# Mathematics Weblog

## A Levels

Monday 20 August 2007 at 11:38 am | In Articles | 12 CommentsLast Thursday the A level results were announced and there were the usual recycled comments with some people attacking and others defending the system. There appears to be three main arguments used:

- A levels are getting easier;
- Teachers are getting better at preparing students for the exams;
- Students work very hard and so it is insulting to them to say the exams are getting easier.

So let’s examine these arguments for A level maths, which is the subject I know about. Unlike some pundits I don’t wish to pontificate about subjects I am not familiar with. My main point is that the arguments above are *not* contradictory and it is quite possible for exams to be easier than in previous years *and* for students to find them hard.

- It is generally acknowledged in the mathematical community that A level maths exams are getting easier and it has been remarked on by a government advisor A-levels are easier says adviser. Yet this headline is misleading because it is only referring to maths and physics which shows just how difficult it is to have a rational argument about the standard of A levels.

It is interesting 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 last hundred years as the subject has been ‘democratised’ and taught to a wider population. I am very much in favour of this but the cost has been the dumbing down of the syllabus as I have mentioned before. I can only repeat my question that*Is it possible to teach mathematics to a larger range of students without compromising on the level taught?* - This is true but nothing to be proud about. Teachers and schools are under extraordinary pressure to get good results. Hence they teach very much to the exams, test and retest, and have no time to explore interesting parts of mathematics which would help to motivate and put things into context.

How politicians can imply that this is good beats me. - Mathematics, as those of us who taught it know, is hard. This has been recognised (finally) by recent research, and it has been proposed that, as happens in Australia, more UCAS points are awarded for harder subjects like maths, though I can’t see that it will happen here.

Also mathematics is essentially linear so unless students are adequately prepared at one stage they will find it very difficult to proceed to the next stage. With dumbing down going right back to the early years of education most students will find each stage hard no matter what the level. The ignorance of this caused disaster in 2000 when A level maths was temporarily made tougher and so the gap from GCSE was unbridgeable for many students, leading to lots of failures, the abandonment of the subject by many and the restoration of an easier system.

Finally, with a greater percentage of the student population studying mathematics many of them are bound to find the subject hard.

It is good that Further Mathematics is becoming more popular and is to be encouraged, though it should be noticed that it too is a pale reflection of when it was last popular.

I don’t have easy answers to the problems of mathematical education but wish to see an *informed* debate on it. I just hope that Alexander Borovik is not correct when he writes

The current crisis in mathematics teaching is a dawn of a much more serious crisis of transition from the mass mathematics education of the past to a more selective and elitist education of increasingly small, in relative terms, numbers of mathematicians.

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Very interesting reading. Boy I really agree with all of that.

I am trying again to qualify as a maths teacher. I am fine as a tutor, and only seem to lack the ability to “tick the boxes” appropriately. Tomorrow I will get the results of the small group of girls I taught GCSE (private school). by the way do you know of any source of silly maths stories/anecdotes maths related. my kids always enjoy them and I know only a few (e.g. the BIG NASA error not converting to cm, and the clever way Euler could add up 100 numbers, and the very very peculiar Pythagorean sect.)

Comment by zzina — Wednesday 22 August 2007 12:26 pm #

Jokes always go down well and the best source of mathematical humour is Comic Sections. Sadly it is out of print but if you look at the end of the posting Comic Sections you may still be able to obtain a copy from the author. There are more jokes from the book here.

In Mathematical Circles: A Selection of Mathematical Stories and Anecdotes looks interesting but I haven’t read it.

Do readers have suggestions of websites or books on light-hearted mathematics which would inspire students?

Comment by Steve — Wednesday 22 August 2007 1:02 pm #

zzina is probably thinking of the story

about *gauss* (not euler) being told

in elementary school to sum the natural numbers

from 1 to 100 … look at this page

for over a hundred (!) versions of this story.

