of progress is being made.
The most tragic part of it is that the kids who would have been the real math enthusiasts under traditional teaching methods never get the chance to see the order and beauty of math, because curricula like this completely hide it.
For more info on this, see the Web site mathematicallycorrect.com .
Because the poor government "education" establishment is failing to really teach math, of course they have to put a happy face on the situation by dumbing down the tests too.
In 1950, the world needed on 1-2 percent of graduates. The businesses and lifestyle was geared that way. Only few engineers were needed for railroad, aviation, shippig, auto, tv and construction.
Today, you need some mathematical background knowledge everywhere. This means that you have to lower the exam standard and let people move on. Today's automobile engineer doesn't sit down with complex geometry solving. Good computer skills with less mathematical knowledge is acceptable too. Such person would have been useless in auto engineering division in 1950.
I have one son, 4 years out of high school and one just beginning. The difference between their exams and the ones I took 30 years ago is shocking. Worse still is that the decline extends beyond math and into many or most other subjects as well. Worst of all is the great pride that so many people take in this ignorance.
No one is going to say that the teachers are doing a better and better job every year. No one is going to say that the students are held to higher and higher standards in math and that they are achieving those standards more often than before.
This is because it would be false. You might get arguments about the extent of the change, but none on the direction.
And nothing in education will ever improve in the US as long as the system is union-controlled.
Bah! Kids today have everything too easy! Why, back in my day...!
What? It's time for my Metamucil? No, I'll come quietly this time...
Chelloveck
I give up on debugging. From now on, SIGSEGV is a feature.
Could everyone put their country in the comment, if applicable? It saves people arguing back-and-forth about the same point, when both are correct for their own country and experiences, but on opposite sides of the world ;-).
has demonstrated that curriculum's have been dumbed down to accommodate a greater breadth of material. The students I see are exposed to more Stuff, but never have any in depth mastery. I am in the U.S., not UK.
To really see how easy school has become over the years just find some childrens books from the early 1900s. You will find that many post-seconday strudents would have a hard time with them.
Undetectable Steganography? Yep, there's an app fo
I'm a math professor and I must say, just in the past 10 years, I've noticed the "average" undergrad is A LOT worse at basic math than they used to be. I don't know which was cause and which was effect, but students are worse at math and we're teaching them less up through high school. This needs to change very soon or we're going to be a nation of mathematical idiots in another few decades. It has already started... just look at the percentage of American math PhDs coming out each year.
I agree with everyone else, we need to pay math teachers more. In states like TX a public school teacher makes barely enough to live poorly, and with a math degree, they can make double working in private industry. It is a very hard sell to convince mathematicians to go into education.
The other thing we need to do is not be afraid to actually fail someone. This society has made it so that everyone feels its their "right" to graduate high school and go to college. We need to change this and actually fail people when they can't do the work. If someone doesn't earn a degree, they shouldn't be "awarded" one.
I did my A Levels at a technical college from which few conclusions can be drawn, but when I arrived at a redbrick University in 1983 I was dimly aware that people with three As, or maybe (whisper it) FOUR As existed over in the med school (I'm excluding General Studies, with good cause: my college didn't teach it, so I entered myself and got an A, so I presume it's worthless). No one on my Computer Science course had qualifications close to straight As, and this in an era where higher education uptake was about 10%.
Today, _everyone_ in a university like that, three or four times larger, will have qualifications `better' than mine. I don't know what sort of University A (computer science) B (physics) C (maths), or perhaps it's B (maths) and C (physics), I can't remember + A in general studies gets you into, but `not much' I think is the answer. With 40% take up as against 10%.
Looking at my kids' maths, at a heavily selective secondary school my daughter is several years behind where I was at the same age. At O level I did differential and integral calculus, with volumes of rotation a favourite sport, which is now optional at A Level.
Mensa won't take SATs from later than 1/31/94 as an indication of your IQ. That says something about changing test difficulty...
Looking at the example questions, the earlier questions look difficult, but unnecessarily so. What I mean by that is, they take what could be a straight forward question and then obfuscate it behind a bunch of random noise merely to confuse the test taker.
The newer example questions seemed more rationalized, they test whether you know the theory or formula needed to solve the question without throwing you a curve ball.
Would you rather encourage people to continue studying onto more advanced levels with easier tests, or throw them a GOTCHA question which will totally turn them off to the subject matter?
There is a difference between testing knowledge of the subject matter, and giving the test taker a hard time. A "difficult" question might be great to ponder when you have unlimited time, but in a time pressured test, it is not appropriate.
I'm sorry but what do we really expect to learn from this research?
Maths in the 1950s was designed for engineers and scientists in that generation. They learned what they needed.
Maths today is exactly the same. The fact is you can't use 1950s standards to evaluate today's exams any more than you can use today's standards to evaluate 1950s exams.
The only real question is - Are engineers and scientists finding their maths education weak?
The answer in my view is no in most cases. In a limited number of careers the maths they received isn't nearly advanced enough but that would have been the case in the 1950s too.
As I said they're using the wrong measuring stick to measure the difficulty of exams. Nobody needs to know half of the useless junk that kids learned in the 1950s when frankly it is less time consuming and more accurate to use a calculator.
That's just my opinion. I honestly think a lot of this kind of "research" is a result of much older people looking at today's maths and thinking "Why aren't they learning what I did?" While completely ignoring what they're learning that the 1950s students didn't.
Look, you can read about it anywhere. We even had math classes in some cities where success was built around "best attempt" or other such non-sense.
What it all boils down to is that no matter what standard the Federal Government tries to set someone tries to cheat it. That is why there is always such an uproar versus standardized tests. Down here in Georgia they failed nearly 40% of all students in tested grades versus a standardized test. They knew it was coming. They even had practice tests. Is it all the schools fault?
No. Students seem have this sense of inevitability. They are still of the belief that they don't have to. After all anything else they complain about in school gets changed. I don't see their attitudes as defeatism, its entitlement that they suffer. They don't have to do this, that, or what not. We don't have the right culture in schools, especially city schools among minority students. Until we change the fabric of society the MTV generations will forever think themselves above "working hard". They are all going to be rap starts, professional sports players, or worse win the lottery!
We gave up control of our schools to "feel gooders". Now its all about grief counselors and no winners allowed because no one should be a loser. When we removed the reward of success what did we expect? I have seen articles where every student got to walk the diploma line regardless if they graduated just so they didn't feel ostracized. Well tough shit. Your boss ain't going to worry about making a failure to feel good. If you don't perform your in for a world of hurt. I guess you could go into government work, of all categories in the job market they have added more jobs than anyone and everyone knows the saying about how its near impossible to lose a government job.
Schools and students are simply trying to cheat the system. The problem is the schools encourage it because they don't allow for losers. They don't want to hurt little Bobby's feelings so they set him up to fail in life. If they want control of our kids then they should be responsible for them. They get hell bent if someone raises a finger about the Bible in school or complains about sex education yet they are completely aloof when it comes to holding the kids to a standard of education.
Private school was the only recourse I found. Standards had to be met or we might not be allowed to come back. Students were encouraged to be better. I don't see that outside of a few select public schools; you know I hear it all the time how so and so's public school isn't like those others but sorry it is.
* Winners compare their achievements to their goals, losers compare theirs to that of others.
I know that this story gets touted around every year but I think there's some truth in it. I tutor some 1st year physics students and their math skills are shocking. They can follow 'recipes' well enough to solve questions they're used to. However, present them with a problem where they have to actually think and they're stumped.
"Physics is to math as sex is to masturbation." -R. Feynman
Maths has definitivly become a lot easier here. It takes a lot less work to get good grades now, and there's an alarming lack of focus on basic math skills. There's plenty of A-students who can't do basic math. The norwegian school-system is really fucked up though. There's so much focus on getting the trouble-makers through school, so they're allowed to basically take over classes. I mean, we don't want to send them to special schools, because that would stigmatize them! Never mind the 25 other students in the class, they'll just have to sit there and feel neglected.. Not to mention, without consequences these students never learn. I've had students yell at me straight off at 08:15 in the morning because the last test had some questions which weren't exactly as the ones in the book. They're so mal-adjusted and unfit for real life it's scary.. (ohh.. and just for kicks.. 90% of the worst students are pakestani.. while they make up about 3-4% of Oslo in total..trying to teach them anything is basically a crash-course in becoming a racist)
That said, I work with a couple of really old math teachers, and there's a few subjects like probabilites that are completely new them.. so math has changed. Don't be fooled though, they've replaced all the hard'n'gritty stuff with fluffy feel-nice stuff.
In Norway, we've had two big reforms in the last ten years, and both made the hardest paths easier. Ironically, they also both made the maths for students taking vocational education harder. It's so tragic I want to cry :(.
"" How about taking the safety labels off everything, and let the stupidity-problem solve itself? """
It's been said before, but (imo) today's students are essentially 'weaker' in 'doing' math simply because they don't have to do much of the doing. The result? Easier tests so that more, or at least the same number of, students pass. Schools funding is often determined on this criteria, so no one wants "below passing" students.
When kids start Algebra I with a TI-89 that is drawing tangent lines and running linear regressions (in between games of tetris) for them, they don't learn any of the basic skills. This leads to a general decline in non-assisted capability, leading to a 'requisite' decline in the difficulty of tests so that more students can perform acceptably and schools maintain their funding.
Perfect Example? Shopping the other day in a store who's register was offline. I was -unable- to make a purchase because the register was down. When I offered that we could simply calculate the tax on the purchase and subtract that total from my $20 you should have seen the look on the kids face; would have thought I'd just asked him to land a hampster on the moon w/ just pencil and paper.
I took Calculus a long time ago as part of my Computer Science curriculum. Now that I am going back to school for a degree in Mechanical Engineering, I have to take Calculus III - Multivariable Calculus. Since it has been so long since I took Calc I and II, I took them over again.
I do think that the classes seem easier than when I took them before, and I think the students are generally not as well versed in the prerequisite material as they were when I took them before.
But I am not very upset about this. The fact of the matter is, except for specialized disciplines, _no_one_uses_this_stuff. Every engineer I have ever spoken with has said they never or almost never use calculus.
I suppose it is good that we are all made to take it so that we have an appreciation for what computers are able to do for us these days, but I'm not upset if there is less emphasis placed on rigorous mathematical study. Such study should be required for people who will be going into fields that actually require it, but it doesn't look to me like mechanical engineering is one of those fields.
A work that expires before its copyright never enters the public domain and thus enjoys eternal copyright protection.
And I found that the math levels are largely influenced by self-determination more than anything. I'd say that standardized tests have become easier, but at least at my school there were tons of kids participating in UIL math events with huge interests in math. When I started college, I found the math to be too easy for me.
One of my roomates was an SS teacher, he quit over No Child Left Behind. Not only does it lead to "teach the test", it keeps good teachers from going into the classroom in the first place.
Prediction: The real iPhone killer is going to be sex robots from Japan. Think about it.
I don't know about high schools, but our local public school has my second grade daughter doing long division and adding and subtracting fractions with differing denominators. I know _I_ didn't do that until much later.
I still maintain that I wasn' taught Maths at A level or GCSEm I was taught how to pass a maths exam. For the entire second year leading up to the exams we were taught past papers. In Maths, (as well as Physics, Chemistry and Electronics) I was set each paper, full and mock exams from the previous 15 years. In the end this meant that I coasted my final exams as 75% of the questions on each paper were reprints from previous years that I had already not only done myself but been taken through ideal examples for afterwards. This didn't help when I reaached University as I had very little idea about the mechainics behind the maths causing me (and many other students) to have to pay for extra maths modules to keep up. The entire focus of the school system is not the education of the students but meeting the targets set by the government. It doesn't help that everytime someone raises a set of valid complaints the government springs into action and sets a completely new set of guidelines and targets which the teachers then have to spend more time working out how they can fudge.
No child left behind.
In my time at school (late 80s), universities selected their students by looking at their A-level grades. 4 good A levels was enough to guarantee you a place at a top university. Today I read that universities are starting to set entrance exams of their own because they can't tell who the good students are anymore, as they ALL have 4 or 5 A-levels. More details in the story from todays Guardian
A pizza of radius z and thickness a has a volume of pi z z a
I went to high school in Finland around 1988-1991 or so. I was in the "advanced math" group, which they did away with and put everyone in the same group.
I was also able to take a look at some high school math books from the '60s or '70s, and they were much harder.
When I went to uni, the math was a shock! But had I studied the high school math a couple of decades earlier, it wouldn't have been.
This educational video explains the biology behind this observation:
http://www.imdb.com/title/tt0387808/
I'm just doing my GCSEs (end of "high-school") and have to say this is all too true. Some of the exams, maths in particular, have been insultingly easy.
I finished both maths papers (calculator and non-calculator) with enough time to do things like trace all the writing on the front of the paper, do a perspective drawing of the exam hall, contemplate shouting out some answers and imagine the various possible consequences, and generally get bored in an hour of sitting around doing nothing.
I think the most difficult thing in all of the two papers was solving a simultaneous equation which was disguised in graph form to kind of trick a few people.
These days it is far easier to use computers etc as a multiplier; one mathematician can be used to do a lot more. For example, one mathematician can work as a consultant to an organisation that develops some stress analysis package/library etc and thousands of structural engineers can use that work without having to personally crank the math.
To know when to use which math tools does need some level of math skills, but far less than actually doing the stuff yourself.
Engineering is the art of compromise.
Well I dropped out of high school 2nd time in 10th grade. Stayed out of school for 7 years, without cracking a book or studying went and took my GED exam, passed first round, I was amazed that there were people on their 4th and 5th tries taking the GED test. Another 7 years pass, I decide to go to college to further my education and to get a job in computers. Again, without opening a book or studying in 7 years I'm in remedial classes, which I expected but what I saw there I had never expected. Fresh high school students that had graduated the year before in courses equivalent to what should have been Junior and Senior year Maths and English.
In a world where it's been survival of the fittest since the beginning of time, why in education is the policy "No child left behind"?
In the end it's the other 97% of students that suffer, and ultimately every other industry from lack of well educated people.
Or parents that have to pay tuition for their child to take Junior and Senior year Maths and English so that they are ready for college.
To the parents of those children that have learning disabilities, I feel for you, but at the same time I do not feel that my child should suffer a lesser education so that your child feels better about themselves. The real world doesn't work like that, and not everyone gets a trophy for playing.
I am Bennett Haselton! I am Bennett Haselton!
Then: Sally is twice as old as Suzy. Three years from now, the sum of their ages will be 42. How old is Sally?
Now: Chloe has 7 apples. How many apples does Chloe have?
Tomorrow: Write the number 5.
I looked at the sample questions, and I have to recommend that math teachers learn English before teaching math.
It reminds me of Lockhart's Lament. We're teaching math wrong. Highly recommended reading:
http://www.maa.org/devlin/LockhartsLament.pdf
Strangely the Putnam exam has gotten harder, or at least more specialized (in a biased kind of way).
I can score about 3 points (of 120 I think) if I'm lucky on a modern Putnam since I don't have the prodigal knack and (more importantly) I never bothered to take a Putnam-prep course since I was more interested in research and diverse study than in tricking people into thinking I was a primadonna.
Just out of curiosity, I took a 60s Putnam one day and many of the questions were largely the "flagpole and shadow" type that used calculus and trig - fairly straightforward. Even the hardest questions were physically-grounded whereas nowadays they are extremely abstract.
I guess everyone was getting the "natural" questions right so they refocused the competition on the high end, but it's not just the difficulty of the questions: it also has to do with the style.
An update on this story today: Imperial College has decided that A-levels have become worthless for deciding which students to admit. This from one of the academically strongest universities in the UK, which specialises in science and technology. Their point is that nowadays, almost everyone gets 3 or 4 As, so they can't distinguish between them. They're going to start setting their own entrance exams.
"...the district is forcing them to dumb down the tests..."
We in the U.S. did the same thing to the Presidency eight years ago, and have gotten similar results.
I thought they had done studies in the late 80's/early 90's that showed that most females have less understanding in math then most males. As a result, didn't they start "dumbing down" the math portions of these critical exams to make them a bit more fair to the females? And the same with the english arts, dumb down for the males?
Also, in general, we are slowly getting away from this idea that memorization is what is important and what makes you smart. Part of that is simply that these days it is much less useful, but there has also been development in educational theory. We do not need or want our children memorizing tons and tons of facts. That really isn't helpful. If I need something remembered, I'll have my computer do it. It's way better than you. We need them learning how to think.
