This extended post investigates resurgent interest in specialist maths schools, as displayed by the Tories under Theresa May. It:

  • Discusses developments during the first half of 2017, foregrounding the May Government’s draft industrial strategy, its spring budget and the Tories’ 2017 election manifesto.
  • Reviews the difficult history of 16-19 specialist maths free schools, beginning with their inclusion in the Chancellor’s 2011 autumn statement and concluding with initial signs of resurgence when May replaced Cameron as prime minister.
  • Assesses the performance of the two university-sponsored schools so far established.
  • Considers future prospects, given a hung parliament, identifying potential obstacles to full implementation and areas of likely compromise between now and 2022.
  • Highlights several factors that limit the overall effectiveness of the default model, as exemplified by the two schools already open.


Pre-election commitments, January to May 2017

Pre-announcing a draft industrial strategy

Early in 2017, the Prime Minister’s Office issued a press release ‘Technical education at heart of modern Industrial Strategy’ (21 January).

It confirmed that this forthcoming strategy would ‘include plans for a radical overhaul of technical education’, outlining four reforms included in an imminent green paper:

  • £170m of new capital funding to establish Institutes of Technology, to provide higher level technical education in STEM subjects across all regions.
  • Various actions to tackle STEM skill shortages including: encouraging the growth of STEM subjects in HE, exploring options to ‘incentivise’ an increased supply of STEM graduates and reducing regional imbalance in the numbers progressing to higher level STEM qualifications.
  • Promoting lifelong learning, considering ‘centres of community learning’, maintenance loans for higher technical education and a UCAS-style applications process.
  • ‘Plans to use the successful free school model to expand the provision of specialist maths education across the country’. This would involve ‘working with local partners including top university mathematics departments’.

Related press coverage suggested that journalists were offered some vague quantification. For example, the Telegraph reported:

‘Theresa May will announce a drive to create a specialist maths school in every British city on Monday to ensure the country “stands tall in the world” after Brexit.’

That implied some 50 schools.

The Sun’s version was even more ambitious, claiming that there would be ‘a specialist school…opened in every town’.

Industrial strategy green paper

The green paper ‘Building our Industrial Strategy’ was published two days later on 23 January, giving a 17 April deadline for consultation.

The Government’s response had not been published before purdah descended ahead of the 2017 General Election.

The green paper describes 10 ‘pillars’ for the draft strategy, proposed on the basis of evidence – some of it from abroad – that they each drive growth. One of these pillars is ‘developing skills’:

‘We must help people and businesses to thrive by: ensuring everyone has the basic skills needed in a modern economy; building a new system of technical education to benefit the half of young people who do not go to university; boosting STEM (science, technology, engineering and maths) skills, digital skills and numeracy; and by raising skill levels in lagging areas.’

The maths schools proposal is included amongst the actions intended to boost STEM skills and address skills shortages.

The text refers back to a related statement (not quite a commitment) in the 2015 Tory Election Manifesto:

We aim to make Britain the best place in the world to study maths, science and engineering, measured by improved performance in the PISA league tables. To help achieve this, we will train an extra 17,500 maths and physics teachers over the next five years. We will make sure that all students are pushed to achieve their potential and create more opportunities to stretch the most able.’

It also mentions the long-awaited Smith review of post-16 maths. This was first announced in the March 2016 budget:

‘The government will… ask Professor Sir Adrian Smith to review the case for how to improve the study of maths from 16 to 18, to ensure the future workforce is skilled and competitive, including looking at the case and feasibility for more or all students continuing to study maths to 18, in the longer-term. The review will report during 2016.’

Terms of reference were belatedly published in a July 2016 DfE press release.

Although the report itself was unpublished (and remained unpublished ahead of the 2017 Election), the green paper drew on its provisional findings:

‘Professor Sir Adrian Smith’s review of post- 16 mathematics has identified that one factor contributing to the shortage of STEM skills is the take up of advanced mathematics qualifications, including A level mathematics, further mathematics and core mathematics. We have already made substantial progress on this since 2010: the proportion of people studying mathematics is now at its highest ever level, and it is the most popular A-level. But there is significant regional variation and students in some areas are much less likely to progress to A-level mathematics than their peers in other parts of the country. There are significantly more students studying advanced mathematics in London and the South East than other parts of the country.

The review will propose solutions to these imbalances and the wider challenges that reduce progression to A-level and other important maths qualifications. These include both cultural factors and practical barriers, including financial ones, for schools and colleges. Furthermore, the proportion of girls studying A-level mathematics and physics still lags behind that of boys significantly.

Maths free schools such as Exeter and King’s College London, have the potential to drive up standards in the subject and ensure advanced mathematics education is available to pupils who might not otherwise be able to access it. The Government will consider how to enable this model to spread and deliver benefits for mathematics education in their wider community. We will seek partners to open mathematics schools of this kind across the country.

This implies that the Smith Review will itself recommend the introduction of more 16-19 maths free schools, as one means of increasing A-level take-up, improving standards and spreading wider benefits through outreach activity. But it is conceivable that the final paragraph is merely government commentary upon Smith’s conclusions.

One might infer from this that:

  • Selective 16-19 maths free schools remain the default model under consideration.
  • Future sponsors might not be confined exclusively to the ‘top university mathematics departments’ mentioned in the press release, though some would ideally be involved.
  • These institutions must be capable of delivering benefits for maths education in the wider community. That implies a substantial outreach programme reaching well beyond the potential future intake.


Spring budget 2017

In the 2017 Spring Budget, the Chancellor announced:

‘…funding for a further 110 new free schools, on top of the current commitment to 500.

