In the November maths resits, the number of students awarded a grade 4 or higher was just 32 per cent with the exam board AQA; 30 per cent with Edexcel; and for those sitting the OCR exam, 27 per cent. Meanwhile, a parliamentary committee heard earlier this year how compulsory maths resits are leading to mental health challenges, heaping stress and anxiety on pupils.

As a former teacher of 11 years, who has worked in school and college classrooms in London and Derbyshire, Geoffrey Wake is well aware of the struggles facing teachers and students stuck in a cycle of resits. “I’ve taught those classes and it’s hard work. The students’ relationship with maths isn’t good, and it’s your job to turn that around,” he says.

It is Wake’s hope that the £640,000 Maths-for-Life project - a professional development programme for teachers based on findings from the University of Nottingham’s Centre for Research in Mathematics Education, of which Wake is convenor - can go some way to tackling the issue. He is currently recruiting teachers to take part in the Education Endowment Foundation-funded trial, which begins in September.

The project focuses on five maths topic areas: proportional reasoning; algebraic expressions; parts of a whole; contextual problems; and handling data. It also aims to form communities of teachers who can collaborate to improve their teaching and students’ learning, and it is hoped that about 60 colleges and 50 schools will work on the project over a two-year period.

For Wake, it is fundamental that teachers examine their own knowledge of teaching. “Professional development is hugely important and, in many ways, it’s sadly neglected in the teaching profession,” he says. “So Maths-for-Life is really about developing teachers and giving them insights into the different ways in which they can work with their students.”

Team review

As part of the programme, there will be “lesson study”, where teachers will work together to understand a particular class and how it was received. “They will all watch one of them teaching it, so they can focus in great detail on the student materials, how they reacted and how they learned. The programme is innovative in that way, particularly in the further education sector,” he says.

Wake and colleagues have been working with 20 “lead” teachers across England during the current academic year to fine tune the programme, and the anecdotal evidence looks promising, with teachers reporting increased student confidence and engagement, and improved results in internal testing compared to students who were not in the study groups.

“One thing that’s become clear is how lacking in confidence these students are. This is about giving them confidence. It’s a gradual build-up of getting them to feel that they can tackle questions that, in the past, they would have shrugged and given up on,” says Wake.

Part of the programme includes developing the use of visual representations to help learners see a topic in a fresh light. “We want students to get a picture of what they are trying to find out before ploughing in with a rule or procedure,” he says. “A lot of students, particularly those who haven’t been successful at GCSE, see maths as a set of rules and procedures, where you have to know which ones to apply to get the right answer. We’re trying to dispel that approach, and to go deeper in their understanding of the subject.”

“A simple example is a task where students are asked to match a fraction to a ratio: Ali has twice as much money as Blair, so the ratio is 2:1. Almost all students match that to a half, which is not the correct answer. So we use a visual representation where we’ve got what looks like a bar divided into sections - Blair’s got two, Ali has one, so students can see straight away that Blair has got two-thirds of it.

“We ask students to match the fractions and the proportions before we give them the picture, and then when they have the picture, the hope is that it helps them to understand the process,” says Wake.

This is just one of many approaches that teachers can implement. So what, then, does Wake believe effective maths teaching should look like in the average UK classroom?

“You really need to have thought through the examples you’re using and why you’re using them,” he says. “For instance, there are better numbers than others to use in questions, which can help students gain a clearer understanding of the concept.

“So, never use 2 squared as an example - I’ve done it myself and I’ve seen student teachers do it at the drop of a hat - because the idea of squaring is ambiguous and misconstrued with this number. It’s better to use 3 squared instead.”

Eastern inspiration

Wake joined the University of Nottingham in 2011 after spending 19 years in the school of education at the University of Manchester. His credentials include work on curriculum design and its associated assessment, and the design of the free-standing mathematics qualifications. He was also on the government’s expert panel that advised on the development of the Core Maths initiative. However, his work hasn’t always been classroom based and he has also researched the way in which people use mathematics in the workplace.

Most recently, Wake has been working with researchers in Japan, and he has been impressed with the maths teaching he has seen there. “They use very structured lesson study, and they have a very different approach to professional development.

“If you work in a Japanese elementary school, you’ll be involved in the professional development process as part of your day-to-day work,” he says. “We are using a modified version of that in Maths-for-Life.”

Department for Education figures from 2015 found that 20 per cent of secondary school maths lessons were taught by a teacher without a relevant degree - up from 17 per cent in 2013. How can schools cope with fewer specialised teachers, and the declining number of teachers with maths degrees walking through their gates?

“A maths degree isn’t a prerequisite to being a good maths teacher,” says Wake, whose own degree is in engineering science. “Yes, you need a mathematically-related degree, but it’s a huge mistake to think that someone who’s good at maths themselves can teach it well.

“Everyone has to go back to the beginning. It’s important that teachers have some mathematical capability; that they have a qualification to a high level. But that alone isn’t sufficient.”

He believes that at the root of the problem is the current approach to initial teacher education. “Government ministers seem to think that you can teach with just a high-level qualification in a subject and, to me, that totally undermines the profession of teaching,” he says. “I don’t know of any other country that has as much on-the-job training for teaching - it’s becoming more and more like an apprenticeship.”

Taking care

Wake would also like to see maths textbooks produced with greater care and planning, and believes that too many textbooks are “written in sections allocated to a team of teachers who write their sections in their spare time”.

This can lead to a lack of careful development of the mathematics across subject topics and over time, he says. “To ensure that we have textbooks that can match those developed in the Far East, we need to take a different approach where a team works over a substantial period with this as their prime employment.

“We need to draw on what we know from research and task design. At Nottingham, we have carried out such careful design of lessons for the US, but even our curriculum and task design experts haven’t had an opportunity to work on a textbook scheme.”

Ultimately, Wake would like to see resources in place for maths students to achieve a deeper understanding of the subject. He believes that, where appropriate, group work between students can be incredibly useful in this regard.

“It’s about understanding the connectivity between the different parts of maths, the structuring. When I was at school, I wasn’t happy with rules and procedures, I had to understand why they work - and that’s why I enjoyed maths teaching so much.

“Because it’s only really when you delve into that - how maths works, how it is structured, how it all connects - that it becomes a beautiful subject.”

Christina Quaine is a freelance journalist