# Practice makes perfect!

Thursday 30th June 2022

It's said that is the only way to get to Carnegie Hall is to practise, practise, practise! And the only way to get good at maths is to keep practising the skills. I remember spending hours at secondary school practising calculations with fractions and it stood me in good stead when it came to algebraic fractions later in my school career. But it was very dull… and nowadays calculators can do these sums!

These days, we have a range of ideas for encouraging our students at every level to put in the time and effort to hone their skills. What could have been a long exercise from a textbook or worksheet can now be presented as a quiz, a card sort, a set of dominoes, or a Desmos classroom activity. If you’ve not tried Desmos Classroom, the AMSP have an On Demand Professional Development (ODPD) course titled Desmos in the Maths Classroom that you may find helpful as a starting point.

Alternatively, we can embed the routine practice into an activity involving higher-thinking skills. For example, ask your students to investigate the answers to $$\frac{1}{2}-\frac{1}{3}$$ and $$\frac{1}{3}-\frac{1}{4}$$ and $$\frac{1}{4}-\frac{1}{5}$$ and so on. They get the practice with common denominators, but then have the opportunity to spot patterns; to explain their thinking; to make predictions and check; and to generalise and express their findings algebraically, if they're ready for that.

There’s always the wonderful question “What if…?” What if we looked into $$\frac{1}{2}-\frac{1}{4}$$ and $$\frac{1}{3}-\frac{1}{5}$$ and $$\frac{1}{4}-\frac{1}{6}$$ and so on instead? Is there still a pattern? How far can you generalise? What if the numerators aren't equal to 1? Doesn’t that sound more exciting than a boring old worksheet? And, with practice, these ways of thinking become accessible to more and more of our students.

This embedding of higher-thinking skills into our teaching could become a habit, but it's not always easy to think of ideas. The AMSP run a range of professional development courses for teachers, and one of them looks specifically at Higher GCSE topics through mathematical thinking. You can view our other professional development opportunities for GCSE Mathematics teachers on the AMSP website. We also run professional development for teachers of A level Mathematics, A level Further Mathematics, and Core Maths.

The remainder of the summer term may offer an opportunity to invest in yourself and your skills – there’s loads of help available from the AMSP. Why not give it a go?