A group of construction students wielding paper aeroplanes in a corridor attracted the suspicion of one teacher. “What are you doing out here?” she asked.

“We’re doing maths,” one replied. “We’ve been learning about angles in maths with the folds in the paper. Our teacher told us that we should now go outside and test out our paper planes.”

This is one of many similar scenarios playing out in colleges up and down the country, as maths teachers work to engage students with low levels of prior attainment.

In his government-commissioned report on post-16 maths published last year, Sir Adrian Smith warned that society’s negative attitude towards mathematics was “a cause for concern”.

“It is culturally acceptable for individuals to confess that they ‘can’t do maths’, whereas this would not be easily admitted for literacy,” he wrote.

Maths teachers, therefore, have the added burden of justifying the importance and relevance of maths against what Smith called “a backdrop of negative attitudes towards mathematics”.

Teachers of GCSE resits face a further hurdle, too. They are tasked with getting students through an exam that these learners were unable to pass after 11 years of schooling.

The maths and English condition of funding for 16- to 19-year-olds, introduced in 2014, compels students who leave school with a grade 3 or D in GCSE maths or English to resit these exams until they achieve that elusive grade 3 or C. Unsurprisingly, this has resulted in a huge spike in the number of older students taking GCSE maths exams.

The pressure of GCSE resits

This summer, 172,291 students aged 17 or over sat GCSE maths- almost a quarter (23 per cent) of the total number of entries. This marks a major increase from 2013, when there were just 77,501 17-plus entries, representing 10 per cent of the total.

Resit pass rates are low - just 19 per cent for maths, according to Ofsted’s 2018 annual report. Research by Impetus-PEF, published in August, shows that 10,063 students taking the GCSE maths exam in 2017 had already attempted it twice before; some were even sitting it for a ninth time.

All these extra students, of course, require extra teachers. But set against a national shortage of maths teachers affecting schools, recruiting them to teach in colleges can be even more challenging. Three in five colleges that responded to a 2016 Association of Colleges survey said they had struggled to recruit teachers in this subject area.

Mike Ellicock, the chief executive of the National Numeracy charity, says FE colleges face an “impossible” task. “Considerable effort has gone into addressing the chronic shortage of maths teachers in schools in the past decades,” he says. “However, nothing has worked there and schools are arguably in a worse place than when Sir Adrian Smith wrote his influential report, Making Mathematics Count, in 2004. I haven’t seen any evidence to suggest this will change in schools - let alone in colleges, which undeservedly continue to be the poor relation.”

The true nature and extent of the maths teacher shortage in FE is not well understood, owing to the lack of good data. This issue was picked up by Smith in his more recent 2017 report. “Little,” he concluded, “is known about the workforce teaching mathematics and quantitative skills in FE colleges.” He recommended that “the Department for Education should improve the evidence base on the FE workforce teaching mathematics and quantitative skills in order to assess supply, teaching quality and the effectiveness of current recruitment measures”.

Subsequently, the Nuffield Foundation, a charity that funds education research, commissioned the Centre for Research in Mathematics Education at the University of Nottingham to provide a snapshot of the maths college teacher landscape.

The report’s authors, Andrew Noyes, Diane Dalby and Yvonna Lavissay, say their survey offers “the clearest and most up-to-date account of the mathematics teacher workforce in FE in England” to date.

They spoke to 480 teachers working in a representative sample of 31 colleges - around a sixth of the total number of teachers at the time the project started. The data they gleaned reveals a striking picture of college lecturers rising to the challenge to try and fill the maths teacher gap.

Around a quarter (26 per cent) taught maths as well as another subject. One in 10 taught mainly maths alongside another subject; 16 per cent were employed as vocational teachers, but taught maths as a second subject.

Teacher trainer Julia Smith says that because recruitment is such a big issue, vocational tutors whose courses have a quantitative element - such as engineering, for example - are increasingly taking on mathematics classes, too.

“A lot of those people would be quite happy to take it on because their own maths is very good, providing they get to know what the syllabus is,” she says.

Steven Wiggins is one of those teachers. For three days a week, he teaches sports BTEC students. The other two days, he teaches maths classes.

Having enjoyed maths at school, Wiggins, who works at a college in Leicestershire, took up the chance to teach it at college to “add another string to his bow”.

Juggling dual priorities was “tough to start with”, but having a good support network of maths teacher colleagues and understanding managers has helped. “The biggest thing is motivation,” he says. “These students have a perception that they are ‘failures’ because they did not get the grade 4.”

This fundamental challenge is highlighted by Ofsted in its 2018 annual report. “The impact of repeated “failure” on students should not be underestimated, the watchdog says. Rather than creating the perception that English and mathematics study in FE is a punishment for not getting a grade 4 at an earlier stage of education, it should instead be pitched as a core part of vocational training”.

Another maths teacher at a college in Northamptonshire admits she has not always been successful in engaging her demotivated students. “The biggest challenge is overcoming the fear of maths that has been built up through years of struggling and the avoidance strategies that they have developed as a defence against failure,” she says.

“Teen bravado would much rather say, ‘I didn’t care, I didn’t try, so it doesn’t matter,’ rather than admit that they hate being hit over the head with same grade in the same exam, year on year.

“I try to work out what they can do and get them helping each other - keep the mood light as far as possible and work on topics that will have relevance to them later. A good understanding of percentages and interest rates is far more important than algebra for most of my learners.”

