Say goodbye to a passive audience, and hello to pupils who give back as much as you put in. Open-ended, collaborative lessons rule for Caroline Besley

Bec Curtis starts each day with her Year 2 class with a maths puzzle. Her questions are deliberately open-ended: “The answer is 20, what could the question be?” or “How many sketches can you draw that have a rectangle in them?” Parents stay and work them out with their children.

Lorna Stokes, who teaches Years 5 and 6, also poses open maths problems. Rather than asking: “What’s the remainder when I divide 52 by five?”, she’ll say: “Working with your partner, you have one minute to find as many numbers as you can that have a remainder of two when you divide by five.” And when they start giving her answers, she might follow up with: “How do you know? Convince me.”

Until recently, these Bristol primary school teachers would not have asked their pupils maths questions that yielded more than one answer. Nor would they have involved other youngsters, let alone any other parents, in finding a solution.

But they knew they needed to make changes. They were fed up with hearing their own voices drifting over a sea of passive faces and were keen to make lessons more collaborative and stimulating. While they were skilled at teaching standard numeracy strategy lessons, they were unsure how to vary this structure and develop lessons that promoted a “using and applying” approach.

So, in collaboration with another headteacher, I devised a programme of support using a number of demonstration lessons, which I’ve tried out in three primary schools in Bristol.

They were certainly not model lessons. Thirty pupils exploring many 3D shapes at the same time was probably asking for trouble. But seeing Year 5 children engrossed in dividing up different amounts of raw pasta shells and so understanding why a remainder can be expressed as a fraction was fantastic.

After each session, we reviewed the lesson. Some common themes soon emerged: those who made the most significant contributions were not the ones who usually contributed to maths lessons, and there were greater opportunities for dialogue between pupils. Above all, youngsters gradually became less reliant on the teacher and on finding the “right” answer.

Our work was not about making massive changes. We simply changed the emphasis of lessons so that they were underpinned by the talking and thinking that using applied maths demands

Caroline Besley is a part-time teacher at Parkwall Primary School in Bristol. She also teaches at the City Academy in Bristol and is an affiliated field tutor with Bath Spa University.

Find your answers

Some useful books for teachers who want to delve deeper into the teaching and learning of mathematics are:

- Maths to Think About by Noel Graham and Richard Trim (Claire Publications)

- The Really Useful Maths Book by Tony Brown and Henry Liebling (Routledge).