Saturday 28 August 2010

Access to University for Children in Care

It is well known that in the UK, the state is a terrible parent, particularly when it comes to educating young people in care and preparing them for the world of work.

A shockingly high proportion of our children in care leave school with no formal qualifications whatsoever, and I read recently that barely 1% of such children managed to get to university in 2003, rising a little to 5% in the last few years. This compares to over 40% of the general population of young people going on to higher education. Now, it is possible that a high proportion of children in care come from social groups where education, in any case, is not greatly valued, so one could argue that even if they had stayed with their families this group might not have done very well. But frankly that is nonsense, and at best a feeble excuse for seriously bad performance by our care system. From what I read, German children in care - often looked after in family group homes - do immensely better than ours.

Children in care in this country generally leave the care system at age 18 and thereafter have little or no public support - financial, emotional and otherwise. This contrasts with most of our undergraduates who have family homes to go back to in the holidays, families who will provide lots of emotional and financial support whenever it is needed, and a supportive environment that values what they are doing and achieving. None of that is available to most children leaving care - they are largely on their own. Given that, it is perhaps not too surprising that few get to university, and that when they do they struggle.

So how could we improve this shockingly bad situation, that deprives many young people of really important life chances - not through any fault of their own or as a result of any formal prohibition, but sadly, as a result of official indifference and lack of support and encouragement? A few ideas occur to me, but there must be many other things that could be done.

(1) Perhaps most useful would be to establish networks of people willing to act as long-term voluntary mentors of children in care, supporting their education and encouraging ambition, achievement, working for longer term goals. Ideally, any given young person should have the same mentor for a number of years to foster consistency of approach and to facilitate the building of strong relationships. I might remark in this connection that with this idea in mind I approached two of my local councils a little while ago, through their social services departments. One never replied, the other replied positively, arranged one meeting, then the whole idea 'died'. This cannot be the best we can do!

(2) We could end the practice of just 'abandoning' young people in care when they reach age 18. After all, most young people in families, even those who feel quite independent, actually need and receive quite a lot of support for several years thereafter (though they don't often like to admit it) - and it's always nice to know that one's family is 'there' in case of urgent need. Young people, I think, need a mix of regular, routine support, plus the knowledge that in emergency there is always someone available to help them. Such knowledge helps to build the confidence to take on long-term projects, such as getting properly educated and going to university. Not many of us could do that without at least the assurance of support in the background.

(3) We need to find better ways of supporting young people financially, not particularly by handing out social security to support idleness, which is unproductive for everyone; but by supporting all forms of apprenticeship, further and higher education for those in care and for those who recently left the care system. Young people often need proper incentives to work, to seek more education, and funding mechanisms should be set up with that in mind.

(4) People who have been in care quite often want to take up education a bit later in life, perhaps 10 or 15 years after they left the care system. At the moment we don't make this very easy for them, I understand - we should be more generous financially, more helpful in enabling these people to find routes to suitable courses or training programmes.

(5) Last, what can universities do? We already accept students who come to us through unconventional routes, for instances via various access courses that prepare for university people who didn't do well at school at the normal time, for whatever reason. That's a good start. And I imagine that in the future more of our programmes will be taught in more flexible ways then they are now - mixes of full-time and part-time study, evening and/or weekend classes, various forms of distance learning, transferable credits (so people can do their study at more than one institution), and so on. All this will help to make university-level study more accessible to people with relatively difficult backgrounds that don't fit the conventional patterns very well.

Whatever we do, I'm certain that we can serve our children in care far better than we do now - and we surely must!

Monday 23 August 2010

More on great universities - The case of China

To most westerners like myself, China is a country of contradictions. This is particularly evident in the country's higher education system, where there is a frenetic country-wide competition for places each year, mostly based on success in a very demanding examination. Yet when students show up at their designated universities and colleges, what do they find? Lots of competent and intensive teaching, to be sure, but not much in terms of real centres of excellence.

Despite growing rapidly for decades now, China's university system, according to an intriguing article by Steven Kuo in The Guardian at the weekend, is not notably characterised by 'critical scholarship' or liberal values. Indeed, thinking of the characteristics of great universities as discussed in my posting of July 5th, it seems that China's higher education system is quite deficient, and may not even be moving in the right direction - for increasing scale at a rapid rate does not imply that quality is also improving.

