A-Levels: Gah.
A-level results day has come and gone and, as usual, we get the “A-levels suck”, “No they don’t, stop insulting my intelligence” argument. Meanwhile, everybody turns off the telly and moans about the same old crap year after year. I figure that since this isn’t really read by anyone anyway, I can probably get away with a bit of a stab at A-levels.
Here goes: A-levels in Mathematics are getting easier, and if you disagree, you are wrong.
So, I guess I should try to back this up before everyone comes down on me like a ton of bricks. Well, tough – I’m not doing the legwork for you. If you took A-level maths in the last couple of years, go back and look at papers written ten or fifteen years ago. There’s such a chasm in the level of difficulty that it is completely impossible to say that the papers being written are not becoming easier. Mathematics papers from previous decades are almost as hard as current day AEA (Advanced Extension Award) papers, generally taken by the more enthusiastic students.
It’s important to note that the increase in difficulty arises not only from the breadth of knowledge that the student is expected to learn, but also the depth at which they are expected to understand the material presented. For the most part, current day papers ask only for the student to memorize and then regurgitate existing knowledge and basic mathematical techniques.
Of course, the exam boards would have you believe that it’s down to students putting more work in, or simply becoming better at answering the questions in the way they want. Neither of these points detracts from the fact that students simply don’t know as much as they need, and the evidence of this is quite apparent.
There is one simple cause for this: statistics. The government wants 50% of people coming out of college to go to University. How might one accomplish this? Well, there’s the obvious decision by many universities to create loads of pointless degrees (tourism management? what?). But if A-levels are watered down, entry requirements won’t be as hard to attain and even then, they can’t go above asking for 4 A’s, right? Genius!
Unfortunately this drive to achieve meaningless and potentially harmful goals is hurting the universities out there that are offering courses that do actually mean something. The mathematics degree at Warwick has maintained the same standards of difficulty for a number of years now. However, many mathematics departments – Warwick included – are now having to water down their first year because the students simply don’t possess enough knowledge coming in from A-level to understand the more advanced techniques.
As a very big example of this, we don’t teach any group theory in the first year at all now – when I enrolled, there was at least 7-8 weeks of teaching on the subject. But this then causes a very big problem, because whilst the jump from A-level maths to 1st year degree maths is large, the jump from 1st to 2nd year is much larger. So then the entire degree has to become easier, and people who struggled at first find themselves facing a virtual impossibility task to maintain on the degree course.
I’d like to point out that this isn’t meant to be a stab at everybody taking A-levels. It is not the fault of the students that their education system is failing them, and it is good that they are making the best of a bad system. However, something needs to be done quickly, or we’re all going to be screwed over by shoddy degrees.
19/10/2007 10:00 am
Very much agreed.
19/1/2007 1:01 pm
As a very big example of this, we don’t teach any group theory in the first year at all now – when I enrolled, there was at least 7-8 weeks of teaching on the subject.
And in my day the first lecture at Warwick was on group theory, part of a 10 week course ending in some field theory.
A-levels in Mathematics are getting easier, and if you disagree, you are wrong.
Even a government advisor agrees A-levels are easier says adviser. But what to do about it? It’s not as simple as it first looks.
A level maths and its equivalent have been getting easier since at least the early 20th century. I remember seeing a paper around 1900 which included some very complicated algebra. In the fifties and sixties extension papers included questions on inversion (part of projective geometry). Clearly they have become easier since then which is why many Universities were forced to introduce 4 year degrees; in the sixties and seventies top grades in a 3 year degree was the entry to postgraduate courses.
But at the same time more people studied mathematics; in 1900 it would have only been the elite and in the sixties, only grammar and independent schools. So the problem is how to attract more people to mathematics without diluting the standard. Following complaints by universities in the 90s that students were not well prepared for degree courses, the A level in 2000 was made more difficult (back to the standard of the eighties). It was a disaster with huge failures because of course the leap from GCSE was too great for many, so later on the syllabus was made easier again.
The only way to improve standards is to start in the primary schools and gradually spread throgh the years on to the secondary school, so that there are no unbridgeable gaps. But this won’t happen because it requires a 15 year programme and governments (which could change 3 or 4 times in that period) work on much shorter time spans. And the experience of the disaster of modern maths in the seventies shows that such large projects can backfire. On top of that government ministers and civil servants tend not to have a mathematical background and are spectacularly ignorant about mathematics and the way it should be taught (though Gordon Brown does have Scottish higher maths).
