At first glance the class of excited nine-year-olds looks like any other when the principal drops in for a visit.

As their teacher, Yaffa Tala, writes each item on the blackboard her pupils shoot their hands up to specify what they hope will be in the brand-new school building that they will be moving into next month and will visit for the first time on a trip which Ms Tala explains will start at 8am today: a cafeteria (no); computers (yes); a proper playground (yes); drinks machines (for water, yes, for fizzy drinks, no); a library (yes); a gym (yes); individual lockers (yes).

"Will they have keys or codes?" one child asks. There's a murmur of approval when the principal, Ala Khatib, announces that there will be two lavatories for every class instead of the six for the whole school in the "temporary" building it has occupied for the last decade. There is a gasp of excitement when Moid Hussein in the back row asks him if there will be an elevator and the head says yes – changing swiftly to disappointment when he explains it will be not for Moid and his classmates but for the disabled, and for elderly visitors to the school.

But in fact these 36 fourth-graders are like no others in any school in Jerusalem. For a start, as in every class here, there are two teachers – sharing the lesson with Ms Tala, an Israeli Jew, is her colleague Rajaa Natour, a Muslim Arab. And then you realise that about half the class are Arabs (including three Christians) and the other half Jews, with Jews and Arabs, boys and girls, paired up on many of the desks.

The lesson itself is in two languages. It begins in Hebrew – with most of the Arab pupils speaking it fluently. When it switches to Arabic – at the suggestion of the principal – the Jewish children feel less comfortable asking questions in a language most of them have not quite yet mastered. But when Omri Bar Giora, wearing a bright blue Israel national team shirt says – in Hebrew – that he hopes there will be "four football fields" at the new school, the face he makes shows he has no difficulty whatever in understanding the principal when he explains, in Arabic, that, sadly, that would be a bit much to expect. "I make a point of never speaking in Hebrew in class," says Mr Khatib, a first-rate Hebrew speaker.

But this is not for the benefit of the Arab children, but for the Jewish ones, who he is anxious to see turn their good "passive" Arabic – the ability to understand – into the confidence and ability to speak it.

But then Mr Khatib is, in truth, not the principal, but one of two co-principals, the other being Dalia Peretz, a Jewish Israeli teacher (who incidentally learnt her Arabic from her Moroccan Jewish immigrant mother for whom it was the first language). And the two close colleagues are equally presiding over a unique and visionary educational venture, the only Jewish-Arab school in Jerusalem.

Any time now (when the Jerusalem municipality gives it the final permit) and thanks to a major donation from the Rayne Foundation, the charity set up by the late British Jewish businessman and philanthropist Lord Rayne, and other funds channelled through the Jerusalem Foundation from Germany, Switzerland, Liechtenstein and Austria, the Max Rayne School and its 406 pupils will move into its $11m (£5.4m) purpose-built premises.

The school is located on the border between the Jewish West Jerusalem neighbourhood of Pat and the Palestinian East Jerusalem neighbourhood of Beit Safafa from which many of the Arab pupils come. The official opening ceremony is on Sunday.

It is hard to overestimate the importance, pioneering rather than merely symbolic, of the school in a city whose religious and ethnic divisions are at the absolute heart of the Israeli-Palestinian conflict.

Two members of the fourth-grade class, Yazid Ershed, the Arab boy, who asked about the drinks machines, and Aviv Pek, the Jewish girl, who asked about the library, have grown up together in the school having been at the kindergarden together. Discussing what the school means to them yesterday, they completed each other's sentences several times. "I like the school and I really like the teachers," says Aviv. "I have lots of Arab friends. One of my best friends is an Arab girl and, of course, she comes to my house."

The point is echoed by Yazid: "I have Jewish friends too," he says. "We go to each other's houses. We play football, we play with computers or we just talk."

Conscious that outside the school Jewish and Arab children remain segregated, Yazid says: "If they all went to school together there would be no war. They would live next to each other in peace and not fighting each other." What did their friends from segregated school think about them coming here? "When I tell them I go to a Jewish Arab school, they are very surprised," says Yazid. "They don't understand it." Aviv recalls: "A woman who is a neighbour started shouting at my father: 'Poor girl, what is she going to learn from the Arabs?' She doesn't understand that Arabs have a life, they are nice people and not the monsters of the city."

Yazid explains that the school observes all the main religious festivals – the Jewish high holidays, the great Muslim festivals such as the Eid al Fitr just passed, and Christmas. Some of the holidays are shortened to ensure that the pupils are at school for as long as other children in the city.

And he adds: "Last year we studied all the religions together but this year each kid is learning about his own religion." In school, the children speak partly in English– which both are learning – but more in Hebrew, in which Yazid is fluent. So again, does Yazid speak Hebrew better than Aviv speaks Arabic? Aviv nods. Her Arabic is "not good enough". "But I am learning to speak it slowly," she adds. Yazid says of the school pupils in general: "If we speak in Arabic part of the kids will understand but if we speak in Hebrew all the kids will understand."

