There were toddlers in prams, babies in carriers, wrapped up against the cold, young children clutching placards and teenagers, thousands of them, banging drums and chanting protests. The energy and sense of urgency among the 500,000 climate marchers through Madrid at the last UN climate talks in December stood in stark contrast to the stalled, static and bloodless conference itself, where talks on the arcane technicalities of carbon markets fell apart amid acrimony.

Schoolchildren have led the way in climate protests and climate action in the past 18 months, with the school strikes begun by Greta Thunberg spreading worldwide. Thunberg herself crossed the Atlantic twice by boat to attend the climate talks, and the Fridays for Future movement has spawned waves of similar protests.

“These [striking] schoolchildren have grasped something that seems to elude many of their elders,” the UN secretary-general, António Guterres, wrote in the Guardian last year. “We are in a race for our lives, and we are losing. The window of opportunity is closing. We no longer have the luxury of time, and climate delay is almost as dangerous as climate denial.”

With so much focus on children – who will have to live with the consequences of climate breakdown and ecological disaster, species loss and pollution – the role of education is key. But in England, climate change barely figures on the national curriculum, and campaigners complain that schools are not required to teach it directly.

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In 2013, a row broke out over changes to the curriculum in which a specific reference to climate change was removed in favour of a more general requirement to teach environmental change. Michael Gove, education secretary at the time, was accused of pandering to climate dismissers. Campaigners say the wording of the requirement is not strong enough.

Jenny Thatcher, campaigner at Friends of the Earth, says: “Young people graduating from school and college in 2020 would be forgiven for believing that two parallel universes exist: one in the classroom, and the real outside world. [Climate change] should be on the curriculum – it is pressing and urgent.”

The Department for Education says primary school children are taught about how environments can change as a result of human actions, while in secondary science they are taught about the production of carbon dioxide by human activity and its effects on the climate.

In GCSE science, they consider the evidence for human-caused climate change and how CO 2 and methane can be reduced, as well as renewable energy sources. In GCSE geography, they look at the causes, consequences and responses to extreme weather conditions and natural weather hazards. Since 2017, pupils have been able to take an environmental science A-level.

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But the climate crisis, and the breakdown of ecosystems caused by our depredations, are not only questions of science. These are economic disasters, too, plunging hundreds of millions of people into poverty and they engender social upheaval, including migration and conflict.

The solutions to climate disaster also offer a range of intriguing possibilities for study, from the development of solar stoves for Africa to the changes needed in our diets, farming and food production.

Properly taught, climate change could fit into subject areas across the curriculum, not just physics, chemistry, biology and geography but economics, history, social studies, media, arts and food technology. Its lack extends to vocational teaching, as Thatcher points out: “Plumbing courses in college are not teaching how to install low-carbon heating systems, and catering colleges are not covering sustainable diets.”

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Some schools and community groups have taken the climate agenda into their own hands. Extra training is available for teachers on how to explain climate issues in the classroom, but it can cost thousands of pounds for a few days, beyond the stretched budgets of most. However, Greenpeace also sends volunteers to classrooms to give talks for free.

Gove, meanwhile, is hotly tipped to lead the UK’s presidency of this year’s crunch climate conference, COP 26, in November, which many experts see as one of the last realistic chances to set the world on course to drastic cuts in greenhouse gases.

Thunberg is likely to attend the Glasgow event, taking the stage along with fellow school strikers.

There will be events and demonstrations around the UK and the world. COP 26 will provide a vital opportunity for children and young people to make their voices heard in the climate crisis, far beyond the classroom.

Fiona Harvey is the Guardian’s environment correspondent