As A-level exams draw nearer, I have returned to teaching Arthur Miller’s Death of a Salesman. A cautionary tale on being wedded to an ideal that is unattainable, it has left my students ultimately frustrated with the central character, Willy. Why can’t he think outside the box he hems himself into, they wonder. He could have been bolder with his ambitions in the way we, their teachers, encourage them to be.

Making young people aspirational is the bread and butter of teachers everywhere. It forms the background noise of our daily dealings with our students. Each lesson of each day, we bargain with them: if you stop fidgeting and concentrate, if you apply yourself with maximum effort, you will, eventually, be rewarded. For students from poor and disadvantaged backgrounds, it’s a carrot forever dangled before them. Hard work begets success, a future of fulfilment and financial ease they are told. Will Smith said so in his umpteenth motivational video, so it must be true. What is left unspoken, but no less definitively delivered, is that failure can only be considered a predictable result of indolence.

But when the government’s own social mobility commission reports that “inequality is now entrenched in Britain from birth to work”, adding that “social mobility has been stagnant for the last four years”, it perhaps befits teachers to better prepare students for the truth. Education may well be presented as the great leveller of an uneven playing field but the lie is that it ensures equality of opportunity for all. At this point, it’s hard to know if this is another falsehood to be maintained, much like fibbing about Father Christmas or the tooth fairy. We must have our young believe in the magic of meritocracy, never mind if failure to climb the social ladder is internalised and felt as individual inadequacy – the bizarre thinking being that it is far more positive to allow pupils to blame themselves for what has been determined as a foregone conclusion mapped out by wider social structures.

If the above reads as dangerous pessimism and anger, remember that, as teachers, we are by our very nature hopeful. We teach precisely because we want to enable “human personality that is able to flower and realise itself” to quote Arthur Miller. We perhaps most keenly understand the tragedy behind the figures of social immobility. It is enraging. No wonder, then, that last year the social mobility commissioners, led by Alan Milburn, quit en masse, so exasperated were they with the lack of political resolve on the issue.

Last week Dame Emma Thompson, an ambassador for the Children’s Future Food Inquiry, expressed incredulity at “Dickensian” levels of food poverty. The fifth richest nation in the world has a third of children living in poverty, with 2.5 million of those in “food-insecure” homes. At the same time, the social mobility report finds that by the age of six, there is already a 14% gap in phonics attainment between children entitled to free school meals and their more advantaged peers. By age seven that gap widens to 20% in writing and 18% in both reading and maths.

We are often told by government that schools are where we must focus attention when considering social mobility. Yet that idea has proved hollow at best. At its worst it simply sounds disingenuous. A Channel 4 survey reported earlier this week that 86% of teachers believe there has been an increase in child poverty over the past five years. It is in this climate that teachers, teaching in schools already facing severe funding cuts, are in many cases reaching into their own pockets to provide their pupils with basic necessities such as toothpaste and toothbrushes. How can a child be expected to excel at a subject when they are busy pushing down their stomach so its growls won’t be heard by classmates?

Some of the most disadvantaged pupils that I come across display the kind of heroism, to call upon Miller again, that the playwright was attentive to. Miller, interested in redefining who could be cast as a tragic hero, writes in Tragedy and the Common Man that the everyday person becomes heroic in their “battle to secure [their] rightful place” in the world. My students display such heroic optimism despite being enmeshed in a society so deeply flawed that it continues to waste their talents.

For Miller, “The Greeks could probe the very heavenly origin of their ways and return to confirm the rightness of laws. And Job could face God in anger, demanding his right and end in submission.” This generation’s young deserve much better than the status quo. They deserve meaningful change.

• Lola Okolosie is an English teacher and Guardian contributor