During a break on Wednesday she admitted: “I’m not sure how much longer I can go on.

“They turn up without pens or books,” she added of her pupils, most of them the children of immigrants from Turkey or the Arab world. “They fight, they set off fireworks, they kick in doors. There’s no point in trying to teach. If you hang up a poster, they tear it down.”

Her fellow teachers — all native Germans — feel the same way and have begged the government to close the Rütli school. “We’re completely exhausted,” they wrote in an open letter. “More teachers are off sick than students. This is a sign of unbearable pressure.”

Their plight has pushed the subject of Germany’s immigrant community to the top of the political agenda.

Government officials argue that Germany must absorb its immigrants rather than isolate them in ghettos where they may fall prey to Islamic fundamentalist groups. “The government sees it as a security issue,” said Tanja Wunderlich, an immigration researcher for the German Marshall Fund think tank.

Although there is widespread agreement on the need for more integration, opinion is divided on how to bring it about.

Angela Merkel, the chancellor, has convened an “integration summit” for this summer. On the agenda is whether the “naturalisation tests” being pioneered by two German states should be adopted nationwide.

An exam for immigrants in Hesse has prompted accusations that it is hostile to Muslims. The test includes questions such as: “In your eyes, were the perpetrators of 9/11 and the 2004 Madrid attacks terrorists or freedom fighters?” Ercan Yasaroglu, a sociologist who came to Germany from Turkey as a political refugee, said the tests were a mistake. “Immigrants who are trying to fit in feel knocked out,” he said. “They think that this country doesn’t want them.”

The same charge has been made against the Netherlands, which raised eyebrows by encouraging would-be immigrants to watch a video about Dutch society that included homosexual men kissing and a topless woman. In France, Nicolas Sarkozy, the interior minister, last week invited those who were “uncomfortable” living there “not to feel uncomfortable about leaving”.

On the surface, Germany might seem to have less of a problem than France, where immigrant suburbs were set ablaze in rioting last year, or the Netherlands, where a film maker critical of Islam was slaughtered in the street. During the uproar over Danish cartoons depicting the prophet Muhammad, Germany, with its immigrant population of 6.7m, was a haven of peace.

However, awareness is growing that the problem in Germany can only get bigger. Few politicians dare to utter the truth that the country needs more, rather than fewer, immigrants. This is because Germany has one of the lowest birth rates in the world.

Even if the annual influx were to double to 200,000, the population would still shrink by 8.5% by 2050.

The country is struggling to integrate the immigrants already there. The children and grandchildren of 1960s “guest workers” often speak little German and have limited chances of finding a job. Unemployment among immigrants is 26%. Their chances of discovering a role model are just as remote. “School for them,” said Petra Eggebrecht, former director of the Rütli school, “is simply a place to fight for peer recognition, where young criminals become idols.”

Young people are also easy targets for Islamist organisations. Outside the Rütli school last week there was something defiant about the way the children greeted visitors, not in English or German, but in Arabic.

Some states have taken measures into their own hands. North Rhine-Westphalia has appointed an integration minister; Hesse and Baden-Württemberg plan the naturalisation tests.

As for the Rütli school, some are advocating punishment for troublemakers, including stints in special boarding schools to give them a taste of prison.

Sommer, who has applied for a transfer, would rather see the place shut down. “If I don’t leave soon, I’ll have a nervous breakdown,” she said. “I can’t wait to get out of here.”

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