New UK Study Shows Math Standards Slipping

[The Grim Squeaker]

The loss of mathematical potential is costing Britain alone billions in productivity, and all signs point to similar slippage in U.S. and elsewhere

A rigorous new study looking at the aptitudes indicated by responses to, formats of, and content presented in math exams from 1951 to 2006 shows a disturbing decline both in standards and an apparently correlated decline in student competence. The study looked at British 16-year old students’ exams and confirmed what many in the educational systems in Britain already recognized -- math competency is in an unprecedented weak state. And similar problems appear to be true in the U.S. and elsewhere.

The study says that the immediate effect of this inadequacy is not always readily apparent, but that the grave result is the loss of a generation of mathematicians that could have contributed diversely to the economy.
Mathematicians are essential to tackle the more cerebral side of problems in topics as diverse as economics, biology, computer science, and mechanical design. Without these mathematicians, many problems go unsolved or have suboptimal solutions, and this translates to loss in domestic product and standard of living.

Of course such slippage is hard to monitor. However, the decline in abilities is far more visible. Despite government claims that it is carefully protecting standards by government testing of students, much like here in the U.S., the testing standards have been in steady decline, according to the study, since around 1970. Between 1951 and 1970 the study found the standards to be quite high and to demand competency in algebra, arithmetic and geometry, all essential topics. By the 1980s the testers began to try to simplify the test.

The study accuses the math education of being shallower and broader. The questions were easier and less demanding. Worse, it says, students were not allowed to independently formulate paths to solutions, but had to follow a dictated path or risk losing credit. Calculators snuck their way into the allowed list of supplies and formula sheets began to appear. This had a net effect of decreasing students’ basic math knowledge and arithmetic abilities.

Additionally, the actual grades themselves fell. The standard for a C fell to a mere 20% mark on the harder British standardized test. The apparent rise in scores from 1990 to present is "highly misleading" it said. It said this increase is due to easier tests, lower standards, and a cram-and-forget mentality on the part of students just looking to use the test to gain college admittance. Says the study, "Exams have changed from being a staging-post to further study to being a series of 'tick-boxes'."

British Deputy director of Reform and a co-author of the report Elizabeth Truss state that the loss of competent mathematicians at the university level is a trend that must be stopped. She states, "In today's Britain it is acceptable to say that you can't do maths, whereas people would be ashamed to admit they couldn't read. We need a cultural revolution to transform maths from geek to chic."

Schools Minister Jim Knight disputes her remarks saying British standards are world class. Perhaps he's right, as many say standards are slipping worldwide. Knight was able to point to minor recent improvements. He stated, "Ucas figures show the number of people who took up places on full time maths degrees has gone up by 9.3% on last year. That is good news, but we agree maths is of vital importance to the economy and it is a top government priority to encourage more mathematicians in the future. In addition, we have launched a campaign to encourage more young people to consider careers in maths and science."

In Britain, where every position has a "shadow" political second in command, Shadow children's secretary Michael Gove was quick to comment, "India and China are producing four million graduates every year. The single largest area of graduate growth is mathematics, science and engineering. A third of graduates in China are engineers - here it's just 8%. Between 1994 and 2004, more than 30% of the physics departments in Britain disappeared."

Liberal Democrat schools spokesman David Laws added, "This is a damning critique of maths education in this country. Our education system is too often failing to get the basics right, which risks damaging the national economy."

While many in the U.S. remain unconcerned about such developments in Britain, similar signs of slippage are showing up in the U.S. In fact many physics programs in the U.S. are gradually losing funding or disappearing. The last U.S. particle physics lab is on the verge of collapse and is only being kept afloat thanks to private donations. As mentioned, such trends may seem harmless, but promise to greatly harm the world economy.

Interesting, if nothing new. The bits about the nature of the changes, and some of the comments were interesting. (Such as some of the changes being due to the tests focusing more on set answers, and not "just" due to NCLA).

[Darth Wong]

It pains me greatly to see this decline, but it doesn't surprise me in light of decades of anti-technology and anti-science rhetoric, not to mention a generation of coddled students whose parents threaten educators rather than their own children when they see a bad report card.

Similarly, university flunk rates have declined precipitously in the last 20 years; they are refusing to flunk students for not meeting the standard.

[Admiral Valdemar]

The system is made to make you an efficient exam passing machine. Nothing more.

[CaptainZoidberg]

In my experience, there are three big problems with mathematics education:

1. Math just isn't all that fun until you get into Calculus and Differential Equations (that's the farthest I've gone, and I find it to be pretty exciting stuff).

