The figures are stark: if you go to a private school to take your A levels, you have about a one-in-17 chance of going on to Oxford or Cambridge (2,800 students out of a cohort of about 48,000); if you go to a state school, it’s one in 60 (4,200 from 252,000); and if you’re on free school meals, it’s only one in 900 (just 50 students out of 45,000).

It seems perverse to argue either that these figures are the result of genetic differences in academic potential or, given the considerable energy expended by the universities to remedy them, that they spring entirely from the biases of the decision-makers (although I am aware that there are adherents to each of these beliefs).

We are left, then, with three choices: to shrug our shoulders and accept that this is an inevitable inequality in an unfair world; to look at the size of the problem and persuade ourselves that if it can’t be completely rectified, then we shouldn’t try; or to put our shoulders to the wheel and do what we can to give young people choices and opportunities based on their talents and decisions rather than on the wealth and class of their parents.

As a school leader, I see myself firmly in the third camp. The question is not whether perfection is possible, but what can be done from here to make things better.

Oxbridge tutors will tell you that they are looking for potential - that they are looking for students who can benefit from the education on offer. Students who want to learn, who know how to think. Students who have the foundations of knowledge required for further building, and who are able to communicate their understanding well enough to take part in an academic community.

The main observation from the data with which I started is, therefore, that independently educated students, as a body, show more of these features than state-educated students and that financially disadvantaged students, as a body, score less well. A second observation is that these attributes are not arbitrary hoop-jumping, arcane skills of use only to the residents of ivory towers; instead, they are skills worth developing in all our young people - abilities to which all students should have access.

Having identified the issue, it remains for us to consider what can be done. What can state schools, their colleagues in the independent sector, the government and the universities do to give more young people the opportunity make an educated choice of whether they wish to head to one of these universities and, whether they do or not, to develop these valuable attributes?

Students who want to learn

It is surely the defining feature of a university student (or, at least, in the Platonic ideal) that they wish to spend some of the best years of their lives in scholarship. In reflecting on different acceptance rates to these universities, it is, therefore, worth thinking about whether there may be differences in the desire to learn and, if so, how one might go about addressing them.

There is something intrinsically pleasurable about learning but it is not an easy pleasure and, like the dark side in Star Wars, there are alternatives that are quicker and more seductive. The learning journey is rather like a long hike: it’s an amazing feeling being in the open air, feeling the muscles stretching, but there are marches that are no fun at all when the drizzle sets in. At this point, those who are kept on the trail by enjoyment alone will surely turn off and seek quicker and more reliable sources of entertainment.

For those, however, who trudge through the sloughs, there are beautiful panoramas, glorious paths through sun-dappled woodland and a sense of achievement at the end of the day. The more you learn, therefore, the more experience you will have of the joys, and the greater the chance you will stick to the task.

To get started, however, there have to be other motivations. Do those around you, particularly your parents, learn and value learning? Do you get praised for learning? Do you get opportunities to gain social credit as a result of scholarship? Do you have examples around you of how learning can lead to desirable ends? There also needs to be something to keep you going: do your teachers crackle with excitement at the thought of learning something new? Is learning offered to you as a good in itself or merely as a means to passing exams? We need to tell students how amazing learning is and, just as a well-timed piece of chocolate can keep tired legs moving, we need to make sure they have regular opportunities to see, and feel, the rewards for their efforts.

Taking advantage of university education is not, primarily, about what you know - it’s about what you don’t know. Wanting to learn is a key attribute for a student.

Students who know how to think

In order to succeed at the most academic universities, students need to know how to think. If we take as our a priori the idea that disadvantaged and state-educated students are less good at the kind of thinking that is being assessed (this is, at least, statistically true), then we can speculate as to the mechanism by which this difference may be created. One source of advantage experienced by some students (who may well not realise the value of their advantage) is the dinner-table conversation. This archetypally middle-class occupation is a fascinating study in the development of intellectual advantage.

Teenagers whose homes include scheduled, effectively compulsory, periods of discussion will be used to thinking that they should have ideas (in order to hold their share of attention) and that the reward for ideas is to have them tested and questioned. Practice at any skill improves performance, and one mealtime a week for 10 years is 500 hours of ideas, games and interrogation that students whose homes are not built around this activity will miss out on.

