It’s the last lesson on Friday afternoon. The period where it is hardest for a teacher to inspire and engage a class of tired kids eager to get away for the weekend. But Year 5 is far from fed up. The buzz in the classroom is tangible. Children sit up straight on the carpet in front of their teacher straining at the leash to take part in a conversation designed to work out how best to take other people’s views into account and to consider all factors in solving a problem.

They talk about how it’s important to listen to what other people say without interruption, even though you want to put your idea across. Should you say “Oh what a stupid idea” if you don’t agree with it? asks the teacher, Hilary Power, who is deputy head of Two Waters primary school in Hemel Hempstead, Hertfordshire.

There is a loud chorus of “No!” Julia says: “That would be hurting someone’s feelings.”

But how do you get your views across if you always think you might be hurting someone’s feelings, asks Ms Power?

“You could say ‘I like that idea but I have another one’,” says one of the boys. There are nods all around.

This is not a class where boys dig each other in the ribs and fidget while taking little part in the discussions, or where girls fiddle with one another’s hair, or gaze out of the window. Or where the teacher provides most of the answers. This feels like a sixth form class being encouraged to produce its own ideas. Everybody is responding. But these children are 9 and 10 years old.

At Two Waters this is not exceptional. The school is run on radical systems which involve no text books, no work sheets, no homework, no labelling of or shouting at the children. Talking is allowed in all lessons. Pupils generate their own work and mark it in consultation with their teachers.

They work in pairs throughout their schooling, but towards the end of their time at Two Waters they have learned to “coach” themselves. Everyone is considered gifted and talented - even those with special educational needs.

The school has a mixed catchment area but gets extraordinarily good test results - among the best in the country. Half of the children, for example, reach level 5 in English and most end up on the gifted and talented registers of the secondary schools they move to.

There is regular brain gym, bottles of water on the desks and fruit every morning. The concept of multiple intelligences is built in to learning.

There are visual, auditory and kinaesthetic sessions for all and Edward de Bono coloured thinking hats for the youngest. (It’s a de Bono-accredited school.) The older ones no longer need the hats because the thinking skills have already been imbued. The school is a magnet for visits from educationists who want to see this for themselves.

Nanette Paine, who has been head of the 240-pupil school for nine years, makes no apology for injecting such a wide range of learning and thinking ideas into Two Waters. She reads books voraciously and diligently trawls the internet to keep abreast of the best ideas.

“If there is something out there that is going to help one of my children, then I want to know about it,” she says.

Ms Paine took over a traditional primary school with average results with a vision to remove worksheets and text books and to lift the ceiling on children’s learning. Watching her own son underachieve at secondary school because of teachers’ confrontational approach confirmed in her a desire to run a school where all children were respected and everyone’s voice counted.

At Two Waters she has had to exclude only one pupil permanently and that was because the child could not be stopped from biting. Two others have had temporary exclusions for hurting other children deliberately- something she will not tolerate.

Very few of the staff were there when she first arrived. Now she has a policy of only taking newly qualified teachers who she trains in the Two Waters style.

It is unique. From the inspirational posters encouraging all to achieve to the bold blue walls and the apparent indistractability of pupils and staff in lessons, this school feels very different from the more traditional primary schools a visitor is used to.

Jessica and James are guides on the day I visit. They love school and look puzzled when I mention that some children don’t like going. They particularly like having a buddy to work with. “It really helps your learning,” says Jessica. “You can bounce ideas off one another - it’s much better than working alone.”

James adds: “If your buddy asks for help you don’t give them the answer.

You have to talk them through it so they can find the answer themselves.”

You can see what they mean in full swing in Hilary Power’s Year 5 class after she gets them to work in groups to decipher a cryptic sentence.

The idea is that she gives them four sentences - the last will explain the full story but, before they get it, they have to work as a team to decide what might be coming next. Each group appoints a scribe, an organiser, a leader, a noise monitor and a researcher.

The children discuss ideas with almost no butting in and no sign of one or two pupils dominating. In one group a boy with special educational needs is appointed the researcher and he diligently goes off to fetch a dictionary to look up the meaning of one of the words. Everyone listens when he reads it out. The children are firing on all cylinders. The atmosphere in the room is one of controlled excitement and fun. It’s a fantastic lesson.