2. Computer Science and numerical methods aren't emphasized enough.

3. At least at the High School level, mathematics is largely oriented around problem solving and competitions like the AMC. A lot of people I know have gotten disillusioned with mathematics because its so competitive and cut-throat.

In my personal opinion, math should be taught with integrated computer science. In elementary school you could start to teach the kids some basic Python and simple ActionScript (for Flash). Then in Middle School you could introduce them to Maple, and perhaps Java. In High School Advanced Placement Calculus could be taught with integrated Advanced Placement Computer Science. For example, an assignment might be to write a program that performs numerical integration then graphs the results.

But I'm not a math teacher, just a student, so you should probably take what I say with a grain of salt.

[Sarevok]

The system is made to make you an efficient exam passing machine. Nothing more.

Funny thing. Going through older british maths text books (70s and such) the question seem a lot more harder ! The syllabus may not have changed much but O and A level questions have gotten so formualic even a computer could do them.

[Fingolfin_Noldor]

In my experience, there are three big problems with mathematics education:

1. Math just isn't all that fun until you get into Calculus and Differential Equations (that's the farthest I've gone, and I find it to be pretty exciting stuff).

Erm, fun or not, these are essential topics to study. It cannot be emphasized enough that you can't be an engineer or physicist or mathematician without being good at Calculus and Differential Equations.

2. Computer Science and numerical methods aren't emphasized enough.

I don't see a point in teaching some of this stuff at a high school level when people are having enough trouble with the existing core which is why more important. Maybe as an extra class but certainly not a core subject.

3. At least at the High School level, mathematics is largely oriented around problem solving and competitions like the AMC. A lot of people I know have gotten disillusioned with mathematics because its so competitive and cut-throat.

Well if they are disillusioned with math, then they have cut out a good number of career options in engineering etc. where it's even more competitive. Of course it's competitive. If it weren't, then any tom dick and harry could claim to be a Mathematician.

In my personal opinion, math should be taught with integrated computer science. In elementary school you could start to teach the kids some basic Python and simple ActionScript (for Flash). Then in Middle School you could introduce them to Maple, and perhaps Java. In High School Advanced Placement Calculus could be taught with integrated Advanced Placement Computer Science. For example, an assignment might be to write a program that performs numerical integration then graphs the results.

What is the point of learning numerical integration at that level, when you have to cut out a good chunk of the theory which incidentally involves a fair bit of calculus and other topics? I would think these courses should be regarded as extra curricula but if students have enough trouble with the basic subjects I don't seriously see a point teaching extra fluff which would be taught at a deeper level in the university anyway!

[Jaevric]

Honestly, mathematics kicked my ass. I made it through geometry (the only math class I've actually enjoyed), trig, statistics, and pre-calculus (with tutoring), but the calculus courses I took at UT Austin killed my GPA. I don't know if it was an issue with the professors, the fact I was getting far too little sleep in the dorms, or my own hang-ups about "not being good at math" but I could not wrap my mind around calculus, even the dumbed-down "business" calculus.

The worst part is I realize how important a skillset advanced mathematics can be, I've just convinced myself that I can't manage calculus.

I took calculus several times and never managed to pass the class, and I suspect it was worse every time I tried it because I was more convinced I wasn't going to be able to pass this time. It didn't help that most of the professors either wouldn't or couldn't explain why the equations worked that way, or in one case admitted to the class that the only purpose of requiring calculus was to flunk students out and that we'd never actually use it unless we were going to be engineers or mathematicians (this was UT Austin business school). Rote memorization of equations was a serious issue for me, and if I forgot any part of the equation I didn't have enough grasp of the theory to figure out what I was missing.

[Admiral Valdemar]

Erm, fun or not, these are essential topics to study. It cannot be emphasized enough that you can't be an engineer or physicist or mathematician without being good at Calculus and Differential Equations.

That's the problem, if it isn't fun, then no one wants to do it. You can't be good at something you honestly don't care for and have no inclination to carry on doing. Maths I knew was important, but despite being a diva at physics, I sucked shit at maths. I was in the top set at school for science, and near the bottom set for maths, one step above learning the multiplication tables by age 16. None of my teachers got it, though I saw it as the application of maths being interesting and worth my time, while theoretical stuff bored me shitless. I won't lie. I'm wary of people who get their jollies off maths, because it's totally alien to me. Then again, they could say the same thing about toying with living organisms.

