UPDATE 16/11/17: After I wrote this post I was contacted by Steve McCormack from the NCETM to discuss the issue directly with Charlie Stripp on the first NCETM podcast. You can listen to the discussion (30 mns), also with the NCETM’s Carol Knights and Secondary maths teacher Rob Beckett, here.

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The new GCSE in mathematics is considerably harder than the old one which has resulted, not at all surprisingly, in very low grade boundaries. For the Edexcel Higher paper in Summer 2017 a score of 79% across three papers earned the highest possible grade, a Grade 9, and this grade was achieved by around 3.5% of the population across all exam boards.

The changes to A levels in England, with no more modular exams, terminal papers at the end of two years, and difficulty increased just like at GCSE, have resulted in most schools and colleges insisting students take only three subjects. Where previously a student would study four in Year 12 and “drop” one at the end of the year to continue with three into Year 13, now it is imperative that students are on the correct course from the beginning. There is no halfway house where they can bin off their worst subject, there are no modules to resit and up their final grade. Get it wrong and two years of study can end with little to show for it.

Charlie Stripp, Director of the NCETM (for those who may not know, this is the National Centre for Excellence in the Teaching of Mathematics, funded by the government to support maths teaching), has written his latest blogpost on A Level Maths and Further Maths. In it he talks about the positive trends in both qualifications over the last decade or so and his idea for ensuring those trends continue. The first set of graphs on the post shows us how uptake of both qualifications has increased considerably since 2003, the kind of graph that makes a maths teacher happy (although, let’s face it, every graph makes a maths teacher happy)^{[1]}.

Then Mr Stripp argues his case for accepting students with a Grade 5 in the new GCSE onto A Level courses:

A long-standing frustration for me in trying to increase participation in AS/A level Maths and Further Maths has been schools and colleges choosing to impose high ‘entry requirements’ for students to embark on these courses. I believe that a student with a strong pass (grade 5 or above) on the new GCSE Maths should be entitled to the opportunity to study AS/A level Maths. The Smith Review includes the stark statistic that, in 2015/16, 92% of students who entered A level Maths had achieved an A or A* grade in GCSE Maths, whereas just 53% of students entering English Literature A level achieved an A or A* in English at GCSE. This is caused mainly by large numbers of schools and colleges imposing high GCSE Maths grade ‘entry requirements’ for students to embark on AS/A level Maths courses, and I believe it is very damaging. There will also be a ‘self-selection’ effect, but if schools and colleges aren’t encouraging students with B grades or equivalent to choose AS/A level Maths, they will be influencing students’ self-selection too.

I’m afraid I am one of those frustrating Mr Stripp (sorry!), but this is not without serious thought and consideration. I am a huge proponent of creating opportunities for students and increasing participation in maths makes me very happy, but lowering the entrance requirements is not the right way to do it.

The post tells us that the results data from A Level Maths are negatively skewed, pointing out that a higher proportion of students last year got A*-A in Maths than did in English or Physics (42.3%, 24.3% and 29.2% respectively) and attributing this to the difference in the proportion of students taking these A levels with A*-A at GCSE (92% for Mathematics vs. 53% for English Lit, nothing mentioned for Physics, I may check sometime).

Forgive me more quoting, but I need to do so to illustrate my point. Mr Stripp then shows us the graphs below, which show data from 2010. The first shows the proportion of students achieving each GCSE grade from A*-C who went on to get each A Level grade from A*-U. The second shows the same data from English in the same year.

We all know that statistics are interpretable, and our point of view will inevitably affect that interpretation. Part of Mr Stripp’s job is and has been to try to increase participation in A level maths, so he understandably looks at these graphs, along with the facts that in the same year 44.8% of students achieved A*-A in maths against 23.1% in English, and sees that “[those] with lower GCSE Maths grades can succeed at A level Maths.”

I look at the same data from the point of view of a teacher, working in the wider context of a school where it is paramount (for the students academically, and for the school financially) to get students on the right course, one they won’t fail or drop out of. Looking at the GCSE grade B and C students on these graphs I notice that 5% of each get A*-A in Maths and 5% and 1% get the same in English. At the lower end, however, 6% and 12% get a U in Maths and only 1% and 2% get the same in English. This suggests that a low GCSE grade has a worse effect in A level Maths than it does in English. If we factor in E grades as well as Us, the effect is even more stark. Grade B and C students got 26% and 36% E-U grades in Maths compared with 6% and 20% in English. Is a student with a lower GCSE grade going to struggle in maths? It would certainly seem so. (This data is also misleading since we do not know how many more students started the A Level course but dropped it after AS in Year 12, which we all know from experience is more likely to happen with those with lower entry grades).

