The transition between GCSE and A-Level Mathematics is one of the largest jumps a school student can make. . There is no getting around it: A-Level Maths can be difficult! I am often called to tutor children who were flying at GCSE level with A or A* grades, only to start really struggling within months of starting an A-Level course. This guide is intended for anyone wanting to help support a student on an A-Level Mathematics course.
Content and exam format
The problem isn’t helped by the size of the learning curve at A-Level. The early modules like C1 and S1 (the first modules in pure mathematics and statistics, respectively) tend to start off with relatively straightforward and familiar content that quickly gets very difficult. For example, the first unit in S1 kicks off with “Representing Data”, where students are taught the use of statistical devices like histograms, stem-and-leaf diagrams and boxplots (I have taught some of these to able year 7 pupils in the past!). From this the traditional next step is a whistle-stop tour of probability, normally taking them up until Christmas or so using a standard A-Level progression, and again likely to be very familiar from previous work. Then, boom! Difficult topics with exciting names like “discrete random variables”, “binomial probability functions” and “bivariate data” follow in quick succession. Core/Pure mathematics follows much the same pattern, moving quickly from familiar concepts like graphs and co-ordinate geometry into new ideas like calculus.
This increase in difficulty is matched by the fairly brutal markscheme on A-Level papers. An A-grade requires 80%, whilst an E needs 40%; the other grades are staggered equally between these in steps of 10%. Papers for Edexcel, the most popular exam board for Mathematics A-Level, are typically marked out of 75, with 8 or so questions of somewhere between 7-10 marks available for each. Missing just one of these out is enough to drop a whole grade! To stand a chance of accessing the top grades, students really need to be understanding and answering every single question.
I am certainly not saying that students shouldn’t be challenged to this degree or recap on key concepts at the start of a course; just that they should be mentally prepared for the difficulty level of what is going to come next. In my experience working as a tutor, this is not always the case.
The differences between A level and GCSE
The key differences between A-Level and GCSE Mathematics are certainly not just about content. One of the most common things my students say to me is their confusion with all the new symbols and terminology. They are expected to look at something like Σ10+2r (r = 10, n =30), identify that they are meant to use the formula S = n/2(2a + (n-1)d) and quickly work out the answer is 987. Assuming this is a question worth 3 marks, they will have no more than a few minutes to do all this. Students are expected to be fully conversant in the meanings of equations and terms within them. Statements like “integrate y=2/√x , x > 0”, whilst short, contain a lot of implicit meaning that it will take both time and confidence to understand. Formula books are handed out in exams, but relying on these is like trying to write an essay in a French exam entirely from a dictionary.
I have tutored several students who were able to get top grades at GCSE by rote-learning solutions and correct methods, then bombed at A-Level as they couldn’t handle the increase in required conceptual understanding. As with anything, the best way to handle the new concepts is to keep track of them as they arise. I recommend the use of a mathematical dictionary, allowing students to look up terms as they go through the course, and perhaps even get students to compile their own list of key terms as they go along.
Study skills and practice
The best way to study any science is by doing, and so it is good to get students in the habit of practicing the use and application of Mathematics from day one. This doesn’t just mean questions from a text book; it extends to understanding the origin of key formulas, deriving one equation from another, making up your own problems, and the old chestnut of doing past papers. It is worth getting students to frankly assess their study skills at the START of any course, and look at how to improve these. On more than one occasion I’ve asked an A-Level student “how do you revise?”, only to be told “I never have”. It sounds obvious to an adult, but students often aren’t taught effective revision techniques by their school. Take some time to assess what they can do already and then augment this with other good practice. Don’t be surprised if this extends right down to concepts like keeping class notes in an organised, logical order!
When to use a tutor
There will be times when students struggle with the material at A-Level Maths. One way of overcoming this is bringing in a tutor to address specific content issues. A good tutor will quickly be able to spot barriers to progress, and with even a short amount of dedicated one-to-one time they will put practical steps in place to address these difficulties. Given the difficulty of the subject, you really want a subject specialist to do this, and so I would recommend looking at Adrian Beckett tutors (a specialist Maths tuition), or Owl Tutors (my own agency).
In a nutshell, I believe the most important success criteria for any student’s successful transition to A-Level Maths is a positive, “can-do” mindset. Mathematics (and certainly Further Mathematics) is probably the hardest A-Level choice. Apart from the junior Stephen Hawkings of the world, all students will struggle at times. By being ready for this, and by learning to recognise a difficulty as a positive obstacle to overcome, students will be in a much stronger position to deal with the challenges ahead.
So, in summation:
- Recognise the challenges ahead; foster a sense of healthy respect (not fear!)
- Get into good habits early. Keep all notes in a sensible place, start practicing and doing Maths from an early stage, and start thinking about how to revise from day one
- Keep on top of new concepts and definitions as they arise by using a Mathematical dictionary
- Encourage and develop positive ways of thinking from day one!
- Don’t be afraid to call in a tutor to address specific subject concerns