This will include new specialist maths schools to build on the clear success of Exeter Mathematics School and King’s College London Maths School – which my RHF the Prime Minister visited earlier this week.

The budget document said:

‘The government… will deliver the manifesto commitment to open 500 new free schools by 2020. The government will extend the free schools programme with investment of £320 million in this Parliament to help fund up to 140 schools, including independent-led, faith, selective, university-led and specialist maths schools. Of these 140 schools, 30 will open by September 2020 and count towards the government’s existing commitment. The new free schools will be located where they are most needed to improve the choice of schools available to parents, following a rigorous assessment of local factors.’

It is unclear what proportion of the total will be specialist maths schools and when these will be operational.

The formulation leaves open the possibility that specialist maths schools need not be confined to 16-19 and need not be university-led. There is no reference here to location in cities. Instead, these institutions will be placed ‘where they are most needed’.


May 2017 Tory Election Manifesto

The Tories’ 2017 Election Manifesto drops the Cameron government’s ambition to make the UK the best place in the world to study STEM subjects as measured by PISA, stung no doubt by our limited progress in the 2015 cycle.

Gone, too, is the reference to providing more opportunities to stretch the most able.

Instead the 2017 edition substitutes:

‘We want British technical education to be as prestigious as our world-leading higher education system, and for technical education in this country to rival the best technical systems in the world.’

It does not name the jurisdictions regarded as having the best ‘technical systems’ or provide any benchmarks to help quantify this level of achievement.

Specialist maths schools are also mentioned in the manifesto, not in the section on technical education but in that dealing with the outcomes from the selection green paper:

‘We will make it a condition for universities hoping to charge maximum tuition fees to become involved in academy sponsorship or the founding of free schools. We will introduce new funding arrangements so we can open a specialist maths school in every major city in England.’

There is scope for confusion here. Implementation is often problematic when a single initiative features in two parallel areas of government policy.

It is unclear why new funding arrangements are necessary, given the existing budgetary provision in the free schools line of the 2017 spring budget. This may point towards more concrete plans to develop alternative models.

Note that the scale of the commitment is now one in ‘every major city’, which probably suggests somewhere between 10 and 20 institutions. Let us assume 15.

Like most of the educational commitments in the manifesto, this one is entirely uncosted.

Much depends on the size, location and nature of the schools created (and especially the scope of the outreach effort), but a commitment on this scale might suggest initial capital costs of £75m and annual steady-state running costs of up to £40m per year. We do not know what percentage of that is already in the baseline


Preparing the ground

Baroness Wolf, the inspiration behind the KCL maths school, seems to have taken on the role of maths school champion, so far by unofficial government appointment.

On 27 April 2017, a few days after general election purdah was imposed but before the Tory manifesto was published, she gave a presentation at the Annual Conference of the Heads of Department of Mathematical Sciences (HODOMS).

Her powerpoint is posted on their website. It describes the KCL school as part of a wider STEM strategy, adding:

‘STEM education now accepted as crucial policy area across Westminster but this was specifically (and unusually) aimed at top end, increasing flow of really good young mathematicians from state system’.

It adds that the KCL school is ‘central’ to its ‘WP efforts’ and has been praised by OFFA’s director. Wolf mentions the school’s outreach provision for Years 10/11 and Easter and Summer Schools supported with additional KCL funding.

She says that current government policy is:

‘…strongly in favour of specialist maths schools. Top priority for No 10 if Conservatives win this election’

She also reminds her listeners of the green paper proposal to link HE tuition fee increases to school sponsorship.

Finally she outlines next steps:


So it seems that universities are being strongly encouraged to consider specialist maths schools as a ‘path of least resistance’ towards fulfilling the new tuition fee requirement about to be imposed on them in the wake of the selection green paper.

But the prime mover is the No 10 policy unit rather than DfE. And they are willing to explore different institutional models, rather than relying exclusively on clones of the KCL and Exeter schools.


A concise history of specialist maths schools


The short and difficult history of these institutions has featured prominently in several of my previous posts, beginning with ‘The introduction in England of Selective 16-19 Maths Free Schools’ (November 2011).

Immediately ahead of the 2011 Autumn Statement there were media reports that funding for the next tranche of free schools would include provision for at least 12 selective 16-19 free schools with a maths specialism, sponsored by university maths departments and located in major cities.

These would be established by 2015 and were intended to make England ‘a world leader’ in the subject. In due course the model would be extended nationally and would serve as a model for similar provision in other subjects.

Government spokespeople were quoted:

‘The first goal is to aim for the highest quality 16-to-18 maths teaching in the world to educate mathematicians able to produce breakthroughs in pure and applied mathematics, or to build innovative companies.’

‘In so far as there is a goal, it is to produce pupils who excel in Cambridge’s entrance papers and similar tests.’

‘This is an experiment and we want people to come up with other projects in other subject areas.’

It is no secret that Dominic Cummings, political adviser to then Secretary of State Michael Gove, was behind the concept.

Cummings has since explained that ‘Gove’s team…pushed the idea through DfE’ so they had something ready-made in case they were asked to flesh out an upcoming announcement.

Their opportunity came when the Chancellor was fishing for a science-related policy to include in the 2011 Budget.

The Chancellor’s statement dropped the commitment to a dozen institutions:

‘These schools will include new Maths Free Schools for 16-18 year olds.

This will give our most talented young mathematicians the chance to flourish.

Like the new university technical colleges, these Maths Free Schools are exactly what Britain needs to match our competitors – and produce more of the engineering and science graduates so important for our longer term economic success.’


Limited progress: 2011-2013

I picked up the story in ‘A Progress Report on 16-19 Free Schools’ (March 2013).

Although there were early examples of other 16-19 specialist STEM free schools these were not sponsored by university maths departments and had been set up within the mainstream free schools programme.