Well, since education used to be so much heavier in the memorization it is no surprise that the tests are "hard" for people today. I remember getting in to this argument with someone I knew. They'd found a test posted online that was a highschool graduation test circa 1900. They used it as an example of how much "harder" school was then and how I couldn't pass it. Well, turned out I could, but only because I'm a trivia junkie. I know lots of useless facts, and there was a whole lot of the test that was full of it. The geography and history sections were nothing but. Things like matching capital cities to states.
Ok, well that's neat and all, but it is quite thoroughly useless. There is no reason to know that. If you want to, great, but don't pretend like it is useful knowledge or that you are smart because you can do it.
So ya, people today had trouble passing the test, but that doesn't mean the test was hard, it meant the test was different.
I remember taking Calculus in High School (basically, a review of trigonometry and other concepts in the first semester, and then finally learning basic Calculus in the second, aka a bullshit easy class), and it's not as though even personal initiative is appreciated. I loved to read ahead in the book, and try to figure out things on my own. Often, I'd already understand the concepts being taught during the class, and the teacher was well aware of this. However, instead of being able to use processes I understood, I had to go through the tedium of the original process, and go through a page of work instead of the quick process that would cut it down to two or three lines. It's not as though it could be excused by my needing to understand how the process worked, considering it was almost never even mentioned in class, and it was always the most interesting part of mathematics to me.
We have maths. MATHS. There's an s.
-1 not first post
I know my fellow coworkers would crucify me for this, but I think the biggest problem with teachers getting a fair wage is the Unions. Are teachers at private schools getting screwed over so bad? I have been working in public education for 7+ years, and the unions have fought hard to ensure that kindergarten and high school teachers of any subject all get the same pay. And what has happened as a result of that? In the democratic process of wage negotiation, few grammar school teachers really care a lot more about teaching than getting paid. With the smaller class sizes necessary for grammar school, there is disproportionately heavy representation for these teachers that "aren't in it for the pay". They have spouses that make all the money they need. These are also the same teachers that have the time to go to all the union meetings while the 20's something, single high school teacher is home grading papers and working on the next weeks lesson plan. I am all for "Same work, same pay", but you just can't say that a high school advanced math teacher does the same work as a grammar school English teacher. I am not going to say one is harder, cause that isn't the point; just let them negotiate for their fair wage separately by supply and demand.
Hope this isn't too far off topic, but what I really think needs to happen is that there should be incentives for people to become math and science teachers. Specifically, let prospective math and science students pay off government loans with years of teaching in public school. This brings more opportunities to poorer students by reducing the up front cost of getting such degrees. While likely many may leave, the public school system would benefit greatly. There must be some figure of tuition costs v. years of teaching in public school that would be mutually beneficial and bring more geeks into the classroom.
Want Big Business out of government? Take away the incentive and start by getting government out of big business!
Here's what helped me- http://www.mathdoesntsuck.com/
Dumbing Us Down
John Taylor Gatto
It took ten years for me to shake off the damage the public education system did to me. Most of you still don't know you're broken.
My son actually went backwards since last year! He was performing double-column addition/subtraction operations in year 3 last year and now in year 4 is only working on single-column operations. Multiplication and division are also pale shadows of what they were in my time. (I'm 39). After chatting to his teacher they have been told to try and make maths "fun", and approximation answers are treated as good enough!
I am not familiar with the American school system, but I don't get why let the district design the tests anyway? If there is such a clear conflict of interest, someone higher up should design the tests, maybe the state.
When I went through the Ontario system (1986), the requirement for engineering was 3 high schoool math courses in: Calculus, Algebra, and "Functions and Relations".
I did some Calculus T.A. work, and the new students are missing certain critical concepts. The new curriculum has eliminated Integration from High School Calculus. It is actually lucky that the students get any Calculus in High School at all. One of the original proposals for the new curriculum recommended eliminating Calculus entirely. The Engineering schools fought hard to keep Calculus in High School.
Some of the first year engineering students have not seen key trignometric functions like the sine function. Other students have not seen Sigma notation, which is used for for finite and infinite series. Almost all of the students struggle with the university Algebra course, which makes me suspect the high school introduction to vectors and matrix algebra was been watered down.
Reducing the high school requirement from three to two high school math courses hurts the undergraduate engineering students. Further, a subject like Calculus benefits from repeat exposures over a number of years. The students would benefit from an introductory Calculus course in Grade 11, a deeper course in Grade 12, and then the 4 more courses in first and second year university. That way, the students have had 4 years Calculus experience before they need to apply the hard stuff in 3rd and 4th year engineering. As it is, students might only see Calculus for 2 years at university, and I'm not sure if this is enough time to really absorb the subject.
As for the quality of the students themselves, the students from the new curriculum are different. They are very fast (faster than me) at solving problems with known forms. On structured problems, similar to ones they have seen before, they are very fast. Unfortunately, they are very poor at solving unstructured problems, and problems where they have not seen the solution technique in advance. It is like someone has beaten the creativity out of the students. They can write tests really well, but they can't do original math. I imagine the students will pick up the creativity as they gain experience. It is just that someone has removed the fun advanced questions that really get the students thinking from the curriculum. The high schools are somehow creating students that can do simple stuff, but lack deeper insights into what they are doing. The students haven't been allowed to try, fail, and sometimes succeed at solving the harder mathemetical questions.
I'm a licensed teacher
Since surely this is at least in part teaching issue, and seems to be commonplace in most of western society (not just nations with the NCLBA or equiv.) doesn't this really suggest a drop in teaching quality/ability? Are we handing out 'licenses' to the wrong people, or too easily (to people with integrity issues who bend to NCLB standards) or some other flawed way? Should we be handing out 'licenses' at all? Can teaching ever be taught, really? Are teaching unions a help or a hindrance to the education product (and not to the teachers standard of living which I agree is generally too low)?
I'm sure this'll kill my karma, but I'd be genuinely interested in hearing thoughts along those lines since pinning it all on some amorphous 'system' or act or generation seems like a bit of a cop out, to say the least.
=======
Science -- Sealed, Delivered.
Not as dumb as boomers
Both my parents are engineers and I am getting the same degree and the math is harder but also thaught better compared to during their studies. And I also have more real engineering courses compared to my parents. Take in account that all the computerrelated aspects of these courses were nonexisting in their time.
I'm not a fan of the specific policies of NCLB, but I don't understand how measuring a schools performance with standardized testing is a bad plan. The current implementation may not be ideal, but the theory seems sound to me.
I want standardized testing to make teachers "teach the test" -- so long as the test covers all the material we want students to understand, that's an ideal outcome. It gives schools and teachers and objective reference to determine if their curriculum is complete and accurate. And the scores give us feedback about the relative performance of schools and teachers, so we can determine when we fail to meet academic goals, and investigate the difference between schools and teachers with different success rates.
It's not like you have to shove all this testing into 2 hours in the last week of class -- a situation where you couldn't possible cover all the requisite information. We could construct a series of short, standardized tests to be given through the year in various subjects, as part of normal classwork. Combine those with more comprehensive tests given on a less frequent basis to ensure retention. You know, just like teachers should be (and for the most part are) doing anyway, except designed by people who are both experts in the subject area and who have experience with statistics and test design.
If you're not first you're last!
9 out of 7 math students agree, standards have not been dropped!
Kindness is the language which the deaf can hear and the blind can see. - Mark Twain
The math curriculum - at least in Columbia MO US - is horrible. Absolutely horrible. My 4th grade son (who can do most 4 significant digit math computations in his head) is still being drilled on counting. 90% of his actual "work" is drawing diagrams of different ways to break down and re-add up numbers. He was capable of producing an answer to the problems, sans the "how I got the answer" part, years ago. They've never even shown these kids a multiplication table. I'm not a big fan of memorizing the multiplication tables, but at a minimum it is a great visual representation tool to expose kids to. Every school year, my son goes backwards in his math abilities. Every summer, we move him forward again.
Then of course is my daughter's experience in 6th & 7th grades. Math class is 35 minutes a day of pure lecture. All actual figuring and problem solving is given as homework. As a parent, I despise that much homework! It's a huge de-motivator. And, the math curriculum still sucks. Some pompous PhD sucking 6 figures a year out of the school district must have put a lot of effort into finding the worst, most convoluted math books on the market. The math itself hasn't changed, but the terms used to teach it have. I suppose there are down-the-line advantages to using the word "mean" instead of "average", but this and similar term changes since I was in school makes it difficult for me to provide assistance. I have to study the whole book (which is very poorly written and very difficult to find term definitions in) to be able to help at all.
As for the testing? It's all bullshit. Over 10% of a student's time is pretty much devoted to preparing for and taking tests. Another 8% of the entire school's budget is handed over to companies that sell the testing materials and services. All while teacher positions are being cut and non-"core" programs (band, choir, art, drama, the like) are being cut as well. I understand the need for occasional assessment testing. But this much is totally out of control.
At least this is Slashdot - someone should be able to reply and give a good argument for WHY we need this much testing.
All pass beyond reach of medicine. None pass beyond the reach of love.
There was a bit more set theory / functions etc. at 'A' Level, but again the teachers were keener to push calculus because they were on firmer ground.
When I got to University EVERYTHING was sets, groups, fields and functions; all that solid, traditional stuff was reduced to background information, I never needed any of it in an exam.
Meanwhile, back at school in Thatcher's britain, even the little 'real' maths there was in the sylabus was discarded in favour of a more 'practical' approach - it was important that everyone should be a competent grocer. Even things like trig and geometry were sidelined as unimportant to creating financially competent 'citizens'.
There was a gap of ten or fifteen years then when I paid no attention to UK school maths, but since various nieces and nephews have been going through the system, I have seen a shift back to more traditional style topics (trig and geometry included), especially compared to the mid to late eighties. None of them so far has made it past GCSE, so I don't know if 'A' Levels are any closer to University maths than in my day, but I suspect not.
The point I am trying to make is that the original article bemoans the prospects of UK maths undergraduates because exams are easier than they were, hence they won't have the necessary knowledge going in. Since the maths taught in schools hasn't bourne much relationship to University maths for a hundred years or so I can't see it makes much difference. If they want better graduates they should sort the sylabus out before they worry about 'slipping standards'.
[ ]Half Empty [ ]Half Full [x]Twice as big as it needs to be
From what I can tell, at early grades at least, since my son is only in 3rd grade now, math is not getting "dumbed down". He is in a charter school with a better curriculum than the ordinary public schools though. I may change my mind when he gets to high school, so ask me again then.
...the future crusty old bastards are already drinking the Kool-Aid.
That parents with kids in school right now may have with regards to testing.
Most parents don't know what's going on in classrooms today, despite the best
efforts of schools to keep them informed.
Sig this!
The recent report of the National Mathematics Advisory Panel is mandatory reading for anyone concerned about math education in the US. The report details exactly how things are going wrong. Our school district (where I have kids in grades 5, 7, and 9) uses a program called "Everyday Math", which is atrocious. (The University of Chicago should be embarrassed.) The emphasis is on breadth rather than depth, and there is a "spiral" so you learn a little bit every year about a lot of different topics. Students frequently have to write little essays explaining how they got the answer. (The linked report explains that spiralling is poor pedagogy, and that good math students can't always write an explanatory essay -- they just know what to do.) The high achieving families all have their kids tutored at the local Kumon center so they can learn their multiplication tables. The low income families just suffer the consequences of inferior education. The school board and district administrators are clueless, having just agreed to try out 3 different math programs in 3 different middle schools. How on earth will they evaluate the results?
In our district, the nonsense stops in high school (which is administratively separate), and and I actually think my ninth-grade daughter is learning more math than I did at the same age. But you have to survive elementary and middle school math to get to the high quality teaching. It's such a waste.
I'm not really an "older" slashdotter, I hit the big 3-0 next year, but from my experience, discussions with parents about their youth, and seeing my neices and nephews, I do have some perspective. In my parents generation the top graduate (valedictorian) in a class *might* have a somewhere between a 3.6 and a 4.0 GPA and there would be just one person. In my graduating class there were 6 valedictorians, all with 4.0's. One of them I remember as being one of the stupidest people I had ever met, she could barely function from being a scatterbrain, but by spending 80+ hours a week doing schoolwork she always got A's.
In my neices class, 10 years after mine (she just graduated) there were about 12 valedictorians, with OVER 4.0's. Aside from the sheer stupidity of a system were a student can graduate with a GPA higher than the maximum, there's an obvious trend here.
Febtober!
The article is quite accurate, although the decline was already in progress by 1990, going by my personal experience.
I was a university lecturer in Electrical and Computer Engineering during the latter part of the 80's, and the maths standards of university applicants were causing us more and more problems as the decade progressed. To put it simply, even the best qualified young people were not really up to the rather tough mathematical requirements of an engineering degree course.
What we ended up doing was organizing a prior summer course to help out those who were nearly there, and sometimes recommending an entire remedial year for the lower median students, mainly focussed on gaining the missing mathematics competence. Sadly, quite a few seemingly good students couldn't even cope with that and dropped out, but better to drop out early than halfway through a hard course.
It's a very bad situation. We live in a technological civilization, and pretty much everything manufactured around us is the product of applying mathematically-based knowledge somewhere along the line. The dropping competence in mathematics, and hence the declining ability to handle the hard sciences and engineering, is extremely worrying.
"The question of whether machines can think is no more interesting than [] whether submarines can swim" - Dijkstra
The Social Engineering, er, Mathematics exam in 2009:
;)
Johnny the hard-working farmer labored hard all season long and harvested 5 bushels of fruit.
Rodney the lazy sod sat on his ass all season crying about how unfair it was he didn't have any fresh fruit.
Uncle Sam took 3 bushels away from Johnny and gave them to Rodney.
Explain:
- Why giving Rodney free fruit is the right thing to do
- How it's fair to punish Johnny for working hard
- Bonus point: what is the percentage tax Johnny was charged?
The Christian Right is Neither (Christian nor right). See: Matthew 23, Matthew 25, Ezekiel 16:48-50
I too have a belief that the system protects teachers too much. However this year my Daughter's eighth grade Math teacher was awful and could not even attempt to keep control of the class. He was let go about 1 month before school was out and it was his first year.
Interestingly the High School that she is going to is aware of that teachers failings and identified all of his students as likely needing extra help in ninth grade.
This was supposed to be the GATE class too. Now most of these advanced math students have lost the edge they had and are behind other GATE students in the district.
Glad they got rid of him.
Life moves pretty fast; if you don't stop and look around once in a while, you could miss it. -FB
I don't know if the kids are dumbing down, but there was a time when I was in high school that I used to be able to answer all of these questions.
I can't. I've forgotten.
Not that it worries me too much, I mean, I never had to take a math class again after my sophomore year and I'm doing okay. And the real-life applications of trig have been few and far between. I did once use the Pythagorean theorem to find out if a corner desk would fit into my apartment. That's about the extent of my higher mathmatics applications.
But still - this is something that I wonder if I'm missing out on.
Maybe we should get together "adult math clubs" to refresh ourselves on algebra, geometry and calculus.
I used to work for NetQoS. I no longer do, but want to keep the excellent karma attached to this account.
Yes they have.
I had my maths GCSE a week ago, and I can confirm that yes, maths is now damn easy. The most difficult question on the paper was to perform a simple proof involving algebraic fractions.
The problem of maths education does seem to be worse in secondary schools, due to the habit of teaching to the lowest common denominator (pun unintentional). For me at least, year 7 maths was simpler than what I was taught in year 6.
One experience that for me really exemplified this decline is the International Maths Olympiad test. During the test, I had to attempt to teach myself how to solve quadrilaterals, as we had not been taught them in class.
For you Americans, UK GCSE = 15/16 years old
If anyone has any questions about learning GCSE level maths, feel free to ask me.
I must be new here...
I went to HS in the mid 80's, undergrad (Physics) and grad (Unclear Physics) in the early 90's: I was APPALLED even in grad school at the people who were supposedly top of their undergrad class and unable to do simple DifEqs! The advantage I think? I had to learn to do it myself. Even in undergrad: I could use a calculator... but no whiz-bang TI-85 (I did end up buying a schweet HP clamshell my senior year - and learned to glory of reverse polish). So you used your Handy Dandy Math Handbook even in the early 90's... and learned how to create your own plug-n-chug. AND you learned to derive your own equations. It was called an education back then. Now? I teach classes for an unnamed university or two on occasion, and cannot believe that inability of the "grad students" to do basic algebra. And that's all I have to say about that!
Kids crave electrolytes, give kids what they crave.. That is the obvious answer to math, ..besides the fact that it sucks.
Bringing liberty to the masses. - http://freetalklive.com/
I can tell you that the quality and the difficulty of the exams in the U.S. is a joke. I feel bad for American kids who really have to dumb themselves down because the system is working against them. We are losing a lot of young talent without even knowing it because our education is designed to educate everybody in the most efficient way of multiple choice tests.
