It only takes a moment talking to Emily Galvin, an apprentice with Ironworkers Local 7 in Boston, to grasp how her first year learning the skilled trades has transformed her life. For one, she has a fresh understanding of the anatomy of a city—of roads, bridges and buildings. She’s taking classes in structural steel, tension, rebar and labor history. “I love how we use mats of rebar,” Ms. Galvin says, “to make reinforced concrete for floors or knee-walls, like for a parking garage.”