*Scope note: this is the first of a series of posts inspired by three recent publications/projects on UK universities:*

*The IPR Policy Brief, **Diverse Places of Learning? Home neighbourhood ethnic diversity & ethnic composition of universities*

*Results from the Longitudinal Education Outcomes study (see **discussion** at Wonkhe)*

*Tim Blackman, **The Comprehensive University** (Higher Education Policy Institute Occasional Paper 17)*

*Since the education systems of the four parts of the UK differ on some ways and most of my experience is English, I’ve chosen to focus on that country.*

I want to start with a statement made by Tim Blackman in his discussion of what a ‘comprehensive university’ might mean, He points out (p. 19) that the published admission requirements for a computer science degree range from three A levels at A*A*A to two Cs at A-level, and states (p. 20): ‘It is unlikely that these are all assessments of what is needed to succeed on a particular course.’ I can’t speak directly about computer science courses: I can, however, talk about the closely-related topic of mathematics courses.

In 1983 I went to Oxford University to study mathematics: although most entry was still via entrance exam, I took an alternative route and after an interview was given a conditional offer of A level grades ABB (my subjects were mathematics, further mathematics and German). In fact, I got all As, and an S level in mathematics. This is very similar to the current Oxford preference for A* in both mathematics and further mathematics and an A in your third A level. In contrast, if you want to study for a BSc in mathematics and statistics at the University of Chichester (the university closest to where I was brought up), you need a minimum of 104-120 UCAS tariff points (equivalent to BCC), including at least a C in mathematics.

I found my mathematics BA the most purely intellectually demanding degree I have ever done (even though I’ve subsequently done two masters and a PhD). It pushed me to the limit of my ability to think mathematically, whereas I’d found my A levels largely straightforward. What do I think would have happened if someone had come onto the course alongside me with only single mathematics at grade C? They’d have been struggling from the very start and would probably either have disengaged from the course or dropped out. From my experience, a very high level of mathematical ability was required for that particular course.

What about mathematics at Chichester? The teaching I had at Oxford was fairly variable: some very good lecturers and some fairly hopeless ones. The terms were short, but we got intensive teaching, including regular small group or even individual tutorials. Mathematics at Chichester is taught within their Institute of Education, so in theory should benefit from best educational practice. I don’t have figures for degree classifications specifically for mathematics at either Oxford or Chichester, but Oxford as a whole had 35% of its students get firsts and 60% of its students get upper seconds. Chichester had 70-71% of students gaining a first or upper second class degree.

All of which information leads to me a key question. Do I think that an upper second in mathematics from Chichester is equivalent to an upper second in mathematics from Oxford? I am sceptical that this is the case. This is because mathematics is a predominantly cumulative subject: you cannot effectively learn a new skill until you have mastered a number of earlier ones. In contrast, both librarianship and history are far less cumulative and have more forms of skills and knowledge that can be independently mastered. In fact, I was able to succeed on a masters degree in medieval history without having a bachelors degree in history or even an A level in it (I did have an A level in ancient history, plus a number of other transferrable skills). I doubt, however, that anyone could have gone from a bachelor’s degree in history to a masters in a mathematical subject without extensive prior study.

If you’re comparing maths students at Chichester with those at Oxford, therefore, you’re looking at ones at Chichester who, based on their A level results, are largely starting from a lower initial basis of skills and knowledge than those at Oxford, and who are likely to find it harder and more time-consuming to develop new mathematical skills. Under the circumstances, it’s unlikely that in three years many of them are going to end up with as advanced maths skills as students who have spent three years at Oxford. Note that this comparison has no connection with ethnic diversity: students at the University of Chichester (and its mathematical students specifically) are substantially less ethnically diverse than those at Oxford, and nor is Chichester a deprived or post-industrial area.

But there’s an important element I want to add to this. The fact that I do not think a degree in mathematics from Chichester is as good as one from Oxford does not mean that I think it is valueless. It’s here that we meet one of the biggest fallacies in English attitudes towards education: that anything but a ‘top’ qualification is useless. This all or nothing approach is pervasive in discussions of education at all levels. It’s there in the repeated denunciations of ‘Mickey Mouse’ degrees and the complaints that there are too many universities and too many students going to universities. It’s there in the longstanding lack of political interest in further education: politicians are forever talking about schools and higher education, but rarely about anything else (with the recent exception of apprenticeships).