I never had a multiple choice test until I came to the U.S. All of my previous science and math tests were written. I had to draw diagrams, explain my line of thought and show meaningful calculations. If my penmanship or analysis of the problem was not clear, I had to discuss it with the teacher in one-on-one fashion. It was quite common to talk to a teacher in order to resolve any questions that he or she may have about the work. If mistakes were genuine and not repetitive, then they did not influence the grade by that much. For example, if you did all calculations correctly and then missed a minus sign when writing the official result, this mistake would be circled and that's it. Overall, I was considered a good student who lacked some attention and I have always received A-/B+ for most of my work. It really sucked to write things out and explain complex problems on paper and then present everything in a legible manner -- if the teacher could not read it, it was a mistake -- but overall I am glad that my teachers pushed me this way. Physics and chemistry were the toughest subjects because you had to write so many freaking formulas that by the end of the test your hands could barely function. Damn, I miss those days.
Fast forward to my life in the U.S. The land of multiple choices really screwed me over because if I could not circle a correct answer I automatically failed the problem. I could hardly discuss any issues with many of my teachers because there was this stupid system in place and everything was decided by punch cards. On top of that, the level of math and science education in the United States was lagging behind of what I have experienced in second world country. Math problems were mediocre at best. Physics did not involve any thinking besides what was in the book -- well, at least in high level -- and for some reason organic chemistry was considered a college subject. Students got away with submitting hand drawn diagrams on what appeared to be toilet paper . And if you had good eye sight you can pass the course by circling the same multiple choice answers as your A-student friend. Are you really surprised that we are in Iraq and a financial mess right now?
You may think that education has little to do with skills in the real world, but I beg to differ. My recent encounters with some IT engineers make me thank all that hard work I used to put in graphs and analysis. The more people I meet the more I realize about the skills that one has to develop in order to do some rather basic tasks, like stating a problem and a possible work flow in a manner that other people will understand. Ask a fresh college grad to describe a problem on paper (no computer) and you'll get a bunch of gibberish written with a hand of what I would consider to be a fifth grader. Who cares about the material if you can punch two numbers into a TI-89 and circle a correct answer. Right?
Okay, smart ass, what do you suggest? Well, for starters let's teach kids who want to learn. Let's not try to teach everybody in the most efficient way possible. Let's not bring everybody down to the lowest common denominator. If school is not for you, then may be you should leave after the 9th grade and pickup a trade. A lower student to teacher ratio will allow reduction of multiple choice tests and more of the one-to-one work most kids need in order to to learn how to learn.
For people not in the U.S., NCLB is the controversial No Child Left Behind act.
As I understand it (I once dated a teacher,) the history of NCLB is basically:
I can only speak for the UK. I finished my GCSE's in 1992, A-Levels (Physics, Chemistry and Maths) in 1994, and Physics Masters in 1998.
There are a few reasons I think it's been happening. At some point the creation of exam papers became a business, so schools started shopping around for the easiest exam board. This has had the effect of driving the difficulty of exams down. This downward spiral should have been stopped immediately by a central exam regulator (I assume we have one) but either they are useless, powerless, or (more likely) they are under pressure by the government to let exams through, since record exams scores "look good".
Another problem in the UK is that Labour have tried to open up University to too many people. My naive idea of education is that by the time you get to University level, only the smart people are supposed to be left. Not rich, not poor, but smart. This is at odds with sending so many people to university because most people are just not that smart. The only way you can have so many people going to university is by A. Letting them take simple things like Media Studies. or/and by making the hard subjects (Physics, Maths etc) much easier. Both of these things seem to have happened.
The other sad effect of pretending everyone is a genius is that it's no longer possible for the government to pay for your university education. The people making the decisions in government today got full grants, whereas students today are often in debt for years. I managed to finish my degree before grants ended, but if I was 18 again, I'm not really sure I could face all that debt, so I would probably never go to university in today's world. The sad thing is, the next Newton or Einstein may make the same decision and end up flipping burgers instead, all so that huge crowds of people can get a degree in media studies.
A child will not be able to find his problems with his/her tests if they are having trouble socially. It is not always that they don't understand how to be social, but the environment itself.
There are those teachers who some children give a bad reputation, and it is hard to feel easy to ask the teacher for advice. How do you improve yourself in that kind of an environment?
Instead of making math exams easier, they should focus on building a strong foundation. How many schools try to get through a certain number of chapters by year's end? They should focus on quality work, not quantity.
So instead of doing like 12 chapters in a year, do like 9, but make sure those students have it crammed into their heads on how to do the material in those 9 chapters. A strong foundation in high school will prove useful when one continues on in the subject in college.
If someone's a bit (or a lot) slower than the rest of the bunch, it doesn't always mean they can't do the same things, but it does mean that they'll need to work towards it a lot more. The sooner they know they're slower the sooner they can figure out how (and if) they can cope with it.
Waiting to start that until college/university/real-world is too late. The habits and coping methods are best learned when you're young -- when you're learning how to learn. Dumbing public school systems down until everyone passes might seem like a cheerful warm fuzzy idea to "some people", but it's actually the worst possible thing you could be doing for those kids.
There are problems beyond math.
.bat "scripting" and javascript for ~2 years before that).
:D) has had the same experience (with her being the "kid", age ~15 at the time). This at least tells me that kids have an inherent drive to not waste their time. If that's true, then why are they so unmotivated to do schoolwork?
The biggest is that the school system is not a great way to learn stuff. I remember (but bear in mind that I'm your average slashdotter, not your average person) at a fairly early age drawing 6x6 grids which taught be that 7 has probability 1/6. I remember my father drawing circles in the sand with dots in the center, explaining the basics of chemistry (and he's not a chemist), and me completely getting it.
I remember at age 14 (laughably late by slashdot standards) that a person I knew had written a program that played chess. Being a moderately skilled chess player at the time (1390), I thought that was awesomely cool and wanted to do that myself. That got me started writing C (I had dabbled in
Where am I? Studying CS & Math. Doing the things I chose to study in my own time, not the things I discovered in school.
Contrast this with school. You're forced into confinement (it wasn't until grade 6 or 7 we were allowed to leave school grounds unsupervised) with a bunch of people that mistreat you horribly and wish you the worst, and another bunch of people who really don't give a rats ass. You're bored out of your mind in the classes that interest you because the material is easy and progress through it is slower than your pace. You're bored in the rest as well, because they don't interest you; the disinterest may arise merely from the fact that they are being forced upon you.
And I went to a private school... with the things my mother has said about public schools (and she's worked at one), I think I should be glad to not have attended one. On top of that, I hear the danish school system is better than the one in USA.
More edibles for cognition: John Taylor Gatto (English teacher) says that we he finds companies that don't mind having the kid do some work, the kids do more and better work than the paid staff. My ex-girlfriend (okay, so not completely an average slashdotter
Not wanting to be completely off topic, the article says that work needs to be done on making math chic. The question is: who has the credibility and influence with kids to make math cool? For young kids, the parents have some influence, although not much in the "cool" department. For teens, it's mostly the peers (not the kinds who reset the connection). That's a network effects problem you have to solve. Who else? Rock stars? Quaterbacks? Miss teen south carolina (everywhere such as maps)? I mean, having math be the Hot Stuff wouldn't be bad, but it would imply (not just suggest, as the decline in maritime piracy has) the existence of the flying spaghetti monster.
(for those not picking up logician's humor, everything follows from a contradiction).
What do we think of online assessment systems provided by the big textbook publishers like MyMathLab? They use a drill and kill approach to the learning of math - do these really help us learn?
I'm in the middle of Part II exams (finals) for the Cambridge Maths Tripos and I certainly wouldn't call them easy! :-S
It's not just maths. I teach science to 11-16 year olds in the UK. It seems like the hard academic subjects have been stripped over the years. I weep at the science syllabus now. I bet many would be shocked to know what is actually in it. Couple of quick examples: First lesson in Year 10 'Carbon Chemistry' - cooking egg and potato. Coursework for GCSE - write an article about a news item that has science in it. Everything HAS to be relevant to the lives of teenagers these days it seems. The beauty of science is that it can show us wonders that are not in our everyday lives. So much for my vision. I'll be teaching the morals of using a mobile phone on the tube soon enough - in science. They're slashing the 11-13 year old syllabus come this September, down to virtually nothing - I kid you not, and I don't exaggerate. From my perspective in science, the kids I teach know NO maths whatsoever. Today I asked a kid what was 0.999 * 10. They couldn't do it. At all. They were set 2 out of 6, and I'm in a pretty decent school. I was dumbstruck, although not as dumbstruck as this generation clearly is.
than others
Engineering is the art of compromise.
so long as the test covers all the material we want students to understand
thats not quite the kind of teaching to the test I'm referring to. Most teachers are given access to the tests before hand, then they can coach students pretty hard on the problems they will see - there is no goal in there to RETAIN(or even get a real understanding) any of that information.
Prediction: The real iPhone killer is going to be sex robots from Japan. Think about it.
The problem is that "teaching the test" does not mean teaching the material that is on the test. It generally means teaching students how to take tests (if you don't know the answer, pick C; try to eliminate one or two wrong answers first; options with "always" or "never" are probably wrong; &c.). Students learn a lot of tips and tricks for taking bubble tests, and they learn facts about the subject areas, but they are unable to synthesize that material in any way. So, occasional standardized testing to ensure that basic facts are present is acceptable, but relying on standardized tests alone is no way to determine whether or not students are actually learning the material, or that they are capable of thinking about it abstractly.
Rhapsody in Numbers
My teacher taught both classes, in a weird integrated block class along with a bit of philosophy and original sources thrown in--some of my favorite parts of the class were struggling through Newton's Principia, or Einstein's Principle of Relativity, or examining Kant's philosophy, along with Descartes, Locke, etc.
He genuinely respected our intelligence and didn't dumb anything down for us, not even the tests, to the dismay of other teachers who (pretty much correctly) claimed that his classes were taking up all of our time. Still, aside from sleep loss, it was one of the best classes I've ever had.
OK, I got off somewhat offtopic there, but to counter TFA's claims I just want to say that high school math tests are still hard. Really hard. At least, the ones at my school, anyways. And because I know it's going to be mentioned, I would like to note that this was the standard class for seniors. Some declined or dropped out and opted instead to take another course online (the problem with a small school is few options) but pretty much all of the seniors took this class.
In case anyone's wondering, I live in the US and go to The Geneva School, a tiny (but expanding) classical Christian school. (And Mr. Brown, I know you're a /.er--if you're reading this, hi!)
Reality is the original Rorschach.
This is an interesting subject. For me personally in my A Levels I found that the older past papers were marked a lot harsher and I did find them harder (but still doable) than the more recent ones. This was for Chemistry in particular.
However, on to Maths at GCSE I remember my dad looking at my work once and saying he does not understand it and wasn't taught it at school. Whether it is he can't remember or not is a different storey. I guess one could argue that although the content may be different it doesn't say anything about the difficulty however.
I remember seeing an article on the bbc comparing what students in China were doing for Maths and what students in the UK were doing for Maths- the china exams looked a lot harder to me. I guess that's going off topic though.
In 1981, when I took it, the age 16 maths exam included simple calculus, matrices and the beginnings of set and group theory (plus, you still had to be able to long division and all that).
In 2008, those are all gone - and even the quadratic equation question is split up into two handy steps for you: (1) factorise this equation (2) now solve it.
To be fair, the matrices, set and group theory were presented as silly things that you had to learn to do to pass the exam - that much hasn't changed.
Of course, back then only about 10% of UK the population went to Uni and you could get into a half decent one with 3 Bs and Cs in the age 18 exams.
Now, 40%+ of the population go to Uni and yet more and more places are insisting on straight As. Clearly there has been an unprecedented surge in human evolution! The signs are plain at any UK university: kids with strange integral-sign birthmarks, men shooting laser beams from their eyes, girls with white streaks in their hair and a predilection for yellow spandex watched over by aging professors with English accents everywhere... Er, no - not really. Apart from the professors with English accents of course (there may be a logical explanation for that).
In a survey of 100 programmers, 111111 thought that duck-typing was a good idea.
When I was in HS, I took the highest math offered (AP Calculus). At least half the kids in the class couldn't subtract two three digit numbers without a calculator. Most couldn't do it without pen (right, most kids didn't even use pencil) and paper.
1. kids are bullied at school...
2. educational standards are dropping there...
3. its food served is unhealthy, due largely to outsourcing...
The list continues to grow.
Just as we (in Australia, at least) were essentially "forced" to implement our own phone service (enabled by excess bandwidth in .AU as well as converging technologies like VoIP & Asterisk ...and cheap VSP rates) - by our monopolistic Testra (gov't majority-owned telco & ISP)...
Let's see WHAT ELSE we have to do for ourselves:
- build electic vehicles (or convert our smaller ones to electric)
- construct our own renewable energy systems (windmills, solar- or geothermal-hot water for showers & heating, etc.)
- design our own energy efficient homes
While it's fun to do all the technologies involved, it sure doesn't leave muc time for living (unless we do these things cooperatively, sharing design results in Open Source documents & photos of our prototypes, etc. and - where possible - helping each other in the neighborhood or larger regions).
Oy! What a future we can look forward to! :-/
Of course, we can also go for a model more like village... (&/or maybe move to India for plenty of examples...?)
Did you mean to say "Fire the teachers and pay the replacements more"? As a taxpayer I'm sick and tired of seeing the awful results of the educational system, and the teachers unions mounting the charge that the reason we have such bad teachers is the supposedly low pay, but at the same time suggesting that if the pay is raised it would be completely wrong to get rid of the current dregs of the teaching profession and replace them with those better teachers that the higher pay will supposedly attract.
I'm an American. I love this country and the freedoms that we used to have.
My father is a high-school mathematics teachers, and he says that parents are the problem. No longer do the parents force kids to do their homework (which he says about a third don't turn in at all). They are their child's buddy, his best pal. They go and fight the nasty teachers for him.
My dad also complains bitterly about the reams of paperwork (being chairman of the math department is an unwanted honor because of it). The principle at his school said he probably spends half his time just making sure the school is compliant with regulations, so they don't lose federal funding.
The teachers at that school also say they have funding problems because are the only school in the valley that doesn't tweak test results to get more govt funding. Overall, the general problem is that kids can't be forced to do anything they don't want to do. Thanks, popular psychology.
(Oh, and one of Dad's favorite cartoon he posts is a calculator saying "I think, therefore, you don't.")
The government can't save you.
I never understood the "need" for all of those "pre-" courses.... I never bothered to take them.
can't teach. I sorry to be so rude but I've talked with my nephews teachers and they don't seem to understand many of the basics of math, science or even some thing as simple as logic.
They seem to be agenda driven, case in point. Recently the school insisted on showing Gore's movie but refused to show any counter point because in their eyes there was only the, and I quote, "ONE TRUTH" Excuse me but that's not education that's indoctrination and very, very, frightening no matter which side is doing it.
The only way this country will get back it's lead in the Sciences, and with that commerce, is if we get people with degrees in science and math, or from industry research and development into teaching.
People that refuse to allow two side to an argument, to give some a choice or allow for discovery have no teaching skills IMHO.
Si vis pacem, para bellum! For evil to succeed good men need only do nothing!
They didn't seem very easy when I was in high school just a few years ago. I even failed one of my math classes, Algebra 2 my last year. I barely missed passing. I never fully understood what we were learning and more complex material like calculus--forget about it. Didn't stop me from graduating though because I had already completed enough math credits; it was only required you complete up to geometry. I always thought that was too low. Even though I failed the class, and it would have kept me from graduating on time, I think it should be a requirement to pass the class I failed. Standards are getting lowered all over the place in public school, of course math is going to be hit too.
It shouldn't be difficult to prove the tests are getting easier, just compare representative samples from each decade. Also you have to take into account that students are allowed calculators on a lot of the exams now and portable programmable graphing calculators didn't even exist 50 years ago.
I have sympathy for students who find mathematics a difficult subject, but lowering standards, dumbing down the material, and providing technological crutches are not viable solutions.
If you build it, nerds will come. Soylentnews.org
Readers with kids in school right now may have a bit of a bias on just how educated and how intelligent their precious little gems are. I'm just saying that there are a lot of different ways to study this issue, but asking parents if they think their kids should be given harder tests (and by corollary, lower grades) many not be the most objective way to look at this.
I'm an American. I love this country and the freedoms that we used to have.
