The potential of student leadership to shape educational experience is not fully understood. As such, I think we are missing the opportunity to unleash huge potential in our schools and communities. In the schools I visit, I see some brilliant examples, but I think we could do more.

There are several reasons why I feel this is a matter for the sector to consider. For one, our schools belong to the communities that they serve and leaders effectively look after schools for the next generation of families. The school does not belong to the workforce of today: it belongs to the community of tomorrow. Children in schools today are the community citizens of tomorrow - future teachers, nurses, doctors, lawyers, accountants, politicians and even national schools commissioners.

Our pupils cannot just be encouraged to engage in leadership; they must create and own their personal leadership journeys, and we know that many want to do this. This is a cultural shift, not a new curriculum innovation.

In these last few weeks, we have seen evidence time and again of students leading in their schools and communities.

We saw it in the run-up to the general election, when young people demonstrated their potential to think about serious matters and form opinions of their own.

We saw a North Kensington student show incredible leadership awareness, demanding to sit her exam only hours after fleeing the burning Grenfell Tower last month.

We saw it in the younger children who attended the Ariana Grande concert in Manchester in May and witnessed a terrorist attack, but turned out in their thousands to attend the One Love Manchester tribute concert less than a fortnight later, as well as making charitable donations in their schools.

Nurturing this is a challenge (not just an opportunity), not least of all because too often we confuse student voice with student leadership. Just creating the opportunity for the voice to he heard is not enough.

Also, we often see students as the recipients of change rather than the change agents for their schools. And too often we assume that students lack a voice to express their ambition to make things better, when it is clear that this voice has power. Their use of digital platforms is ample evidence of student leadership in its embryonic form.

These three challenges can only be met if we look beyond personal and local context. The best leaders I have been privileged to work with operate beyond their own horizons and this is why, for me, building the capacity of young people to lead is such an unrecognised challenge in the system.

Leadership has its roots embedded in these communities: family, peer group, community, town, regional, national, international - clearly, not everyone can lead in all seven contexts, but I am certain that every young person has a role to play in at least half of these.

5 steps to foster leadership

As an advocate of a new approach, I would want to expose young people to at least these five experiences in their school careers:

1. To work with leaders in different contexts who might hold different views to the young person, but would challenge thought processes and help develop the power of persuasive argument.

2. To read some of the great leadership speeches from history to see that context matters, but not as much as the motivational language of powerful moral purpose.

3. To deepen their awareness of the spectrum of political thinking and how leadership in a political context shapes actions and outcomes for communities.

4. To take on difficult personal challenges to build confidence and resilience - from taking on a public-speaking task to confronting and diminishing a fear or challenging discrimination wherever it occurs.

5. Last but not least, to behave as a leader. Not waiting to be told to lead, but identifying a challenge and taking responsibility for making something better. Wearing the leadership mantle with confidence so others follow.

If we were to achieve something close to this, we would see a more equal and just society. We would move beyond the language of disadvantage to one of opportunity and we would empower generations of young people to grow as responsible and tolerant citizens.

In doing so, more adults might take responsibility for improving their own lives and those of people around them, too. Student leadership is the most under-recognised challenge being faced by schools today.

This is an edited version of a speech delivered by Sir David Carter at the Institute of Education’s summer reception last month. Sir David Carter is national schools commissioner