In her first year as Fed chairwoman, Ms. Yellen has made a point of showing public interest in the plight of the unemployed and in programs seeking to help them. Her first public speech after assuming the helm, in Chicago in April, highlighted the stories of three workers. That trip included a similar visit to a job-training program. She has maintained the view that the job market is far from good health, and that monetary policy can help, even as some Fed officials argue the Fed’s work is done.

On Thursday, Ms. Yellen took evident pleasure in hearing the stories of people who found jobs in recent months, beaming and congratulating them. She also pressed for information about the experience of looking for work.

Are there particular skills that make candidates more desirable? If math makes a difference, how much math do people need? And several times, in slightly different ways, Has it gotten any easier to find work? Does it feel like it’s getting better?

Bin Qamruzzaman, a 34-year-old Marine Corps veteran, lost his job at a military contractor in a mass layoff in November and spent nine months looking for a new one. Ms. Yellen asked if the problem was a lack of skills or a lack of opportunities. Mr. Qamruzzaman, who has a degree in engineering, said that he saw plenty of listings, and shipped off plenty of résumés, but that companies did not respond. The Connect program was able to help him by identifying companies that really were hiring, he said, and by putting him directly in touch with their executives.

Ms. Auerbach said little things often made the difference. Many employers, for example use computer programs to screen résumés, so she teaches student to repeat the exact phrases in the job posting. “If it says ‘outstanding interpersonal skills’ we make sure they write ‘outstanding,’ not ‘excellent,’ ” she said.