In a playground outside a YMCA, Mayra Aguilar rolled purple modeling dough into balls that fit easily into the palms of the toddlers sitting across from her. She helped a little girl named Wynter unclasp a bicycle helmet that she’d put on to zoom around the space on a tricycle.

Ms. Aguilar smiled, the sun glinting off her saucer-sized gold hoop earrings. “Say, ‘Thank you, teacher,’” Ms. Aguilar prompted Wynter, who is just shy of 3 years old. Other toddlers crowded around Wynter and Ms. Aguilar and a big plastic bin of Crayola Dough, and Ms. Aguilar took the moment to teach another brief lesson. “Wynter, we share,” Ms. Aguilar pressed, scooting the tub between kids. “Say, ‘Can you pass it to me?’”

Ms. Aguilar and Wynter are both new at this. Wynter has been in the structured setting of a

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