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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?
...teachers unions and the fear of lawsuits make firing the awful ones nearly impossible. I call B.S. on that one. In my time teaching, I saw several bad teachers let go. Problem was, there wasn't anyone better to replace them.Changa hates change.
Teachers aren't paid enough?
I live in Calgary and teachers here are well paid and we still see this problem. One of the biggest problems I see here is that we've created a system where you can not "Hold a student back" and thus students move to the next grade regardless of being prepared for it or not. Eventually these students get to highschool and can not pass the courses without a lot of help from teachers (yeah, as if that is going to happen) so they reduce the complexity of the courses in order to continue to pass these students.
Craft Beer Programming T-shirts
That said, in the linked PDF a 1951 question is stated as: Solve the equation:
9 * (1-x^2)/(1+x^2) - 7 * 2x/(1+x^2) = 3 A 1970 question is: Show that (x â" 3) is a factor of
x^3 - 5x^2 - 18x + 72
then find the three points where y = x^3 - 5x^2 - 18x + 72 meets the x axis While a 2006 question is: Find a and b when
x^2 + 8x + 21 = (x + a)^2 + b
Use your answer to find the minimum value of
x^2 + 8x + 21. I can see why someone might say the 1951 question was harder than the 1970 question which was harder than the 2006 question.
"Goodness me, how unlike the FBI to abuse the trust of the American public." -- The Onion
I'm from Canada, and we learned fractions in grade 3 or 4, the early 1980s.
testing out my trending skills
Ok time to take a Karma hit for telling the truth. Minorities have been screaming for years that the SAT Math section somehow discriminates against them because their scores are so low. So they had no choice but to dumb them down. The more you lower the maximum score, the more equal everyone's score is.
Welcome to the wonderful world of multiculturalism and affirmative action.
When I went through the Ontario system (1986), the requirement for engineering was 3 high schoool math courses in: Calculus, Algebra, and "Functions and Relations".
I did some Calculus T.A. work, and the new students are missing certain critical concepts. The new curriculum has eliminated Integration from High School Calculus. It is actually lucky that the students get any Calculus in High School at all. One of the original proposals for the new curriculum recommended eliminating Calculus entirely. The Engineering schools fought hard to keep Calculus in High School.
Some of the first year engineering students have not seen key trignometric functions like the sine function. Other students have not seen Sigma notation, which is used for for finite and infinite series. Almost all of the students struggle with the university Algebra course, which makes me suspect the high school introduction to vectors and matrix algebra was been watered down.
Reducing the high school requirement from three to two high school math courses hurts the undergraduate engineering students. Further, a subject like Calculus benefits from repeat exposures over a number of years. The students would benefit from an introductory Calculus course in Grade 11, a deeper course in Grade 12, and then the 4 more courses in first and second year university. That way, the students have had 4 years Calculus experience before they need to apply the hard stuff in 3rd and 4th year engineering. As it is, students might only see Calculus for 2 years at university, and I'm not sure if this is enough time to really absorb the subject.
As for the quality of the students themselves, the students from the new curriculum are different. They are very fast (faster than me) at solving problems with known forms. On structured problems, similar to ones they have seen before, they are very fast. Unfortunately, they are very poor at solving unstructured problems, and problems where they have not seen the solution technique in advance. It is like someone has beaten the creativity out of the students. They can write tests really well, but they can't do original math. I imagine the students will pick up the creativity as they gain experience. It is just that someone has removed the fun advanced questions that really get the students thinking from the curriculum. The high schools are somehow creating students that can do simple stuff, but lack deeper insights into what they are doing. The students haven't been allowed to try, fail, and sometimes succeed at solving the harder mathemetical questions.
The union would say that they weren't convicted,
Those commie bastards, actually believing in that commie philosophy of "innocent until proven guilty."
Yes they have.
I had my maths GCSE a week ago, and I can confirm that yes, maths is now damn easy. The most difficult question on the paper was to perform a simple proof involving algebraic fractions.
