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?
.
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.
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?
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
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.
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 ;-).
And you carry your TI-93 round with you? I don't, but I still use very basic maths at the supermarket.
Brand X: "Buy one, get one free!"
Brand Y: A few pence cheaper, and a larger pack too.
Brand Z: "25% off!"
How many people today can't work out which is best?
(UK supermarkets even do most of the work for you, below the price for every product is printed something like "1.50 per kg", so it's very easy to compare prices -- you only need to work stuff out if there's an item on multi-buy promotion, in which case the 'per' price will still be for a single item.)
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
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.
WalMart here in the US generally has the price per unit marked.
:P
And yeah, I do carry my TI-89 with me, but I'm an Aerospace Engineer. Without that, my mechanical pencils and my ID card I'd be naked!
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.
Sure, not everyone is going to go on in mathematics; some will be poets, some will be historians, and so on. It is also true, however, that most people don't have their future that well written by the age of 16, and having a solid enough background in a variety of subjects, including mathematics, literature, and history, to be able to keep future options open to exploration is important. 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. No, doing the mathematics is not going to be easier; sure the computational grind is easier, but mathematics is not arithmetic. Constructing rigorous logical chains of argument, and symbolic manipulation within formally defined systems; understanding how abstraction can be used effectively, and how it can be taken too far; and being able to think coherently and correctly about abstract entities -- these don't magically become trivial given a calculator. Personally I think part of the problem is that we've lost sight of what mathematics is, and what mathematics is not. Modern mathematics courses are simplifying away what matters in favour of shallow coverage of surface material.
Craft Beer Programming T-shirts
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!
You're modded Funny, but that's worryingly accurate. Today's kids like being told they're number one, and if they get dragged down for poor marks, they'll just complain to their parents, who'll complain to the schools, who'll start making cutbacks for other similar children until everyone is told they're outstanding when they clearly are not. I can't talk, though - that sentence was huge. Sigh.
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).
On the other hand, they should be smart enough to know that the SAT was never meant to measure your IQ. In fact, they should be smart enough to know that IQ tests themselves only measure certain abilities, and are not really a good measure of intelligence.
I normally score around 135 in IQ tests (of course it depends on things like time of the day, quality of sleep on the previous night, BAL, etc), and in my opinion IQ tests and Mensa-like organizations are only good to inflate egos, as they have little relevance to real life.
By the way, did you know that "mensa" means "fool", "stupid", or "jerk" in Spanish? How fitting...
As an engineer today however, I have zero need for knowing trig simplification identities, calculus proofs, and the like beyond a high conceptual level, but I have far more need and usage of logical and discrete math fields, programming concepts, vector operations, statistical methods, and other "math" topics that are still completely absent from any high-school math curricula that I've seen.
And I'm afraid that you are, indeed, a victim. You see, the reason why you learn geometric proofs and calculus proofs is to assist with developing problem-solving skills that require an individual to reason a problem from start to finish, much like real life. It scares me that you claim, as an engineer, that all you need to know are the rote mechanics of math (and yes, that is what you describe: number crunching as opposed to critical problem analysis).
Unfortunately, at least in the US, proofs of any type are becoming rare to non-existent in many curricula. I see the direct result of this every day I'm in school and a student stares at me with a blank look on his/her face when I ask him/her to analyze and determine the best course of action for solving for some quantity X given Y and Z.
You didn't mention what type of engineer you are. Computer/software/hardware, perhaps? Then yes, I'd agree that programming logic, vector operations, and the like are probably a valuable intellectual commodity. But I know many engineers who work day in and day out designing things, and this takes more than a simplistic knowledge of how to perform statistical computations.
Craft Beer Programming T-shirts
Calculators are good, if you can already do the sum you want to do in your head.
I know that 1234+2345 is ball park 3500. If I grab my calculator and get something that is about 3500 I'm happy. The point of doing stuff without a calculator is so that you don't depend on it. It is way to easy to make a mistake using a calculator, and if you cant at least estimate the right answer then you have no way of knowing if you operated the calculator correctly.
This skill becomes even more important in physics later on, when you want to neglect terms but cant work out their exact contribution without solving the very problem you want to neglect them from.
A student should be able to ball park the square root of 10 in their head, or work out the sine of 0.1 radians, or estimate what the sum of some set of numbers is in their head because they can simplify the problem to the point that they know they have the right answer.
Then you use a calculator to get it precisely.
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
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.
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 racist when you massage the numbers to make it look like 90% of the worst students are Pakistani.
However, if that genuinely is the case then IMO it's not racist at all. There may be underlying reasons for it that are racist in origin, but if you refuse to acknowledge the problem you're never going to find those underlying reasons.