What if education policy was made by teachers? And not just any old teachers, but younger ones, new to the classroom, who can cast a completely fresh eye over school practice and procedures. What would it look like?

There would be a new way of teaching maths, a certificate of general knowledge, a bigger teaching load for heads and different assessment at the end of primary schools, according to a group of new teachers on a policy internship week organised this summer by the Centre for Policy Studies (CPS), the right-of-centre think-tank.

These half a dozen teachers, fast-tracked to the classroom on the elite Teach First scheme, are putting forward ideas about what they would do if they ran education policy.

The most advanced policy proposal comes from English teacher Daisy Christo, 26, who recently taught in south-east London on the Teach First programme.

She was shocked to discover how little general knowledge pupils can draw on in lessons. As a result, she researched the area and is now lobbying for a new certificate of general knowledge for secondary pupils.

“Children lack really important knowledge,” Ms Christo says. “Most pupils, for instance, probably don’t know Churchill was a wartime leader. They think of him as a nodding dog who advertises insurance, and there is some recent research which shows that even Russell Group university students can’t name one 19th-century prime minister, and don’t know who fought on each side of the Boer War - so you can imagine how much worse it is in schools, and with a different kind of pupil.”

Knowledge needs to be built upon within a systematic framework, Ms Christo says, “but the current approach doesn’t help with this. In history, for instance, you may be doing the Victorians one week and the Vikings the next. A hell of a lot of teachers know that there is a problem with this sort of approach.”

The Teach First interns agree. “It (the certificate) definitely appeals to me,” says David Lovell, 24, who is teaching in the West Midlands after studying history and politics at Birmingham University. “An awful lot of reading comprehension comes from knowing references and being able to read between the lines.”

“It would be a challenge to get it into the curriculum,” says Henry Dobson, 24, who is teaching in west London after studying history at Newcastle University, “but it seems like a good way of giving pupils a lot of knowledge, without it necessarily taking up a lot of time.”

Other participants are also enthusiastic, pointing out that they had been trained to deliver a skills-based curriculum without any suggestion that the transmission of knowledge could also be important.

In contrast, at least one the interns’ proposed policies focuses on the intersection of classroom skills and subject content.

Katherine Webb, 23, teaches maths in Bradford and graduated in geography from Bristol University. She suggests re-ordering the maths curriculum so that instead of pupils having to constantly spread themselves across the four interwoven curriculum strands of number, algebra, space and measure, and data, they can concentrate in a more sequential way, first on number, then on other things.

“If you haven’t got the greatest number skills in place, you shouldn’t be moving on to algebra,” she says. “All the levels should progress, but it should be number first, then the processing skills.” In fact, Ms Webb explains, she is already working with colleagues at her school to rewrite schemes of work.

Mr Lovell wants to reform school management structures so that those involved in leadership are still actively involved in teaching and learning.

“My idea is that schools should run on the same lines as independent schools, where they have bursars and school administration and teaching are separate things,” he says. “I’m not saying that school leaders should have a full teaching load, or anything like that, just that they should stay focused on teaching and learning; they should stay in touch with what goes on in the classroom, and not be distracted by administration.”

Another intern wants to see breakfast and after-school clubs used more strategically to support pupils’ learning. At present, although schools are encouraged to run such clubs, “they are not as much geared towards homework being productive as they could be”. He suggests involving more teachers and teaching assistants, so that clubs can give struggling children proper professional help with their work.

Another wants to see a system of entirely independent external assessment at the end of primary schools, so secondaries can be given a reliable picture of their incoming pupils’ levels of attainment. Secondary schools, several interns feel, are getting false reports under the current system, which includes national tests and teacher assessments.

“You’re told a child can do this or that, and then you find they simply can’t,” says one intern. “So, you have to go right back to the beginning and teach it to them again.”

Other participants are obviously ahead of the curve - they put forward policies that the Government is already planning to implement. One intern proposes ways of simplifying the bureaucracy around school trips; another suggests that GCSEs should be 80 per cent linear.

Almost all of the interns point out that the day-to-day grind of classroom life leaves no time to stand back and think about the theory or practice of teaching. “So, this (course) is a brilliant chance to consider wider education policies and issues,” says Mr Lovell.

Tom Burkard, education researcher with the CPS, who led the week, says that group discussions include how the cognitive sciences are being ignored by schools, which are not even starting to apply the flow of new findings about how the brain works to the processes of teaching and learning.

Interns also debate the “madness” of thinking that one teaching approach can be laid down for all classroom situations, and consider how old- fashioned “chalk and talk” can sometimes be the best way of putting something over.

They also look at the possibilities for using computer-adapted multiple- choice testing for independent assessment at the end of primary school - a favourite idea of Mr Burkard, who has long argued that this is an efficient, effective and reliable way of assessing pupils.

All of the interns emphasise that, while the CPS is associated with the political right, this did not reflect their own views.

“But it is really refreshing to think about things in a different way from the `academies bad, free schools bad’ kind of way that you always tend to get when you’re in school,” says Ms Webb.

And Ms Christo points out that although many people see political biases in educational ideas, this is often wrong.

“Knowledge has become associated with the right wing, but to the extent this has happened, it’s an historical accident,” she says. “There is nothing right wing about knowledge. I’m not proposing that we fill children’s heads up with knowledge and deny them critical thinking.”

The participants are also challenged to think hard about the basics of education and school life by a series of speakers brought in via the education forum of the radical Institute of Ideas.

Alka Sehgal-Cuthbert, an arts teacher and lecturer, asks if education should be about increasing social mobility, arguing that there is little, if any, evidence that current policies designed to “level the playing field” have improved the life chances of disadvantaged children, and that education should be pursued for its own sake.

Science teacher Dave Perks argues for more pure science teaching and a return to hands-on lab work, and Dennis Hayes, professor of education at Derby University, wonders, “Is education bad for you?”, which leads to a heated debate for and against the national curriculum.

Meanwhile, Dr Shirley Lawes of London University’s Institute of Education, asks: “What do teachers need to learn in training?” She leads an argument for much greater emphasis on subject matter - the interns agree that they are frequently called upon to teach subjects they know little about, and point out that this inevitably affects their enthusiasm and effectiveness in the classroom.

All the participants say they went away with practical classroom ideas, including how to ensure their pupils take in every step of a lesson and how to address a whole class more effectively.

Mr Lovell says he left having spent time thinking about the big issues of education, such as “What is education really for?” and “Is a C grade what pupils really need?” “But most of all,” he adds, “I realised that you have to be your own teacher, develop your own ideas within the system and imprint your own personality on your teaching.”

The internship is one of a number of placements offered by Teach First to participants in its programme over the summer. It also runs its own policy initiative, Policy First, to channel ideas from the classroom to the wider educational world.

This is something that now seems set to happen with Ms Christo’s proposed certificate of general knowledge. Details of her proposal are outlined in a paper coming out from the think-tank Civitas shortly.

Since her inspiration is the longstanding work of American educationalist ED Hirsch, and since education secretary Michael Gove is known to be another of Hirsch’s fans, her idea looks well on the way to gaining political traction.