Mr Stripp also said that, “a grade D or E in AS/A level Maths can represent success for many students, opening opportunities for further study.” This is interesting. I had a quick look on UCAS and really struggled to find a degree that states mathematics as a prerequisite that wanted less than a C. They may be there, but there aren’t many. It would seem that most courses that want you to have A Level Maths want you to actually have done quite well in it. There are probably other “mathsy” post-Sixth Form options (an apprenticeship in accountancy for instance), but how many of these would actually require A Level in maths over any other A Level, or even a decent GCSE grade? This I can’t answer, I would like to know.

From where I am standing, if a student is going to get a D or an E in A Level Maths and is capable of getting a better grade in a different subject, then that other subject would be, in most cases, better for that student.

Since the most recent data Mr Stripp could find was from 2010 I decided to take a look at 2011-2017 from my own school, and the wonderfully pragmatic and highly experienced Adam Creen contributed data from his school too (thank you, Adam!) I have a sample size of 387 students across the seven years. Both schools allowed students to take A level Maths with A*-B at GCSE, although many students with a B never chose it in the first place. Here is the result distribution, in a lovely Sankey diagram:

We would always allow B-grade students on the course if they opted for it, but those with a B generally struggled, their background and knowledge from GCSE was often simply not strong enough. We offered interventions throughout both years, put on extra sessions at lunch time and after school and, even with these, most B-grade students still didn’t get more than a C. Of those who dropped Maths at the end of Year 12, most were students with lower prior attainment – these results are from those who stuck the full two years.

According to my data, 28% of B-grade GCSE students got a U at A Level, 53% got E-U and 75% D-U at A Level. Of all those who got a D-U at A Level, 58% were B grade students at GCSE.

So when Mr Stripp says that students with a Grade 5 on the new GCSE should be allowed to study A Level Maths, I’m afraid I balk. We are told that students with a “strong pass” (DfE official phrase for a Grade 5) now have a more rigorous mathematical background due to the increase in difficulty of the new GCSE.

On the Edexcel Higher paper in 2017, a student with just over 28% got a Grade 5. Twenty-eight percent!

That shows me someone who either really didn’t understand most of what they were taught, or someone who was only taught enough content to access about a third of the exam. That is not someone with a “rigorous mathematical background”. The issue is compounded by the fact that students can get a Grade 5 on the Foundation paper, which means they will never even have *seen* a huge number of topics that most of us would consider prerequisite to A Level study. Outliers aside, these students would have the most humongous uphill battle to access A Level Maths.

At my school we will accept students with a Grade 6, but I fully expect to have to give them a huge amount of extra support in order to succeed. We won’t accept students with a Grade 5. That would be massaging the figures of A Level Maths uptake at the expense of getting students on the right course. When their next two years and, by extrapolation, a big part of their future depends on the course choices they make then I would be doing them a disservice by allowing them onto a course which they would, in almost all probability, completely or very nearly fail.

I understand Mr Stripp’s sentiments, but I think they are setting students up to fail, and that is not fair. What we need to do is get it right earlier on, so that more students finish GCSE with better mathematical knowledge, but that is a whole other issue.

^{[1]} These graphs should come with a note: the raw numbers of entries have increased but since 2010 the *proportion* of the entire A Level cohort taking Maths has remained pretty consistent (see the Maths and Science tables here). Raw numbers have increased since the overall number of A level students has increased.

UPDATE 16/11/17: Following the podcast with Charlie Stripp, we were curious about the difference between the DfE data I mention above and the JCQ data he presented. Some lovely people at MEI have looked into it and it seems that the JCQ data counts how many candidates in a given sitting got a qualification, where the DfE data counts only those in State schools and Sixth Forms. Stella Dudzic (MEI) wrote this:

*Firstly, if the graphs of numbers are restricted to 2010 onwards (to match the SFR range of data) then the increase in numbers does not look as dramatic.*

*Secondly, plotting the SFR percentage of candidates with A level maths and FM gives the following graphs (using final figures rather than provisional for 2015/16):*

*This raises the question of what happened between 2014/15 and 2015/16? The footnotes in the DfE SFR explain this:*

*4. Figures for 2015/16 onwards cover students at the of advanced level study who were entered for at least one A/AS level, applied single A/AS level, applied double A/AS level or combined A/AS level during their 16-18 study. As a result there has been a large increase in the number of A level students since 2016 and therefore figures are not directly comparable to earlier years.*

*So it’s not right to join the graph between 2014/15 and 2015/16 because the number of students is being counted differently (which accounts for the drop in the percentage). Once you erase that line segment from the graph you see that the percentages for both maths and FM are going up.*

*The JCQ and DfE statistics count different things but sticking to one set of statistics (for comparability year on year) should show the same trend. JCQ data counts how many candidates in a given sitting got a qualification. DfE data counts how many students coming out of school sixth forms and colleges have a qualification (I think it does not include private candidates which is one reason why the figures with maths are smaller than the JCQ England figures)*.