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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.
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.
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
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.
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.
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.
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.
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.
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.
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.
When I took my A-levels back in 1987, I'd reviewed all of the papers going back 10 years. The exams had definitely gotten harder. The problems from the 70's were somewhat simpler.
Not quite the same thing as here, but standards, for Maths A-levels at least, had toughened between the 70's and 80's.
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 think that is more likely the case of pushy parents.
Education is turning into almost a two tier system. There are those kids which are pushed by their parents and aim to succeed and then there is everyone else.
The kids who push hard all fight over a small handful of places in top schools fighting off with multiple public and private schools (who often are rubbing the Uni's asses).
It does amuse me that we have these moral panics about exam difficulty without really addressing the key question - Does it teach then what it intends to? And are the subject's goals in line with what is needed?
Looking at grades as an answer to either question seems about as intelligent as asking the cows about the weather.
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.
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.
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 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!
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.
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Science -- Sealed, Delivered.
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.
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 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 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
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!
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:
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).
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 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.
Math does not go together with multiple choice tests. Many math problems are hard to solve but easy to check, meaning it can be much faster (and easier) to just run each answer backwards than solving the original problem. As a simple example: suppose you're asked to integrate sin(x)*cos(x). Since differentiation is easy, you just differentiate all the answers and see that sin(x)^2/2 differentiates to sin(x)*cos(x). You could do an entire test on indefinite integration and *never even perform integration*. (Another example: prove X vs which proof proves X)
Of course some math problems don't have that 'easy to check' property, and they are more appropriate for multiple choice tests. Definite integration is an example of such a problem. But even then multiple choice tests are easier, because you can catch your own errors by comparing against the possible answers (not to mention the non-negligible chance of just guessing the correct answer).
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?
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
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 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?
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.
Geology - it's not rocket science; it's rock science
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...
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 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