"We haven't had such a dramatic lack of teachers in Germany in three decades," Heinz-Peter Meidinger, the president of the DL teachers association, told media days before school started in many parts of the country. "All together, 40,000 teachers are missing."

Those positions are being filled temporarily by novices, retirees and students — or they are simply vacant.

Read more: German elementary schools 'rent' male teachers

"The beginning of the school year in many of the states has shown that our country is in danger of gradually moving toward an education emergency," the conservative politician Volker Kauder, one of Chancellor Angela Merkel's closest confidants, told the dpa news agency on Monday.

The problem is the result of many factors: an increase in births, a large influx of refugees, a generation of teachers retiring, a lack of investment in education and high hurdles to get into teacher training programs at universities.

And worst hit are schools where teachers' pay is lowest: elementary schools, trade schools and schools for children with learning disabilities. Inner-city schools in Berlin's poorest neighborhoods and schools in rural areas find it hardest to attract new teachers.

Read more: Berlin and beyond: Getting into the right school

Some states are trying to address the shortage by allowing people without teaching degrees into classrooms. North Rhine-Westphalia, for example, Germany's most populous state, is recruiting university graduates with work experience to get hands-on teacher training in schools. After two years of practice and theory, they should be fully qualified as teachers.

Outside the box

It's controversial in a country where sales clerks, waitresses and tradespeople can spend years getting diplomas in their fields. There's even a special word for those who take unconventional career paths: "quereinsteiger," or people who get in from the side.

Read more: Germany exports a secret of its success: vocational education

Back in 2013 the 16 state education ministers agreed that quereinsteiger could be allowed as a last resort and only to plug a gap temporarily. But they are becoming a "long-term solution" to the dearth of educators, according to VBE teachers union head Udo Beckmann, who called for uniform standards for training the newcomers in an interview with the public broadcaster ZDF on Monday.

Last year about 4,400 people who had qualified through one of these programs were hired to fill some of the 34,300 new contracts nationwide. The highest numbers of career changers were in Berlin (1,270), Saxony (1,100) and North Rhine-Westphalia (800). Berlin and Saxony are among the states most desperate for teachers, but also where educators are provided the least job security. In most other states teachers are civil servants with permanent contracts and attractive benefits.

'Very worried'

Some have scoffed at the idea of hiring teachers from the ranks of people who are striking out on new career paths. Though quersteiger deserve recognition for wanting to work with children, the conservative Kauder said, "I am very worried about the quality of teaching."

Experts such as the education professor Jörg Ramseger argue that people who get into teaching without taking the traditional route don't have time to consider whether they are cut out for the job.

"At university students have five years to experience how small children think and how they learn and how to shape modern learning environments," he told the Tagesspiegel newspaper. "During their studies and internships, the students can examine and think through for themselves whether they really want to and are able to teach small children."

Read more: Education and digitization: Germany should invest in teaching before tech

The traditional route to become a teacher is demanding. High school graduates must show near-perfect grades in numerous subjects to be accepted to universities' teacher-training programs, which take seven to eight years.

Critics of the traditional path, such as Peter Struck, professor of education at the University of Hamburg and a former schoolteacher, say the hurdles are too high and there are too few places, which result in too few graduates.

"The quality of a teacher has nothing to do with his grades," he told the weekly newspaper Die Zeit. "In Passau, high school graduates have to complete a many-week internship in a school before their first semester [at university]," he said. "A course facilitator tells them afterwards whether or not they are suitable for the teaching profession. Everyone who is still interested then should be admitted."

A recent study by the Bertelsmann foundation estimated that 105,000 teachers would have to be hired by 2025 to meet the needs of Germany's elementary schools, while a maximum of 70,000 university graduates could be expected to begin working in the field in that time. If those figures come to be true, quereinsteiger are likely to become even more common.

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