The bigger number of Mickey Mouse subjects doesn't help either (media studies, American studies, programmingHAHA! etc.) since people have been told you're nothing without going to uni, and if they can't do a core subject like the Big 3 of science, maths or engineering or even English, then sod it, they'll take air guitar 101.

[chitoryu12]

Standards have gone to shit in elementary schools down here in Florida. My friend's sister is 13 and just passed 5th grade this year. She would actually still BE in elementary school because of her grades, but they're so desperate to get her out to avoid looking like they can't teach for crap (a common accusation when parents see a teenager still in grade school) that they're just passing her on to middle school. She'll be 20 years old by the time she gets out of high school, and that's assuming she gets her act together by then. It's far more brutal here at Lake Mary High. 9 absences (and she's a known skipper) gets you automatic credit denial, and if you're even half a credit off of the 24 you need as a senior you don't get to graduate. For a girl who's spent her life just being passed by desperate educators, she'll drop out in a heartbeat.

[CaptainZoidberg]

Erm, fun or not, these are essential topics to study. It cannot be emphasized enough that you can't be an engineer or physicist or mathematician without being good at Calculus and Differential Equations.

Nearly everyone I know who does math for fun got excited about math through programming or solving problems. I really got interested in math when I started to explore it as a way of solving problems, and way of exploring the mysteries of life. I think Mr. Wong's Star Wars vs. Star Trek site was a little bit of an eye-opener since it showed how seemingly impossible problems (like figuring out how powerful the death star was) could be solved through math and physics.

And as Admiral Valdemar said, people won't really get into math if they don't think its fun.

I don't see a point in teaching some of this stuff at a high school level when people are having enough trouble with the existing core which is why more important. Maybe as an extra class but certainly not a core subject.

I think there's a lot of merit to that point, but I still think that math could be a lot more fun if it was integrated with programming.

Well if they are disillusioned with math, then they have cut out a good number of career options in engineering etc. where it's even more competitive. Of course it's competitive. If it weren't, then any tom dick and harry could claim to be a Mathematician.

My experience is of course pretty limited, having only had taken a few college math classes, but from what I've seen engineers have an attitude where they want others to succeed, where mathematicians are more cut-throat. It seems like in engineering the goal is to overcome a natural obstacle, while in mathematics the goal is to be better than other mathematicians.

What is the point of learning numerical integration at that level, when you have to cut out a good chunk of the theory which incidentally involves a fair bit of calculus and other topics? I would think these courses should be regarded as extra curricula but if students have enough trouble with the basic subjects I don't seriously see a point teaching extra fluff which would be taught at a deeper level in the university anyway!

In my HS class, numerical integration and symbolic integration were taught together. I think numerical integration is important since it's more directly applicable to real world work.

And when I say numerical integration, I'm just saying definite integrals, not anything funky like Runge-Kutta.

[The Guid]

I actually read the report and it was a load of bollocks. For a start they started using this funny symbol ---> %, all the time at the end of some numbers. This happened too often to be a typing error. They also talked about using letters instead of numbers, which, ummm... died out with the Romans for christ sake. What a load of crap.

Take no notice. Mathematics education in Britain is fine.

[Dooey Jo]

I was in the top set at school for science, and near the bottom set for maths, one step above learning the multiplication tables by age 16.

In 5th grade, I remember, we used to have these tests. We would get a paper with 100 or something single digit number multiplications, and have five minutes (or maybe three, I don't remember that well) to fill in all the answers. I could never do it on time, and got really stressed out every time we would do it. Eventually I figured out a system, where I'd fill in one difficult answer (I didn't do this for multiples of five, one or zero, and other numbers I was better at), then search the whole thing for equivalent numbers, which for me was faster than actually doing every number. I didn't memorise the multiplication table, but I did figure out how to solve the test.

But that's okay. I've never intended to become a calculator, and surprisingly, taking a few seconds to solve some multiplication in my head has never been quite the impediment one might expect. I have, however, hated school maths ever since, even though I am good at it, and prefer to learn it on my own.

[Rye]

The study accuses the math education of being shallower and broader. The questions were easier and less demanding. Worse, it says, students were not allowed to independently formulate paths to solutions, but had to follow a dictated path or risk losing credit. Calculators snuck their way into the allowed list of supplies and formula sheets began to appear. This had a net effect of decreasing students’ basic math knowledge and arithmetic abilities.

