By Mike Baker
Education correspondent, BBC News
It is the biggest question for teachers and parents: what sort of minds should we be trying to develop in our children?
Is it the traditional educated mind, able to master an academic discipline?
Or should we be nurturing the "creating mind", encouraging young people to "think out of the box"?
According to the world-renowned psychologist, Professor Howard Gardner of Harvard University, there are at least five kinds of minds that we should be developing.
Gardner has already had a huge influence on educators with his theory of the multiple intelligences that exist among different children.
This underpins theories such as "personalised learning" that are rooted in the belief that different children learn best in different ways.
This week, in a lecture at the Royal Society of Arts in London, he outlined the five minds that he believes future generations will need if society is to flourish. The lecture was based on a book, Five Minds For the Future, due out next year.
When applied to education policy and practice, his theory raises some difficult questions.
To oversimplify his thesis, the five minds are characterised as: disciplined, synthesising, creating, respectful, and ethical.
The "disciplined mind" covers the conventional approach of developing an ability to master an academic subject, a craft, or a profession as well as, in the other sense of "discipline", the ability to apply oneself to the business of learning.
The "synthesising mind" is the ability to absorb, sift, select, and make sense of the vast and indigestible amounts of data that surround us in the internet age. This could be the most important of the five minds for survival in everyday and working life as we flounder in ever-higher tides of data.
The "creating mind" is Gardner's third category. This is the mind that "forges new ground" and discovers new ways of doing things.
This raises the question: "can creativity be taught?" Is creativity inhibited, rather than encouraged, by traditional education with its focus on learning the best of what has been thought and said in the past?
Gardner says he now believes that personality and temperament, not education, are perhaps the most important factors in developing the would-be creator.
This is a challenge to teachers who like to think their role is about encouraging creativity.
If Gardner is right, it may be counter-productive for schools to try to develop creative minds.
Moreover, he argues, the creative mind needs repeatedly to come up against obstacles and to experience failures. Are schools willing to put children, quite deliberately, through the experience of repeated failure?
The fourth category is the "respectful mind". This is about recognising the "otherness" of people different from ourselves and respecting the differences of, for example, traditions, religion, and ethnicity.
Schools clearly do believe in developing respectful minds, even though they cannot be measured or included in league table performances.
But how easy is it to develop the "respectful mind" if children rarely meet peers from other religions, ethnic groups, or social classes?
This is where we start to run into difficult policy issues.
Should governments be forcing integration? Should they continue to encourage faith schools when those schools tend to isolate children of one religious and ethnic group from others?
If children grow up apart, and are educated apart - as happens in Northern Ireland - how much chance is there of developing respect for each other's religions?
In an interesting coincidence, this week also saw a reopening of the debate about ethnic quotas for schools.
The head of the Local Government Association, Lord Bruce-Lockhart, said it was unacceptable that non-white pupils should form 90% of the population of one school when white pupils form 90% of another school just down the road.
He suggested it might be time to introduce ethnic quotas to school admissions to end this segregation.
This follows the decision by the Church of England to take 25% of its intake at all its newly-opened schools from families of other faiths or no faith at all.
This issue carries a lot of historical baggage. The practice of bussing pupils from one district to another in the USA, to overcome racial segregation, proved unpopular and problematic.
Quotas do not go that far. They are not about trying to overcome the fact that racial and ethnic groups sometimes choose to live apart or are forced apart by housing costs.
The concern of Lord Bruce-Lockhart and the Church of England is, more modestly, to ensure that schools better reflect the religious, ethnic and social composition of the neighbourhoods they serve.
But by highlighting the importance of the "respectful mind", Gardner raises a challenge to current policies such as the state funding of faith schools and the emphasis on parental choice.
Most of the evidence from the newer faith schools, and from research into the effect of school choice policies, suggests they increase social sorting and segregation.
There is therefore an uncomfortable clash between two government aims: greater parental choice and more integration.
Gardner's final category is the "ethical mind". This goes beyond simply respecting others towards actively striving to do good, trying to make the world a better place.
The "ethical mind" encourages us to do what is right even when it clashes with self-interest.
This is difficult in a highly competitive age. Should a school accept, or retain, pupils whom it knows will damage its results, its truancy record and its league table position?
Moreover, should it do so when it knows that the school down the road is excluding pupils, or framing its admissions policy, to improve its league table standing?
In my experience, teachers are very ethical people. Yet we hear more and more cases of teachers, and head teachers, who have cheated in coursework or national tests in order to protect their job or their school's reputation.
At a less extreme level, many teachers feel pressured into narrowly drilling pupils for exam success rather than teaching them the broader aspects of subjects. They are therefore putting self-interest, or self-preservation, ahead of what they think is right.
Perhaps the lesson of Gardner's lecture is that it is time that more teachers found the confidence to exert their professional sense of what is right and wrong over what they feel external pressures are forcing them to do.
That is not an easy lesson.