Building great universities, by which I mean universities actively engaged in research at a serious level, at or close to the world frontier in some areas, is not just a matter of throwing resources at the 'problem'. Neither a big university system nor a smaller élite system offers any guarantee of producing world level research. Nor does it much matter what governments say. They can make plans and express the intention of building world-class universities until they are blue in the face, but they won't succeed, in my view, unless the academic culture they foster is 'right' in some very important ways.

When I first started visiting Eastern Europe in the early 1970s, the academic culture did not seem to me particularly vibrant or healthy, for several key reasons:

(1) There was little knowledge of other countries, and more importantly, little knowledge of relevant research going on elsewhere. So competition in research was missing, and much that was done was repetitive, second hand, derivative; the resulting research papers were mostly of a poor academic standard.

(2) Research was done within a bureaucratic, hierarchical structure, also usually highly politicised - institute directors, for instance, were commonly (communist) party members or at least had party approval (so they belonged to the so called nomenklatura).

(3) Although I couldn't observe this directly, as an outsider, I gained a strong impression that while academic merit had some influence on appointments and over promotions, party approval and patronage had at least as much influence.

(4) Discussions and debate - both at internal seminars and at more open conferences - were typically constrained and formalised. I have never seen a senior researcher's work criticised in public, and it was normal practice for institute directors to be deferred to by all their junior staff - after all, jobs and careers were probably at stake. Often, discussion didn't even get going until the director had had his say. Yet in western universities, especially the better ones, lively critical debate goes on all the time, and the norm is that one should not take personal offence if a colleague criticises an idea or a piece of writing. That's just part of the normal process of developing research ideas. One needs a fairly thick skin, of course, and a degree of personal self confidence, in order to work well in such a critical environment. But this is indeed the 'culture' that enables a university to become great.

Since communist governments collapsed and transition started in 1989-91, there has been a process of slow reform going on in Eastern European universities and research institutes, generally in the direction of improving international links, raising teaching standards and strengthening research. But it is a slow process, since it is not easy to transform the academic culture of a country; such change always meets with resistance from the beneficiaries of the old model.

And China will be no different, except that the near decade long closure of most of the country's universities during the dreadful Cultural Revolution (CR) (1966-1976) has left a big 'hole' in universities' academic staffing. There remain some older professors, trained and in post before the CR, though their academic lives were badly disrupted and many of them will have been political appointees. There is also a rapidly growing cohort of younger academics, some trained wholly in China, but increasing numbers trained in overseas universities (such as the UK, Australia, the US) and returning to China.

This latter group, I think, are really important for the future vigour of China's universities, as they have experienced the more open, liberal, competitive ethos of western research universities. However, being away from China for some years will have loosened the personal connections that often help Chinese academics to find posts in good universities, and returnees might also find themselves less trusted politically than those who never travelled. All this makes changing the culture pretty difficult. China is still quite far from having a system of academic appointments based largely on merit and open competition.

Given the recent growth in the sheer scale of Chinese universities and research centres/institutes, we shall soon reach a position where over a third of the world's research publications in science, engineering and other disciplines will be written in Chinese. Some of this research will undoubtedly reach the highest standards to be found around the world, but one suspects that the prevailing academic culture - still only changing very slowly - will ensure that the proportion of top class research remains relatively low.

Thursday 19 August 2010

UK Universities - Business Models

As I noted in an earlier blog posting (May 19th), who 'owns' UK universities is not entirely clear. More importantly, what sort of business model or business type should our universities adopt, in order to enable them to function best as universities? This is a surprisingly tricky question. For in practice quite a few business forms can be found across UK higher education, mostly the result of historical accident, statutory provision, and occasionally, private initiative.The result is a typically British, rather messy picture. Thus the varied landscape currently includes:

Private institutions, profit seeking

Private institutions, not for profit (e.g. University of Buckingham)

Companies limited by guarantee (e.g. London School of Economics)

Statutory corporations (with charter and statutes needing Privy Council approval for changes) (this covers most universities formed as a consequence of the Further and Higher Education Act 1992)

Chartered corporations (with charter and statutes needing Privy Council approval for changes) (this covers most pre-1992 universities)

Ancient universities, established neither by Act of Parliament nor by Royal Charter (Some changes need Privy Council approval) (Oxford and Cambridge Universities).

Unlike in some other countries, where universities are formally part of the public sector (and university staff are civil servants), UK universities are all legally independent bodies. They normally enjoy charitable status (which confers a variety of tax privileges upon them), and they each have a governing body responsible for all aspects of managing the institution, within the framework of whatever regulation and oversight is currently in force.