The problem of maths education does seem to be worse in secondary schools, due to the habit of teaching to the lowest common denominator (pun unintentional). For me at least, year 7 maths was simpler than what I was taught in year 6.
One experience that for me really exemplified this decline is the International Maths Olympiad test. During the test, I had to attempt to teach myself how to solve quadrilaterals, as we had not been taught them in class.
For you Americans, UK GCSE = 15/16 years old
If anyone has any questions about learning GCSE level maths, feel free to ask me.
I must be new here...
For people not in the U.S., NCLB is the controversial No Child Left Behind act.
As I understand it (I once dated a teacher,) the history of NCLB is basically:
Other than the 10 weeks or so off in the summer, teachers don't really work that little. Most teachers I've known (including mine) put in around 10-12 hours per day and a good chunk on the weekends. Okay, any good teacher. Plus you have to add in all sorts of meetings and weekly side deals all over the place. Once you start doing any extra-curricular activities for your students you're pushing 60-70 hrs a week. No thanks.
This sig isn't original enough, it's time to come up with something witty...
I agree with you for the most part. However the one issue with that is that in the US it is the people who drive the politicians to do what they do. Our vote matters to some degree but to a much higher degree is popular opinion, if someone is just "liked" they can get elected. So if the people are uneducated and don't understand the whole picture they very often drive the politicians to do things that don't make sence for the Nation as a whole. In the end it's best that everyone is well educated but I do like the idea of letting people fail. I think you learn much more from you failures not your successes.
Saying "all faiths are equivalent" is akin to saying "all drugs are the same".
Actually, if it's a set of angles, you can do some cosines and sines by hand.
Take an equilateral triangle of side length 2. Cut in half, so you have hypotenuse length 2, base length 1, and vertical length sqrt(3). Now you can find the cosines and sines of both 30 and 60 degrees (or pi/6 and pi/3 radians, respectively).
Now take a right angle triangle with base and vertical length 1, and hypotenuse length sqrt(2). Now you can find the sine and cosine of 45 degrees (pi/4).
So with a few simple skills: basic geometry, SOHCAHTOA, Pythagoras's theorem, you can find the sine and cosine of 3 different angles. Now learn your CAST rule (where the different trig functions are positive based on the quadrant) and you can do it for up to 12 different angles. Then learn your double angle formulas and you've got another 4 angles. Then learn the period of trig functions and you can now find it for any of those 16 angles plus the period of the function. Anything other than that, and yes, you'll need a calculator, but knowing those rules (which can be taught progressively throughout high school) and you'll find doing certain things much easier. Now, granted, trig isn't for everyone. However, it's not unreasonable to expect people to do certain calculations sans calculator. Like multiplication, addition, and division.
Cynical Idealist
Math does not go together with multiple choice tests. Many math problems are hard to solve but easy to check, meaning it can be much faster (and easier) to just run each answer backwards than solving the original problem. As a simple example: suppose you're asked to integrate sin(x)*cos(x). Since differentiation is easy, you just differentiate all the answers and see that sin(x)^2/2 differentiates to sin(x)*cos(x). You could do an entire test on indefinite integration and *never even perform integration*. (Another example: prove X vs which proof proves X)
Of course some math problems don't have that 'easy to check' property, and they are more appropriate for multiple choice tests. Definite integration is an example of such a problem. But even then multiple choice tests are easier, because you can catch your own errors by comparing against the possible answers (not to mention the non-negligible chance of just guessing the correct answer).
God this sentiment irritates me.
You are evaluating the work teachers do based on your experiences as a student.
When class is in session, I work far more hours a week than my software development friends. Basically, I can't play when school is in session. There literally is no end to what needs to be done.
When class is not in session, I can scale back to about 40 hours a week.
I'm so sure you think that just because students aren't at the school, teachers have nothing to do (eyeroll).
Part of the reason it's hard to get good people to teach is that it's an abusive amount of work for very little pay.
I only taught at the K-12 level for 2 years before I said "screw this." I'm at the uni level now, and while the hours don't go down much, the pay goes up a lot. Also, you don't have to deal with parents!