I don't know about them getting easier, but two years ago I got an A* in my GCSEs with zero revision outside of class and I'm certainly not a genius. Based on that I'd have to say they are pretty easy. A levels have been more difficult, though I've got an A in all my current modules (final result coming in August) - but they were after doing plenty of revision.
Brilliant paper; thank you for linking it.
...but so are the people taking it.
I'm 18, British, and currently doing one of my A-Levels in Mathematics, and while I'm generally seperated from the lower years (13-16 year olds) I occasionally find myself interacting with them. These kids do not understand maths at all.
Now, I know I'm doing A-Level Maths, but is it really unreasonable for the concept of pi-r-squared to be simple? While the top set maths (year 10/11) are at their usual level, the bottom sets continue to drop off the scales as our society's education system struggles to accommodate them. The exams have to get easier because more kids are failing, it seems.
Last year trigonometry was missing from an exam paper my friend's sister sat. She was doing an intermediate paper (and it's on the syllabus for it). Wasn't trigonometry mandatory for even the lower band paper, in days gone by?
I never felt compelled by any of my math tests and always found expectations to be what I would consider subpar. That being said, numbers do kind of come easily to me.
I generally feel that America tends to appeal to the people more than the proper education. We need to make budget cuts? Let's make it seem like we're doing better by raising the amount of Math they need to graduate but lowering the standards in all the classes. In doing so, the kids will no longer be able to be enrolled in those expensive art and music courses and then we won't have to offer many of them anymore (that's an almost literal example from my alma mater after I left).
I just feel that the US school systems are going to hell.
"Don't meddle in the affairs of a patent dragon, for thou art tasty and good with ketchup." ~ohcrapitssteve
Examples of the evolution in teaching math since the 1950s.
1. Teaching Math In 1950:
A logger sells a truckload of lumber for $100. His cost of production
is 4/5 of the price. What is his profit?
2. Teaching Math In 1960:
A logger sells a truckload of lumber for $100. His cost of production
is 4/5 of the price, or $80. What is his profit?
3. Teaching Math In 1970:
A logger sells a truckload of lumber for $100. His cost of production
is $80. Did he make a profit?
4. Teaching Math In 1980:
A logger sells a truckload of lumber for $100. His cost of production is
$80 and his profit is $20. Your assignment: Underline the number 20.
5. Teaching Math In 1990:
A logger cuts down a beautiful forest because he is selfish and
inconsiderate and cares nothing for the habitat of animals or the
preservation of our woodlands. He does this so he can make a
profit of $20.
What do you think of this way of making a living?
Topic for class participation after answering the question:
How did the birds and squirrels feel as the logger cut down their homes?
(There are no wrong answers.)
6. Teaching Math In 2008:
Un maderero vende un camión de madera de construcción para $100. Su
coste de producción es $80. Cuántos de su familia pueden usted alimentar
desde los $20 beneficios?
MyMathLab may well have some benefits for the students; however, the main reason that the publishers are pushing such programs is because it gives them a revenue stream even from students who purchase used textbooks.
You are absolutely wrong from my perspective as a college instructor of freshman physics students. Few students today would have survived the freshman physics courses I took back in the 1960's. They don't know simple trig identities, and the modern trend is to even take calculus out of the calculus based physics courses because they do better on standardized tests which basically use 7th grade math! I have had tears from female students who got a C and who "just have to have above average grades". Hell, she/they should have had a D but you cannot give anyone a "bad grade" or you will get a reputation as a hard ass and you will get creamed on the student evaluations at the end of the semester, which has career implications. And we in physics are the last bastion against grade inflation on most campuses these days, since we are generally used by colleges of engineering to eliminate the radically unworthy. As if ill prepared students are the best judge of what they need in a career in science-an area of academia where there are objective standards of what you need. Really!
Some areas of engineering have changed requirements for their freshman classes, particularly in the electronics and computer areas-areas Slashdot readers tend to be concentrated in. But, for example, you might need a basic understanding of trig and geometry to do decent computer graphics today, and those math skills are not taught or badly taught today, judging from the "brighter" and "more able" students I see today. There are some basic skills that haven't changed and the ability to use a calculator that contains every formula known to science and engineering (I can remember one that advertised exactly that a few years ago) doesn't help you understand what you are doing. And understanding is the difference between being a valuable worker in any science/engineering field and being a hack.
You sound exactly like the caricature of an engineer one sometimes encounters: someone who doesn't want to understand anything, just which engineering handbook to look up the right formula in. The requirements of a basic science and engineering degree have not changed in the 45 years I have been around academia. Computer programming at the freshman level is probably the sole exception-but I learned Algol 60 and assembly along with Fortran IV back in the day, and all in one semester. A freshman course in electrical engineering will probably say more about transistors today, but not a lot of deep substance: Ohm's law and basic circuit calculations are exactly the same and involve the same math techniques today that they did in 1950. If you went through a dumbed down math curriculum in high school, even if you took a calculus class, if you don't know some basic trig and geometry, if you have to wait until late in your sophomore year to learn about the determinants and matrices I learned about in a hick high school in Texas in the 1960's, you simply are not going to be able to advance as far in your learning as you should be able to in your freshman year of college. And you will emerge at the end of your four years of college less prepared than your predecessors did even 15 years ago: the worst of the decline has been in the last 20 years.
My next door neighbor is a high school teacher at a local public high school. He teaches Chemistry, and also coaches the track team. He pulled in $160k last year. He's been on the job for 23 years, which has a huge impact on a teacher's salary, and he makes a little extra for the coaching gig, but not a bad salary for the 9 months of work. While teaching may have a low entry level salary, their raises and bumps for tenure are nothing to sneeze at, and can support a fine lifestyle.
I am an American high school student who attends one of the top public high schools in his area. I'm not saying I'm a genius, but I know that I am not a dumbass either. I am a product of the education I have received from 12 years of public education. I personally find standardized tests incredibly easy and dare I say it, fun to take. They take very little mind power to take and get a good score on. This shows the sad decline in standardized tests.
In comparison, upper level high school classes make you work and you can't slack off or you will suffer. This is really true with AP classes, as teachers are teaching college material. That is, unless the teacher does not actually teach on a high level. I have taken AP classes where both are the case. And in both cases, my scores and college credit for each class is reflective of it. Nothing works unless you have a teacher who knows what they are doing teaching you.
Also, the lower level classes, which I have taken some of, are shockingly bad in terms of actual teaching/learning. You don't learn shit, and it is presented in a way in which you baby along the kids. Teachers also do their best to make sure every kid passes. Hell, I had one teacher who was so intent on making it easy to get kids to pass, he gave 85%+ an A, whereas the rest of the building does 90%.
So basically, in the US, it comes down to the teachers and NCLB. Teachers are not respected nor paid enough. Their job is hard, and there is a great dearth in good teachers. We need to promote this. That way, we can actually have children who do not think elephants are bigger than the moon. Teachers are dumbing things down because they have to for NCLB, and because they are are afraid to teach at a high level and see students suffer. Let's get with it. Not everyone is a perfect student, and no matter what some people try to do, its never going to be that way. The education system is holding back the smartest and brightest kids.
For an example, I had a good friend who attended our school as an exchange student from Sweden. He was amazed at how little we did, and how low the standards were. He had never learned American history, yet in that class, he consistently was the best and got the most out of it. As we used to sadly say, "The Swede is kicking American ass at American History. Pathetic!â American standards are low, and our children are suffering. This needs to change.
I know from experience in New York State that the Mathematics system is extremely flawed in the public Schools. You Spend your Freshman and Half of your Sophomore year learning something called Math A (early algebra,factoring etc.) Then through your Second half of Sophomore Year and Junior year is spent Learning something Math B, which consists of Quadratics, Proofs, More advanced Algebra etc. The Argument over the validity of this system has been going on for the past 8 years its been in the works. Before this system there was a much easier system with one math class per year. Spending a Summer off and then continuing a math class is just absolutely ridiculous.
Full report here: http://www.reform.co.uk/documents/The%20value%20of%20mathematics.pdf)
The argument goes, so far as I understand: Mathematics education has "declined" since 1990; therefore, this is the single cause of nine billion pounds of lost gain to the economy. No, sorry, there are many other factors contributing to this supposed "decline".
I think it would do Reform some good to learn some basics of sociology first. THEN, they are welcome to try writing an unbiased research study telling us why mathematics have gone downhill.
Is there ... perhaps... just a slight little chanse... that it's improving the education? I remember in the extras of the game portal, in the first level with azidfloor, the commentatory said something in the line of "This used to be the first level introducing the powerball element, but to many people got confused because to many elements where introduced to fast"
I for one havn't yet found any insufficiencies in my math background, And I'm currently spending my time crunching quantum mechanincs. I think there is a point in not "trowing" it all at the kids.
If I became a teacher, sure the first thing I'd try to teach would be pythagoras, followed emidiatly by trig differential equations, integration, and moving on to eulers identity, since these are the things I'm currently using the most, but a 2nd grader would properbly just go into brainshock and learn absolutely nothing.
Besides, the level of a test does not equate student levels, however levels of understanding are extremely hard to define.
The NCLB isn't the cause of the focus on testing, it's a symptom. Note that the math tests started becoming noticeably easier a full decade before NCLB.
The true source of the focus on testing is the involvement of the federal government in education. The larger the beaurocracy involved in education, the more people will want to look at raw numbers. Private schools don't have this insane preoccupation with test scores, and neither did most public school districts or states before NCLB.
It's easy to point at little quirks of the public schooling system like NCLB and declare that they are the reason behind the failures of public scooling, but the truth of the matter is that the system is designed in a way that inevitably leads to these types of failures.
So these are exams for 16 year olds; what is a 16 year old supposed to do with this education ?
I was educated in the UK, and I left school at 16 to start an apprenticeship - I'm not sure that there are many of those left.
If I had stayed at school I would have done "A" levels - the (at the time) horribly hard exams designed to stop people from going to university.
I'm not kidding, the public wanted value for the money they spent on university education and A levels were a way to screen out those that might struggle to make it. In some ways they help make a "4 year degree" only take 3 years to obtain in the UK.
If I had done the A levels and not gone to university I would have been considered an academic oddball, who really did not fit into the scheme well.
So there were two streams of people doing exams; the university-bound and the apprenticeship-bound and the exams were tailored to those needs.
Needs must have changed...
1) UK and other nations want to encourage further education, not put a barrier in the way
2) Many of the traditional forms of employment for 16 yr olds have gone, 16 years is a waypoint in a normal schooling to 18 now.
3) Universities have welcomed "nontraditional" academic backgrounds for years, and indication to me that the old way of doing exams was not considered optimal.
I think it's inappropriate to expect the exams to stay the same when their context has changed.
Nullius in verba
Here's an interesting statistic. This is for all students who took the GRE between 1998-2001.
To get a scaled score of 800/800 on the Quantitative (math) section, you needed to be in at least the 94th percentile.
To get a scaled score of even 730/800 on the Verbal Section, you needed to be in the 99th percentile.
Of course, the data could be biased (perhaps more science and math majors took the GRE than liberal arts majors? perhaps engineers suck far more verbally than our liberal artists suck at math?), but even so it shows the GRE math section doesn't do much to challenge and separate the brightest minds.
I know that many math topics that were in standard math courses in the 70's are now AP (advanced placement) material. In the private, Christian school my kids attended, they worked really hard to keep the standards up. Parents then started to complain that their kids were not scoring as high as they had in public school. So the school changed grading for tougher courses without changing the difficulty of exams or the content of the classes. I don't think kids are dumber. I do believe the time spent watching TV and playing video games has a negative impact on intellectual curiosity and on creativity. But I think the key factor is that we expect less of the kids and more of the system. There is a new sense among parents that, not only are their kids, on average, above average but that any failings are the fault of the system (teacher's not paid well, NCLB issues, unions, etc.). IMO, most of the fault sits squarely on parents. If they expect more and hold their own kids accountable, then the kids will do better regardless of all the rest.
http://xkcd.com/135/
I think the problem is more that the test structure is poorly designed (e.g., bubble tests with no written portion) than anything else. Yes, it's profoundly more difficult to score an exam manually than by computer, but we're not talking "rocket scientists needed" here.
Let's not forget about one of the fundamentals of population and bell curves: proportional growth. When Gen X begot Gen Y, the problem of the Boomer-era population growth got worse. So we have a populace, X percentage of which has problems with math or logic or something that causes issues. When operational cash is granted from the public based on performance, and X being unevenly distributed through the system, the motivation is to induce success by inching the bars lower in those schools that got stuck with a greater percent of X. Now throw in national correlation for education 'standards' and the bars all over start moving. The net effect seems to be lowered expectations, and thus lower student motivation to push their own envelope. I've heard entirely too many new parents talk about brush off low (70 and lower) math grades in a conversation about art, plays, music, or sports. Or worse still, altered grades based on performance in those areas. A prime example of this is a fellow student of mine in the electrical engineering program who slipped through the cracks, was told to sit in a corner and do something else while the others where testing, and has left this one to this day with 5th grade language skill, and intellectually lazy to the point of not caring if they understands the concepts when guessing answers on (multiple choice math) tests. By the way, that's another problem with education: multiple choice only encourages this sort of behavior. Problems have been more frequently reverse-worked from the answer list than actually solved among my classmates. It encourages leaning on the mental cruch of the easier operations rather than learn new ones. So here you are, motivated to just move the kids through meaningless grades on salaries built for college students and you're wondering why the net education level has disintegrated? Maybe you're not wondering, in which case you should be part of a grassroots crusade to expect more out of rising generations, and get them to think.
It's education in general. The problem is that up until the 80's, there was a general understanding that education was above and beyond politics. Overall policy was in the hands of Local Education Authorities and the government pretty much set the funding levels. During the 80's and early 90's however, Margaret Thatcher's conservative government took control of education in the name of "improving" it. Part of this was down to crushing the power of the teacher's unions and a claimed influence of political bias on the behalf of teachers and the other was a pathological hatred of the very left wing Inner London Education Authority (ILEA). One of the signs of the animosity between the government and ILEA was the appearance of anti-Tory Easter Egg type messages in ILEA produced software (I know a teacher that found a few).
Anyway, the conservatives set up OFSTED to monitor schools and started issuing diktats regarding what should be taught and how it should be taught. A whole generation of 80's kids was created that couldn't spell or string a sentence together because someone high up decided that grammar and spelling weren't important as long as people could make themselves understood.
And now we reach the real point which is that education in the UK was truly screwed when Tony Blair made his Education, Education, Education speech. At the moment this statement was made, Blair's was declaring "Judge my government by the success we have in education" and being able to show that standards were improving became more important than improving standards. One prime example of this was the introduction of the GNVQ qualification. Unlike the GCSE, the GNVQ is a quantitative measure so a GNVQ in ICT would be along the lines of:
1/ Open a word processor
2/ enter a block of text
3/ Insert a picture into the document
4/ Add some more text and centre it
As long as you performed those 4 tasks, you got your GNVQ. The content could be utter bollocks but as long as you did it you got the ticket. The GCSE however, included a qualitative component so the effort and skill involved was higher. So why you may ask did David Blunkett declare a GNVQ to be the equivalent of 5 GCSEs? The effect of this was rapid. Schools that were towards the bottom of the performance league tables switched to GNVQs and rapidly shot to the top leaving those teaching the more difficult qualification looking like poor performers.
And this happens with every new scheme the government brings out because they always leave a loophole that can be exploited by school heads desperate to show improvement. It isn't just education either. In hospitals, the government was under pressure to end the situation where patients were left in corridors on trolleys. Quick witted hospital managers saw the loophole, had the wheels removed from the trolleys, called them beds and designated the corridors as wards. Problem solved overnight, performance related bonus secured. Another example was when hospitals were being criticised for having empty wards. The managers worked out that it cost less to decorate a ward than it did to staff it so some wards were being decorated every three months or so.
Make no mistake, it is easier to lower the bar than it is to make people jump higher and so long as league tables and performance related funding and bonuses exist the bar will continue to be lowered. As it is, bosses and university lecturers are complaining that they are getting kids with A* qualifications who are pretty much illiterate, innumerate and have no common sense, with universities spending the first year of a degree course bringing the kids up to a level that they'd have left school at 15 + years ago.
The government has one thing right though and that is that education needs reform, but the reform they are bringing in will only compound the problem as it's purpose is primarily to pass the schools system into private hands. The education I'd like to see would focus on English, Maths and practical subjects with the first two applied to th
Hmmmmmm..... Deep fried and look like Squirrel.
