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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.
Craft Beer Programming T-shirts
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.
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...
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
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!
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!
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.