University involvement remained a non-negotiable for authentic 16-19 maths free schools. A contemporary FAQ briefing published online said:

‘The common feature of all specialist maths Free Schools is significant involvement from a university maths department. Universities can apply to set up a specialist maths Free School on their own, or in partnership with another strong education provider. Similar specialist maths schools, with significant input from universities, already operate in the United States, Russia and China.’

Cummings has claimed that many university maths departments were privately supportive but unable to give public support, let alone a commitment to pursue such an ‘elitist’ project, some being over-ruled by their more cautious vice-chancellors.

Finally, in January 2013, a press release confirmed two successful applications, one from King’s College London, the other from the University of Exeter, both schools to open in September 2014.

Cummings highlights the involvement of Baroness Wolf in the KCL project. The Exeter project followed the KCL blueprint in most respects, though it had joint sponsors with Exeter College playing a role alongside the University, and also included a residential boarding facility.

My 2013 post observed that neither Kings nor Exeter could then boast a highly ranked maths department. Perhaps they thought that free school sponsorship might help to push them further up the rankings.

If so, I could detect no tangible improvement to date.

To take an example, the Guardian’s 2018 University Guide rates Exeter’s maths department at number 27 and KCL’s at number 52 in the UK. Exeter is outranked in the south-west by Bath, UWE and Bristol; KCL is outranked in London by Imperial, UCL, Greenwich, City, LSE, Royal Holloway and London Met.

Other university rankings give different outcomes, some more generous to KCL and Exeter, but one would be hard-pressed to claim a significant impact.

During this period the Government’s wider ambition was unchanged:

‘The ultimate aim is to create a network of schools that operate across England which identify and nurture mathematical and scientific talent.’


Progress stalls: 2013-2015

I reported subsequent developments in a further post: ‘16-19 Maths Free Schools Revisited’ (October 2014) the second edition of which reflected a Twitter discussion with Cummings.

In June 2013 education minister Liz Truss wrote to the heads of university maths departments to encourage more bids.

She argued that universities could use their access agreement funding for this purpose, citing support from OFFA’s Director:

‘Professor Ebdon has… confirmed to me that he considers the sponsorship and development of Maths Free schools as contributing to higher education ‘widening access’ activity, and that it would be perfectly legitimate to allocate funding ring-fenced for improving access for under-represented groups towards the establishment of such schools.’

But this statement was not enshrined in OFFA’s official guidance to institutions on preparing their access agreements.

A November 2013 press release about a maths competition provided another opportunity to drum up interest. It mentioned in passing that:

‘The KCL and Exeter schools are the first to take advantage of a development grant made available by the Department for Education for the creation of university-led specialist maths free schools.’

Shortly before this the TES had submitted a Freedom of Information request asking how many expressions of interest and firm proposals had been received, and which of the latter had been approved and rejected.

It took until June 2014 for the ICO to issue a Decision notice insisting that DfE should release the information.

The notice itself revealed that a third proposal – presumably rejected – had been submitted by the University of Central Lancashire.

A TES follow-up story revealed that five more expressions of interest were received that did not result in formal proposals. The identity of those institutions has never been published.

But ministers still had not given up. According to the decision notice, DfE argued that:

‘…funding arrangements were only confirmed for the development of maths free schools in February 2014 and many policy decisions on this issue have been shaped by the specifics of the two schools that are due to open soon. It expects the policy to develop even further as more maths free schools are approved.’

When Cummings commented on my post in October 2014 he claimed there was a further project confirmed but still under wraps.



It never materialised

Meanwhile both the KCL Maths School and the Exeter Maths School opened on time in September 2014.

Another TES article reported new Secretary of State Nicky Morgan saying at the launch of the KCL School:

‘I think that some [universities] are clearly waiting to see how the King’s and Exeter schools go. Clearly there is a huge amount of effort required, but I think King’s will be enormously successful, and I am hoping they will be leading by example.’


Sidelined by the 2015 Cameron Tory Government

As noted above, the 2015 Tory Manifesto included a highly ambitious commitment to make England the best place in the world to study maths, science and engineering, but specialist maths schools were no longer mentioned as a means of achieving this end.

It seemed that the Tory policy-making machine had finally recognised it was flogging a dead horse.

When a Cameron-led Tory Government was duly elected, attention had shifted from the maths-specific to embrace the wider concept of university-sponsored schools, although initially on a voluntary basis.

A new ministerial letter of guidance from BIS to OFFA, published in February 2016, said:

‘We would like you to encourage universities to work with all types of school, including free schools and academies, building on their existing work including in sponsoring schools. You might also encourage universities to become involved in setting up free schools where this will have an impact on widening access.’

The DfE white paper ‘Educational Excellence Everywhere’ (March 2016) was launched at KCL maths school, which was duly lauded in Secretary of State Morgan’s launch speech.

The text also includes a case study of Exeter maths school, apparently to illustrate a commitment to continue encouraging, through the free schools programme, more ‘innovative models of education’.

But there was no explicit commitment to develop a national network of maths schools. Other, separate maths-related commitments, including strengthening teachers’ professional development and improving provision for the most able, would be achieved by other means.

Despite this, the maths free school concept was kept alive through media coverage of the two working examples.

As early as September 2015 Baroness Wolf published an article in the Spectator called ‘What I’ve learned helping to found a specialist free school’.

This argued that the KCL school ‘exists to nourish untapped potential’ and demonstrates that:

‘…specialist schools work, not just because students find their tribe and learn from each other, but because teachers do the same’.

That prompted a further post from me ‘Progress report on KCL and Exeter Maths Free Schools’ (September 2015) which interrogated the claim that small specialist 16-19 institutions of this kind were particularly effective.