This is the background against which some new ideas need to be considered. Thus Nick Butler argued in yesterday's Financial Times that UK universities should be freed from much of the existing government regulation and control so that they can 'manage their own numbers, costs and charges' and hence be 'responsible for their own successes and failures'. This presumably would entail flexible fee setting, something that might come out of Lord Browne's on going review of university funding. And the resulting higher fees could be more manageable for the government, in principle, if the student loan book were also taken off the government's balance sheet and turned into a private sector fund. Thinking logically, too, an institution free to succeed is also free to fail, but I wonder how prepared our government would be to see one or more universities go under either as a result of generally tough financial conditions or as a result of particular bad (or unlucky) decisions. This is quite normal in the private sector, of course, but would this competitive mechanism be allowed to work in higher education? An interesting line of thought, though I have a feeling that actually doing it - making it happen - might be quite difficult.

Another idea was introduced by Simon Baker in the latest Times Higher Education. Instead of focusing on regulation, as the previous point did, this contribution makes proposals about university ownership. In particular, it suggests that the current UK government is contemplating new legislation that could result in universities being owned - wholly or partly - by their shareholders. This idea would turn universities, legally, into something like the familiar public limited company (plc). But why would we want to do that? The claim in Simon Baker's article is that transforming universities into shareholder-owned bodies would make it easier for them to raise money from investors. However, I'm not sure this is right, for several reasons:

(a) Why should anyone buy shares issued by a university unless they expect a decent return on them, namely a suitable mix of dividend payments and capital gains? Hence any university issuing shares will have to offer an attractive return to investors, but it can only do this by investing the funds so raised in sufficiently 'profitable' activities. Many universities might not be very comfortable at the idea of being pushed towards profit seeking in this way.

(b) A few universities have already issued bonds to fund some of their new developments, without any accompanying shift to a shareholding model of the university. It's not clear why this could not be extended without changing the basic 'model of the university', and I don't understand how adding shareholders would make such funding any easier.

(c) Most UK universities exist to deliver high quality teaching and research in a not-for-profit manner and this type of institutional goal sits quite uneasily, I think, beside shareholding and profit seeking.

Hence although there might well be room in the higher education landscape for some private, profit-seeking, shareholder-owned institutions delivering a variety of profitable, specialist courses, it's hard to see much of the existing sector moving in that direction. I fear that sitting and thinking in my office, which is what I like doing best, would not be greatly appreciated by shareholders seeking short-term profitability!

Saturday 14 August 2010

Research degrees and supervision

This summer marks the end of a significant aspect of my academic career, as both my last research students have recently submitted their theses and await their oral examinations (more formally known as the viva voce, or viva).

One of these students,a Ukrainian, has been doing full-time research for her PhD in economics at my university for over three years and I have been her principal supervisor. We have met often, or exchanged e-mails, and I have read several drafts of most of her work; other colleagues have made big contributions to the supervision, especially for the more technical econometric part of the thesis which has never been my forte. The whole process has been hugely interesting, and I keep my fingers firmly crossed that she will manage the oral successfully - in fact my last stage in advising her will take place next week, when we meet to enable me to advise her what sorts of question to expect in the viva. Other than that, I am not of course involved at all in the examination process, in keeping with standard UK practice (this would be different in the US, for instance).

My other student is a Norwegian whom I have not yet met - with luck we shall finally meet on the day that he comes over to Edinburgh for his viva, and I look forward to that. He is a distance learning DBA (Doctor of Business Administration) student of the Edinburgh Business School (EBS), where I was working part-time until end-April this year. Despite formally ending my employment at EBS, however, I agreed with the School that I would continue supervising this particular student through to completion, since anything else would have been quite disruptive to the student concerned. He is already employed and works full-time at a Norwegian consulting firm, so for the most part his research has had to be fitted into spare time, including holidays, though his employer is also very supportive. The research is not in economics, but in risk management, a subject quite new to me, and about which I have learned a great deal in the past couple of years.

Supervision 'at a distance' is very different from what I have been used to, and has taken the form of a mix of e-mails and telephone conversations, the latter almost weekly at critical points of the research. Some of the correspondence has involved detailed commentary on draft chapters or longer chunks of the thesis. What is missing from this sort of supervision is the quick informal chat resulting from a chance meeting in the corridor, the sort of link that has been very useful with my on-campus students. But I think we have nevertheless managed to establish a good working relationship and mostly communicate quite well.

