The good society, the British historian R. H. Tawney once wrote, is not just one in which people can rise up the social ladder, but one in which they can lead a life of dignity, “whether they rise or not”.

Teachers might bear that in mind when they think about the role so often allocated to schools in fighting economic inequality. In the last 30 years, a huge imbalance has been created between the rich and the rest: incomes for the richest New Zealanders have increased by around $60,000 a year, while those of the poorest have risen by just $2,000 a year. That leaves many families struggling to pay the bills, or afford the growing number of household items – like personal computers – that are deemed necessary as society’s affluence increases.

The answer, we are often told, is education. Barack Obama’s education secretary, Arne Duncan, once described having a job in education as the ultimate in social justice work, and similar – if less emphatic – ideas get thrown around here.  Schools, we are often told, can help poor children lift themselves out of poverty, improve their life chances, and reduce the imbalance between them and richer children.

The problem is that this is a zero-sum game. If you give the child of cleaners a good education, so that they don’t have to become a cleaner, all that means is someone else’s child has to become a cleaner; and if, in between times, you haven’t done anything to improve the terms and conditions of cleaners, if you haven’t lifted up their pay and increased the respect in which they are held, then you have literally achieved nothing, only changed the name of the person who gets to be paid, and treated, badly.

That isn’t to say that schools can’t transform the lives of children in poverty; of course they do. But that transformation should only be about helping them to discover their talents, not to rise out of poverty.

In other words, we need a decoupling. There is the question of what talents children have, and how they are developed; that is properly the task of teachers –  the task of nurturing kids, of imparting knowledge and skills, of unearthing and even to some extent creating talent.

Secondly, and separately, there is the question of what rewards those talents earn. And that is society’s look-out. Society should be able to order things so that there are few imbalances of wealth and income, barring whatever extra rewards are given to those who have genuinely worked harder or made a greater contribution to the general good.

Given that, even on a conservative estimate, socio-economic status explains 60 percent of the differences in kids’ achievement, it is in fact essential that we work out how to redress the imbalance – otherwise poverty will keep on making it hard or impossible for teachers to fulfil their part of the pact. In other words, rather than trying to fix education so that society can function properly, we should fix poverty so that education can function properly.

That, of course, is an aspiration, and the reality for many teachers is that they do have to try to lift their pupils out of poverty. Even if it’s a zero-sum game, you can’t ignore the needs of those who are right there in your classroom day after day.

But it’s important to hang on to the ideal, especially when there is so much muddled thinking in evidence. And that ideal is that society should aim not for social mobility, which presumes a huge distance between rich and poor within which people are ‘mobile’, but for greater equality, so that, whatever talents children develop, they can lead lives of dignity and fulfilment. It’s about ensuring all the rungs on the ladder are comfortable, and reasonably close together, rather than ensuring people can move great distances up and down among them.

This kind of equality is sometimes seen as an anti-achievement, tall-poppy-cutting mission, but nothing could be further from the truth. As Tawney pointed out, “Individual differences, which are a source of social energy, are more likely to ripen and find expression if social inequalities are, as far as is practicable, diminished.”

In other words, if everyone, regardless of their social position, can live comfortably, they’re much more likely to give full rein to their talents. And that, as opposed to the pointless pursuit of social mobility, seems like a prize worth winning.

Max Rashbrooke is a journalist, author and researcher based in Wellington. He is a well-known commentator on the rising gap between rich and poor in New Zealand, with his book Inequality: A New Zealand Crisis being released in 2013.