This all sounds reminiscent of when I was at school. I was 3-4 years ahead of where I should've been when I started high school maths and due to the frustratingly set curriculum, I couldn't carry on at my own pace. Thus I turned into an extremely lazy maths student that doodled most of the time (never did homework) and then did everything in the last 10 minutes to try and make it interesting. Eventually even that got tiresome, I kept getting in trouble for not doing homework, I had shit teachers, etc. All of which made me not give a shit about the subject at all. We really were on rails to the exams, nothing more, the teachers as much as said so.

[Minischoles]

The system is made to make you an efficient exam passing machine. Nothing more.

This. I can barely remember any of my secondary maths purely because all I learnt in class was how to pass the exam. Nothing more, nothing less. The schools are so under pressure to perform well in league tables and get good results its all that ends up getting taught because they can't risk anything else when not getting good marks can mean a cut in funding (where the logic to cut the funding of low performing schools instead of you know giving them more to improve came from is beyond me) and even the loss of a headteachers job.

[Psychic_Sandwich]

Erm, fun or not, these are essential topics to study. It cannot be emphasized enough that you can't be an engineer or physicist or mathematician without being good at Calculus and Differential Equations.

While this is true, bear in mind that you're trying to teach things to children. They inherently have shorter attention spans and don't concentrate as well as adults on boring but necessary things. Saying 'this will be important later in your life' just isn't a convincing argument for many (most, even) children.

As an anecdotal example, when I was in school, I was in the top set for maths. We had a brilliant teacher; he made the subject fun and thus managed to hold our attention and actually teach us stuff, rather than just turn us into test passing automatons. Unfortunately, he was pretty old, and had a number of rather serious medical conditions, which forced him to retire. The replacement we got was an arrogant, self absorbed twat hated by everybody. His teaching method was 'Page X to Y. Solve all the problems,' and he couldn't eve be bothered to mark out answers. As a result, our grades tumbled, and we did really poorly in pretty much every test we took.

[Fingolfin_Noldor]

While this is true, bear in mind that you're trying to teach things to children. They inherently have shorter attention spans and don't concentrate as well as adults on boring but necessary things. Saying 'this will be important later in your life' just isn't a convincing argument for many (most, even) children.

As an anecdotal example, when I was in school, I was in the top set for maths. We had a brilliant teacher; he made the subject fun and thus managed to hold our attention and actually teach us stuff, rather than just turn us into test passing automatons. Unfortunately, he was pretty old, and had a number of rather serious medical conditions, which forced him to retire. The replacement we got was an arrogant, self absorbed twat hated by everybody. His teaching method was 'Page X to Y. Solve all the problems,' and he couldn't eve be bothered to mark out answers. As a result, our grades tumbled, and we did really poorly in pretty much every test we took.

Point taken. Though I can't think of any way where Calculus could be taught in a any more interesting way, at least from the way I was first taught. A difficult subject definitely requires a dedicated teacher to do a difficult job, which I guess I was fortunate enough to get one way back then.

[Darth Wong]

Counting on exceptional teachers is not a strategy; it only works when you have exceptional teachers, and cannot be taken seriously as a solution for a society-wide improvement program.

Personally, I think a better approach is to have different grades of high-school diploma: Basic, Advanced, and With Honours. In order to get the Advanced or With Honours diplomas, you must take all of the advanced maths. In order to get the With Honours diploma, you must do very well in certain core subjects: language, math, and science.

Right now, everyone gets the same diploma even if they took the bare minimum of maths. But people are conscious of prestige and accolades, and if they know they get the dummy diploma if they don't do well in math, that might provide some extra incentive.

[Coyote]

Prioritizing academic achievement as well would help; the sports stars pretty much get all the accolades. But I remember a lot of kids in my HS math classes (admittedly long ago) who felt that math just wasn't that relevent. Cash registers counted change for you; there was always a calculator somewhere, no one knew anybody that needed to do a square root on the job--

--and yes, it's true, you can counter that by telling those kids "if you're content to pilot a cash register until you're 60, fine" but faced with a bunch of kids whose idea of "planning ahead" means whose fake ID will be used to get the beer this weekend, it becomes one of those subjects that they miss out on, and then look back at later and wish they'd payed more attention.

[CaptainZoidberg]

Personally, I think a better approach is to have different grades of high-school diploma: Basic, Advanced, and With Honours. In order to get the Advanced or With Honours diplomas, you must take all of the advanced maths. In order to get the With Honours diploma, you must do very well in certain core subjects: language, math, and science.