Re-emergence under May’s 2016 Tory Government

Maths free schools had not been forgotten by the Director of the New Schools Network (NSN), Nick Timothy, who was subsequently installed as May’s joint Chief of Staff.

In March 2016 the Independent had published a story about KCL’s school which once more concluded:

‘…ministers have not abandoned the idea of similar colleges being set up in the future.

Nick Timothy, chief executive of the New Schools Network, the charity which supports free schools, said: “If the best universities are serious about taking on more pupils they need to take direct action to make sure schools are giving children the right opportunities.”’

The Guardian also published the note of a discussion hosted by CMRE in May 2016 at which Timothy:

‘…offered for discussion a number of other ideas for how to increase capacity – not just via free schools but in the academy sector more generally’.

These included many that resurfaced a few months later in the schools green paper, but there were others too:

Should the government fund the establishment of specialised school chains – for example with specific focus on maths or science or foreign languages? Given the likely future of 16-19 provision, specialist sixth forms might be the only way to guarantee some important A-level subjects.’

This highlights two potential developments to watch, as and when the Tory’s commitment is implemented.

Following the replacement of Cameron by May, the latter’s ‘Great Meritocracy’ speech (September 2016) again used the example of KCL maths school, as one of four to illustrate the successful involvement of universities in sponsoring and supporting schools.

The subsequent DfE green paper ‘Schools that work for everyone’ (September 2016) followed suit, using it to exemplify the claim that ‘some universities already run excellent schools’.

It proposed that, as a condition of charging higher fees, all universities should sponsor a state-funded academy or establish a new state-funded school, but it did not specifically encourage institutions to consider 16-19 maths free schools. Nor were they mentioned in the chapter devoted to increasing selection.

It may be that the revival of 16-19 maths free schools was only held out of the green paper because it had already been earmarked for the Industrial Strategy.


Performance of the KCL and Exeter maths schools

On the basis of the evidence then available, I judged progress by September 2015, when the first cohort took AS levels, as warranting an Ofsted rating of ‘good’ for KCL and ‘requires improvement’ for Exeter. My judgements took full account of the highly selective nature of both intakes.

This cohort went on to record impressive A level results a year later, including very high progress scores.



This extract from the 2016 performance tables shows 65 students entering A levels at KCL, compared with only 35 at Exeter. (For September 2017 the PANs are 70 at KCL and 60 at Exeter.)

Both schools returned progress scores well above the national average, but the KCL progress score is substantially stronger.

These outcomes come with a health warning since they most likely reflect the proportion of each intake with a ‘spiky’ performance profile – exceptionally strong attainment in mathematics/physics but rather weaker grades across the remainder of the GCSEs included in the progress measure’s baseline.

At KCL 69% of students achieved A level grades of AAB or higher with at least two in facilitating subjects. The average point score is 49 and the average grade is A.

By comparison, some 46% of Exeter’s students achieved AAB or higher with at least two in facilitating subjects, their average point score is 43 and the average grade is B+.

KCL claims 94% of its cohort progressing to study a STEM subject in higher education, with 14% securing Oxbridge places.

Exeter also claims 94% of students progressing to higher education, but with 18% securing Oxbridge places. Just two students chose to study at Exeter. Only six students (18%) chose to study straight maths degrees.

While Exeter reports 100% retention for their first cohort, this data is ‘not entered’ by the KCL school, which operates a performance-related exclusion policy at the end of Year 12:



The initial September 2014 cohort began with 69 students, so it seems likely that four failed to make the cut.

Reliable information about the number of disadvantaged students and their outcomes is much harder to track down. Separate measures for disadvantaged students are not yet included in the 16-18 performance tables, though they should be introduced when the 2017 results are published in December.

The Economist ran a story which says that 14% of the KCL intake had ‘qualified for free school meals’. It is unclear whether or not this is the ‘ever 6 FSM’ measure, though that seems most likely. It is also unclear whether it applies across all three intakes since 2014, or only the 2016 intake.

This is respectable – significantly higher than the average for 11-18 selective schools, but also significantly lower than the overall incidence of pupil premium eligibility in the school population.

On the other hand, we also know that 15% of the first intake was not formerly attending state-funded schools.

KCL’s most recent access agreement says:

‘KCLMS opened in September 2014 and now has 130 students split evenly across two year groups. Of these students, 37% are girls, 25% are classified as living in ‘urban adversity’ by the ACORN dataset (compared to a national average of 17%).’

KCL representatives additionally state that 22% of maths school students are from Acorn quintiles 4 and 5 and that 31% are ‘first generation into university’.



It would be helpful to see reliable data showing the proportion of each intake at each school that was formerly eligible for pupil premium.

Ofsted inspections of both institutions had to be undertaken within three years of them opening. Exeter’s inspection took place in January 2017, at the beginning of the second term of its third year of existence.

The report published on 28 February rates the institution ‘Outstanding’. It says that ‘approximately 20% of learners are from deprived backgrounds’ (though it does not state the measure) and that:

‘…learners from lower-income families, who are in receipt of a bursary to subsidise the costs of living away from home, achieve as well as other learners’

Exeter’s most recent access agreement sheds no further light.

The inspection of the KCL school took place on 25 April 2017, so it has enjoyed almost the maximum three-year grace period to get its house in order.

The report was published on 5 June and it is no surprise that KCL, too, receives an ‘Outstanding’ judgement.

The report says that the proportion of learners from disadvantaged backgrounds is ‘high’ but offers no quantification. It adds that ‘learners from disadvantaged backgrounds outperform their peers’.


