# What can we learn from last summer’s GCSE Maths exams?

From last year’s headline figures and the increasing grade boundaries it seems that most pupils are being prepared well for the new(ish) 9–1 Maths GCSE. A benefit of the course is that it provides welcome additional challenge for the most able pupils, preparing them better for future study. However, some teachers are concerned about how accessible the papers are for the less able or those who struggle with the comprehension aspect of questions. Here are some key areas to consider that will help prepare students for this year’s exams.

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Some of the topics that have been recently introduced at GCSE are quite challenging. Perhaps your pupils have got to grips well with many of these – such as finding expressions for the nth term of quadratic sequences and using iterative methods to solve equations – but still have problems with others. Topics that may be worth focusing on include

• algebraic proofs – pupils often struggle to ‘get started’ by giving a correct expression, e.g. for an even or odd number,
• interpreting the gradient as the instantaneous rate of change, so recognising the need to draw a tangent to a curve to estimate this,
• explaining what a gradient or area under a curve represents (they need to answer in the context of the question),
• composite functions – pupils don’t all understand the meaning of fg(a), sometimes thinking it means the same as f(a) × g(a).

Basic numeracy skills

Pupils often lose marks needlessly due to simple arithmetic errors. The new National Curriculum at primary school places a greater emphasis both on recall of multiplication and related division facts and on formal written methods. However, the pupils we’re currently preparing for GCSE obviously haven’t benefitted from this, so you may need to go back to basics and practise these key skills. Perhaps build regular lessons into your scheme of work or focus on numeracy skills at the start of each lesson. It’s worth encouraging pupils to use formal methods such as column multiplication as they do tend to make far fewer arithmetic errors with these methods.

Using calculators

Bizarrely I’m sure we all know pupils who still make simple arithmetic errors in calculator questions because they either can’t use, don’t use or perhaps don’t even have a calculator! A knock-on effect of this is that pupils can run out of time in calculator papers because they’ve been spending far too long on questions that could have been done quickly on a calculator. Now that a greater proportion of the total marks at GCSE are on calculator papers, perhaps we should be using them for a greater proportion of class time?

Losing ‘silly’ marks

With any Maths exam, some pupils will lose marks due to small slips such as rounding errors or mistakes with negative numbers. An easy win could be to remind pupils to always read the question again at the end to ensure

• they have used and given the correct units,
• their answer makes sense in the context of the question.

GCSE formulae T-shirts, designed by Jenny Walker

Remember that pupils also need to learn all the required formulae for the exam. The Head of Maths at my school had the super idea of having GCSE formulae T-shirts made for staff to wear in lessons with Year 11 pupils.

Problem solving

Finally, to access the top grades available in either tier, pupils need to be able to apply their knowledge to a range of contexts and to attempt more challenging, multi-stage problems. There’s potentially a lot we can learn here from the mastery approach to learning maths which is often used in primary schools. Pupils learn a topic thoroughly before moving on, including applying the skills learnt to a range of contexts and in combination with other areas of maths. Consider looking at your KS3 and KS4 curriculum to ensure it is geared up towards developing problem-solving skills with plenty of opportunities to apply knowledge and skills in every topic studied. This may reduce the number of pupils who are fazed by this type of questions and could improve the way they structure and explain their solutions.

Author bio

Katie Wood combines her part-time work as a Maths teacher in Surrey with authoring for Oxford University Press and marking exam papers for Edexcel. She also has two primary-age children and is a school governor.