Teaching on the 50/60's: A farmer sold a basket of potatoes for 50$. His expenses for production were 4/5 of the selling price. What was his profit? Teaching on the 70's: A farmer sold a basket of potatoes for 50$. His expenses for production were 4/5 of the selling price wich were 40$. What was his profit? Teaching on the 80's: A farmer sold a basket of potatoes for 50$. His expenses for production were 4/5 of the selling price wich were 40$ so his profit was 10. Underline the word potatoes and chat about it with your classmates. Modern teaching: A farmin persun got a subsidy of 40 to plant any potatus then he sells fur 50. Draw 1 putato an state what u thinc about getin rish.
Don't forget we have to make all the smart kids dumb so that the dumb kids don't feel so dumb. Not to mention failing is almost impossible these days.
There is a clear dependence how valid a test is, on it's difficulty. Make it too hard and you will have bad "resolution" make it too easy and the same will happen. Ideally you PDF (probability distribution function) covers the whole scale of grades AND maps out the interesting level of skills to meaningful values.
Ahhh, but how do you explain private schools that take the *public* school rejects and somehow educate them? There are plenty examples of this. Your point is just FUD.
Perhaps the researchers are just angry they had to use sliderules and plot points on paper and now we have HP and TI calcs to do it all for us. Not to mention if they can't, there's always TI-BASIC for that.
Though at my university, they barred the use of calculators for calculus and above courses, meanwhile, at the jr college down the road, they allow them and the credits transferr one-to-one. I totally agree it keeps you from relying on it as a mathematical crutch, but graphing calculators do have their merits when you opt to build your own programs for solving things and to save on time when they only give you 45 minutes for a huge test.
When I was in... grade 9 I think, my father, who was a Math and Physics teacher, gave me an exam he had given his grade 9 students back in the seventies. I could do about half of it.
When I was in high school I tutored. One of my (junior high) math students had a problem where she was supposed to add two vectors. So I started to show her how to decompose them into orthogonal components and... she told me that's not how they learned in class. Oh? So how did they teach you how to do it?
Well, first you draw a diagram. So far so good. With a ruler. Uh, okay, seems a bit over the top, but whatever. Then you draw a line from the start of one vector to the end of the other. Mmm kay. Then you measure the distance with your ruler....
Flash forward to my one (required) undergrad business course where the recommended method for solving a system of linear equations was... drawing a graph and visually identifying where the lines cross.
I was tutoring a student in trig. They can use their full graphing calculators and the questions were multiple choice....
This was a college prep private school.
Makes it easier to do it the dumb way then to know the right answer.
83% of public school math tests are easier today than 30 years ago. That's nearly half!
Having recently graduated from the University of California, Irvine, with a degree in Mathematics I can tell you that it seems very unlikely to me that the exams are any easier at the college level. Many of the texts we used in partial differential equations, Fourier analysis, complex analysis, etc. dated back to the 1950s an onward. The exams I took were based on the material in the books, so if this is how exams were made 50 years ago, the only way they can be easier is if they are based on the "easier" concepts being covered. I find that unlikely.
Even the more modern textbooks were by no means simple to understand. The book I used for a course in cryptography and number theory was written in the 1990s, and the exams in that class were as hard as everything else.
Try using a zero-knowledge proof to show you don't know anything!
Today, a teacher is someone who lacks the knowledge and communication skills to get a real job.
Teachers were once a respectable profession. Now, their job is to rig tests to make administrators look good, while taking shit from pipsqueaks.
The politics of protecting kids and teachers unions make it impossible to punish bad students and to punish bad teaching respectively. Imagine the hell that would be raised if half of kids were told they have below average intelligence.
http://www.accountkiller.com/removal-requested
I realize that this is the last place in the world that I should say this, but it needs to be said:
There is no need for most math instruction in school!
Everybody has to take algebra in school. Everyone must pass it more or less to graduate from high school. You can't get any kind of decent job without a high school degree.
But less than one in a hundred thousand people will every use algebra. For anything. For the rest of their life!
"But learning algebra helps students to learn how to think!" So does spending four years learning 13th century Ukrainian grammar. So does learning anything stupid and useless.
So if the math tests are getting easier, fine! The vast majority of people who aren't destined to become rocket scientists don't need to learn math and don't need to put into a situation where their future career depends on learning a difficult subject that they will never use.
Math is a fetish of the educational establishment in the US and other countries. It used to be learning Latin, but that requirement was finally waived about thirty years ago. After the language had been dead for 1800 years. That goes to show what a bunch of cement-heads the teachers and the educational establishment are in the US. I understand that the situation is worse in other countries. So if the youth of America are the dead last of the civilized world in their mastery of mathematical concepts, so what!?! If you are never going to use a subject, what the fuck difference does it make if you don't learn it well?
I'm a firmware programmer and electronics technician. I've used algebra once in fifty years. I did OK in it in school, but I hated it. I wish that every hour spent learning this stupid and worthless subject could have been spent instead learning the Beatles and Rolling Stones guitar licks. Something fantastic that would be useful for my entire life!
But no, some asshole with a Master's degree insisted that we all had to learn fucking algebra.
Now I know that you like math. You're reading this on Slashdot, for Christ's sake. But seriously, guys, it's not for everyone. Don't judge people by their fucking math scores.
Before this continues, can people *please* indicate what they mean by "being paid beans" and include numbers? That would make this a bit more scientific, and if you could include that number as AFTER TAX (including after pension and average retirement savings taken out), that would also make this more scientific.
I am here in the U.S. north of Chicago, in an admittedly very well-off suburb. Our teacher clients tell us about the math they are teaching the kids around here, and yes, it is much harder than what I had at that age.
So, perhaps the higher grades are getting easier? The high school (year 9-12) and university math I've seen that isn't Honors (advanced) level is woefully simple.
However, I know that at my university (6-10 years ago) the calculus there was REALLY hard. I may just be daft, as I'm not the very best at very complex math, but after struggling 3 times with Calc II (I should have passed it the first time, but that's a different story) I took the class at a local college and got one of the highest grades in the class since I had drilled myself into the ground on much harder problems. So I think difficulty also varies by institution.
My verdict over here? It depends where you go. The teachers I know (clients, friends) who are teaching well seem to be getting about $70-90K US Dollars per year to teach. Of course, pension benefits and retirement are taken from that, so it's less, but that's still a pretty decent wage in my book.
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What I see here is a global conspiracy to get the people of the world to dumb down into a pre-industrial era average intelligence.
The people behind this once controlled the world by exploiting people who didn't know squat about how the world works. They ask for tributes to a higher being in the guise of a comfortable life after death.
These guys who are lowering the math standards are the same people behind the entire 'taking evolution out of the classroom' BS.
I was one of the second year to sit GCSE's after the switch from O-Levels. They hadn't got around to introducing course work when i took my Maths GCSE but after revising from O-Level papers it was obvious even then that they were simpler and according to the study this is before the really big decline set in. No wonder shop assistants can't cope if you give them an extra 10p plus a note to get a round number of pounds in change etc.
Blame also the politicians who want "no child left behind"
Blame also the parents who want every child to have a college education
Blame education departments for tragically underpaying educators and then responding to the diaspora by licencing anyone who couldn't make it into a medicine, law or engineering course.
And blame the political/industrial system that really, really doesn't want the serfs to be able to "call bullshit!"
... and one of my maths exams was pretty hard. I was told going in that %50 was a good mark, and that anything much higher than %75 or so was excellent. It covered the trickier sides of integrals, complex numbers, 3D trig, motion problems, and lots and lots of tricky little proofs. If you're interested, take a look. (PDF warning)
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
Here in Brazil stuff is really screwed up!
In short, students do not want to learn and teachers do not want to teach. So they make a deal -- the mediocrity deal -- in order to relieve the effort from both parties.
Teachers who would not accept it get threatened and students who demanded better classes (like me) are tagged "nerds" and submitted to physical violence.
I had to study maths mostly by myself, but I also got the help from some teachers which were friends of mine and indicated me nice books.
The results. I am a second year undergrad in CC and people in my university (even the vast majority of teachers) find calculus too overwhelming for first years, so they removed it.
Algorithms? That is reinventing the wheel! All of this crap has been solved, of course.
The good deal is use proprietary framework and code websites and apps in java. That is what a computer scientist is for.
A (good) teacher exposed the results of a test and he found out more than half the class (second years and beyond) do not know a byte has 8 bits. He also gave a 6GHz CPU for runtime analysis, and some retarded idiot wrote it would execute 10^-3 instructions per sec.
Seriously, I lost hope. What I do is gather a group of friends and study for ACM ICPC. Fuck the rest of the course.
BTW, a probability teacher once told us a certain property of a function holds. I exhibited an counter-example to him silently and he purposedly ignored me. Then I said: "You are lying, this is false, that is bullshit, this does not work, here is the proof, you can not move on on this hypothesis." I said it less rudly, of course. Still, he told the class to laugh at my ignorance (the precise argument was my function was so bizarre only "nerds" would actually come up with it) and moved on, knowing it would get nowhere.
Well, the problem is students are corrupt, teachers are corrupt, this whole shit is corrupt.
Of course, there are exceptions. But I have lost hope in this place...
I know even if I give my best, I cannot stand before guys from eastern Europe, for instance. That is very sad...
I can't believe nobody included the obligatory joke on this. Also, my first post on slashdot :)
Teaching Math in the 1950's:
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit ?
Teaching Math in the 1960's:
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?
Teaching Math in the 1970's:
A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?
Teaching Math in the 1980's:
A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Underline the number 20.
Teaching Math in the 1990's:
A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers, and if you feel like crying, it's ok. )
Teaching Math in the 2000's:
Un hachero vende una carretada de maderapara $100. El costo de la producciones es $80. Cuanto dinero ha hecho?
At the risk of sounding like some kind of language-related Nazi, "College Preparatory Mathematics" is more of a misnomer than an oxymoron. An oxymoron is just a pair of words that seemingly contradict each other (e.g. "Microsoft Works").
You know, there is a difference between trolling and pointing out the flaws in your reasoning. Just saying.
I was in the supermarket today looking at the ad board and saw an ad reading "fore sale, roaller blades" made me wonder exactly what children are being taught these days.
Blazing Spiders
Many people in the US equate the college degree with getting a job. They take the "right to work" and backtrack to "right to school after high school" because you need college training to get a good job. The New York State Teachers Union newspaper recently featured a picture of a rally with a sign reading, "Keep SUNY [the state university system] open to ALL!"
Huh? Since when did university become a right rather than a privilege one earned? Oh, that happened a few years after we decided that everyone had to finish high school and made high school a college prep program.
I'd rather have someone respond than be modded up.
Dash: "Dad says our powers make us special"
Mom: "Everyone's special, Dash"
Dash: "Which is another way of saying that nobody is"
Life is hard, and the world is cruel
Geology - it's not rocket science; it's rock science
So you're saying the NCLB act of 2001 is responsible for test difficulty dropping precipitously in the early 1990s UK?
see subject
- Paper 1
- Paper 2
I took the exam in early nineties and had a tough time preparing for it (I cleared first attempt and got admission in a good college, happily). It is heartening to see that the standard of the exam has not gone down.Private school teachers are typically paid less and have lesser benefit and retirement packages. In exchange, they deal with far fewer student disciplinary problems and less meddling from state and local bureaucracy. On the other hand, they can be fired for pissing off students with well-connected parents.
If you talk to people who used to be public school teachers and have moved on or changed to private schools, I think that very few people would tell you that the union is the problem. Private school teachers readily accept lower pay in exchange for not having to deal with 20-year old ex-cons and not being lectured every three weeks on the latest educational fads, typically, by "educational consultants" who were in the classroom as little as possible before moving on to more lucrative careers- if they were teachers at all.
Loan forgiveness programs are nice, but compared to comparably educated people teachers are treated very poorly. Compared to other professional workers, they have much less control over their schedules, fewer job perks, and significantly lower pay. If you have a science or math degree, if you go into something other than teaching you can probably afford to pay off your loans and still have more take-home pay than a new teacher who is getting subsidized loan repayment.
Teachers without unions generally have lower pay and lower job security. My guess is that this stems from the fact that large numbers of educated women traditionally had few other choices for their occupation, not from unions.
Having short tests throughout the year does not work. I work in an elementary school in the USA where this is done. What happens is that these tests are mandated by the state and half of them must be done online. The tests are given out of order from the curriculum so you are constantly just teaching the kids a snippet of information here and there so they can pass their tests. Very little quality work gets done because of this.
The worst part is that they use several different (4 iirc) testing methods to decide how well the kids are doing. All this testing is a nightmare. The only class where work could actually get done somewhat normally was in math, where they were tested every ten lessons.
Keep in mind, this was all created by experts in their areas of expertise and are supposed to know what's happening. The teachers in our school district have no say over what is and isn't taught. Most of it is direct instruction (which my 86 year old grandma could show up tomorrow and teach), which is horrible. We also use Saxon Math, which leaves the teachers with little to no input on their students' education.
Everything is all decided elsewhere and the students just take test after test from September until April, 3-4 times a month. The kids hate it. The teachers hate it. Administration loves it.
First, what is to be assessed. The states, due to a annoying thing called the constitution, are free to set what they consider to be reasonable standards. This in itself makes NCLB a joke. Combine this with no significant federal financing to encourage high standards, as it down say with the speed limit, makes any testing data unreliable.
Second, what passing standards are to be. It appears that these are often set on the same basis as the need to escape a bear. You don't need to outrun the bear, just your friends. In the same way, no state wants to look bad, so standards are set to insure a healthy number of students pass, not on any absolute level of demonstrated ability. This tradition of fungiable standards and data crunching are deeply rooting in the origin. Rod Paige, the man Bush broght with him from Houston to create NCLB, had a lot of experience laundering data.
Third is when should a topic be tested. Should topics be tested the grading period in which they are taught, at the end of the year, in the next year? Right now many topics are tested in the year after a student typically takes a class. This is benificial to advance students, as topics are often repeated every other year, but regular students are at a disavantage, as the NCLB tests not what they are currently learning, but work they did the previous year.
Fourth, when should the test be held. If the test is to be a measure of progress, ideally the test would be given as a final exam, and the grade used as such in the course. Technology and security does not allow this, so the test is given at various times during the year, over material the student may or may not have covered. One consequence of this is that for many students, learning ends when the test is over. That can mean that what is supposed to be at least 30 weeks of classes becomes as few as 20.
Fifth, how should the data be used. Even though students take some subject every year, generally only a few of these tests are used for federal compliance. Furthermore, this compliance is based on the arbitrary standard set by the state, and not based on improvement by the student. Certainly it would be more important to expect the students scores to grow year to year, instead of just passing. To make matters worse, only the aggregate score is used. No attention is paid to the broad topics. This means that a student can consistently fail a topic, and as long as that student passes the test, everything looks ok. To put this in perspecitve, a student can theoretically graduate without ever knowing how to find the area of a square.
Finally, how do we insure that students are being taught. As mentioned above, one way might be to look at individual student growth. Is every student learning something every year. While this is gaining some traction, this is not what is done at the federal level. What is done is to break the students into demographics, say white,asian, hispanic, etc, and also socio-economic status designation. A school must meet minimum passing requirements for each group. The simplest way to meet these standards is simply to make sure that you only accept kids that pass the test. if this is not possible, then the second best thing is not to have too many of these groups, i.e. make the school as homogeneous as possible. In any case, the whole thing is a farce as it does not guarantee that no child is left behind. Many, many children are left behind, and students that traditionally have not been taught still are not.
That said, the general idea is good. It is generally accepted that fewer teachers are jus
"She's a scientist and a lesbian. She's not going to let it slide." Orphan Black
I'm almost 4 years into an engineering program and I still have peers who just fail to grasp basic math concepts. Part of the problem is in how engineering is taught, at least in my schools. There are so many old exams floating around and so many teachers teaching straight from the formula that I'm pretty sure half these guys just memorize the method/paper/exam and spit it right back out for the exam (plenty of stories of kids not even using the proper #'s 'cause that's the one thing the professor changed on his new exam.) That's not even counting the ones who cheat their way through the exam.
open source modern art: laser taggi
This has been around the net a few times... And it may have been posted *cough, cough*, in my faculty lounge once or twice.
Teaching Math in 1950:
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?
Teaching Math in 1960:
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price, or $80. What is his profit?
Teaching Math in 1970:
A logger exchanges a set "L" of lumber for a set "M" of money. The cardinality of set "M" is 100. Each element is worth one dollar. Make 100 dots representing the elements of the set "M." The set "C", the cost of production contains 20 fewer points than set "M." Represent the set "C" as a subset of set "M" and answer the following question: What is the cardinality of the set "P" of profits?
Teaching Math in 1980:
A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.
Teaching Math in 1990:
By cutting down beautiful forest trees, the logger makes $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the forest birds and squirrels "feel" as the logger cut down the trees? There are no wrong answers.