Another complication, though, is that because the DBA is quite a new 'product' of the Edinburgh Business School, some of the supervision is - in effect - conducted by committee, something I haven't encountered before and don't like very much. What happens is that a draft of all or part of the thesis is circulated to some or all of the DBA research committee, with comments coming back to the committee for discussion, then being cast as advice to go back to the student. With the best will in the world this is a problematic approach to supervision, since it's extremely hard to avoid mixed and confusing messages going back to the student concerned, though I've done my best to act as a 'filter' where I thought this would be useful. Officially, though, I'm probably not supposed to do that as this could be viewed as 'diluting' the committee's views. That said, my guess is that this fairly inefficient approach to supervision will be largely dropped once the DBA is more established and the School feels more confident that good standards of research and scholarship are being maintained.

So, my last two research students, and two very different styles of supervision. This makes me wonder how I learned to be a supervisor in the first place. But I started supervising PhD students back in the mid-1970s, only shortly after I finished my own PhD, and I have no recollection of receiving any formal training at all. As far as I remember, my first few students always had someone more senior as principal supervisor, so I guess I learned quite a lot from observing their practice - this sort of on-the-job learning was standard in those days, as there was very little proper training for anything then. Before long, I was encouraged to take on students as a principal supervisor in my own right, and also saw the other end of the process as I was increasingly invited to serve as a PhD examiner by various universities. Gradually, therefore, I picked up the elements of what supervision was all about.

Nowadays, the same learning process takes place but it is more formally structured, with more systematic training of new supervisors (to which I have contributed on occasion); clearer codes of practice for research students and supervisors so everyone knows what to expect and how to operate; and regular reviews of progress to identify emerging problems in good time (I don't recall any reviews taking place in my early years as a supervisor). All this makes the supervision of research students rather more professional than it sometimes was in the past, though I doubt whether good practice has really changed all that much. Supervising bright and imaginative research students has always been fun, and long may it remain so!

Sunday 8 August 2010

Funding Scottish universities

It was a little alarming to read in today's Sunday Times (Scottish edition, p2) that Scottish universities seem to be heading for a funding model that makes little economic sense, while rejecting out of hand the one model that - when carefully designed - offers a promising way forward. For the moment, sadly, politics seems to be ruling the roost, and is certainly well ahead of some basic economics in terms of its apparent influence on current thinking. Let me explain what this is all about.

Of course we all know the context, namely tough spending cuts that will shortly be feeding down from the UK government (spending review expected to publish its conclusions in October), through the Scottish government, then down to the Scottish Funding Council, and finally down to the budgets for individual further and higher education institutions. Given the scale of the UK's budget deficit, still exceeding 10% of GDP, and the determination of our new government to get the deficit down to more manageable levels quite rapidly - which I fully support - most UK government departments are likely to find their budgets cut by 10-20%, I imagine, and in a few cases by even more. For Scotland, which has already quite foolishly decided to defer this year's cuts, the budget reductions will in due course be no less severe. Hence it would be more than a little risky for Scottish universities to be planning for budget cuts of less than 10% in the next couple of years. We don't know the real numbers yet, but this indicates roughly the order of magnitude involved. The outcome might be even worse, but is unlikely to be any better than this.

So what should the Scottish universities do? Their first step seems remarkably sensible. The umbrella body that represents the Scottish universities and liaises between universities and government, Universities Scotland, has set up a working group of university principals to examine a variety of ways forward for the sector. Their remit apparently includes consideration of possible institutional mergers, reviewing the length of degree programmes (most Scottish honours degrees are four years, most English degrees are three years), and various funding options. On the latter, the Scottish government has already stated firmly that it is opposed to fees, whether these are paid up front, or deferred and paid back through the income tax system once graduates are in work and earning at a sufficiently high level (as is, in essence, the system already operating in England). Instead, the Scottish government has expressed support for some form of graduate tax, and the Sunday Times article claims that the university principals support this idea too.

If so, one hopes there will be some rapid re-thinking, as the graduate tax is not really a very smart idea, despite being widely 'floated'. Repetition, unfortunately, does not turn a bad idea into a good one! I imagine, though, that the idea is coming up not because many people really like it, but because of what is or is not perceived to be politically acceptable given present Scottish government policies. For in May 2011 there will be new elections for the Scottish Parliament, and one doesn't need to be unduly cynical to suspect that the present Scottish Government might be rather reluctant to modify any of its headline-grabbing, populist policies before then. One of these policies is their strong opposition to university fees.