Smith stresses that college maths teachers need to take a different approach to their counterparts in schools to allow students to “put their pasts behind them”.

“One of the problems is most people tend to teach maths in the same way they were taught,” he says. “College maths cannot look, feel or sound like maths or else you are just going to get the same results. When teachers are innovative and creative, that is when you start to get better results.

“The skill of the GCSE resit teacher is finding different ways to do things. There are various ways to do long division or fractions. If the student can’t do it one way, the teacher can show them a different method and they will still get the same answer. It’s about helping them to build their maths toolbox. If they are showed a new way to do it aged 16, the learner is more open to it because no one has ever showed them that before.”

Another role for a college maths teacher can be chasing students to make sure they attend classes. Monitoring attendance is a function that almost a quarter (23 per cent) of college maths teachers said took up between two and five hours a week, according to the results of the University of Nottingham study.

Catherine Sezen, senior policy manager at the Association of Colleges, says that this is a necessary evil: “Chasing attendance is part of what you have to do. You can’t teach a young person who isn’t in the room. You have to get to the reason why they might not be attending. As colleges, we know the importance of English and maths to our students. There’s a requirement in the condition of funding that students have to attend for at least six weeks.”

The workforce survey also reveals how college maths teachers ended up where they are. The data shows that the most common area of employment prior to becoming a college maths teacher is working in industry, business or self-employment (24 per cent). Other common entry routes include transition from teaching another - usually vocational - subject (19 per cent) or from teaching in schools (23 per cent).

One of the research authors, Diane Dalby, a senior research fellow at the University of Nottingham, says that this diversity is fundamentally different from that of schools - a fact that has until now been neglected by policymakers. “There is a message for government in this. Unless you worked in an FE college you would not be aware of this,” she adds.

This diversity is one of the strengths of the maths FE workforce, Dalby says. “A teacher who is stronger at maths within a team can support someone who is less strong. A teacher who is stronger at engaging 16- to 19-year-olds can support someone who is less strong in this area.

“You have these assets there, so you need to train managers to encourage a professional learning community among their staff. This takes leadership but also outside intervention from time to time for sustainability. It is about seeing this workforce diversity as an asset rather than something that is a problem.”

The survey also highlights that many college maths teachers do not have an undergraduate degree in maths.

More than a third (34 per cent) of college maths teachers only had GCSE maths as their highest qualification level on the subject. A further 30 per cent had a bachelor’s degree in maths and 7 per cent had a postgraduate qualification. The report authors state: “There is an outstanding need for subject knowledge enhancement in professional development plans.”

Dalby adds: “College maths teachers are, by and large, not mathematicians who become teachers in the same way that in schools most maths teachers will have at least maths undergraduate degree before starting teacher training. In schools, they expect their maths teachers to have a degree in maths. In college, a whole range of skills are just as important. You need the whole toolbox.”

Sezen adds that you have to be a teacher of maths but also, crucially, a teacher of young people, so it “doesn’t matter if [college maths teachers] have level 2 or if they have a master’s”.

“It depends on the individual. You have got to be able to teach the whole person. If the teacher is motivational and engaging, then they are the best person for the job,” she explains.

But David Russell, chief executive of the Education and Training Foundation, believes that having the factual knowledge necessary to guide learners into different ways of exploring maths and understanding concepts is essential, especially when dealing with demotivated learners.

“Excellent teaching involves the ability to use deep subject knowledge to skilfully connect learners with the subject and move them past misconceptions about the value of the subject, or about the subject itself,” he says.

“In the deregulated teaching environment which is FE, there is currently no requirement for teachers to be qualified to a level above that which they are teaching. However, we believe that the quality of teaching in FE would be enhanced if all maths teachers held a subject qualification at least a level above the highest level they teach at, and had successfully attained Qualified Teacher Learning and Skills or Advanced Teacher Status.”

Wiggins, whose highest maths qualification when he started teaching was GCSE, has since achieved level 3 teaching numeracy qualification, and another teaching course at level 5. Other lecturers who have a passion for maths but who teach another subject should not to be scared to give it a try, he says.

“If you feel you have something to offer, don’t be afraid. Coming from a vocational background, most people will have some life experience that helps you relate to your students more and gain their respect.”

George Ryan is an FE reporter for Tes. He tweets @GeorgeMRyan

Teaching GCSE maths ‘is a balance of support and sanctions’

Simon Ball, a maths teacher at Newcastle and Stafford College Group, has been teaching maths for 16 years.

He started teaching in a secondary school and now teaches in a sixth form attached to an FE college.

He says he enjoys the college setting because it is much more relaxed than a school, and he teaches both GCSE resit students as well as maths A-level students.

“I feel that some of them engage once they realise that you can help them succeed. A good portion of the students resitting GCSE maths did not have great experiences at schools, for whatever reason, so the chance to make up for that and get the qualification can be quite motivating.

“Before I even started this year’s first GCSE maths lesson, a student whipped out a soft drink and started to have some, which is not allowed in classrooms. When challenged, they responded negatively.

“A week later, it became apparent that the student might have to move out of my class. She became upset - I like to think it was because she felt she would have the chance to succeed with me. Some students display lower levels of engagement, which is a massive issue.

“Then you have to strike a balance between supporting them positively and sanctioning them for behaviour that disrupts the learning of others.”