This asymmetry isn't hard to understand in a city in which the mainly Arab families whose children go to the school – most of whom have Israeli citizenship – deal every day with the many institutions of a city which has been under Israeli control since the 1967 Six-Day War. Arab children are much more likely to be exposed to Israeli entertainment and media than Jewish children are to their Arab counterparts and the principal attractions, such as the city zoo, to take a single example of many, are Israeli.

Improving the Arabic language skills of Jewish children, says Mr Khatib, who like Mrs Peretz, has two daughters at the school, is one of the challenges the school faces. As he points out, "no one told us" how to run a school with Jewish teachers teaching Hebrew to Arab children and vice versa.

Indeed the training, as Mrs Peretz, who happens to be the sister of the former defence minister and Israeli Labour leader Amir Peretz, is very much "in service". But the other challenge is to persuade the Israeli Ministry of Education, having fully accredited the school up to the ninth grade, to allow it to build the high school for which level the school's first pupils will be ready next year. The school is one of three across Israel in what is known as the "Hand to Hand" project – the others being in the Galilee and the northern Wadi Ara triangle of Arab towns and villages. The project's mission statement says that the growth and success of the schools already "testifies to the extraordinary power of a simple idea – that by coming together, face to face, Arab and Jewish children can study side by side, learning each other's languages and cultures" – in turn teaching "that our common humanity is more important than any differences that divide us".

So far, of course, many of the parents who have chosen the school are middle-class professionals. (Aviv's father is a business consultant; Yazid's a lawyer) But Mrs Peretz, who would like to see 10 "Hand to Hand" schools across Israel in the foreseeable future, says that the school is already making strides – partly through scholarships to cover the relatively modest £600 per year costs to families – in attracting more lower income families. Some residents of Pat, a lower middle-class Jewish neighbourhood, alienated from the ethos of the new school being built in their midst, have even held protest demonstrations. But the school is planning intensivediscussions with local community leaders, not least to persuade them to encourage local children to become pupils.

Meanwhile one of the school's many important functions is to confront both communities with the different, and indeed wildly contradictory, narratives of the other. To Israelis, 1948 is the victorious War of Independence and to Palestinians the Nakba, or "disaster", in which hundreds of thousands of Palestinians fled or were forced to leave their homes. That can be painful for Jewish as well as Palestinian pupils.

"Some of them feel guilty saying 'Did my people really do what you are saying'," says Rajaa Natour. "Others feel very proud of their state. In one class a kid got up and said 'We won the war'."

Such a statement, she explains, then provoked a deep discussion about what that victory meant. Ms Natour adds that she works in the school because it "is a very leading project and this may be the only place to make education a tool for change".

And, as Ms Peretz points out, the Jewish parents have already signed up, before their children come, to a school "ideology" which provides for such debate. One parent, an Israeli photographer, Quique Kierszenbaum, who took the pictures for this article and who serves on the school parents' committee, sums up why he and his wife, Sharon, wanted his five-year-old son, Guili, at the school. "We are a very liberal family and we feel that normal schools in Jerusalem have an atmosphere of not knowing anything about the others who live in this city," he says. "For us after six or seven years of the intifada the school seemed like the only solution to staying in this place.

"If you are not part of the solution you are part of the problem and we want to be part of the solution."

This, he believes, translates "into normal life in a way that is easy and natural". Whether it is the pleasure his son has taken over the last month of greeting everyone he meets, Jews and Arabs, with the seasons-old Arab greeting Ramadan Karim, or the Arab and Jewish intensive and free-ranging parents' discussion about how exactly to commemorate the 12th anniversary next week of the assassination of the Israeli premier Yitzhak Rabin by a right-wing fanatic, there is more emphasis on the discussion of democracy, peace and non-violence, and less on mere ceremony.

"We are living co-existence here, not just dreaming or talking about it," says Mr Kierszenbaum. "We're giving to it the most important thing we have –the education of our sons and daughters."

One of the school's newest pupils is Maria Amin, a six-year-old Palestinian girl from Gaza who is confined to a wheelchair which she navigates with a joystick operated by her chin. A patient at Jerusalem's remarkable rehabilitation hospital, the Alyn, she was paralysed from the neck down when the car she was travelling in was caught in an Israeli missile strike on an Islamic Jihad commander which killed her mother, uncle, grandmother and elder brother.

She wasn't at the school yesterday because of medical problems, but Mrs Peretz hopes she will be at the school for several years to come.

You can't miss, fixed to the door of her classroom, under inscriptions of greeting in Arabic, a colourful painting – a house a flower, a tortoise, a vivid rainbow – by her new classmates. In large letters on the painting are written the words"Welcome Maria". In Hebrew.