It’s a difficult subject but one that needs to be more widely discussed and understood.
19/7/2007 7:22 pm
Agreed entirely. I have testimony from A-level Mathematics teachers to this effect. The solution?: Bring back older syllabi; let teachers teach in what ever fashion they feel will benefit their students; and most of all, get the Government out of the schools!
19/10/2007 10:00 pm
Thanks for your responses guys, makes for very interesting reading.
Steve, it’s clear you know a lot more about the situation in mathematics education than I do so take everything in this with a pinch of salt – but this has been aggravating me so had to get it off my chest
I think I might have died if this was the case in my first year
This emphasizes the point even more, I guess.
Interesting point.
To build on something that Tozznok has said, I think part of the key to this is that students don’t find the current syllabus interesting at all. In fact, the only reason I ended up taking mathematics at university in the first place was because of an excellent teacher who was willing to teach beyond the syllabus, and cover interesting and challenging problems.
In my mind, part of the solution is to give the teachers more scope in the classroom to teach in a more interesting fashion. Learning basic calculus methods out of the textbook without some decent, interesting applications is just plain dull. Together with this, introducing some of the easier concepts from STEP/AEA papers – with more emphasis being placed on proof and logical progression – could spice up the subject and make it a bit more appealing.
The exact same thought had crossed my mind. As it stands, the fact that the Government is involved so critically in the role of education is harming future generations of children, solely because their primary goal is to be re-elected and maintain power.
Ultimately I think the Government should have no say in education. A separate organisation needs to be established, full of people who have real experience in these issues (i.e. experienced teachers and lecturers), in order to make sensible suggestions to improve things.
19/10/2007 10:32 pm
Ultimately I think the Government should have no say in education. A separate organisation needs to be established, full of people who have real experience in these issues (i.e. experienced teachers and lecturers), in order to make sensible suggestions to improve things.
Yes, I very much agree but the cynic in me would also argue that is what the QCA should be doing. But anyone who has dealings with such bodies knows how bureaucratic they are. They tend to change the syllabus every year, insist on endless testing in schools and become every teacher’s nightmare.
There is also another problem that was brought home to me when I came to the opening of the new Warwick mathematics institute three years ago, when we were told that if every mathematics graduate went into teaching there would still be a shortage. And we desperately need more well-qualified teachers to to teach in a more interesting fashion as Dave says.
Professor Alexander Borovik thinks that mass science and maths education in the west is dying and we should concentrate just on the top 5%. But I was drawn towards mathematics by people like Martin Gardner and would like to think that it should be open to as many people as possible and that people like Ian Stewart and Marcus du Sautoy should be praised for their efforts to help explain and enthuse the public about mathematics.
Can I draw readers’ attention to a couple of blog postings I made Dumbing Down and Dumbing Down 2 and the links in them? I want to encourage as wide a debate as possible on this topic and seek ideas on what to do about the problem.
20/11/2007 11:39 am
[...] to see the effect this is having on university mathematics courses even in the last few years A-Levels: Gah. However, A level mathematics and its equivalent has become steadily easier over at least the [...]
21/12/2007 12:02 pm
There’s an entry on Peter Hitchens’ blog about this issue. He quotes an article written by current Tory Education spokesman Michael Gove back in 2002: in that piece, Gove attacked Estelle Morris, the then Education Secretary, for trying to blame the QCA for this, when the QCA was merely acting on orders from her department! Gove’s article is here: http://www.timesonline.co.uk/tol/comment/columnists/michael_gove/article1171095.ece
However, as Hitchens points out, now that Gove is in the Shadow Cabinet, he is silent. The Tories aren’t going to help solve this problem, then. Actually, they’re the ones who started it!
25/4/2007 4:47 pm
Just for the record, Mathematics is clearly not alone. I recently graduated with a First Class degree in Computing from supposedly one of the best universities in the country for that subject. It was not difficult. I am not amazingly clever but the course was amazingly dumbed down. I looked at exam papers from only five years ago and they were much harder than the exams I sat. Some courses had had their syllabus cut in half over the last few years.