‘Managers recognise that they need to focus more closely on the proportion of disadvantaged learners and those from a Black or minority ethnic heritage who progress to the most prestigious universities, including to Oxford and Cambridge.’

How to summarise this evidence? There is no doubt that both schools are extremely successful, but to what extent that success is attributable to their highly selective intakes (and the ‘spiky profile’ of many students) is a much more open question.

It seems fair to conclude that both schools are exceeding expectations to some extent, KCL a little more so than Exeter, but neither is quite as exceptional as the (previous) government would have us believe.


Future prospects

Even before we factor in the uncertain Election result, the plan to resurrect – and to some extent reinvent – specialist maths schools throws up a cloud of difficult policy issues.

This is associated with an unreasonable expectation that they will contribute simultaneously towards several different policy objectives including:

  • Increasing substantially the national supply of highly qualified undergraduates in STEM subjects.
  • Safeguarding national provision of maths and further maths A levels – and substantially increasing take-up in those subjects, so helping to secure universal post-16 provision.
  • Helping universities to fulfil their widening participation and fair access commitments, as well as a related requirement that they engage in school sponsorship.
  • Increasing choice and diversity in the school system, pioneering a tranche of new specialist 16-19 institutions and supporting a commitment to introduce new selective schools.

There is some recognition that replication of the default model, exemplified by the KCL and Exeter schools, is problematic. But how might it be adjusted to secure a national network of some 15 schools by 2022?

The sections below look first at the policy issues before turning finally to consider the impact of the Election.


Leading university maths departments as main sponsors

Even allowing for Baroness Wolf’s powers of persuasion, the next government’s chances of recruiting sufficient ‘top university maths departments’ to act as lead sponsors for 15 maths schools look extremely slim.

On the face of it, specialist 16-19 institutions might seem more closely aligned with HE-level expertise than primary or secondary schools and so a ‘path of least resistance’ for other universities to follow.

But, if one accepts the argument that few volunteered the first time round because of concerns about ‘elitism’, there is no obvious reason why that would have changed.

The pre-Election May government seemed prepared to force universities to adopt or found a school of some kind, but there were signs that it was already rowing back from its earlier position. The threat of compulsion is articulated rather differently in the green paper and in the Tory manifesto.

The green paper says it intends to require academy sponsorship or founding a new state school ‘as a condition of charging higher fees’. It goes on to propose that this expectation would ratchet up over time.

It threatens new guidance to the Director for Fair Access (DFA) to issue in early 2017:

‘… with a clear expectation that universities would contribute to school-level attainment as a condition of charging higher fees, and that we want them to do so by sponsoring academies or establishing new free schools.’

This would inform the DFA’s own guidance to universities on their 2018/19 access agreements.

It hints that the DFA might be instructed to reject access agreements that fail to follow this guidance, but it will also consider further potential measures to impose this requirement ‘including potential legislation’.

The Manifesto speaks only of imposing ‘a condition for universities hoping to charge maximum tuition fees to become involved in academy sponsorship or the founding of free schools’.

This suggests that the condition would be restricted to those universities charging maximum fees, rather than applying to any universities that wish to increase their fees. Moreover universities need not be the lead sponsor; they might simply offer peripheral support.  Nothing is said about how the condition would be imposed.

No published guidance was issued by DfE to the DFA in time to inform OFFA’s 2018/19 access agreement guidance, which said:

‘We are therefore further strengthening our guidance by asking you to increase the pace and scope of your work with schools to raise attainment, so that the teaching and learning outcomes for schools that work with universities are enhanced. This includes:

    • the sponsorship of schools where there are issues around attainment and progression;
    • the establishment of new free schools (including mathematics free schools) to support disadvantaged and under-represented students
    • other significant partnerships, support and activity with schools.’

This falls some way short of the formulation proposed in the green paper.

Note that, while maths schools are specifically included, they are directly associated with support for ‘disadvantaged and under-represented students’.

That is, of course, the only real justification for their inclusion in access agreements, but it is hard to make a case that the two existing schools are operating primarily as engines of social mobility. They make some contribution through their intakes and via outreach activity, but only at the expense of considerable dead weight.

It might be possible to improve their record by radically revising their admission arrangements, in line with those of selective 11-18 schools, to take in much larger proportions of disadvantaged students, but it would be difficult to do so without lowering entry requirements.

Prior to the Election it seemed likely that specialist maths schools would be expected to give new emphasis to ‘ordinary working families’ (as would university access agreements). I have shown elsewhere that this would have negative consequences for those from genuinely disadvantaged backgrounds.

Thus far, universities have been highly sceptical of the government’s proposals. UUK’s response to the green paper says:

‘The main issue with the government’s proposals for universities is the relatively narrow scope of what is being proposed. Raised aspirations, improved attainment, increased teacher ability and retention and improved school success can all be achieved through a number of partnership and engagement mechanisms between universities and schools….

… If the government chooses to adopt the proposals as currently set out in the Green Paper, essentially prioritising school sponsorship over other types of contributions, it is inevitable that this will result in some unintended consequences. These would include damaging existing partnerships between schools and universities, focusing resources on fewer schools, skewing incentives for university involvement, and potentially undermining an institution’s financial viability in the case of smaller or specialist institutions.

Lastly, this is a fairly evidence light area and it will be essential that further evaluation of existing forms of sponsorship is undertaken to determine which approaches work best within different contexts before a much broader extension in school sponsorship is considered.

UUK does not mention that any condition tied to fee levels would cut directly across the new TEF regime, only just finalised by the passing of the Higher Education Act 2017.

From 2019/2020, providers awarded a Bronze TEF rating will be restricted to increasing their maximum tuition fee by half the forecast inflation rate, whereas those with a Silver or Gold TEF rating will be able to raise maximum fees in line with inflation.