Comment by vlorbik — Wednesday 22 August 2007 8:46 pm #

Thanks for all the interesting stuff. I am now tracking e-bay for cheap books. I have also e-mailed Prof Des MacHale at Cork.

My “know-all” mentor from my first school told me the story about Gauss – he told me it was Euler.

I have followed some of the links and now I find that the pocket book “Mind-Bending Lateral Thinking Puzzles” I bought from ASDA has some input by Des MacHale & Paul Sloane. It is well liked by my students. I do have some cartoons and diversions like learning to draw the “impossible” trident etc.

Comment by zzina — Sunday 26 August 2007 10:35 pm #

Here’s the problem from the perspective of a student. Teachers are competing with a variety of issues and jobs that students have the opportunity to achieve nowadays. Let me clarify. Many students are disinterested with the schooling route with the quick rich schemes of many Americans. I dont think many are willing to put in the time and effort. So teachers have to come up with clever ways to keep students interest in and out of the classrooms. One of my professors actually made it mandatory that we pull his lesson plans off his website, The Cyber Professor if we dont come to class that way he can interupt our normal web browsing. Although its not a long distance online enviornment, it’s easy to access, it shows me our teacher relates to new ways of thinking and its easier. This wouldnt work for all teachers, but I would like to see teachers come up with news of getting their lesson plan across. Difficult, I know and I feel for all of you out there! Keep up the good work.

Comment by Ernest — Sunday 2 December 2007 4:03 am #

sorry! The teacher’s website looks more like this!!! The Cyber Professor I also found some viral media streams that teachers are adding to teach their students over sites like youtube. Kinda entertaining, but I dont know how effective that is.

Comment by Ernest — Sunday 2 December 2007 4:18 am #

I live in Japan, a country where pretty much everybody goes to university. Therefore, instead of A-levels, the focus for teachers is to help their students learn enough to pass university entrance exams which vary in difficulty depending on the university. My point is, students are accepted into a university based on the requirements of that university, not some arbitrary pass-mark decided by the government.

There are, of course, problems with this, too. Since, students all take different tests, it’s impossible for teachers to cover every possible question posed by the hundreds of different universities. So what happens is that the students study all day, then go to specialized “cram” schools every evening to study specifically for the entrance exams of their desired university. And these cram schools are hugely profitable! 🙂

Comment by Nick Ramsay — Thursday 10 April 2008 9:36 am #

lol I don’t care if it is getting easier lol, I just want to get my degree

Comment by www.algebrasolver.totalh.com — Monday 26 May 2008 4:46 am #

hi. I programmed an online gcd calculator that calculate greatest common divisor between two integers in 4 methodes! (euclidean,rootfinding,recursive,scalar).

I will be happy if see my link in your site.

thank you

bye

Comment by mohammadrdeh — Wednesday 2 July 2008 7:02 pm #

I agree with the article. I’m getting a degree to be a Math teacher, but when I mention it to others they shy away or anounce their distast for the subject.

Comment by Tara — Wednesday 5 November 2008 3:41 am #

Hi I’m from Czech Republic. I went to UK to study AS-levels and I was very very displeased with the level and the way how the math was taught there. Just pass the exam, no I wanted to learn some math. Unfortuneatly I knew all the stuff already from czech, ok my problem, but I was basicly discouraged to do some extra study. When I asked for something extra I was told that I don’t need that for the exam. And I have to say that further math was the same we just learned more “usless” stuff than in normal math but the way It was taught was the same. Please do something with A levels.

Comment by Tomas — Monday 7 September 2009 6:15 pm #

As a parent of younger children (pre-teen), I see them forming opinions of math. A lot of these opinions seem to be based upon how well they (think they) are doing, and how relevant math is to them in lives.

As with many skills, you have to know the basics before it becomes fun. Just think of learning the piano. That takes time before you can actually “play” and for it to be really fun.

We have to help kids at the early stages to get the basics of math down pat, otherwise higher maths will forever only be reachable by a minority.

Comment by Math Game Review — Thursday 25 February 2010 11:51 am #