A decade back I sat opposite a very little boy and his mum on the train to Sheffield. I wanted to do some work, but the little boy was absolutely determined to talk to me, although conversation with a boy who wants to say “red” earnestly and repeatedly isn’t the most scintillating. His mum was trying to study, and kept apologising to me. I gave up trying to work and talked to the little boy, much to his mother’s delight.

After a while, and grateful that I had kept her little one entertained, we struck up a conversation. She had left school at 16, with good GCSEs, including some A*s – and a U in maths. She was pregnant by 17 and a mother a few months later. She worked – from memory – in the local Premier Inn, where someone had spotted that she was clever. They wanted to put her on a management course – but she had to pass maths GCSE first. Hence she was studying maths, by herself, from textbooks.

I asked, cautiously, how she got a U. She told me that it was genetic. Her father had failed maths and told her she too would be bad at it. As Larkin remarked, “They fuck you up, your mum and dad”, although in this case there is no evidence to convict her mother.

I said this was nonsense, and that I reckoned she had skipped loads of lessons and never done her homework. She was amazed at my perspicacity – “How did you know?” – adding that obviously she had played truant because there is no point going to lessons if you are genetically bad at maths.

I told her, as the Department for Education chief analyst, that it is impossible to be A* in most subjects and fail maths. As Professor Rob Coe has remarked many times, all core subjects are expressions of a single unidimensional trait, “general academic ability”. If you are that clever, then unless you have extreme dyscalculia or the like, you can get a decent grade in maths.

At this point the fourth person around the train table – a university student – took out his ear buds and said: “He is right. I am Chinese. We all do well in maths. That is because we are taught well and work hard. You will be fine”. He then went back to work.

She told us that we were the first people to have faith in her ability to do well in maths.

Maths is a cruel subject. You literally and obviously get things wrong. A history essay can be weak, but at least it is an essay. Sometimes in maths you do not know where to begin, and nothing is harder on self-esteem than handing in a blank sheet of paper.

Since I met that lady, thousands upon thousands of people have had to resit maths GCSE in further education colleges, having failed maths in school. Some have passed, but the majority have not. This is a tragic failure for them, and for us as a nation. Maths is important, and we know – as the Chinese student remarked – there are societies that show that pretty much everyone can get to a decent standard.

That is why I am so pleased that the EEF has stumped up £600,000 for an RCT for maths mastery in further education colleges. There is good evidence that this approach works, but – given covid and everything else – not enough to be certain that it should be the norm.

Maths mastery costs £50 per student per year. As far as we can tell, students make a month’s more progress, and students from poorer backgrounds make double that. Two month’s progress for £50 is a bargain. Now Tim Leunig’s rule of thumb is that RCTs can and do overstate the final benefit by two to one – because in an RCT everyone concentrates hard, and it is all shiny and new – but even if it is only half as effective once rolled out, this approach would still be worth every penny.

The EEF are recruiting colleges for this trial now. We all know that teaching maths to people who think they can’t do it can be a hard, hard grind, painful for teacher and student alike. If we can build up their confidence, make them realise the truth which for many of them is that they are perfectly competent, they can and will learn enough maths to pass. And then, like this young lady, more doors will open for them.

So do sign up, get trained, and let’s change some lives.

This is great news. However, the CFEM PROJECT has started this work and the NCETM is recruiting teachers to become Mastery specialists. Also, Maths Hubs are carrying out workgroups looking at GCSE Resits and Functional Skills all with an emphasis on Mastery. I hope we are not reinventing wheels but building on all existing work and evidence.