Needless to say, no one greatly likes fees, any more than they like paying for any other large item such as a new car. But we don't expect our desire for a car to be met through a government grant, not do we expect to pay for it through the general tax system. Instead, we either pay cash if we have it, put most of the cost onto a credit card, or, if we want cheaper credit, we take out a bank loan and repay that over a period. We're all perfectly used to buying things that way nowadays, so why not something really important and valuable such as university education?

Moreover, a system of student fees can be set up in such a way that no one has to pay up front. Instead, students would take out loans and then repay them once they are in work. Ideally, this can be done in an income-contingent manner so those who don't earn a lot pay back little or nothing; and also be time limited, so outstanding debt is written off after 25 years, say. These are features of the current English model, and they are highly desirable ones. For universities, this scheme means universities get their fees when the students walk through the door, but the students themselves pay nothing until later, as indicated. Two aspects of the present fees system in England do need some reconsideration: (a) at present, a zero real interest rate is charged on student loans taken out to pay the fees, and this is both very inefficient (no one should get a 'free' loan) and very expensive for the public finances; and (b) the stock of student loans outstanding can be regarded as part of the overall public sector debt, and governments are not keen to see that going up at present for obvious reasons. This aside, the student loan scheme is an excellent one and should be extended to Scotland in my view. It will, in any case, be very interesting to see what Lord Browne's committee recommends in the Autumn when he is expected to report.

Meanwhile, we have the idea of a graduate tax popping up here in Scotland. As normally discussed, this would entail all graduates paying more income tax than non-graduates for their entire working lives, the differential not usually depending on the institution at which a person studied, the length of degree course, the subject area, etc. So unlike the fee system discussed above, where the associated loans that students get can depend very much on these features, the graduate tax is 'fair' in the sense that all graduates pay the same (as a function of their incomes, naturally). But this isn't really fair in any meaningful sense, for it means that what students pay bears no relation to the costs of the degrees they have undertaken. Why, also, should graduates pay higher tax for their entire working lives? That can't be fair surely?

In addition, it is worth asking when universities get their money. Is it only when students graduate and start paying their extra income tax? Or is it right at the start, in which case one has to ask where the money comes from. Thinking about this quickly pushes the graduate tax system more and more in the direction of the fees system that has apparently been rejected out of hand. All very confusing! Under the fees system, part of the income tax that graduates pay would go to repay their student loans without ever passing though the public exchequer. Is this also what is envisaged for the graduate tax? If not, then the revenue from the graduate tax becomes part of general government tax revenues, with a presumption that it will be handed over to the universities. But in the UK we have no tradition of hypothecated taxes, in other words taxes collected for a specific purpose - people often think of the car tax, or taxes on fuel, as such a tax, but they aren't, as there is no link - formal or informal - between such tax revenues and spending on roads, say. In fact the only truly hypothecated tax I can think of in the UK is the BBC licence fee. Can we really imagine the graduate tax becoming a new hypothecated tax, guaranteed to be handed over in full to the universities? And even if we believe this, what is to prevent the government from surreptitiously easing back its other contributions to the higher education sector. I think if I were ever running a university I would be feeling very nervous about these ideas. At the moment they are not taking us in a very sensible direction.

Wednesday 4 August 2010

Teaching maths in the UK

Proposals put forward about a month ago by our new coalition government education minister, Michael Gove, to reform A and AS levels (essentially in England and Wales, since the normal school examinations are already different up here in Scotland) have already provoked a good deal of controversy. Mathematics in particular has attracted critical attention, with both Cambridge University and the Royal Society (via ACME, the Advisory Committee on Mathematics Education) opposing the announced reforms.

Now Michael Gove's intention is to scrap the present modular A and AS levels, and replace them with old-style two-year A levels, with assessment largely based on examinations at the end of the second year. The Minister's aim, supposedly, is to "revive the art of deep thought". It's hard to quarrel with the Minister's stated aim here, since the inculcation of better thinking skills in the population can surely only be welcomed. So why are Cambridge and ACME objecting to these reforms to the examination system, and are they right?

Several arguments have been advanced. Let me comment on the major ones.

(1) Harder examinations and the move away from modular courses might discourage more students from taking mathematics at school after age 16, and this in turn would reduce the pool of people from which future mathematics students are drawn. In the worst case, this could even lead to the possible closure of some university mathematics departments.

