Maths A-Level 2010

After reading a recent article in the press about Mathematics A-level in the UK compared with other countries, I decided to look again at the statistics for maths A-level as I had done in previous years (see previous discussion).

The number of Mathematics A-level candidates has certainly gone up for the last 5 years. The Guardian thinks that the number of Maths candidates is at all-time highs, but I disagree. My numbers (from the UK Mathematics Foundation report in 2005) are for England only, but show a larger number of maths candidates back in 1989. Hmm, so where did the Guardian get its numbers from ‒ ah, the TES quote Mathematics in Education and Industry (MEI) as saying that mathematics entrants are at an all time high since records began 20 years ago; I guess my "approximate" source goes back further than the records that TES and the Guardian are quoting from.

Maths as a percentage of A-levels taken has now passed back above the level of ~9% that it was at prior to the disasterous Curriculum 2000 changes that caused a sharp decline in entrants (see Making Mathematics Count 3.23, 3.26). In 2000 Mathematics was 9.8% of A-levels taken. The Guardian looks at the percentage of students taking maths, which it says is 14%, and says that that is still low compared to other countries, citing 85% of students in Japan taking Mathematics post-16. That has to be partly a mismatched comparison, since UK students specialise more so the 14% who do do maths are doing more of it than most of those 85% in Japan; and yet maths is a basic subject that underlies many other fields, so few people taking it at all post-16 is still a valid concern even if there are a minority who do more.

The pass rates for maths are interesting though. The percentage of candidates getting A or A-C grades jumped in 2002, when lots of students dropped out because of the Curriculum 2000 changes. Supposedly the changes made the first year (the AS level bit) too hard, discouraging weaker students, so that seemed to make sense: weaker students were giving up instead of persevering to get low grades, while the top students saw it through, so the number of students getting A and B grades fell very little. At the time, I worried that exam boards might be pressured to make the exams harder, since Maths had the appearance of giving a much higher rate of As than other subjects or Maths prior to 2002.

But it seems that Maths has the opposite problem: instead of making the exams or grading harder to get the A rate back to pre-2002 levels, the rate of As has continued to rise despite the number of students taking it reaching and suppassing the 2002 level. So both the percentage and number of students getting top grades at maths has climbed sharply over 10 years. For the last 2 years, around 45% of students taking maths in the UK have got A or A*. The only subjects with a higher A rate are the modern languages (and Further Maths). In 2002-4, when Maths had scared off weaker students, that made sense; but it is harder to justify now. Modern languages have an excuse for polarisation ‒ some students may have spent a lot of time in the country concerned or be bilingual ‒ but maths does not, that I can see, and has recent history from only 2001 showing a different distribution.

Indeed, from the JCQ A-level statistics I noticed that Maths & Further Maths have the highest rate of A* of all subjects, and one quarter of all the A* graded A-levels awarded in 2010 were for Maths and Further Maths.

Perhaps mathematics teaching and/or mathematics students have got that much better since 2001. It is hard to make a clear-cut case for that, though, when the largest jump in the pass rate was in 2002 and we know that was due to a serious worsening of the mathematics course (albeit not of students or teachers but of the assessment structure). Conversely, I suppose one could continue my argument from 2004 still and say that mathematics might be attracting more students, but perhaps the assessment structure is still causing the weaker students to drop out and not take the exam. We could call that an improvement in teaching efficiency. But since changes were made in 2003 to try and reduce the drop-out rate, is that a likely explanation?

There is certainly concern about whether mathematics has been made easier to attract back students after the Curriculum 2000 debacle:

Changes announced this week let students gain maths A-level with four AS and two of the harder A2 modules. All other A-levels require three AS and three A2 units. There will be two applied and four pure units.

TES 2003, presumably in direct reaction to the Curriculum 2000 problems.

[UK exam regulators] deny that the changes - first published last year - mean the qualification is being made easier.

BBC coverage of the same, 2003.

Alan Smithers, professor of education at Buckingham University, said the standard of A-level maths was “deliberately lowered” amid fears over a slump in entries after the introduction of new-style courses in 2000.
“The fact is that the content was adjusted in light of a dramatic fall in entries and, as a result, we have a much higher proportion of A grades being awarded. This is why we see people being offered Cambridge places on the basis of projected As who do not turn out to be good enough."

in 2006

Many teachers believed the changes have "dumbed down" the exam, an interim report by the Qualifications and Curriculum Authority (QCA) found.
Meanwhile others saw the reduction in content as a "positive move in terms of helping all students to succeed", the report said.

'Split' over A-level maths reform . I like the euphemism "helping all students to succeed" :-)

It is very difficult to judge whether or not exams are easier now, but it shows amazing ignorance to attribute the change in pass rate to the difficulty of the exam.… Now students take their AS mathematics exam at the end of the first year. If they fail, they cannot continue. If they pass AS, they have the ability to pass A-level. So unless there is an unexpected problem in the second year, the A-level pass rate should be very close to 100%.

Counter-opinion from a maths teacher. (But I would note that this does not seem to have caused 45% A rates in other subjects, which were also affected by Curriculum 2000 changes.)

Christine Blower, general secretary of the National Union of Teachers (NUT) said: 'For all those critics who can't bear the idea that the improvement in A-Level results is attributable to the hard work of young people and their teachers, they should have a look at the trend in improvement in the so called 'hard' subjects of mathematics and science.

Daily Mail, 2009 — well that's amusing in the context of worrying about mathematics being made easier.

Rosemary Bailey, professor of statistics at Queen Mary, University of London … described A-level maths as "like using a satnav" where the questions have become "orders: do this, do that", with "hints and instructions about which method to use".

Reform think-tank, 2010