Teaching children to think, not just calculate

By Darran Kettle, Head of Mathematics at Bedales Prep

You may already be familiar with White Rose Education from your children's homework. The teacher-led organisation provides maths and science resources, training and digital tools for schools, students and parents, and is used by about 85% of primary schools in the UK. What you might not know is that Bedales Prep is a White Rose Champion School In September, White Rose published a blog I had written about the role of assessment in teaching, and the importance of using it as a tool for improving learning, not just measuring outcomes. It got me thinking about what makes maths teaching effective at Bedales Prep, and why building confidence is just as important as getting the right answer.

I was a maths ‘failure’

The first thing you should know? My own maths teacher told me I would fail GCSE Mathematics.

Fortunately, this didn’t put me off. Instead, I went to the library, took out every book I could find on maths and decided to teach myself. That’s when I fell in love with the subject.

I don’t want my students to have a maths teacher like the one I had. But the experience did at least give me an in depth understanding of why students can struggle and the fundamental importance of confidence.

Here at Bedales Prep, we develop confidence in a very intentional way. For example, we plan for consistency. Students know what’s going to happen because we always structure lessons in the same way. We begin with a starter, such as times-table practice or going over questions from previous lessons. Only then do we move on to new learning, which students then practise. We also pitch challenge carefully, stretching students without overwhelming them, especially in the early years.

We remove the stigma around getting things wrong. In this subject, mistakes are unavoidable! So we say, ‘Yes, you got it wrong…and it doesn’t matter.’ I know a student is beginning to understand when they can say, ‘I got this question wrong, and I know why.’

One of the things we're particularly keen to develop is children's ability to think for themselves. It's tempting, when a child gets stuck, to step in and show them what to do. But sometimes the most valuable thing we can do is resist that temptation. Instead, we ask another question, encourage them to try a different approach or get them to explain what they've already worked out. We want children to become comfortable with not knowing the answer immediately, because that's often where the real learning begins.

We also work hard to find methods that suit the individual. For example, the standard method of long multiplication involves several steps, and one small mistake can affect everything that follows. But alternative approaches, such as Napier’s Bones (also known as the Chinese method), can make the process easier to follow by keeping place value clear and helping students align numbers correctly. (It’s also a method they’re allowed to use in GCSE papers.)

Maths teaching doesn't have to be Victorian

Traditionally, the way maths is taught can be very old-fashioned. But when we have the technology, why not bring it up to date? After all, we’re Bedalians – we don’t just do things because they’ve always been done a certain way! So, last September, I set up a trial to use videos in class with our Year 7 and 8 students.

Instead of the usual classroom method of me standing at the front and teaching everyone the same thing at the same time, I provided pre-recorded videos on specific topics through Teams, which students watched individually on their school laptops.

Each video was structured around three levels: ‘Must do this’, ‘Should do this’ and ‘Could do this’. Less confident students could focus on the essential learning, while those ready for more could move on to the next level. An exit question at the end of each video checked their understanding: if students got it right, they could move on; if not, they could rewatch the video as often as required. Meanwhile, I was free to move around the classroom and help those who needed it.

This meant children in the same class could be working on the first or fourth video in a topic. It involved a lot of planning, but enabled everyone to learn at their own pace, and for individual help to be given.

And once the videos are made, we can, of course, reuse them. In fact, I’m about to start developing videos for Version 3 of White Rose.

Assessment for learning

Although students might not know it, we are constantly assessing. At the start of each topic, we consider what the class and each individual is ready to tackle, and take all the students’ work into account, from the questions they ask in class to their homework and workbooks.

We’re not just looking at scores, but at the skills behind them. It’s less about whether someone got six out of ten, and more about what they don’t yet understand.

This means we can tailor a roadmap to improvement for every child. For example, we have a master copy of each prep, which I then adapt to suit individual needs. If three or four children in a class need an extension, but two or three are still grappling with the basics, I can swap easier and harder questions in and out as needed.

Maths is hard…but it doesn't get much harder

Sometimes, I get the lower sets in Year 8 to look at GCSE work. For example, we might look at straight-line graphs, gradients and writing equations, or index notation.

I want them to recognise that, yes, what they're doing now is hard, but the maths they'll be doing in three years' time won't necessarily be much more complicated. Maths involves spinning a lot of plates and returning to the same subjects time and again, building on what students have already learnt.

Interestingly, students who've been with us since Prep or Pre-prep often go on to achieve some of the highest GCSE and Bedales Assessed Course (BAC) grades at Bedales Senior. I think that's because when unexpected questions come up in exams, they have the understanding to tackle them rather than simply giving up because they've never seen them before.

Maths is one of the most popular A Level subjects in the Senior School. This summer 77% of students achieved A*-A in Mathematics A Level and 88% achieved A*-A in Further Mathematics A Level.

This is an exciting time for the Maths department at Bedales Prep. White Rose has welcomed the way we've adapted its resources, and our feedback may help shape future versions of its workbooks. Given its global reach of over 140 countries, that could benefit teachers and children well beyond Bedales Prep.

But for me, it always comes back to the students. We care, and I think that's obvious in everyone in my department. I've been here for 25 years, and, a bit like the Sugababes, people have come and gone. But one thing has never changed: we want every student to love maths and feel confident doing it, whatever their starting point. Because maths is about more than getting the right answer. It’s about having the confidence to have a go. Crucially, we take away the fear of making mistakes.