It is rumoured that several prestigious institutions – possibly including KCL and Exeter – will be Bronze-rated when initial assessments are published shortly after the Election.

One route a next government might consider is to make a Silver or Gold TEF rating conditional on the right level of involvement with schools.

It seems doubtful that they would guarantee institutions a minimum Silver rating if they comply. That could be attractive to high-status institutions struggling under the burden of a Bronze rating, but it would make the hugely bureaucratic TEF process entirely meaningless.

It is also important to bear in mind that legislation to enforce this – or indeed any other legislative provision – would struggle to pass the scrutiny of the House of Lords.


Universities as junior partners

Perhaps the best the next government can hope for is that a handful of universities will become junior partners in setting up new institutions of this kind. They might not have leading maths departments – and their maths departments might not even be involved.

According to HEFCE figures dating from late 2016 some 60-70 HEIs were engaged in some form of school sponsorship, though in many cases they were co-sponsors or worked through the sponsor rather than taking lead responsibility.

A study commissioned by HEFCE in October 2016 identified some benefits flowing to HEIs as a consequence of such relationships but, balanced against this, it pointed to significant workload implications and reputational risk if the school is not successful.

HEFCE itself provided a similar but rather more negative judgement in a discussion facilitated by CMRE:

‘HEFCE’s efforts at understanding patterns of HE academy sponsorship found few Sponsors express regrets, but that few have been able to identify immediate tangible benefits to their institutions either..

.. Accordingly, not all see the case for getting involved in quite such clear cut terms as the government, which appeared to regard universities as relatively well-resourced and prosperous organisations. HEIs express concerns that focusing on one or two schools may have negative consequences for universities’ existing – looser, but well established and highly productive – networks of schools. It’s not as if sponsored academies can be groomed as feeder schools. There is also considerable reputational and financial risk for HE providers associated with school sponsorship, particularly where it involves struggling schools in the most deprived areas, which is where the government feels they are needed most.’

There will be more opportunities for universities to associate themselves with specialist maths free school projects originating elsewhere, including some of those already in existence.

Some of these relationships may be fairly tenuous – and potentially contentious too.

The Wave 12 list of free schools approved in April 2017 included a 16-19 institution called ‘Cambridge Mathematics School’.

The NSN mentioned it in a list of groups it was helping to prepare bids:

‘This is a proposal for a specialist Maths 16-19 provision in North Cambridge. All students would study Maths, Further Maths and Physics with a further range of complementary subjects offered. The proposal, led by Chesterton Community College, will meet a need for specialist sixth form places, increase high quality STEM graduates and has support from universities and various industry partners.’

Chesterton College has established a multi-academy trust (MAT) – Cambridgeshire Educational Trust – which would presumably undertake the free school project. The active officers of the Trust include the Director of Studies at St John’s College.

When DfE announced its approval, a website associated with the project was available online. It claimed St John’s College and Cambridge Mathematics (essentially a Cambridge University subsidiary) as partners.

Then the website was made accessible only with the author’s approval. Cambridge Mathematics said its involvement was restricted to curriculum design



It subsequently published a statement:

‘Firstly, this is not one of the Government’s Maths Specialist Colleges announced in January, and modelled on the Kings and Exeter schools. As we understand it, it is intended to support A level Maths and Science learning for the community which Chesterton Community College currently serves.

Secondly, despite the name, the Cambridge Mathematics project is not a sponsor of the school. Cambridge Maths is not sponsoring any schools; however we were happy to support their application as we support the aims of a rich curriculum offer for all.

We have contacted the leaders of the new school regarding the confusion over the name and their use of our logo without permission.’

Cambridge Mathematics will have been keen to distance itself from any suggestion of direct involvement in a specialist maths school on existing lines. In February 2017 its Director published a piece in the TES:

‘On Monday 23 January, Theresa May announced a £170 million package to establish “Institutes of Technology” and specialist maths schools in every British city, to ensure the country “stands tall in the world” after Brexit…

… We at Cambridge Mathematics are firmly committed to championing access to excellent mathematics teaching for every student, not just the most able, and certainly not just those in certain schools…

… We receive this news, therefore, with mixed emotions: we are pleased that the government has recognised the importance of an excellent mathematical education in terms of the future economic prospects of Britain, but cautious as to how we might encourage our brightest mathematicians without detriment to the mathematical education of all others…

… The questions we would like to ask are crucial ones: how does the government plan to recruit for these schools, what will be the admissions process, and how will it ensure it is as unbiased as possible?’

Cambridge is already off the hook by virtue of its involvement with the University of Cambridge Primary School, a university training school opened in 2015.

It seems unlikely though that Oxford will follow suit. When the green paper was published its Vice-Chancellor described involvement in schools as ‘a distraction from our core mission’.


Alternative models

One obvious strategy would be for the next government to ensure that each new Institute of Technology had a linked 16-19 maths free school.

In February 2017 DfE was envisaging an initial network of 10-15 Institutes, very similar to the projected number of maths free schools. The first Institute was expected to open in 2018 and capital funding of £170m had been made available until March 2021.

The pre-Election May government was open to a variety of delivery models, including basing Institutes on an ‘existing high-performing college’, delivery through partnerships between further and higher education institutions, delivery through partnership between a group of employers and an educational institution and the development of completely new institutions.

The 2017 Tory manifesto adds:

‘We will establish new institutes of technology, backed by leading employers and linked to leading universities, in every major city in England. They will provide courses at degree level and above, specialising in technical disciplines, such as STEM, whilst also providing higher-level apprenticeships and bespoke courses for employers.’