Teaching Math in 2002:
A logger sells a truckload of lumber for $100. His cost of production is $120. How does Arthur Andersen determine that his profit margin is $60?
Teaching Math in 2010:
El hachero vende un camion carga por $100. La cuesta de production es . . .
Yeah, OK, teachers are being paid less, standards are dropping. I would have thought that the point to education wasn't just teaching algebra, or English, or Esperanto, or how to climb a rope or dodge a wrench. I thought the point to education was to teach you how to teach yourself. Teach you how to use a library, teach you how to do research, so that when (if you are lucky enough to get to go) to college, you can get by. I'd be interested to see a study of the ability of 18-year olds to navigate through an old-fashioned library, or write a short essay on a topic they originally know nothing about, but have 1 week to research. I for one saulte the diaper-wearing genius babies who are still a twinkle in the milkman's eye.
Have you tried teaching better?
OK, so I went to relatively good (public) schools in the US, but I think some of the most important things I learned from my teachers of Math and Chemistry was to read and learn directly from the textbook. I never really learned much from the teachers, and many of them were considered at the top of their field. To me, the only function of the teacher was to assign a subset of problems from the book for homework, grade papers, and go through some examples in class (which I usually wouldn't be able to follow unless I already read that chapter/section in advance and attempted at least some of the homework).
:P )
So I might be biased in saying that the teachers have a huge impact on the content learned, since I guess I've never had particularly bad ones. I still support raising teacher pay and quality for them to take care of all the administrative, motivational, and social classroom tasks. But I think students can learn the content fine from the math textbook if they go through it at the correct pace.
I acted as a teaching assistant for a summer school for bright children, and their math program was basically a bunch of kids working independently through advanced math textbooks. A small team of us assistants would just roam around and administer chapter tests occasionally and give help and motivation when necessary (I wasn't very good at the motivational parts
As far as exams and assessments go, I'd think they're most useful as a measuring tool when a histogram of the results from all students form a nice bell curve distribution. If it's skewed or clipped by a bunch of scores at the extreme low or high end, then you're essentially throwing away data. On the other hand, you're also losing fidelity if you have a wide range of scores, but all the "normal" people score within a narrow band... say 80% +/- 5%. There's not much point in having strong differentiation between a few people in the tail so that a handful of students who scored 95% could say they're better than the handful who scored 90%, and yet there's no way to distinguish the performance of the thousands who scored 81%. So in this case it makes sense to adjust the test to give the bulk of the bell curve some more "spread".
The SATs went through such a "recentering" in the late 90s. But I think that was mainly driven by their desire to have 1200 / 1600 be the "average score". The recentering gave slightly boosted everyone's Math SAT score. Which in essence was truly lowering the expectations of the test.
I'm in the interesting position of being partway through training to become a High School maths teacher. I finished high school in 1979, where I came 23rd in the state. I did 4Unit NSW HSC maths, which had 8 or 9 hours of teacher contact in maths alone each week.
In the early 90s I ended up back at uni, where I did a maths degree with a minor in computing. I ended up with a 1st class honours, and was part of the teaching team in maths for 1st and 2nd year science and engineering students. We found that close to a third of 1st yr students, in week 1 of semester 1, could not calculate the volume of a rectangular prism!!!
Now that I have kids at high school, I've decided to become a high school maths teacher. My 15 yr old (year 10) has yet to see a quadratic equation (yr 8 when I was at school). My 12 year old (yr 7) does not understand that -5 -2 = -7, though he does know that negative integers exist.
In my course last semester, on middle years maths education, I was the only one out of the group of 24 who could express the relationship between yards and feet correctly. The rest of the class said 3F=Y was right when F is number of feet and Y is number of yards.
I expect to get about $45k-$50k as a maths teacher when I finish. With my quals and experience I can get $100k+ in industry, or $500+/hour as an actuary. Where is the incentive for people like myself who are good at maths, can teach it and enjoy it to teach in schools knowing that the vast majority of the kids hate maths and will hate me for teaching it, unless I can show them how to discover their inner maths nerd?
I was at a school for gifted kids the other week, a school that uses the IBL instead of the std Queensland senior syllabus. Kids doing IBL SL get 3 hours of teaching per week. Those in HL get 1 additional hour. I don't think the problem is restricted to only one school system, state, country or syllabus. There are some serious resource shortfalls in maths and science education worldwide, which are being masked by lowering the standards, so showing the same proportion passing. This will bite us on the arse in a few years when there is massive shortage of physicists, engineers and statisticians.
Expenditure in education is investment in the future.
This is probably an appropriate place to put this anecdote.
GCSE-level equivalent physics exam, 1997: Bicycle weighs 20kg, you carry bike from point A to point B. Distance from A to B is 5 metres. How much work does Bob do moving the bike? g=9.2ms-2
If you wrote down g x d x m = 1000, you got the right answer. If you wrote, 'you guys are idiots' you got it wrong. Personal experience.
Note, I've probably made some basic mistake in the retelling, but hopefully the point is clear enough
Insanity: voting in the same two parties over and over again and expecting different results
Pick up a book meant for grade school math from the 1800s, then pick up ones for each decade till the present.
Grab copies of history text books for a certain grade for each decade from as far back as you can go and compare how they treat the subject of the bill of rights, how government works and what government is intended to do.
Home school your children when little. You will get to teach them what you believe which important in a near theocracy. You can teach them enough critical thinking, math, english and other skills to survive the propaganda, indoctrination and idiocracy of later schooling.
Even keeping them out of the public system for a few years is of benefit.
I'd go on a Vegan diet but the delivery time from Vega is too long. --brownkitty
There, fixed that a bit for you, and added some emphasis. :)
But seriously, it's not just the schools, it's the whole blooming economic system. We're going though a period of extreme flux right now. The economy is a vast and chaotic system, and anytime you have a big, chaotic system and you put a lot of stress on it in a short period of time, things get fugly before the various patterns sort themselves out. The next decade or two (or three or four?) are going to be very interesting times, and not necessarily in any good sense. I'm reminded of the old Spanish proverb here:
May nothing new happen.
Cheers,
"What in the name of Fats Waller is that?"
"A four-foot prune."
I just graduated high school in the US. I don't know about the national trend, but I do know that the difficulty of math exams varied wildly even within my (public) school, which Newsweek tells me is one of the top 900 in the country, for whatever that's worth..
My teacher for AP Calculus BC gave extremely difficult exams. We were almost never allowed to use calculators. The smartest kids in the school (not bragging, just saying) were almost never able to finish his tests in the time allotted. When I took the actual AP exam, I found it relatively easy, as did my classmates. Mostly this is from the tests in class being difficult. I couldn't say whether the AP exam was too easy. Of course, I haven't gotten my score back yet, so take my impression of the exam with a grain of salt.
Another math teacher in my school is famous for the easiness of his classes. I have never taken one, but some of my friends have. One of the courses he teaches is Functions, Statistics, and Trigonometry. (The sequence at my school is weird. This course is like the end of Algebra II and the beginning of precalculus with some stats thrown in.) He lets you use the calculator for absolutely everything. I know a kid who aced a trig exam without knowing what sine actually meant. This teacher also gave a kid points back on a test because he messed up the same concept on two different questions. He guarantees everyone in his classes at least a C+ on the final exam. It is routine to get an A in his class by playing AoE while he lectures (we have laptops), telling him you're getting there when he checks to see if you did your homework, and not finishing tests just because you don't feel like it.
The other math teachers that I had in high school (at the regular and honors levels) were somewhere between these two extremes. The calculus teacher gave the same difficulty of tests in Honors Precalculus as he did in AP Calculus BC.
This space reserved for administrative use.
State run education boards (as opposed to country wide 'central syllabus') introduced a system a couple of yrs ago where kids can pass till 10th grade without writing a single word. The question papers have multiple choice questions making up for 60% of the total marks.
I can't speak for maths, but I'm a physics teacher in a London school and am disgusted with what the exams have become. The government introduced some changes last year that have made the subject into a touchy-feely environmental subject. There's also almost no math. No math! Who heard of a physics class without calculations? If you're interested, I wrote an article about the downfall last year.
-Grey
Silver Clipboard: Time Management Tips
Here in Belgium they train the kids to become dumb calculator slaves. About 10 years ago we had to be able to do trigonometry by hand. Now the only skill they need is being able to read the graphic calculator's manual and operate it. *sigh*
I'm not speaking for all school boards in Canada, but two school boards I've noticed in Toronto (York Catholic District School Board, and Toronto District School Board) had very qualified teachers. From my experience going to the YCDSB, my Grade 12 physics teacher was an ex-geo-physicist with post university education. Every other teacher I had during my time in highschool also had at least a Masters degree in their respective field. Also, for the TDSB, I specifically remember my ex-girlfriend's Calculus and Algeo teacher having four different degrees in Mathematics from university. (They complained he was a bit obsessed with math, but such credentials should surely be a good thing). Maybe a little off topic from math, but my English Literature teacher was a straight A arts student from Queens University (A very reputable Canadian university). And had just finished her masters when I was studying under her. (I believe I heard that a masters increases your pay... Maybe that's just specific to the school board.) Anyway, hope this offers some insight. I was actually very happy with my highschool education. I entered post-secondary education with existing knowledge of almost all the first-year courses I took, and have received similar regards from other peers I've known.
Let me start off by owning up to my bias -- actually, twofold. First, my wife is a middle school teacher, and I have volunteered in many different ways at her school as both elective teacher and simple extra pair of hands. Second, I have found very little in Milton Friedman's writings that I can wholeheartedly agree with. The man seemed to think that private enterprise was a panacea for all of mankind's various ills. He somehow seemed to miss the problem that the underlying profit motive is often at cross-purposes with many of the not-really-business areas he advocated for privatization.
To extend this and dig into the meat of your post, let's look at your postulation. Schools are, ostensibly, there to provide a public service. There is some real debate at certain levels in education circles about how much that public service really has to do with teaching, and how much has to do with daycare. No, I'm not just being cynical -- a large part of why schooling in the US plays out the way it does is because, historically, mandatory schooling for certain age groups was instrumental in allowing for the 9-5 working day for both men and women, which became very important during WWII.
So let's say we assume that schools are there to provide the public service of actually teaching kids, with daycare as a nice side-effect. Fine.
Now let's look at the theoretical private company under Friedman's model that would step in to fill this sudden demand for private education. It would ostensibly be a for-profit corporation, given Friedman's leanings, which means a number of things. For starters, the corporation's management is under a legal obligation to ensure that the company makes as much profit as possible -- by deliberately taking in more money than it costs to do business. This is diametrically opposed to how not-for-profit corporations (i.e. most private schools that I'm aware of) operate -- by deliberately spending all funds alloted in the budget for that year in order to ensure that the services provided are the best possible.
With those *very* different directives, a few moments' thought should be enough to show that any for-profit entity operating in the field of public services is going to provide the least possible service at the highest possible rates. We've seen that time and again, in country after country, in sector after sector. Medical services in the US? Check. Water utilities in the UK? Check. Power companies in the US? Check. Major ISPs in Australia, Canada, the US? Mobile communications services just about anywhere? Check.
Fobbing such services off onto the private sector produces other problems as well, as corporations are by their very definition protected by legal limits on their liability. Given the intimate roles that teachers play as in loco parentis, it is important on many different levels that parents have a serious say in what happens at schools -- which is where PTAs come in. I could well be wrong, but I strongly suspect that no for-profit company would really allow a PTA to have much authority over what goes on.
Part of the problem in the Friedman model is the simple issue of motivation. Why would companies suddenly spring up to take over the role of schools? Private schools that exist at present are there in large part because of an organic need in the community, combined with the presence of people with the motivation to be teachers. The Friedman pipe dream instead seems to be based on the profit motive, which is, as noted above, largely incompatible with public services. His model is also flawed in ignoring the very real geographical constraints of schools -- even assuming real market-style competition
"What in the name of Fats Waller is that?"
"A four-foot prune."
It's pretty bad being a teacher. Had a partner teaching first then second grade -- not all of the kids, but enough to create a problem had the rebellious chip-on-the-shoulder attitude that came around 7-8th grade when I grew up. One issue is there is no way to discipline the children that they care about. Since corporal punishment was stricken, I don't think teachers have found an effective replacement. But "time-outs"...they don't care, their minds are off most the time anyway -- and sending them out of class, or suspension/expulsion -- many of them don't care -- they don't want to be in school anyway. Many of the kids had behavior issues that might have put them in a remedial class (apparently, like Bush was). That's a major problem that's come up in the past several years since Bush's "No Child Left Behind" act. Instead of holding kids back or allowing kids to progress at different rates, all must wait for the slowest child (little Georgie). The regular testing of the kids is more or seems more to evaluate the teachers than the children. Now, it's no longer a child's responsibility to behave or learn -- it's the teachers responsibility to "emote" knowledge into them...kids are simply being trained to be passive receivers and the learning is predictably suffering.
...several or dozen or more years -- too much focus on remedying the lowest rung at the expense of dragging down the whole -- but that's part of the "false dichotomy" -- that there has to be a trade off.
That's been a bad trend over the past
It's the same "root cause" as teacher's not being able to afford to live in the communities they teach in. Not enough resources into education -- too many resources invested in high-end of life and the adult stages (including, recently, this war that is causing oil prices to go up (war->deficit spending->'printing' money (how close is US debt to 3 T$ (Tera-$)?)->dollar deflates in value as massive 'unbacked-money' is created, commodities (incl oil) go up) -> US goes bankrupt)). But look at how much the rich spend on luxury goods --- increase in cruise ships, vacation spots -- extremely expensive hobbies/sports...so much wealth concentrated in top 1% people -- but it's the 'masses' that are taught in schools -- and that's where the dollar share has been shrinking the most.
There was an opinion piece in the WSJ that tried to show how increasing the top tax rate didn't increase the government's tax-income as a percentage of GDP -- what it unintentionally showed, actually was GDP going up as
the top tax rate rose, and GDP going down as it fell -- so the % going to government appeared level. GDP going
up or down reflects almost directly goes into a rise or fall of the "standard-of-living" of the nation. That meant that as the top tax rate fell, the average standard of living for the nation as a whole fell -- and vice versa.
GDP has fallen to lowest levels in my lifetime under the top tax rate falling from over 70% to the 20-25% it is now. All that was Reagan-& the Bushes rolling back taxes on the rich while using government deficit to inflate the economy. While Clinton didn't raise taxes -- he did manage to get the deficit from around 2-billion to almost breaking even by the time he left office -- now it's up higher than ever.
Bush needs to be out of office so yesterday. I think my postings are too long and people don't get this far...
*sigh*...just supposed to shut-up while the nation is tanking to hell...
Anybody who wants to check the watering down process in education, check out the old New York state regents math exams dating back in the 1950's. http://www.nysl.nysed.gov/regentsexams.htm
The upper age limit of compulsory education differs by state in the US. Some places, it's 18; in others (California included, IIRC), it's only 16 -- meaning most folks can legally walk after grade 10.
Also note that, historically, compulsory education in the US only really came about with industrialization and the rise of the more modern labor economy -- at which point, schools provide a very important social service in terms of daycare while parents at at work.
Cheers,
"What in the name of Fats Waller is that?"
"A four-foot prune."
While I do not think people will disagree with the dumbing down of math, the interesting part is what else does math teach us? Unlike English, math has set rules that need to be followed and not broken or you reach incorrect results. Does this mean people now days are less likely to follow the rules too? As for the English Language, I see people proudly messing up words; aka slang. What about the value of logical thinking/problem solving; this too is a useful talent. Are we less likely to think through ideas and use logical reasoning? I can reason out the answer or feel the answer; which one is correct and which on is done. Example: the President of the US is not the most important person do to the balancing of power related to the way the government is setup but go out and ask people and they will happily tell you that He/She runs the country. So is there a relation between a nation falling apart, like Rome, related to the devalue of math? Mostly likely not, but it bringing up the point if you are unable to reason out the answer and only are feeling the answer can you really make good decisions? Or do we avoid the harder problems because we are unable to reason it out due to a lack of training?
(US) The GRE is not supposed to be equivalent to the SAT, much less IQ tests. Since learning how to read and write well is central to every career path out there, it is unsurprising that the literature sections are more competitive than the math.
But this has nothing to do with the original point, which is that basic (In a US curriculum I'd call through trig/algebra 3 basic) math is not what is used to be. Calc is easier to learn that a lot of the finer points of algebra, so why are we forcing people into doing 'pre-calc' when actually they'd be better off learning Calc after a year of basic algebra and geometry (so they don't have the false idea that it's difficult), and then work into linear algebra, more advanced techniques in algebra, etc..
