# Help your students improve their problem-solving skills to master A-level maths

Many maths students come to A level with good GCSE grades and a good work ethic and yet they do surprisingly poorly in their maths A level exams. Why is this and how can we help these students to succeed?

A level maths exam questions are not just straightforward application of the knowledge learned during the course, there is an element of problem-solving or 'figuring out what the examiner wants'.

Students typically practise questions which focus on one isolated skill at a time, for example differentiating curves. There is a good reason for this since students need lots of practice to become fluent in techniques.

However, fluency in isolated skills is not sufficient unless you can combine those techniques and choose the appropriate technique for any particular problem.

I don't believe our students get enough practice selecting techniques and applying them to longer problems like those they will face in their exams.

For example, many students know how to differentiate and know how to find the equation of a line and yet, faced with a question asking them to find the equation of a tangent at a given point on a curve, they freeze as they do not know which maths they are being asked to apply. Knowing how to choose and apply techniques in different situations is just as important a skill for a mathematician as differentiating.

Since choosing and applying techniques is such an important skill, our students need to practise it like they practise other mathematical skills.

How do they do that? Past papers are a great resource for students to practise deciding which skills to apply.

To save time (and fit more practise papers in) students should read through questions, decide which techniques they will need to apply and skip the actual calculations.

This makes a great pair exercise where students read a question together then take turns being A and B. A will say which techniques they would use to solve the question and B has the job of asking A questions until B is confident that they would have no trouble solving the problem using A's method. For example, an exchange might go like this:

Question: Given the curve C with equation y = x^{3} + 2x -5 and the point P=(1,2) find the equation of the tangent to C at P.

A: I would use the curve to find the gradient at P and then use the gradient to find the equation of the tangent.

B: How would you find the gradient?

A: By differentiating.

B: Ah ok. How would you use that to find the equation of the line?

A: Using (y – 2) = m (x – 1) where (1,2) is P which is a point on the tangent and m is the gradient I found by differentiating.

Working together in this way, pairs of students get through an exam paper quickly and while the learning objective for this lesson is to practise choosing and applying A level techniques to exam style problems they are of course revising all the topics on that exam paper at the same time.

I have found this to be a really effective way to translate all that hard work honing techniques earlier in the year into high marks in the exam.

*Anna Granta is on a break from teaching and tutors maths at KS3,4&5 in Cambridge.*