4 October 2014

Bridging the Gap to A Level

At 7pm on Tuesday 7th October I'm hosting a Twitter chat on the topic of bridging the gap from GCSE to AS level. Please join in using #mathscpdchat. If you haven't participated in a Twitter chat before, this guide explains what it's all about. I recommend you set up TweetDeck in advance so you can keep track of the conversation.

In preparation for this chat, this post outlines some of the issues that I want to discuss. First I'll look at why there's a gap, then I'll look at some possible strategies for bridging it. I'm really keen to hear others' ideas on Tuesday.

1. Why is there a gap?
A. The problem with GCSE grades
Most schools require that students get a grade B at GCSE to do maths at A level. This year your AS level classes will contain a mix of students who got anything from 48% to 100% in their maths GCSE. This lower bound might surprise you. Yes, students can get less than half of the answers right and still get a B. That means a student can embark on A level maths with absolutely no understanding of algebra, or no idea how to add two fractions without a calculator.

Students are often 'taught to the test' so have little conceptual understanding - they can get a decent GCSE grade by learning some tricks and doing lots of practice questions. Around 15% of students who achieve a B in their maths GCSE go onto to take maths at A level. The graph below, taken from this 2012 report, shows that of those students who got a B in their GCSE, only 20% achieved A* - B at A level. The majority got a grade D, E or U. Were those students given the wrong advice about their post-16 options? And why did they not drop maths at the end of Year 12? Bear in mind that having got a B at GCSE, they would have expected to achieve at least a B at A level, so these students may have been bitterly disappointed with their results.
Maths GCSE also doesn't do enough to differentiate at the top end. Around 5% of students nationally get an A* at GCSE. These students range from those who are incredibly intelligent to those who were well-taught and hard-working. This will change - the new 'A**' grade (Grade 9) will be awarded to the top 3%. When the new grades come into play from 2017 onwards, I hope to see schools setting a minimum requirement of Grade 7 to do maths at AS level (Grades 7, 8 or 9 will be equivalent to today's A* and A). Am I being elitist? The new core maths qualification will be suitable for others.

The problem is that GCSE grades currently do not give us a clear indication of who is suitable for A level maths and who isn't. I've taught many students who got an A or A* at GCSE but went on to get a D, E or even a U at AS level. Why did they suddenly stop being 'really good' at maths?

Last year I introduced an entrance test in Year 12 - more on this here. It revealed shocking gaps in basic skills and knowledge. Students who got an A* at GCSE could not do long multiplication! I recommend that all schools do an entrance test for two reasons:
1. To identify weaker students and intervene with extra support from the start.
2. To manage expectations - students who got a good grade at GCSE will be surprised if they get a low mark in a basic skills test. They'll realise that they can't coast through the course and will be motivated to work hard.

Is there a case for setting at A level? I know some schools that give a maths test at the beginning of Year 12 and then put students into sets.

B. The problem with GCSE content
I did some analysis of the marks available on last year's higher Edexcel GCSE papers. This is what I found:
  • Approximately 40% of the questions tested skills that are absolutely essential for AS core maths eg fractions, algebra, arithmetic, Pythagoras
  • Approximately 35% of the questions tested core maths skills that are taught again at AS level eg surds, indices, trigonometry, simultaneous equations, inequalities, quadratics and coordinate geometry. 
  • Approximately 25% of the questions tested applied topics (eg statistics) or topics that don't come up at A level (eg loci, transformations).
A student can easily get a grade B with very few core skills.

I wonder if schools that have embedded a mastery curriculum from a young age have managed to eliminate the problem of Year 11 students lacking core skills.

Upcoming reforms will help to address the current problems with GCSEs. Until they are implemented, what can we do with our Year 11s to better prepare them for A level?

There are extra qualifications to consider - the Certificate in Further Maths has some great content like matrices and functions. Additional Mathematics is a challenging course, particularly suitable for students looking to take Further Maths at A level. Regardless of whether your top students are taking these extra qualifications, do you look at interesting, non-curricular mathematics with them in Year 11?

At A level, students often struggle with the change in the way questions are worded. Perhaps we should start looking at these kinds of questions earlier. For example, the question below is from a C1 paper but would be suitable for a GCSE student.
C1 Edexcel May 2013
2. Strategies for bridging the gap
So let's just accept our current predicament - students commence their A level maths course totally unprepared. What can we do to support them? Here's a few ideas and questions.

A. Bridging resources
On A level induction day (at the end of Year 11), many schools give their incoming Year 12s summer work to do. They also recommend resources that students can use over summer to fill in any knowledge gaps - here are a few examples:
In my experience, urging students to do work during the summer preceding Year 12 isn't particularly effective because students just don't see the necessity. I've considered running a 'summer bridge' or transition course in the week before term starts. I'd be interested to hear from teachers who do this.

B. Intervention
At my school we run compulsory remedial sessions in the Autumn term for students who don't do well in their entrance test. We also offer an optional weekly Help Club to all students all year round. When I was Key Stage 5 Coordinator I offered additional support through a student blog. What does your school do to support students who are struggling?

C. Course structure
Does your school offer students flexibility over modules? Which applied modules work best? We find that M1 is too difficult for many of our Year 12s (except those taking Physics) so is best tackled in Year 13. The planned changes to A level maths will standardise the course, removing the element of choice.

How many hours a week should students spend in lessons and doing homework? When my A level teaching hours were cut from 4.5 to 4 hours a week due to budgetary constraints, my students suffered.

How big are your classes? At my school we currently have 18 - 20 students per A level class. I've heard of schools with even bigger classes. At A level I think 10 - 12 students per class is far more effective.

D. Delivery
How do you organise the delivery of the course content? Do sixth form classes have more than one teacher? What order do you tackle the modules in?

At the beginning of Year 12, how much time do you spend re-teaching GCSE topics such as algebra, surds, indices and quadratics?

Do you have any particular strategies for teaching A level lessons? Any particular resources?

E. Effort
How do you encourage students to work hard? Do they do as much practice as they need to? At my school we set out our expectations and outline the support available in a student handbook.

My students are given Alps estimates as targets to work towards, but these are based purely on GCSE grades and in my opinion (partly for reasons outlined above), they are meaningless without teacher input.
Target setting (source: FFT)
I've made an infographic to summarise my thoughts and questions about the path to A level. On Tuesday I want to focus on two key questions:

1. What structures should we have in place at Key Stage 4 to help our students prepare for A level?
2. What support can we offer during Year 12 to ensure students hit the ground running and don't fall behind?

I look forward to hearing your ideas. If you can't participate in Tuesday's chat then please share your ideas in the comments section below.


Update: 6/10/14
All four posts contain lots of good ideas and insightful reflections.

Thanks also to @paulsuvs for pointing me in the direction of these National Transition Matrices which provide interesting information about the grades achieved at AS level. 


  1. Here is a summary of the Twitter chat: https://www.ncetm.org.uk/resources/45796

  2. Another useful analysis of results here: http://www.cambridgeassessment.org.uk/Images/153531-progression-from-gcse-to-as-and-a-level-2010-.pdf

  3. Thanks for posting this information.

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