All institutes are expected to involve themselves in:

‘….developing a strong pipeline of provision at Level 3 either as part of the IoT offer or else with clear pathways of progression to the IoT’s level 4/5 provision’.

Institutes will be expected to deliver a variety of such provision including higher apprenticeships, HNCs/HNDs and the new technical education routes (T-levels) to be introduced from 2019.

It is possible to see how local partnerships might wish to secure a close relationship between the academic and technical strands of STEM provision, enabling students completing A levels at 16-19 maths free schools to opt for higher apprenticeships as well as university degrees.

A variety of different models might also emerge in parallel from the selection green paper. Following Timothy’s earlier thinking, one might envisage, for example:

  • New selective 11-19 free schools with a maths specialism
  • New selective sixth forms with a maths specialism linked to a group of existing 11-16 comprehensive schools
  • MATs running chains of schools – either 11-19 or 16-19 – with a maths or STEM specialism

Some of these would require the ‘new funding arrangements’ mentioned in the Tory manifesto.


Impact of the Election

In the short term paralysis ensues. None of the relevant policy strands can move forward until the next government has been formed and the broad policy agenda clarified in the Queen’s Speech.

The future of specialist maths schools depends on the outcome of one of two green papers – on schools and the industrial strategy respectively.

Consultation on both is complete, but the Government has yet to publish its responses, or the white papers that will set out their detailed plans. Given the policy backlog and the wider political uncertainty, they might not appear much before 2018.

One can expect the more contentious policies – such as removing the ban on new grammar schools – to be dropped. But other parts of the schools green paper might still survive and the industrial strategy might also be taken forward in broadly the shape it was proposed.

The introduction of more selective specialist 16-19 institutions does not require new legislation,  so if a minority Tory government were determined to pursue increased selection in some form, new specialist maths schools would be the obvious place to begin.

Much then depends on the personalities involved. For as long as May remains in place as prime minister she will want to implement what she can of the agenda sketched out in the manifesto.

It remains to be seen whether new Chief of Staff Gavin Barwell will continue to intervene directly in education policy, following the precedent set by Timothy, or whether he will be more content to leave the Education Secretary to make the running.

Given the Election outcome, the cabinet reshuffle was more limited than it might have been. Now that Greening remains education secretary, enthusiasm for maths free schools – clearly a priority imposed and directed from Number 10 – might be rather less than if a known maths education enthusiast, such as Truss or Gibb, were to have taken over the portfolio.

More generally, a minority Tory government will be much weaker than its predecessor. Universities that might have been persuaded to sponsor a maths school will now feel emboldened to resist any pressure imposed on them.

In sum, the prospect of several new 16-19 maths free school proposals emerging during the next two years are very much reduced, but not entirely eliminated.

Are specialist maths schools effective?

The existing model, as exemplified by the KCL and Exeter institutions, is open to criticism on several different fronts. Some of these arguments would also apply to the most likely alternative models.


Limitations of small specialist institutions

Small specialist institutions do not necessarily provide a higher quality educational experience to the students that attend them.

When existing academies add a new sixth form, RSCs apply quality criteria which include an expectation of at least 200 students and a choice of some 15 A levels across a range of subjects. I could find no justification for a different assumption for stand-alone 16-19 free schools

There are examples of extremely successful generalist 16-19 free schools – for example the London Academy of Excellence and the Harris Westminster Sixth Form – and it is arguable that mathematics students attending those institutions are equally successful.

A level examination results at KCL and Exeter are comparatively strong, but heavily dependent on selection. They must also be set in the context of national outcomes.

Provisional 2016 data for England shows 43% of all candidates achieve A*/A grades in A level mathematics – some 18% are awarded A* alone. In further maths 57% of all candidates achieve A*/A grades, with 29% achieving A* grades. In physics about 31% achieve A*/A, with over 9% at A*.

Students’ choice of A levels is far more constrained than in a generalist institution and they miss out on opportunities to interact with peers pursuing a variety of different subjects.

Such interdisciplinary activity is greatly valued by universities, which are almost exclusively multi-disciplinary in nature, so it seems odd that these same universities would restrict similar engagement between younger students.

Wolf argues that subject teachers also benefit more from working in specialist institutions, but supplies no evidence to support this statement.

Although evidence is limited, it seems likely that the strengths of such institutions are offset by comparable weaknesses.

Some students will certainly thrive in such settings, perhaps benefiting from being a big fish in a small pond, but others will do better in more inclusive surroundings. There is no obvious reason why disadvantaged students should perform better in these institutions.


Selectivity versus participation

Much of the media coverage of the KCL and Exeter schools is fixated on them being ‘clones’ of the super-selective Kolmogorov School in Moscow (although there are many similar institutions throughout the world).

Kolmogorov is not the only institution of its kind in Russia, but it draws students from throughout the country. Although the KCL and Exeter schools are highly selective by English standards, they are nowhere near as selective as this.

Cummings repeatedly uses the analogy of Kolmogorov and also draws on evidence from the US Study of Mathematically Precocious Youth (SMPY) even though its least selective cohort is the top 3% and it most often concentrates on the top 1% or even more selective subsets.

As we have seen, KCL and Exeter take in relatively small proportions of disadvantaged students, even though the case for their inclusion in access agreements hangs largely on them operating as engines of social mobility.

Were they to become more highly selective – and so more accurately reflect Kolmogorov and most other international precedents – it is almost certain that the proportion of disadvantaged students would be much reduced.

There is a difficult balance to be struck between these two competing priorities which pull in opposite directions. Admissions reform will be necessary if these schools are to fully justify their inclusion in university access agreements.

They might be ‘reimagined’ as more academically inclusive institutions, potentially with a more technical bias, or a ‘twin track’ approach.