You can also see the same attitude when grammar schools are discussed. Their supporters almost inevitably make the same claim: grammar schools are needed so that bright and hardworking working-class pupils do not have to be in the same classes or schools as disruptive children and have their education impeded by them. The question that is never asked to such grammar school enthusiasts is: what should happen to hardworking but less academic pupils in such schools? Is it OK for them to have their education disrupted by the disaffected? The fact that such a question is never asked, let alone answered, reveals how frequently education is still seen as a privilege for a deserving elite of the academically able and not as a right for all.

To go back to someone who’s gained a 2.1 in mathematics at the University of Chichester: what does it mean for them? Firstly, it’s a confirmation that they are among the best mathematicians in the UK. To give a feel for this, in 2016, there were around 770,000 eighteen-year-olds and around 90,000 people passed A level maths. And in 2015/2016, 8,425 students gained a first degree in mathematical sciences (HESA Table 12). Obviously, not all A levels are taken by eighteen-year-olds or all degrees by these eighteen-year-olds three years later, but you can still see that getting a degree in mathematics implies you have more mathematical knowledge and skills than around 99% of the population of the UK. It’s also interesting to look at data from the Longitudinal Education Outcomes project. There isn’t data specifically on long-term job prospects for mathematicians of the University of Chichester, but there are for the income of maths students at the University of Chester, which has similar entrance requirements and comparable ethnic diversity. After five years, their median salary in 2014-15 was £22,300, against a median salary for all 24-29-year-olds in work in 2014-15 of £20,800 and a median salary for non-graduates age 21-29 of £19,000. In other words, getting a maths degree, even from one of the lower-ranked UK universities, demonstrates that you have unusually high mathematical skills and will probably boost your earnings potential. Even by these relatively crude measures, it is a worthwhile qualification to gain. Any sensible discussion of higher education has to start from the principle that even if there are differences in the relative value of degrees obtained, that does not make any particular degree ‘worthless’.

A real and appropriate crie de coeur in this discussion about education. I appreciate that this is a scoping paper.

There are other points to consider, especially about the undergraduate teaching patterns at the ‘other’ institutions. We know that all establishments offering degrees have to meet qualification criteria and standards before they are ‘licenced’ to go live. The content of degrees has to follow standards and requirements of awards bodies. I have reservations about the model of intensive undergraduate tuition of Oxbridge you outline as a superior one against other models followed by different universities. It has to be remembered we all have different ways of absorbing learning and at differing paces. It is likely that Oxbridge select candidates who they feel will operate well in their pressured environment. Their intake filters will be the higher pass grades they request. In your case an interview, (I had a similar experience With a Russell Group Uni) in which, that element of the assessment would have been covered.

I have some other general thoughts that are germinating , which, if they come to anything, I will feed them back to you.

Very interesting post. I hope it obtains wide circulation.

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Thanks for your comment – you’re right to point out frameworks like the QAA (http://www.qaa.ac.uk/en) which focus on the standards of UK higher education and ensure that universities meet minimum thresholds. And there are also practices like external examiners which can help prevent differences between universities become too substantial.

I probably wasn’t clear enough when talking about teaching methods. I’m not sure that the Oxbridge tutorial system is necessarily the best approach for teaching mathematics, but I think it may be the fastest one and hence the one that allows the coverage of most material. In mathematics, at all levels, the time required to master a particular skill varies greatly. Some students will almost immediately understand a theorem or procedure and will be ready to move onto a higher level very quickly, but some will need repeated working through problems and different approaches to explaining the issues around them until they can grasp its essence.

The course at Oxford was taught at a very high level of abstraction and assumed that students could immediately grasp almost any proof if it was shown to them in logical steps. There was also no more than a minimal attempt to show why any of the maths we were learning might be of any practical use. For the particular kind of students in our cohort, this approach allowed us to learn large amounts of material quickly. For students who were less dedicated to mathematics and less inherently attuned to particular forms of abstract thought, it would almost certainly have been a deeply discouraging and terrible course.

I think most people at all levels of study could do much better at mathematics if they were taught at a pace suited to them and with a variety of methods. Universities such as the OU and Birkbeck and school projects such as the Khan Academy have shown that learners who don’t start off with particular mathematical aptitude, and may even have a phobia about maths, can achieve impressive standards at degree level and beyond. But it is almost certainly going to take them longer to achieve these standards than those who find mathematics easy from the start. If you have degree programmes that are a standard three years in length, maths students at highly selective universities are largely going to come out knowing more mathematics than those at universities which teach students who need more support and a slower pace of work. That makes degrees from highly selective universities better in that sense.

I’d add that all this is specific to subjects (like mathematics) where there’s a certain body of knowledge and techniques that has to be mastered to make progress. There are other subjects, such as history, where there’s far less of a defined body of knowledge to be learned and skills development happens in a rather different way. I may talk about that a bit more in a future post.

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