Meanwhile, some workforce experts find Trump’s ideas on apprenticeships worrisome. In a June executive order, the president called for the creation of fast-tracked “industry-recognized” apprenticeships to reduce regulations and paperwork on companies seeking to roll out the earn-and-learn model. The concern among some is that this parallel push for industry-recognized apprenticeships could be a stealth means of watering down standards for apprenticeships, making it easier for businesses to avoid wage gains and other requirements of the apprenticeship model.

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“We’ve gotten some signals that some of those standards might be loosened under this new model,” said Mary Alice McCarthy, director of the Center on Education and Skills at New America, a left-leaning think tank. The current system “does need to be modernized and made more flexible and updated for certain industries,” she said, “but creating a parallel system is not something I think necessarily seems like the best approach to the problem.”

The Department of Labor did not respond to requests for comment.

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Zurich’s apprenticeship program is highly structured. On Mondays, Wednesdays and Fridays, Atobajeun and the 22 other members of the company’s two apprentice classes pass through the Zurich lobby in Schaumburg by 8 a.m. and make their way to their assignments in claims, underwriting or finance. They each have a mentor, a prescribed training plan, an hour a day free for homework and plenty of opportunities to ask questions. On Tuesdays and Thursdays, they study at Harper, in Palatine, Ill., a 10-minute drive away.

“Programs like this create an opportunity to understand what path is right for you,” said Atobajeun, who recently rotated to finance after finishing her first four months in underwriting. “That’s probably what school doesn’t have that this place teaches you.”

While white-collar apprenticeships like this one are often sold as on-ramps for people who’ve never been to college, that’s not always the case at Zurich. Roughly two-thirds of the apprentices entered the program with a high school diploma or its equivalent, according to a spokesperson for the company, while 27 percent held a bachelor’s and 8 percent had a master’s. For some, the program is as much about getting a foot in the door or switching careers as it is earning a degree.

A native of Nigeria, Atobajeun enrolled at Harper to study nursing after graduating from a high school nearby. After two years there, she matriculated at Rockford University, about an hour’s drive away. But her schedule was grueling. All through college, Atobajeun worked overnights as a home health aide, earning $9 to $12 an hour. She studied at night, too, then attended classes during the day, catching sleep when she could.

She made the schedule work for a time, but the juggling act became more complicated after the birth of her son. The final straw was when she arrived at work one evening to discover that her patient had died. “You form a relationship with patients and their families,” she said. After learning of the Zurich apprenticeship from her brother, who works at a nearby call center, she left the health care field and hasn’t looked back.

A fellow apprentice Colton Wright, 24, already holds a bachelor’s degree in business. He applied to Zurich after searching for marketing jobs and getting stuck in a Catch-22 familiar to many job seekers. Most positions required relevant experience, yet it was impossible to acquire that experience without a job. Plus, the positions he investigated looked unstable, as if these small companies might blink out of existence at any moment. Zurich, with nearly 85 offices throughout the United States, seemed like a smart long-term bet.

“I knew what I wanted in a company and that’s why I ended up here,” Wright said. Like all apprentices, he is required to work an additional third year at Zurich. After that, he said he hopes to become a claims handler, which pays a median salary of nearly $64,000 a year.

The attrition rate at Zurich has been relatively high, with seven of 48 apprentices dropping out before completing their two years. Jennifer Schneider, a spokeswoman for Zurich, said the company isn’t concerned about those numbers. Some people have left voluntarily to pursue an education elsewhere, she said. With the insurance industry facing a tsunami of retirements that could free up some 400,000 jobs, Zurich and companies like it have plenty of incentive to find new ways of recruiting workers. But if businesses burn through apprentices and the programs don’t end up benefiting employers, it’s easy to imagine how some apprenticeships could disappear.

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Apprentices study for an associate degree in business at Harper College, which is working with community colleges nationwide to help them develop apprenticeship curricula.

The apprenticeship program reflects a broader shift toward occupational training at Harper College and institutions like it. Kenneth Ender, the college’s president, said that two-year — and even many four-year — liberal arts degrees no longer hold currency in the labor market unless they’re paired with industry-specific skills.

While some decry this departure from academic education, Ender said students are still being equipped with the solid foundation in math and English that will allow them “to continue to learn the rest of their lives.”

“The slow, four-year baccalaureate is a privileged way of getting an education,” he said. “Some will be able to do it; most won’t.”

Harper has started seven different apprenticeship programs since 2015, and it has two more in the works, in cybersecurity and IT. Models differ slightly: The cybersecurity apprenticeship offers a certificate, not an associate degree, for example. All the companies working with Harper pick up the costs of school — about $15,000 per student for white-collar apprenticeships — but that’s not a requirement of the model. Apprentices participating in a program run by the professional services giant Accenture, for example, must pay for their own courses, officials with the company said.

Rebecca Lake, Harper’s dean of workforce and development, said she doesn’t tailor the programs narrowly to fit the whims of any particular employer. “I don’t sell it that way,” she said. “It’s an associate degree in business.”

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Apprentice Tommy Dowd is studying for an associate degree in business administration at Harper College while working three days a week at Zurich.

One afternoon this year, Wright and his fellow apprentice Tommy Dowd sat in Harper’s no-frills cafeteria discussing the three-hour insurance class from which they’d just been sprung. The course material was dense, Dowd said, but sometimes “something will click. This is what I’m doing right now [at work] and my class is talking about it.”

Dowd, 21, who is working toward his first degree, isn’t sure exactly what he wants do after the apprenticeship. But, he said, he likes the practical nature of his coursework and appreciates the chance to gain concrete business skills. Atobajeun, meanwhile, said she has a plan — she wants to transition into human resources at Zurich once the apprenticeship ends.

She has already identified a future mentor in human resources: the manager who first interviewed her for the apprenticeship. When he called Atobajeun to offer her the position, he gently ribbed her for accidentally cursing during the second day of interviews. (She’d been mortified.) The HR manager told her she had impressed him and would receive an offer, but he issued a good-natured warning: “Don’t embarrass me.”

So far, so good. Atobajeun’s job performance has been anything but embarrassing. Last semester, for the first time in her academic career, she earned a 4.0.

CORRECTION (April 20, 2018, 12:56 p.m. ET): An earlier version of this article misstated the cost to companies of Harper College apprenticeships. It is $15,000 total, not annually.