Lack of funding forces universities to take on foreign students who are not up to scratch (I sat through some tutorials with someone who didn’t even know what computer science was before he arrived in England) and to grant places to home students who have not been adequately prepared by A-levels (the ability to demand top-up fees is dependent on the university meeting certain discriminatory admissions criteria.)
As a result, when I sat through training for my new job at an American company, I was embarrassed by the vast chasm between the British and the American graduates. I wish I had gone to university in America.
27/2/2007 2:28 pm
How did it even come to pass that the onus falls on universities to correct the sub-standard education of new students? It should be the case that the syllabus is the syllabus, and if you want to do well then you make sure you are prepared for the course before it begins.
31/11/2007 11:56 am
Very good points from Charles and Sayo.
I completely agree that it should not be the place of universities to be teaching students stuff they should already have known. As far as I can tell, making the students learn the knowledge themselves isn’t going to help matters.
Apart from a small minority, most students will simply not be able to cope with the amount of knowledge that needs to be absorbed, and when it comes to exam time, they’ll simply fail or get much lower marks. Universities will then moderate the marks upwards, and we’ll be in the position where people are coming out with 2.1s or even 1sts who don’t know what the heck they’re talking about – this is probably an even worse position than we’re currently in.
22/2/2008 2:47 am
[...] to see the effect this is having on university mathematics courses even in the last few years A-Levels: Gah. However, A level mathematics and its equivalent has become steadily easier over at least the [...]
8/5/2008 5:40 pm
I have an ‘O’ Level maths book from 1977. Today this would be considered ‘A’ Level material. Indeed the material on Matrices, which involves a simple electrical circuit filter. I have studied on a BEng electrical eng degree course. Maths has been made easier to pass. On the first day of my degree course me all took a maths test which hasn’t changed for years. The average score has been dropping for every year. Its not the students fault. 50 % of students going to uni is a unrealistic target. It can’t be more than 25 % of the whole population capable of uni study. I have heard that its getting easier even to pass a Phd. If this carry’s on we will not have the universities that we should be proud off. Alot of students at uni now don’t deserve to be there and do not go for the learning expereience.
9/1/2008 1:48 pm
Neil,
Thanks for your comments. I couldn’t agree more with what you’ve said – 50% is wholly unrealistic. Further, I don’t believe that there should be any goal with the aim of getting x students to university. To do so simply devalues the degrees of people passing through and doesn’t help anybody in the long run, with the possible exception of the universities themselves. Some people will simply not need to go to university, and I think this is something that the government refuses to accept.
You need to couple this with the education system we have in place to supposedly prepare under 18′s for university. Unfortunately I think we’re at the stage where a lot of – or possibly too much – damage has been done. Having two teachers in my immediate family (one primary and another secondary), I know that they would just like some common sense to be used. Those going through primary education and now into secondary education are going to be seriously disadvantaged due to similarly stupid schemes and unnecessary paperwork for teachers brought in by the government.
Anyway, I’m glad you found this entry. I feel that I should write something else on this topic soon as it’s proven to be the most popular by far!
1/7/2008 7:58 pm
I have a problem with taking Neil’s comments seriously when he cannot use the English language correctly. It should be ‘it’s’ not ‘its’, ‘carries’ not ‘carry’s’ and ‘a lot’ not ‘alot’. Please don’t make judgements about others’ motivation for being at university (and whether or not they deserve to be there)in such a flippant and illiterate way!
2/3/2008 3:15 pm
Ange, whilst Neil’s comments were not grammatically correct, it is a clear ad hominem attack to disregard anything he says out of hand. As I made clear, I do believe that his opinion carries considerable merit.
I do agree that the comment about whether students deserve to be there or not was not appropriate. Clearly, students have to make their own mind up about studying at university and their motivation should not be questioned, nor should their right to be there. Whether or not their chosen course will benefit them and/or the country as a whole — in my view, the chances are that it won’t — is probably the point that Neil was trying to convey.
18/7/2009 7:25 pm
[...] to see the effect this is having on university mathematics courses even in the last few years A-Levels: Gah. However, A level mathematics and its equivalent has become steadily easier over at least the [...]