Teaching Math In 1950s
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit?
Teaching Math In 1960s
A logger sells a truckload of lumber for $100 His cost of production is 4/5 of the price, or $80. What is his profit?
Teaching Math In 1970s
A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?
Teaching Math In 1980s
A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.
Teaching Math In 1990s
A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers, and if you feel like crying, it's ok. )
Quidquid latine dictum sit, altum viditur.
You must be kidding. It's not just math, it's a general trend.
School has found itself in a bind. In addition to teaching knowledge, lots of parents have started to expect that their kids will receive education in school, instead of at home. So school has to do more in the same amount of time, with less pre-educated children.
In addition to that, the cultural climate has changed. For you, "no child left behind" might be a slogan, but for many schools it has turned into an order: Leave no child behind, no matter how dumb it is.
The solution for many elements in school was to make things easier, so the time available is enough and even the dumb kids can pass.
Assorted stuff I do sometimes: Lemuria.org
Rodney then beats the crud out of Johnny and takes his fruit trees.
Because Johnny didn't pay taxes, there aren't any police to get Rodney to give Johnny his trees back and Rodney is bigger than Johnny.
How much does Johnny get from his taxes?
How much does Rodney get from Johnny's taxes?
Answers: Johnny gets 2 bushels
Rodney gets 3 bushels
We live in the UK and we have a nine year old son at a pretty good state primary.
First off. I don't think that it is fair to blame the teachers for any 'decline' in standards. From what I can see, the teachers are about the same as they always were; there are some good ones and some bad ones. However, the teachers are now under tremendous pressure to teach to the exam and parents will increasingly blame the teacher when their child's results do not match their expectations.
As it happens teachers in the UK are now pretty well paid compared to other professions and, again, compared to other professions they have a pretty high degree of respect in the local community. The head teacher of a local school is still a person of standing in the community, well in this part of the UK anyway.
I do think that a couple of things have changed over the years.
First, there is now a tremendous emphasis on 'practical' maths: so our son is never asked 'What is 9 x 5?' No, it has to be 'John has five bags each with nine apples, how many apples does John have in total?' It gets very tiresome for the child.
Second, I do think that the proportion of disruptive children has risen and that makes teaching the class a whole far more difficult.
Our son's school is a 'good' school with a significant cohort of very bright motivated children going to selective grammar and private schools but there is a rump of children, often from affluent middle class families, who are off the rails and simply have no understanding of appropriate behaviour in the classroom.
Last point, it depends very much what exam you use for comparison. Over the next two years our son will take three maths exams: the Key Stage 2 exam, the 11 Plus and the junior entrance exam for a good private school.
The level of mathematical knowledge required and in particular the different grasp of mathematical principles expected by the three sets of exams is hugely different.
The level has dropped. In High School and at University. And now the latter is gaining even more speed downwards with the Bologna Process.
Those who can make you believe absurdities can make you commit atrocities. - Voltaire
Twenty five years ago, here in NZ, about 30 students from a school of 1000 would take a calculus and/or statistics-based math course in the final year. Most would "pass" ie about 3% of the school population.
Fast forward to NZ 2008. Now a school of 1000 would likely have 120+ students taking similar courses. (Why? Because *everybody* wants to go on to university, and first year uni maths is a *requirement* for many many courses of study.) As things stand today, maybe 100 would likely "pass". 10% of the school population...
So either today's students are on average smarter, more talented, more diligent, and better taught, OR teachers and students are pretty much at the same level as they were 25 years ago but today's maths content and assessment is watered down. Yes, of course it's easier!
Here in NZ we have a high school qualification called NCEA - designed around "standards based assessment." A qualification that is intellectually bankrupt and morally indefensible. But that's a whole different story again.
(I have a BSc with a "major" in pure maths, and taught maths for 10 years in NZ high schools.)
I find it interesting that your complaint is that the teacher couldn't keep control of the class and not that he couldn't teach them Math (sic) at the appropriate level.
A maths teacher shouldn't be there to teach your child self-discipline. They are there to provide education, yes, but there is a responsibility for the student and their parents as well as the teacher. You cannot teach someone who doesn't want to learn (without resorting to corporal/fiduciary incentives at least).
When I'm president of the world we'll bring back the cane for the most disruptive children (to be administered by an official of a high-school court, not the teacher). However you'll be able to leave school early (about 12 years), provided you have basic maths and English language ability, and enter a vocational college.
First year university physics student in Norway:
I agree. Looking at the exams 5-10 years back, in almost every case it gets harder the longer I go back. Just last year to this year, two large chunks in two of my math subjects are gone (laplace-transform and multiple integrals), and I see that happening again and again as I'm going back in the exams.
Its only after he is tenured (depends on the school system, could take a year or three) that he is unfireable deadweight for life (or until he gets a student pregnant... and even then I'd give him better than even odds in NYC). Until he gets tenured, he "merely" gets a union and an absolutely byzantine system of grievance protections to keep his lousy carcass in the job.
New York City decides to fire a 5 year veteran (tenured after 3) for gross incompetence. Costs $250k, 2 years.
http://www.nypost.com/seven/05272008/news/regionalnews/253g_to_fire_one_teacher_112703.htm
A flow chart of what you need to do to fire a NYC teacher. Warning: PDF. And its big, and I'm not talking file size.
http://oldsite.reason.com/0610/howtofireanincompetentteacher.pdf
Help poke pirates in the eyepatch, arr.
I'm not a teacher, so my experience comes from being a math student at university. It was a long time since I started, then I went to work and now I'm back to finish my degree. So I have noticed a difference, from personal experience and talking to my fellow students and just observing them and how they go about solving and talking about problems.
I can see there is a slight change in focus in how the courses are taught. What was concidered important previously is not as important anymore. I don't think they have removed all the hard parts, but they removed some unnecessary once. The focus of what is important has shifted.
It used to be a lot about memorizing information such as formulas and applying that to fairly straight forward problems.
These days there seems to be more of identify the problem, remove the fluff information and look up the formula in a book. Which can naturally have a big drawback cause now some people don't bother learning anything but instead just troll thru the formula compendium trying to find something to apply on their problem. The upside being that some of the things you had to memorize previously where perhaps not that useful except for finishing your math courses.
The teachers I have spoken to have mentioned that new students tend to have a lower level of understanding these days compared to previous generations. So they have to spend more time explaining things that they should already know instead of progressing ahead and explaining new things.
On that note I spoke to a guest teacher that was from southern Europe and apparently there is quite a difference in what is concidered important there compared to here (northern Europe). They apparently have a more proof based teaching method, (dis)prove this or that statement, while we in the north are more into solving problems; Identify it, prepare it and then "crunch the numbers". Clearly there might also then be a cultural difference on what is concidered to be important.
So I'm not certain it has actually become so much easier, I might have just become better. But I'm certain that the focus on what is important has changed.
I took my exams at the beginning of the current "downward spiral", I've heard past teacher's opinions on the situation and recently trained to be one myself.
Back in the mid nineties the government decided it needed schools to be more accountable and so began publishing league tables of exam results and judging schools by these. THe gamesmanship rapidly began and many schools began teaching to pass exams rather than to learn - I did not go to one of these schools, when we all reached the town's joint sixth form to take A-levels the pupils from my school with C grades in maths outperformed most of those with A grades from the schools known to be playing the game.
At the same time the government in andother inspired spark of Thatcherism had the wonderful idea of commercialising the examiners boards setting exams. That's right - exam boards made profit based on how many schools took their exams.
The rest is history, we have schools who are judged by how good the grades they produce are and exam boards who profit by being the ones whose exam is most likely to give the highest grade.
I was the part of last year whose maths A-level was judged on two final exams (one pure, one applied) in which you had to know the entire course to pass. Our teacher admitted to us that the school was changing exam boards to keep its results up. It now uses a modular course, there is an exam on each module straight after it (no need to remember the teaching after that) and if you fail you are free to retake that module as many times as you like until you do.
Here in Belgium, we spend more than 1/3 of our GNP on education, as opposed to 3.7% in US. Result: we rank in the top 5 for Maths and Science, right along countries like Japan where students work 52-hours/week.
:-)
Maybe the US could spend a little less on defense, and a little more on education?
Belgium, it's a good country to live in
Humor-impaired people, please don't read.
Last week I purchased a burger at Burger King for $1.58. The counter girl took my $2 and I was digging for my change when I pulled 8 cents from my pocket and gave it to her. She stood there, holding the nickel and 3 pennies, while looking at the screen on her register.
I sensed her discomfort and tried to tell her to just give me two quarters, but she hailed the manager for help. While he tried to explain the transaction to her, she stood there and cried.
Why do I tell you this?
Because of the evolution in teaching math since the 1950's:
1. Teaching Math In 1950's
A logger sells a truckload of lumber for $100. His cost of production is 4/5 of the price. What is his profit ?
2. Teaching Math In 1960's
A logger sells a truckload of lumber for $100 His cost of production is 4/5 of the price, or $80. What is his profit?
3. Teaching Math In 1970's
A logger sells a truckload of lumber for $100. His cost of production is $80. Did he make a profit?
4. Teaching Math In 1980's
A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Your assignment: Underline the number 20.
5. Teaching Math In 1990's
A logger cuts down a beautiful forest because he is selfish and inconsiderate and cares nothing for the habitat of animals or the preservation of our woodlands. He does this so he can make a profit of $20. What do you think of this way of making a living? Topic for class participation after answering the question: How did the birds and squirrels feel as the logger cut down their homes? (There are no wrong answers, and if you feel like crying, it's ok. )
6. Teaching Math In 2008
Un hachero vende una carretada de maderapara $100. El costo de la producciones es $80. Cuanto dinero ha hecho?
I live in Calcutta, India. Over the past couple of decades, we have seen a steady decline in the quality of the base-line students who qualify at the secondary and 10+2 levels. I teach English to undergraduates. The kind of student I find in my classes now is definitely poorer in intelligence and ability than I used to when I started nearly a decade ago.
I place the responsibility for this directly on the state government's policy to gradually simplify syllabi and relax qualification criteria at those levels, so that the false rise in pass percentages casts their education policy in a favourable light. Of course this fucks up the state's talent pool, but who cares. They're only interested in retaining political power at any cost. And they've been doing that here in the state of West Bengal remarkably efficiently for an astounding three decades and more.
First they ignore you. Then they laugh at you. Then they fight you. Then you win. -Gandhi
Sure, they're getting easier. Tell that to my Differential Equations teacher (yes, I am still in high school): the latest test was a pain where the average grade was in the low 80's out of 100. /me runs off to study for the final in 7 days.
A more objective measure, as opposed to observations made by parents with children,
is to examine the textbooks published during the 1960's with those published today.
The physics texts -- and physics is highly infused with mathematics -- from
forty years ago, many of which can be found at used book stores or even libraries,
are noticeably more comprehensive, mature, and sophisticated than their current
counterparts. Textbooks on physics from today seem almost childlike by comparison.
In fact, for reference purposes, I keep a copy of a basic college physics text
that is copyright 1965. Although it lacks the coverage of some more modern technical
development, its treatment of the fundamental concepts is far more rigorous.
There should be little doubt that times have changed for the worse.
Super. A licensed Social Studies teacher who appeals to 2001 US legislation to explain results in 1990s UK.
Remind me why I send my kids to private school, again?
w00t
Somehow the UK is supposed to better at math than the USA?
My math classes were far more rigorous than this. I had calculus I and II in 10th grade.
I am a licensed High School Math teacher in MA (so my experience is limited to the US, but it probably parallels what the UK is seeing). Here, students take the MCAS exam in the 10th grade. The adjusted scores are reported in the 200-280 range; up until this year, "passing" was a score of 220. For this year's test, they've effectively doubled the passing score, to a 240.
NCLB mandates that we get everyone to certain standards, notably graduation. This forces teachers to focus on the bottom 10-25% of students: those students who wouldn't be able to navigate high school curriculum without significant help. "Letting" them fail is not an option. If a student fails a class, current thinking is that it's because the teacher did not teach effectively, and if this becomes a pattern, licenses and federal school funding are on the line.
While I certainly am in favor of accountability (I work for a private school without a union, and am thankful for it!) somehow it's become dishonorable for a student to graduate without intentions to head to college. But the effect of trying to raise the bottom up is that there's less time to focus on the top students. Many of them can succeed without help, but they certainly aren't reaching their true potential.
How is it obvious that the 1950's question was harder than the 2006 one? They were both easy. There wasn't a question on there that I couldn't solve in my head.
Granted, I'm a University Math and Engineering student...Maybe I should go back to high school.
i agree that math exams have been sweetened for the general population but on the other hand the fast-track students, you know the ones that show up, care, and make large efforts, on a daily basis have access to more now than ever. i have two in a inner-city public school that is notorious for under-achieving, although this is changing, but has phenomenal tech roots believe it or not but is masked by the under-achievers, and this is what I see.
A hand up and a foot on every chest...
The problem may be that we are requiring students to use the WRONG type of calculator.
When I attended high-school, students were encouraged to purchase and use graphing calculators. The expectation was that a quick graphical representation of a function would increase the understanding of the function.
Almost everyone bought those silly TI calculators - math teachers expected to see them, and assisted the students in using them.
My math teacher almost shit a brick when I showed her my HP 48G. She asked why I bought it and I told her that I liked the way a fully programmable RPN calculator worked. Sadly, she had no idea how to use it.
That calculator (and my Radio Shack COCO2 with embedded basic) started me off into the Engineering and CS course of study.
Calculators aren't the enemy of math education any more than power tools are the enemy of the trades.
-ted
One thing I didn't understand in my school (NY, USA) was that they had changed th requirements to graduate. We had to take four years of Social Studies and English and two years of Math and Science in High School.
So, English for four years; wtf do you learn in an extra year or two that you shouldn't already know by now? I know, most people lern 2 type leik this LOL!@!@112 But seriously, this is a noun, this is 1984, we own your soul.
Now Social Studies. I love history. Never had a problem with it aside from remembering specific dates and people. I always felt that taking a message away from past events was the whole reason for studying them. Even so, it was useful and very thought provoking at times.
On to the sciences. In my school, 9th grade was Earth Science. (HS in NY is 9-12 for those in other locales) 10th grade was Biology. Both great classes, very interesting, great teachers. 11th grade was Chemistry and 12th grade was Physics. Now, 11th and 12th were not mandatory. However, to me, they were the most interesting. If they are going to mandate four years of English reading books I have no intention of actually reading, why not mandate four years of science?
Lastly, the maths. 9th was algebra. 10th was geometry, 11th was trig and 12th was pre-calc. (I ended up skipping 9th and moving ahead a year rounding HS out with calc in 12th) Now, I understand not requiring pre-calc and calc. Most people who don't go into technical fields will never use it. However, no trig? Trig isn't even that hard. And it has uses galore in real life. I'm sorry, but requiring me to read catcher in the rye, Of Mice and Men, and Lord of the Flies (please god, no more Jesus references) and not requiring me to take basic maths and sciences is just wrong.
Oh, one last note. We weren't allowed to take a light load our senior year and have half days. If we were done with our core classes, we had to fill up with electives. However, this got me into Computer Science and AutoCAD so I wasn't complaining. Even so, if they won't let you not take an elective you might not like anyway, why not require something that might actually be interesting and/or useful?
The whole part about requiring four years of english and history and then only two of maths and science is absurd. If you are going to skew it, let the kids decide which way they'd like it skewed. Tell them 12 courses between the four subjects. Be it 4,4,4,0 or 3,3,3,3 or 4,4,2,2 or 2,2,4,4 etc. At least then, if they expect to be a lib. arts major candidate, they can get their englishes out of the way. If technophile-land awaits, maths and sciences. And ffs, teach these kids how to use full and gramatically correct sentences. lolfu2
-SaNo
I have been tutoring high school math for 15 years. I can assure you that the demands of high school math have dropped dramatically. 15 years ago students did 20 or 30 proofs a week in geometry for weeks at a time. Now, it's a miracle if they do 20 the entire year.
It's that in the future all kids will be required to know advanced particle physics and warp field design by the time they graduate from high school. We shouldn't tolerate any sort of decline in classroom rigor. Quite the contrary. We should have legislation that requires that by the 9th grade any student can build a flying car capable of Warp 1 using only parts available from Radio Shack.