(2) Only a minority of students taking A level mathematics go on to do maths at university, but many others might well use their maths foundation in a wide variety of other degree programmes. Hence at the A level stage, it is more important to get lots of folk to do the course so that the general level of maths education is higher than it would otherwise be.

(3) In any event, for those who do actually wish to do mathematics degrees at university, A level maths has always been a necessary but not sufficient qualification for doing so. Rather, potential mathematics students have always been advised to take additional courses and/or examinations, such as Further Mathematics, AEA papers in mathematics (Advanced Extension Awards), or STEP (sixth term entry papers).

(4) Nowadays most university degrees are modularised, so surely it makes sense for the school exams like A levels to be modular too.

What should one make of these arguments? Point (4), I think, can be dismissed out of hand. It's a silly point, partly because it seems to imply that all stages of education should be done in the same way, and I'm unaware of any good arguments for that; and in any event, it wouldn't surprise me if the current university fashion for modular degrees eventually went into reverse, as I'm not sure there are terribly good educational arguments for such degrees either.

The numbers game
Points (1) and (2) are really about 'bums on seats', encouraging as many people as possible to take mathematics as far as A level, and if need be making sure the course is not perceived as 'too difficult' in order to achieve that result. I understand the argument, but must confess to finding it profoundly depressing as it seems to imply that school pupils in the UK are such a feeble bunch, and have such limited ambitions, that they cannot (or are unwilling to) cope with a course that is perceived by them, their parents, or their teachers as 'difficult'. This is a great shame, if true.

Why might we not wish to accept this line of argument? Well, I can think of lots of reasons. First, UK school pupils do not come out enormously well in objective international assessments of mathematical attainments - see, for instance, the OECD's PISA surveys. Yet our governments constantly remind us of the importance of international competition for the UK economy, and of the need to raise our achievement levels in science and mathematics, and rightly so. Thus simply accepting fairly weak performance as the best we can do is surely not really very satisfactory. Somehow, we need to shift the whole culture of learning in the UK so it is much more widely understood and accepted that young people need to work hard from an early age in order to learn and succeed. It sounds terribly boring, perhaps, but what's the alternative? And in maths, we might also need a new generation of superbly well qualified, enthusiastic and inspiring teachers.

Second, comparisons that I am able to make personally with other countries don't leave us looking good. Thus I have looked at syllabuses and textbooks from Russia, Kazakhstan, Hungary and to a more limited extent from Singapore, and the level they expect young people to reach is significantly better than what we expect in the UK. True, there is more rote learning than we seem to be comfortable with in the UK nowadays, and probably less 'problem solving', but in terms of basic knowledge and techniques we are well behind.

Third, from talking to my own students over many years, it is almost invariably the case that UK students struggle with the maths they need for economics, while our overseas students almost always cope far better. In fact a few foreign students have even commented to me how shocked they were to discover how little maths many UK students actually knew and could use. This is not a very comforting situation for the UK.

Overall, then, it seems to me that a case can be made for raising maths standards at all levels in our schools, and in that wider context the Minister's proposed reform is perhaps an important first step. The Cambridge and ACME arguments are not, in the end, wholly convincing.

University entrance
Point (3) is about doing maths at university, and the extras that good students need to secure university entry, notably to English universities where degree courses normally last three years. The situation is a bit different here in Scotland as most degree courses are still four years' long - though that might change soon if the forthcoming budget cuts really bite hard.

I'm familiar with these 'extras' partly because I taught STEP mathematics to my son to prepare him for Cambridge entrance, and he was successful; and partly because for the past three years I have taught some advanced maths to an out-of-school extension class at my son's former secondary school. The school itself, and I suspect many schools, is just not resourced sufficiently well to be able to cope with this level of maths teaching. Yet although the STEP syllabus is largely the same as most A level courses, or the Advanced Higher in Scotland, the type of question one encounters is a world away from the typical A level question. For the latter normally splits each question into a series of parts, each following logically from the one before. This is fine in terms of showing that the students have grasped a particular mathematical technnique, but is not so good in terms of creativity and problem solving.

In contrast, a typical STEP question basically says, 'here is an interesting question, solve it', without giving any clues about the area(s) of mathematics that need to be deployed, or the sequence of steps needed for a solution. This is a lot more challenging, especially when the questions have to be done under the usual examination-type time pressure. But this kind of maths is both fascinating and fun, and it would be great if more people could be exposed to it.