3 Things I Learned as a GCSE Maths Examiner That Every Parent Should Know

Matthew is a qualified Teacher and GCSE Maths specialist whose experience spans across 10 years and includes multiple leadership and teaching roles, including Maths Teacher, Assistant Vice Principal, Head of Sixth Form and Lead Teacher.

What Marking Thousands of GCSE Maths Papers Taught Me About Student Mistakes

By Matthew | GCSE Maths Specialist | Sherpa Tutor

This year I worked as a GCSE Maths (Higher Tier) examiner, marking thousands of student responses. It gave me a fascinating insight into the mistakes students repeatedly make - even for those who know the maths.

I love teaching. One of the things I get most pleasure from in the classroom is accurately predicting where students may struggle and using my planning to create strategies to help. 

This is ironic - when I started teaching, I could never predict where or how students would struggle. I felt this was some sort of teaching superpower I just did not possess. 

I watched others teach, spoke to them about upcoming topics, and was amazed by the accuracy with which they could predict the exact point in a lesson that students would struggle. For example, whether to add or subtract when carrying out Pythagoras' theorem, or opting to divide by the number of rows when finding the mean from a table.

For a few years, I genuinely thought my teaching practice would always be limited by my lack of all-powerful foresight - but then I realised it was just a case of experience. The more you teach, the more you see that many students are united by common mistakes that are the same in classrooms across the world.

Then, after 10 years of teaching, I thought I had mastered the ability to predict mistakes and how to combat them...until I marked the GCSE paper this year!

Working as a GCSE examiner was brilliant - the experience and insight gained from marking thousands of responses was invaluable. This post highlights three of the key takeaways I took from the experience, and what you can do as a teacher or parent to ensure the young people you support can be successful in next year's exam.

1. Memorise Key Formulae

The debate between learning and memorising material in education is one which has raged for years. But ultimately, some of the current GCSE maths formulae just need to be remembered - as many are not given on the formula sheet.

If you start a question on density or proportion by using the wrong formula, you stand very little chance of getting any marks. So make sure you mix up revision time between knowledge recall and knowledge application.

There is plenty of evidence to support quizzing and recall, so I would suggest getting all the GCSE formulae down on flashcards and practising saying them aloud and writing them down as a key part of your revision.

2. Practise Written Explanations

A significant number of students struggled on questions that required them to provide reasoning in written form.

Examples of this type of question include comparing the distributions of data sets (often using cumulative frequency and box plots) or explaining why, when working with grouped frequency tables, we can only estimate the mean. Many students clearly knew the maths but could not explain it clearly enough to gain full marks.

Like most things, practice is key to improving student responses for this type of question. Do not accept verbal responses or keywords when practising. Insist on full written answers. This would be a great time to look over mark schemes too, so students can explicitly see the sort of responses they need to gain full marks.

3. Explicitly State Working Steps

Many of the marks in GCSE maths exams are awarded for 'process'. This is often misunderstood by students as being marks for simply writing 'lots of working out'. These two things are different.

Students are not awarded marks for any old working out, but process marks enable them to attain marks for carrying out the correct step, even if they make a calculation error in it. This is best explained in an example - see below.

This is a two-mark question requiring students to solve a two-step equation.

In both responses, the students attempted to multiply both sides of the equation by 4 as step one. The purple response has not made this step explicit, while the red response has (see the x4 in circles).

Both students then go on to make a calculation error: 12 x 4 = 48, not 44.

The red response picks up the process mark, but the purple does not. The second mark is for an accurate answer - neither student scores this mark, as their answers are incorrect.

Despite the students doing the same thing, one scores a mark while the other does not. Across three papers and 240 marks, every mark matters and could mean the difference between grades!

What does this mean when supporting young people? Do not just talk about working out - talk about making our steps explicit. The examiner should be certain which step is being taken at every stage.

Small Habits, Big Gains

None of these suggestions require students to spend hours doing extra maths. Instead, they encourage students to revise more effectively.

Small habits - such as learning key formulae, practising written explanations, and making each step of their working explicit - can make a real difference when every mark counts.

If you want to ask any questions or find out more - drop me a line via my profile.