All the Math I need to know I learned from Slashdot: 2 + 2 = 5
I too have a Masters Degree, albeit in Taxation. I say that not to impress but to let you know that you are not the only educated person that reads this blog. A couple of points. I'm not sure that our kids are more intelligent that ever. More educated maybe, but I'm not so sure about intelligence. Another point. I have run across many, many people that are incapable of doing math in their heads or on paper. This is a real cause for concern. I have blown many an argument out of the water because if you apply math to the argument the argument produced ridiculous results. For instance, if someone argues that there are 10,000,000,00 tires put is the waste stream every year in this country I would apply the following math. 10,000,000,000/300,000,000=33.33. On it's face this beccomes a ridiculous arguement because we all know that we don't replace 33 tires every year for every person in the country. This is why it is important to learn some math by rote. It comes in handy.
# Congresscritter 1: We should improve education.
# Congresscritter 2: How about we tie test scores to school funding?]
# Rational Person 2: If the tests are constant, wouldn't that just lead to worse schools getting worse and better schools getting better? There's a reason the worst team in any professional sport gets first pick in the draft....
-- Political fascism requires a Fuhrer.
"Under this plan there would always be the option of sending the kids to a better school across town if the nearby school got too bad."
1. If they can afford the transport costs
2. If they live in a town or another location where there's more than one school: are you writing off the rural population of your country?
Being a parent and having been through the US school system myself, I still can't see the need for Algebra, Trigonometry, and Calculus in the day-to-day lives of at least 65 - 75% of the population. I liked Algebra for its logic training but due to the lack of real-life applications, have never used Algebra to solve real-life problems. After high school I took classes in Geometry, Trigonometry, and Calculus in college -- a useless set of knowledge and money maker for the book manufacturers. Obviously there is a place for these high-level mathematical courses but the average American would do better getting training about balancing their budget, evaluating interest rates, and solving real-life math problems. High schools need to focus on the basics. Without a solid knowledge of the "times table" and how to calculate the amount of change one gets from buying an item, the student will not be comfortable with their math skills in real-life situations. To help drive home the value of math training, centralize it around money. When the student learns how to save money and not be ripped off when purchasing a car or home, they will learn the value of math. The training has to be built around real-life situations and not lofty formulas that the typical student will never come across.
Help, I'm trapped in a carbon-based life form.
I don't think teachers are being paid enough... I honestly think it has nothing to do with pay, and everything to do with the lack of insulation from the whims of public opinion, which is much more powerful on local levels than national or even state. This means school officials can be voted out if they do not bow to parental pressure.
One good solution to this would be to have the public school system directly subordinate to a council of department heads chosen at random from the given states' accredited universities (both public and private).
Mind you i'm not blaming most parents, because I honestly think such pressure is coming from a vocal minority of individuals who feel their children are "entitled". Now i'm about as liberal as you can get for an american, but I believe our welfare systems should be limited to monetary assistance and post-secondary retraining programs, not grades.
Otherwise, I have to agree with the lack of basic math skills. I graduated high school in 2k1, and while my curriculum included thorough trig, certain pre-calc concepts were not properly covered. This particular shortcoming was pervasive enough for my school (which was top 20 mind you) to offer an "augmented" version which included that remedial material.
In other words, when I graduated high school college curricula were already being stressed by this trend, which is forcing them to shoulder more of the load.
Sooner or later American colleges will either require another semester to make room for the necessary extra math courses, or they will lose their competitive luster by sacrificing some mathematical depth to maintain the traditional four years. Either of these alternatives will mean US colleges become more expensive, either by reduced value of the diploma or the extra semester's fees.
I'm sorry to hear the bar dropping even further. It is yet another reason
The problem
VLC FOR MAC IS DYING! IF YOU DEVELOP, PLEASE SAVE IT!!
im just testing...
Help test the
"This has led to mathematics at university being compromised and able-students being neglected, and has cost the economy billions of pounds in lost mathematicians."
This is a ridiculous quote from the report. If one were to take the trouble to even glance at the appendix A of the report it is easy to see the grand pronouncements have slim foundation. The A and O level exams in the UK are without question significant but they are just used to make relative judgments among current students. None of the cited questions bear on anything that rises above the level school book arithmetic, algebra and geometry. For instance note that algebra in this context has very little to do with what is studied in a university level algebra course.
If this were a report about "dumbing down" of the mathematical tripos exam at Cambridge or the Putnam exam in the US, then the conclusions might not seem as silly. Anyone with a meaningful interest in math is way beyond the standard of the O level exams.
On a more general level people need to come to terms with the gradual but unmistakeable increase in the level of achievement in general intelligence tests over time. That's right, the trend is exactly the opposite of what the old fogies are always claiming (claimed in every generation since the ancient Greeks and probably before).
Rather than publishing silly reports like this one, they could better spend their time exclaiming: "You kids get off my lawn!"
I took British 'O' and 'A' level exams in the 1980s and now invigilate them at my local school. I would liken exams to eating a plate of sprouts [substitute your least favourite vegetable here]. In the 1980's we studied for two years then sat down and over the course of 2 or 3 hours we tried to eat the plate of sprouts. In these days of modular exams taken during your studies you get to eat your sprouts a few at a time, and to try again later if you can't manage them. The coursework components of some courses allows you to imbibe just a few leaves each day (or if you are a member of the Royal Family you can get someone else to eat them for you). The end result of both courses is that you have eaten the plate of sprouts, it is the process that has become much easier these days... Karl (Grade A 'O' level, grade C 'A' level maths!)
I have found very little in Milton Friedman's writings that I can wholeheartedly agree with.
Well that says a lot more about you than about him. Friedman, a Nobel Laureate, was one of the most important 20th century economists. His contributions to the field are on the level of Friedrich Hayek. If you ever find yourself disagreeing with Friedman on monetary theory or consumption analysis, then you should engage in some serious self-reflection on why you have gotten it wrong. You will find that the overwhelming majority of economists will tell you the same thing. I highly recommend that you put down Free to Choose, and pick up A Monetary History of the United States.
[a] corporation's management is under a legal obligation to ensure that the company makes as much profit as possible
Well, I own three corporations and no one has ever made me aware of that law. Could you please cite it? I'll not hold my breath.
a few moments' thought should be enough to show that any for-profit entity operating in the field of public services is going to provide the least possible service at the highest possible rates.
This is absurd, and patently so. A few moments' reflection would yield this: Let's say you run a school under your model (lowest service and highest cost), and let's further say that I open up a school next door to your school that provides higher service at the same cost. Whose school do you think would be more profitable?
In reality, the free market will supply many different products and many different price points. Can a Safeway survive next door to a Whole Foods? Of course it can. And what can you see happening? Have you been inside a Safeway recently? You'll see better quality foods and more organic foods. That's free market competition raising the bar for everybody.
Fobbing such services off onto the private sector produces other problems as well, as corporations are by their very definition protected by legal limits on their liability.
This is silly. There are plenty of private daycare centers, and those are incorporated. Private schools are incorporated. You'll find that the officers of corporations have little liability protection for willful misconduct and illegal activity. Just ask Dennis Kozlowski or Jeff Skilling, both of whom you'd have to visit in prison.
Why would companies suddenly spring up to take over the role of schools?
What difference does it make? So what if private enterprise does not create any schools? Or did you not even read Free to Choose? Friedman advocated vouchers, not the selling off of public schools to private enterprise. If public schools are meeting the needs of the community, then certainly no for-profit schools would survive. But then, how is that a problem? All that means is that the public school system is A-OK.
His model is also flawed in ignoring the very real geographical constraints of schools
I don't get your point here. If the market dictates a need for a school in a certain location then it will spring up there, not 1 hour away.
Why would parents just suddenly decide they wanted to give money?
You ever hear of private school?
But if, as Friedman apparently describes, the basic idea is that the government would subsidize education, then the basic budget should be completely covered,
Ahh, OK. I see you haven't even read Free to Choose, yet feel the need to open your mouth anyway. That explains a lot.
Primer: Friedman envisions a voucher system where each pupil gets a voucher equal to the amount the public school system spends per pupil. That pupil can take that voucher and enroll in any school, including the local public school. Private schools could open up and accept as tuition either the face value of the voucher, or the voucher plus a supplement (just as private schools currently charge tuition). I suppose if a school
They don't grade fathers, but if your daughter's a stripper, you fucked up. --Chris Rock
Well, what you say may be true, but the decline in the difficulty of math tests can't be used to prove anything one way or the other.
A more difficult test is not a better test -- as a test. The function of a test is to yield information. I can make a test that 99% of graduating seniors will get statistically close to zero on, but it serves no more purpose than a test that 99% will ace.
If I am interested in ranking students by "mathematical ability" (assuming such a thing exists in a way that can be measured precisely), I want a test that maximizes the most likely score difference between any two randomly chosen cadidates. If I am interested in determining the qualifications of students for some particular purpose, then I want the test to have a grade that corresponds as precisely as possible to the divisio between "good enough" and "not good enough". It would make sense that that divisio be on the midpoint of the test grading scale. If I am qualifying students for a variety of purposes, then my design task is trickier, but one thing remains constant: a "tougher" test doesn't mean a better one.
Nor, in education, do you want a "tough" curriculum. "Tough" is just a security blanket for when you don't know what to do. If you designed a curriculum that only 1% of the students could follow, it wouldn't be much, if any more useful than one which 99% of the students found easy. What you want ideally is a curriculum that maximizes the mathematical competence of each student. If that is not possible, then you want one which minimizes the difference between the societal need for certain mathematical skills and the supply of people who can fill that need.
Different societies have different needs. India has a huge middle class, but a massive underclass. India's opportunities were historically limited relative to its total population, so a culture of "teaching to the top" made a grim kind of sense. If you couldn't keep up, it was not much loss to society, because somebody sharper is ready to step on you as they climb the ladder of economic advancement. The United States has had for most of its existece an environment of opportunity for all. It makes sense, therefore, to start by teaching to the middle of the class, and sorting out the tail ends of the distribution with special needs programs ("gifted" is really a different form of "special needs").
Now, I know less about the UK than the US, but in the post WW2 decades the UK economy was far less dynamic than the US. Historically, the UK was probably between the US and India, albeit closer to the US. Therefore it makes sense that its educational system was more elitist. However, the UK economy is stronger and more diverse now, so the population the tests characterize is different.
I've been following the testing "sky is falling" phenomenon for decades now. In the 80's, I ran a volunteer group that prepared low income kids for college entrace exams, so I've always been interested in the topic. When dealing with population numbers, you have to consider the sample you are measuring. Are the same proporition of the population preparing for the same mathematical tasks? If not, then you can't use the tests or their score distributions as proof of anything.
For years the college entrance exams became easier in the US, and scores fell on the exams, but it is critical to realize that the scores are calibrated to produce precisely that decline. College bound seniors have become, as a group, stupider. However, they're just as smart as individuals as they ever were. If you took the top 10% of students today and gave them the same tests as their predecessors from fifty years ago, they'd be pretty similar.
I could go on and on about this. Do the curricula have the same diversity of topics? At one time, mathematical education consisted mainly of Euclid, and a student raised on Euclid became very good indeed in the topics in the Ele
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You know, you may have really hit upon a solution to getting a really great education and paying teachers a reasonable amount of money. In the elementary grades, one teacher could cover all the subjects easily. 12 kids (or less) paying 4-5K per child per year would pay this teacher well. And, the instruction could be targeted toward what the kids want to learn. So you get a group that lean toward science, and one that leans toward art, and while covering the basics, you also get more depth in certain areas. Again, parents are in control because of the funding. And as long as taxes are going to be taken out for schooling, you should get a voucher equal to what they give the local public schools to teach your child. You can spend it at any approved "teacher" that you want. Teaching as a cottage industry sounds like a great idea. This doesn't work so well when you get to high school, then you begin to need the specialization (especially with the smart kids) however a group of teachers might rotate their groups of 12.
Here in California. The standards have actually gone up. I graduated high school in 1976. Back then kids who were on drugs and slept in class passed but now I have a kid in high school and I see they do have objective standards that seem to be reasonable. Teachers tell me the same thing, that I went to school during a period when standards were low. Schools are controls at the local and state level so I don't know about what happens outside my local areas
That said student achievment is way, way down on average. This is most due to demographic. Now we have so many more children of poor recent emigants as well as a general broadening of the lower economic classes. But if you control and only look at middle class americal families they are doing as well or beter as ever.
I learned more calculus in my economics classes than I did in my calculus classes. Why? Well, because my calc classes were taught by eccentric mathematics PhD holders who stood up in front of the class writing Greek nonsense with their right hand and erasing it with their left hand (not an eraser, mind you). The only thing accomplished in those classes was the prof getting covered in chalk dust, and no student learning anything about calculus except for the 2 students who were math majors.
My economics classes were taught by ordinary human beings who are wired correctly, so through them, I was finally able to understand calculus. Anyone with a degree in mathematics has no business teaching basic math.
They don't grade fathers, but if your daughter's a stripper, you fucked up. --Chris Rock
By your arguments the problem is that the teachers aren't good enough, therefore shouldn't we be paying them less? How much do you think you'd have to raise teacher salaries to get the kind of people you want to get? It would take decades to see any real change. There would be very little turn-over for a obvious reasons. The people that put up with being teachers now will not go quietly into the night if you quadruple their salary. Older teachers will probably stay as long as possible and teacher's unions are notoriously powerful (at least in the U.S.). There simply won't be room for new graduates and they will have to take other jobs. The unions of course would forbid hiring only new teachers at higher salaries.
Since there are adequate numbers of graduating teachers now, how do you propose to separate the 'better' teachers? Being a 'good' teacher is about more than just knowing the subjects yourself. A teacher that cannot teach the material in the district-mandated textbook should not be teaching now. Maybe the problem is simply with curriculum and not with the teachers.
It's funny that this article should come up a scant few days after I was discussing this with my maths teacher. Over the last 15 years it's clear that the Ontario school board has been hacking away at maths. She explained to me that when students come back to see her they often ask things like "But why didn't you teach us integration, or Euclidian geometry?" These are essential concepts for studies in science and engineering, and now students don't get the opportunity to learn them. However though the fault was initially in the high school segment, universities are not doing much to improve the situation, in that they assume anybody still going into those courses would know how to do that kind of stuff. As an aspiring physicist I find it imperative that schools should get back on track with math, because the way things are going Calc won't even be taught in high school anymore, and I wouldn't want to be the sad bloke who has to teach it to himself from an old text book just to pass his university science course.
The new official way to teach adding numbers is now something like "5 with 3".
So they are removing mathematical operators, and putting natural language in place, because the abstraction of the operators is considered too high.
No joke.
At the bottom of the
"Marge, it takes two to lie. One to lie and one to listen."
-- Homer Simpson SOMETIMES, and just enough to get upset, evidence is just a game because there are too many people with enough investment (financial or otherwise) to support the lie than the truth. I am not talking government conspiracy, just convenient ignorance.
Want Big Business out of government? Take away the incentive and start by getting government out of big business!
In Western Canada here if anything it seems that higher level maths are being taught at lower grades bit by bit. I actually went through early high school as one of these waves took effect and anyone who failed that term would have a harder course than they failed to redo. My parents did not believe me until I showed them that we had to do precalculus in high school.
I've also been reading articles that we've shifted too much emphasis onto homework and it's killing the kids bit by bit. I can believe it since my choice was homework or a social life, but both wasn't really an option. Each teacher would give an hour or two each every day just as a matter of course, as if they weren't doing their jobs if they didn't. Well... that comes to like 5 hours of homework a day.
The dumbing down of A levels in England is indicative of the dumbing down of education in much of the Western World and of how we're treating our kids. They're idiots because we treat them like idiots. We lower the bar so they never develop the muscle to jump higher bars. We're not readying kids for life. I would like to put a lot of it at the feet of parents who don't see their children as individuals wholly seperate from themselves, but rather as pets who need to be coddled and protected. My intelligence tells me that it's all a part of a larger societal more though.
But as GP said, it used to be that teachers were respected. Nowadays, not so much anymore. Also, work has become harder in general I think, because children tend to be less well-behaved than even a decade ago. So the incentive to being a teacher is going down and needs to be replaced with something else. Money is the obvious choice. Even though I would personally like being a teacher, I would never even consider becoming one; firstly, because I see what my mom has to go through as a teacher; secondly, because I make about three times as much money as a software engineer.
wow bravo BBC atlast have got it right.well yeah maths exam do have got easier.first it was like climbing olympus mons(highest mountain in the universe which is on mars)and now its like just going to mars. see how much easier.we have just got to go to mars but not climb the mountain. on a serious note it is now that is tougher. earlier there was not much competion but now every one wants to succeed.do the BBC people know that the correction now a days have got stricter.ofcourse not they wont bother to know this aswell will they? what do they want to prove in their recent "study". that they have got more knowledge of maths or that they have passed more difficult exams than us? am waiting for an ans.