There might even be a case for creating a pyramid structure with a single super-selective entity like Kolmogorov at its peak. But perceptions of ‘elitism’ would probably continue to dissuade the very best university maths departments from hosting it.


Limited input from sponsor HEIs

In super-selective institutions like the Kolmogorov School, the students are so advanced that they need access to extensive university-level maths teaching.

This fundamental justification for university involvement in the school’s core business is largely absent here. At KCL and Exeter university involvement in teaching appears peripheral and mostly confined to enrichment activity. What input there is comes mostly from graduate and undergraduate students.

According to Wolf, the main contribution made by sponsor universities is to governance:

‘With a major university for a sponsor, the governors could offer some substantive help and, above all, reassurance: focusing on what was important wouldn’t bring disaster upon the school. That was our main contribution to the year’s success…’

Similarly the study conducted for HEFCE describes sponsor universities as involved in the management of new schools projects; governance, financial and human resource management; curriculum design; resource sharing; learner enrichment; and occasionally the provision of teacher training opportunities.

Most of the contribution made by universities could equally be provided by other large sponsors. Moreover, their limited contribution to the central business of teaching and learning is not dependent on sponsorship.


Limited outreach activity

If small, localised ‘bricks and mortar’ institutions are to impact on a wider constituency than their own very restricted intakes they must offer an extensive outreach programme.

If they are to justify additional funding through universities’ access agreements they must invest heavily in preparing potential candidates from disadvantaged backgrounds.

But they must also extend their reach further down the range, to counter perceptions of elitism by ensuring that they benefit middle and lower attaining students to some extent.

They must also push below KS4, into primary as well as lower secondary education, connecting as seamlessly as possible with other maths education initiatives locally, regionally and nationally. They must be fully integrated into the national network of maths hubs.

Both the KCL and Exeter schools can boast substantial outreach programmes relative to their size but, even with additional funding from their parent universities, their ‘footprint’ remains comparatively small.

For example, KCL’s most recent access agreement highlights a flagship outreach programme that benefits 200 KS4 students annually. Additionally there is an Easter revision course for 100 Y11 students, a summer school for 100 Y10 students in physics and a professional development course for teachers new to further maths A level.

KCL has:

‘a long-term vision for the school to become a centre of excellence for the teaching of mathematics and thereby to have a positive impact on learners across London’

but their present offer is not commensurate with that aspiration – and it will not be achieved without substantial additional funding.

KCL already claims to be ‘raising GCSE attainment in maths across London’ but there is at present no hard evidence to support this claim. One suspects that, without an expensive RCT, causation will be hard to establish.

It seems likely that the lion’s share of the benefit provided by such schools will always be absorbed by the small cohort of students fortunate enough to attend them.


Cost and efficiency

Small specialist institutions are expensive to run because economies of scale are limited.

  • The KCL school’s financial statement for the year ended 31 August 2016 says it received £1.325m from the EFA for running costs. Assuming 130 on roll, this equates to a per capita cost of about £10,200 per year.
  • The Exeter school’s financial statement for the same year shows it received £1.04m including funding for some boarding places which, given 94 students on roll, gives an average per capita cost of over £11,000.

Both schools received additional top up funding by virtue of their status as specialist maths schools.

The high capital costs sunk in the creation of new free schools are no longer available to spend directly on teaching and learning (assuming funding can be shifted between capital and recurrent budgets). They also create a proportion of surplus places for, if they do not, they cannot be said to increase choice.

The continued promotion of such institutions is inconsistent with the recently completed area reviews, which were justified on efficiency grounds (but which exempted post-16 provision in academies, free schools and UTCs).

The small cohorts of students that are privileged to attend benefit disproportionately from the high per capita investment. Wider outreach provision is rationed by the budget available and the limited capacity of a small staff.

Two schools have very limited capacity to service the national talent pool of the most able mathematicians. It is extremely doubtful whether either can service fully the talent pool within its own region. A national network of 15 schools would have wider reach and should be able to pool limited resources to strengthen outreach capacity.

But annual ringfenced expenditure equivalent to the cost of 15 specialist maths schools could be used far more efficiently to support the national talent pool within its own existing schools and colleges.

A carefully designed initiative deploying a blended learning model would reach more students and should be capable of achieving commensurate outcomes. If access were restricted to disadvantaged students substantial deadweight would be eliminated.



There were signs that the pre-Election May government was attracted by the Gove-Cummings blueprint, seeking to extend the totemic status of grammar schools to a new tranche of selective 16-19 specialist maths schools, each ideally sponsored by a selective university with a top-rated maths department.

But recent history suggests that it would not have been able to persuade enough universities to play ball – and that forcing them to do so could have had negative consequences. So it was wise to explore a variety of models, some of which did not depend on lead university sponsors.

One option would have been to make this tranche of schools integral to a parallel skills strategy, linked closely with an emerging network of institutes of technology and a set of wider technical education reforms. But that is a very different approach – and it is very doubtful that these institutions could serve both purposes.

Given the result of the 2017 Election, what was allegedly a ‘top priority’ for the next government is now markedly less urgent. But if there is a determination to pursue increased selection, institutions such as these could fit the bill. Alternatively, they could be hidden away within a less controversial industrial strategy led by a different government department.

But plans for increased selection and the proposed industrial strategy are both still at the green paper stage. If and when the new government proceeds with them, we should expect to see parallel white papers. Between them they ought to offer a statement of exactly what the government is seeking to achieve and how it proposes to set about the task.

Given the level of political uncertainty we are unlikely to see new institutions on the KCL and Exeter model much before 2020. The chances of seeing any more are radically reduced, but not entirely eliminated. A network of 15 institutions remains a distant prospect.