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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?
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.
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.
In Slovenia I'm noticing quite a different trend and it also seems to be making the policymakers look good ... or something. My sister is 8 years younger than me and is now in primary school - she's learning stuff I only learned in high school. She was being taught things like fractions in third grade, I didn't even know what the hell fractions were back then.
But maybe we're just being weird here.
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.
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.
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.
Teaching the masses in free public schools has never historically been a profession ones chooses if they want to do well financially. And it's not just teachers either. I work in the education sector as a IT engineer and get paid significantly less than I could get in the private sector doing the same job. I took this job, not for the money, but because I wanted to contribute something to the community and still be able to make a modest living. Also (just like teachers) I get PTO on par with Europe (about 45 days off per year).
I judt got a nre Kinesis keybiartf so please excusr ant egregiou typos.
I too have a belief that the system protects teachers too much. However this year my Daughter's eighth grade Math teacher was awful and could not even attempt to keep control of the class. He was let go about 1 month before school was out and it was his first year.
Interestingly the High School that she is going to is aware of that teachers failings and identified all of his students as likely needing extra help in ninth grade.
This was supposed to be the GATE class too. Now most of these advanced math students have lost the edge they had and are behind other GATE students in the district.
Glad they got rid of him.
Life moves pretty fast; if you don't stop and look around once in a while, you could miss it. -FB
I can attest to that first hand: When I started my engineering program [only 1.5 semesters to go :)], I had never heard of imaginary numbers before. Granted, I was able to grasp the concept rather readily, but even am I shocked at the inability of some of my peers to perform basic algebra. I spent most of my first semester trying to explain, repeatedly, the distributive property to one fellow (who is still enrolled, and who still fails to grasp the concept).
:)
Part of the problem, as seen from my view, is the complete and utter dependance on calculators, especially those fancy, programmable Texas Instruments ones, that can practically do the work for you. I have one (it was considered 'required course materials') that I have used maybe a handful of times, preferring my old two-line Casio scientific calculator, particularly now that I know what the little cursive 'i' does.
Lose: misplace or fail || Loose: not bound together
"Pay teachers more..."
Sorry but I don't believe this is the case at all, the culture of "pay me more" is bullshit. Many teachers and experts can't teach, but there are those in both groups who can. Paying teachers more is not the issue in many places, in Canada highschool teachers after a good decade or so can pull in 60,000-100K per year and student disengagement is at recrod levels. The idea that the private sector will 'solve everything' is also bullshit, it's cultural and it's complicated, people have made the same argument your making throughout history, yet the same problems occur you're not a unique snowflake here.
The problem is really about the culture itself, it goes deeper then that though it's north american insitutional and business culture that is the problem. See here:
See: http://www.youtube.com/watch?v=gG3HPX0D2mU
Listen to the comments of "calcification" of kids in the school system and adults in the workplace. It makes a lot of good points about self management and responsibility.
I don't agree that all kids are just "lazy", they are disengaged because most of the time we don't allow their curiousity to blossom by killing it early through 'school'. The other problem is that we don't have a place for certain kinds of people in the job market that will pay decent wages. That is the REAL problem, technological displacement, and trying to achieve the impossible (i.e. raising the bar and expectations to unreasonable levels and then being disappointed when kids don't meet them)
Modern schools are often harmful and disengaging enviornments, for many it's positively toxic to someones development. No amount of paying teachers more, or accountability will deal with forced schedules and irrelevant curriculum, the lack of alignment of student curiousity and interest with what they want to learn vs the boring pablum clueless teachers, businesses and government elites, pushing their pablum as 'education'. Many slashdotters can no doubt attest to the low quality of the curriculum and their teachers and school simply not being relevant to what they are interested in, so they 'carve their own path'.
I think something is to be said by not killing childrens motivation and curiousity, which we do very young.
Teaching the masses in free public schools has never historically been a profession ones chooses if they want to do well financially.
The caveat is that you frequently have to go to grad school to be qualified to teach, and grad school prices are rising much faster than public school salaries. Of course housing prices and food prices are also rising faster than salaries. Every career that used to be "just enough to get by" is in danger of falling out of the bottom of the middle class. When you have something like modern public school teaching, where most of the potential creativity and chance to influence young intellects has been replaced with neck deep bureaucracy and a focus on preparing for the next evaluation test, there isn't even a "contribute to the community" sliver lining any more. Public schools in America are broken.
We are all just people.
A problem I'm seeing with my granddaughter is the geeky pantywaist types that were given wedgies in the gym locker room when they were 13 are now the people teaching our 13 year olds and most of them haven't matured any in the mean time. An interesting solution might be to allow temporary teaching certs to seasoned mature professionals and a major tax break to industries that allow their seasoned and mature professionals to take sabbaticals to teach in our schools. A little fresh blood tends to raise standards a bit.
Apocalypse Cancelled, Sorry, No Ticket Refunds
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...
Knowing more advanced math is not required to be able to teach high school mathematics; it does, however, make a teacher better able to teach high school math by giving them a better and richer understanding of the material they have to teach. Sure, a terrible teacher who has that extra appreciation of the material isn't a great substitute for a fabulous teacher who doesn't, but in general I think we can expect the distribution of quality teachers to be roughly the same between those who seek a degree in math and those who don't... given that, on average, those with a degree in the subject will be that much better.
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