Schools, meanwhile, can promote thinking by challenging “correct” answers, creating a classroom ethos in which supplementary questions are to be expected: “Is that quite true?”, “Is that always true?”, “Can you generalise?”, “Is there a specific example?”, and so on. The opposite environment is when a question is asked that seeks a specific answer and the giving of the correct answer heralds the move to the next question. Teachers have to be allowed to challenge students and allow themselves to be challenged.

This is not a question of imposing middle-class habits and values on those who have no wish to adopt them, but uncovering the joy of hard-thinking, the delight that comes from winning a logical argument. It is also a matter of deepening understanding and developing an expectation that the subjects studied should make sense, that we can look for patterns, make predictions and solve problems. It is turning knowledge from a collection of facts to a tool that can be used.

No academic subject allows for absolute truths - not even pure mathematics - and, in order to relish the hurly-burly of academic debate, students need to have their answers challenged (even the correct ones). Being able to think is at the heart of university scholarship and so students have to get over the idea of education being a process of absorbing, unchallenged, the knowledge of the sages and regurgitating it on to an examination paper.

Students who have the foundations of knowledge

Universities say that they are looking for students who have academic potential. This means much more than innate intelligence - it is a measure of a student’s ability to make progress, to know more (much more) at the end of a three-year regime than at the start. The distinction is important because existing knowledge is irrelevant to ultimate academic ability but key to engagement with a specific course. Universities, understandably, do not want talented ignoramuses - to natural ability they want to see yoked knowledge and understanding, and there are two levels of knowledge to acquire: a common core and a wider hinterland.

There are some things that all students for a course must know - a syllabus that could be (and, in many cases, is) tested by A levels - but this is not enough. In addition, students should have some knowledge from beyond the core: the syllabus is a starting point, not a limit. No student can know all there is to be known - there is too much - but all students are expected to bring something of their own to the conversation, to have some kind of hinterland to draw on.

The most effective resource that a school can offer to students who wish to develop their intellectual hinterland is a well-stocked library and a knowledgeable librarian. With these in play, all the teachers need to do is to bang on about reading. Unfortunately, both the resource and the banging-on can be squeezed out in a financially stretched and syllabus-driven environment. Without a library, students only get the drip-feed of what we offer in lessons; with one, they can gorge themselves on all mankind has said, done, thought or been.

Universities expect that students will know things before they join. This means sixth-formers need to use as much of their two years to learn things as possible, and so schools need to be places that are brimming full of fascinating information.

Students with the ability to communicate

Elite universities that use interviews as a primary means of selection rely on students not just knowing and understanding, but being able to communicate their learning in conversation with an academic. Universities that use the quality of written work to select allow this to be factored into measures of pure subject ability. Students who are comfortable and confident in communicating their thoughts beautifully and precisely will, therefore, have an advantage over those whose language use is muddled or awkward.

Schools need to face up to this and push students into formulating their ideas, into writing and speaking about what they think. Debating should not be restricted to those keen enough to attend the society.

Universities also have a responsibility not to overemphasise this aspect of their selection process. Articulating ideas to a high standard is an important aspect of an undergraduate degree, but it can be taught.

Social mobility?

We don’t choose our parents or the community into which we are born and yet these have an enormous impact on the opportunities that come our way. Some of this variety is beneficial to society - it provides us with a vibrant and heterogenous world in which new ideas can flourish; some, however, is damaging - it cuts off access to talent and embeds inequality. Education cannot rectify all the ills of society, but we can do something; we can push our students beyond their natural or comfortable level and stretch them to be the best. Ideas and thoughts, after all, cost nothing.

Social mobility is not forcing young people into middle-class moulds against their will; it is offering them the opportunity to choose their path, to make the most of their time and talents. Social mobility is not something that can be delegated by society to schools. But schools should be proud to have a central role in this challenge. Dreaming of social mobility is not ignoring the barriers faced by the disadvantaged - but it is believing in a better future, accepting that being disadvantaged is a disadvantage but refusing to give up. Just because some people have a head start in life, it doesn’t mean they can never be caught.

James Handscombe is the principal of Harris Westminster Sixth Form in London. He tweets @JamesHandscombe

This article originally appeared in the 5 April 2019 issue under the headline “Breaking down the door to the ivory tower”