The problem is that the schools will start to lower the criteria for advanced maths and core subjects because they want to give EVERYONE the award. Once our school started creating honors classes, the school felt pressured to let everyone into the classes, and then virtually everyone was taking honors classes.

What we'd need to do to make your system work would be to tie the diploma tiers to national academic exams. For example, one would have to get in the top 20% or so of those exams in all of the core areas to get an advanced diploma, and one would need to get in the top 5% in all the core areas to get an honors diploma.

I also think it would make sense to put areas of concentration on the diploma. For example: math, science, auto technology, etc.

Right now, everyone gets the same diploma even if they took the bare minimum of maths. But people are conscious of prestige and accolades, and if they know they get the dummy diploma if they don't do well in math, that might provide some extra incentive.

I agree with that. The US already has a National Merit Scholarship program, where the top 5% on the PSAT exam get commended, and the top 1% become National Merit Scholars.

If that was tied in with the diploma than I think it would be a good policy, and there would be no way for schools to arbitrarily start giving them out since they're tied to a national standardized exam.

[Darth Wong]

What they should do is post examples of qualifications wanted for various kinds of jobs, and whenever those qualifications include an educational background that requires university-level math, make a note that exceptional math performance is required.

If kids start seeing how many jobs they can never do if they suck at math, that might open a few sets of eyes. Unfortunately, they don't do that in school. Either this idea has not occurred to anyone or the liberal-arts set (which dominates the education hierarchy) doesn't want any of the kids finding out how much less valuable their skills are in the job market than those pesky hard-tech skills.

[Darth Wong]

What we'd need to do to make your system work would be to tie the diploma tiers to national academic exams. For example, one would have to get in the top 20% or so of those exams in all of the core areas to get an advanced diploma, and one would need to get in the top 5% in all the core areas to get an honors diploma.

Standardized exams are highly overrated. It's better to simply limit the proportion of kids who can get the Honours diploma, so that it's defined as a percentile instead of an absolute mark (in a subjective grading system). If only the top 20% of performers in the core subjects get the Honours diploma, then all of this grade inflation won't help anyone.

Although I do agree with some attempt to clamp down on the absurd levels of grade inflation we've seen in the last 20 years. Perhaps some combination of the two approaches.

[CaptainZoidberg]

What they should do is post examples of qualifications wanted for various kinds of jobs, and whenever those qualifications include an educational background that requires university-level math, make a note that exceptional math performance is required.

A lot of the high prestige jobs: doctor, lawyer, senator/representative can be attained without taking any high-level math.

[Darth Wong]

What they should do is post examples of qualifications wanted for various kinds of jobs, and whenever those qualifications include an educational background that requires university-level math, make a note that exceptional math performance is required.

A lot of the high prestige jobs: doctor, lawyer, senator/representative can be attained without taking any high-level math.

Incorrect. Pre-med studies require chemistry, biology, and math. Lawyers and politicians don't require any math, but MDs are a pretty important example.

[Steel]

What we'd need to do to make your system work would be to tie the diploma tiers to national academic exams. For example, one would have to get in the top 20% or so of those exams in all of the core areas to get an advanced diploma, and one would need to get in the top 5% in all the core areas to get an honors diploma.

Standardized exams are highly overrated. It's better to simply limit the proportion of kids who can get the Honours diploma, so that it's defined as a percentile instead of an absolute mark (in a subjective grading system). If only the top 20% of performers in the core subjects get the Honours diploma, then all of this grade inflation won't help anyone.

Although I do agree with some attempt to clamp down on the absurd levels of grade inflation we've seen in the last 20 years. Perhaps some combination of the two approaches.

If there was to be a system where the top 20% get the honours diploma or whatever a nationally standardised exam system is required. Without that then the top 20% of dipshit emelentary school get honours but the bottom 79% of an elite school get no honours despite being superior to every single one of the people at dipshit elementary.

This is one of the problems in UK eduaction at the moment. The really good schools are so vastly superior in terms of quality of teaching and resources and in terms of the pupils actually wanting to learn, that some places can get over 95% As (or top grades at all levels) and take more subjects than the rest of places which struggle to get even half the number of subjects taught to grade C standard.

[Illuminatus Primus]

The doctor case alone would be a big thing. Even softier majors like economics, many kids I know were horrified to learn that proficiency in basic calculus and statistics was absolutely mandated. There is poor communication about solid standards and requirements between the high school and undergrad levels.