It's just not true. Your job is always in peril, you get crap for benefits, you get no breaks in housing, and the pension is thirty years away... I can't pay my bills now! Couple that with principals who are more afraid of parental law suits than maintaining order, many principals who view teachers as easily replaced, and a society wide dis-like of education and the educated and it's a recipe for failure.
Icing on the cake: candidates running from the position that they need to "break the back" of the teacher's unions. Wow. Low pay, Walmart style bennies, no support, no respect, and then they want to break the back of the union that's giving you those low wages, low benefits, and lack of support.
Yeah. Makes sense... I follow the logic: Schools in America would be better if we paid teachers even less, gave them even fewer incentives, made them work harder, and took their pensions. I know the same logic did wonders for the American Auto industry... just look at Toyota.
Who in their right mind would want to be a teacher in the USA?
Studies have found that children are more likely to do better in school if they believe that they're...well, better.
Er, no, that was a popular idea in the 60's but recent science has shown that as students grow up with false praise (to make them think they are better) eventually (early/pre-teens) they realize they're being lied to with counterproductive results including low self esteem and social problems. In the long term it's best to be perfectly honest; by all means praise specific accomplishments at but don't pretend they're doing well when they're not.
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Stop using tab characters in your code!
I've been a researcher in applied science for some 30 years, and have never used a trig identity since graduating from high school, so I would certainly agree with the idea of flushing that from the math curriculum in favor of some combinatorial math.
BUT flushing the calculus path? I don't think so. That is still ultimately fundamental and critical to all of the sciences and engineering disciplines. I use it all the time, along with the discrete stuff I picked up in college that I had to learn to do some types of work - statistical mechanics. polymerization theory, etc.
Aside from the trig identities everything I learned in high school (and college) in math some 30-40 years ago is still absolutely relevant.
And the idea that calculators have changed the way math should be taught? Very little in my opinion. If anything they should alleviate some of the tedium in the lower grades, but that is it. By the time you are in middle school math should be about symbol manipulation, NOT crunching numbers.
As far as maths being useless unless you are a scientist or engineer ---- HAHAHAHA, ask anyone in marketing, business management, investing etc. about that. It is famous how many rich physics PhDs are working as analysts for Wall Street companies.
Yep, my wife is a K-6 teacher, and I'm a System Engineer. She leaves home before me, gets home after me, and every minute of her work day she is working, not looking at pr0n ;)
Most days for lunch she is 'on duty' which means working, and the odd weekend she has to go in for extra-curricular activities. I'm usually at the pub for lunch at least once a week.
She does get 10 weeks holiday though, however she has no choice when they are. Oh and it's always peak season so we pay premium for everything when on holiday. A lot of holiday time is used to do marking, reports or catch up or prepare for the next term.
She gets no free lunches or bludge meetings, and no work or vendor-sponsored drinking sessions.
For all of this, she earns a little over half of what I do, with zero perks or kickbacks to be had.
Anyone who thinks teaching is a bludge, doesn't know anything about teaching.
Or maybe it's all about not screwing up the store's inventory tracking system and not screwing up the accounting so that your drawer counts the way it should.
Purchases from a modern store are not as simple as "I give you some money, you give me some product", even if it may look that way from the point of view of the customer.
If you mod me Overrated, you are admitting that you have no penis.
Wow, it's nothing like that here. My city is divided up into districts, and each district has a bunch of schools, and each school has a section of town assigned to it. Your kids go to the school who's area you live in. If you bitch enough (and I mean a LOT) you might get to move your kid to a nearby school in the same district. Going to a different district is right out. Unless you move, of course.
In the US the majority of public school funding comes from property taxes (PDF). Poor neighborhoods get less money from property taxes, which means they get less money for schools.
Maybe not
According to http://www.merriam-webster.com/dictionary/bludge it's a slang word used in "chiefly Australian & New Zealand". That's not "most of the English speaking world" AFAIK. And something that "googling it" turned up quite easily. I'm not a native English speaker, but I had 4 years of education in English-speaking schools. I had never heard of a bludge.