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?

Comments

Pay teachers more

[kramulous]

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?

Re:Pay teachers more

[shadowkiller137]

instead of a dumbing down I would say that there is more of a split happening between the people in advanced courses and those in the lower level courses. those in the lower courses are not being taught as well and like you said basic concepts are being removed but those in the higher level courses I think are being taught more advanced concepts than previously at that level and age. The standardized tests however must be able to access the whole range of people taking the test so they must be made easier because if the people with the lower training in math got all 0's on the test it would not show at all what they learned, in their own basic way.

Re:Pay teachers more

[sedmonds]

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?

Not only do teachers not get paid enough to attract and retain the good ones, but teachers unions and the fear of lawsuits make firing the awful ones nearly impossible.

Re:Pay teachers more

[homer_s]

...can keep up with the shear numbers of parent classified geniuses.

Clearly, your English teacher wasn't paid enough.

But other than that, the problem I see in this country is that the consumers of education have no choice. And like in any other monopoly, the provider gets away with poor quality.

Re:Pay teachers more

[thtrgremlin]

I don't necessarily get the compulsory education to 18 thing. Get everyone through 8th grade, and if they don't cut it let them go. Work with the kids that want to be there: Want to be there, not necessarily those that get the highest grades. However, off set this with these same kids getting a future opportunity to go back t school when they are older, you know, like after they have learned their lesson that maybe they should have paid better attention in school. Give these misfits an opportunity to do things their way and possibly fall on their ass and learn their lessons. When they want to get their act together, have good opportunities in doing so. The system isn't designed for everybody. Alternatively, kids that aren't so hot in academic courses, let them go to a trade school. Sanitation is a whole lot more recession proof than IT, not to mention there are really great opportunities in those industries for the extremely bright. Construction, demolitions, customer service, automotive repair, and many other fields don't require quite so much general education. IMHO, I think a forcing every student to learn things that are not going to directly influence their economic value in the work force is a major contribution to political and academic apathy. Enough students do not see the value in what they are learning. That doesn't mean the information would be any less valuable IF they learned it, but what is the risk in letting people learn what they want. For those that don't want to learn, save the money to give those same people an opportunity to use it when they get things straight in their head, versus spending it all now when they don't want it. I think all people would benefit, would take greater pride in their education, as well as their chosen career.

I would really like to know what others think. Btw, I am in the US (as one poster asked people to add)

Re:Pay teachers more

[Solandri]

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?

Not only do teachers not get paid enough to attract and retain the good ones, but teachers unions and the fear of lawsuits make firing the awful ones nearly impossible.

Another consequences of the "not paid enough" line of reasoning is that if we did raise teacher pay, we'd have to fire most of the current teachers and hire new ones. The teachers unions get in trouble with this double-edged sword since ultimately their goal is to increase pay for the current crop of teachers, the ones the pay increases are supposed to filter out by attracting more capable teachers.

Re:Pay teachers more

[billcopc]

I used to think that way, I briefly experimented with teaching, early in my career. What I realized is there's no amount of wisdom that's going to un-fuck the educational system. The pay sucks, the students mostly hate you (because _they_ suck), and the whole system is not designed to improve, but merely to survive financially.

I wasn't exactly in the public sector, but it was one of the cheaper and thus more popular private vocational colleges. My already modest expectations were far beyond what this enterprise was offering, which is probably why all the grads wound up either in brainless government jobs (lucky them), or call centers.

The day we rid schools of the financial burden, is the day they will start churning out smarter grads.

Re:Pay teachers more

[RockModeNick]

While I agree with the sentiment, I don't like the word broken. Broken implies they aren't doing what they're intended to, but I don't think thats the case. They're generating the needed numbers of Walmart clerks and other low wage workers, which is success if preparing students for their most likely future occupations is the goal.

we don't want to upset them

[spir0]

we don't want to upset the poor children or make their lives too difficult. their parents might sue.

Finally

[Zelos]

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.

education policymakers need to look good

[amrik98]

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?

General request!

[xaxa]

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 ;-).

Re:tools

[Coryoth]

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. It's interesting you say that, because the actual report was noting the economic impact of the lower numbers of students actually going on to complete higher level mathematics (in part, they claim, due to poor preparation based on lower standards). Apparently there is actually quite a demand for the skills that mathematics education can impart; high enough demand that employers in the UK are noting the lack of suitably qualified candidates (apparently financial insitutions in the UK are looking to France these days, since they produce more and better mathematicians).

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.

Re:First post!

[Anonymous Coward]

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.

Re:Mensa and testing...

[Smurf]

Mensa won't take SATs from later than 1/31/94 as an indication of your IQ. That says something about changing test difficulty... It sure does.

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...

Re:Maths has changed / evolved...

[pongo000]

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.

Privatizing *really* not the answer (long post)

[zooblethorpe]

My favorite idea for "fixing" schools comes from Milton Friedman's book "Capitalism and Freedom". The basic idea is that the government would subsidize education and set some minimum requirements, while the actual schooling would be done by competeing private companies.

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