The past few weeks have been full of high-school and college graduations, but we shouldn’t overlook the 3-year-olds who stood still in their caps and gowns just long enough to receive their diplomas Tuesday evening.

High-school and college degrees are markers of achievement, potential and hope for the future, which we celebrate partly because reaching them isn’t a given. What’s great about the graduation I watched Tuesday evening is that it was celebrating the success of children whose new learning skills will make it much more likely their parents will get to cheer them on as they walk across a stage as young men and women years from now.

Some solutions work, and it’s nice to take a moment now and then to acknowledge that.

The Parent-Child Home Program helps shrink the opportunity gap that exists between different groups of Americans. It’s a national program sponsored locally by the United Way of King County with a number of partner agencies, including the YWCA, serving families. The graduation I attended was held at the YWCA East Cherry Branch, where families in the program have all struggled with homelessness.

Elfnesh Wolde and her husband, Alemayehu Feyissa, watched their son, Leoul, get his certificate. Leoul, who’ll be 3 in August, was one of the younger participants in the ceremony.

Feyissa said, “The fact that this program is out there makes you feel comfortable … that there are people out there who want to help children.”

The family, including a daughter a little older than Leoul, came to the United States from Ethiopia in 2012 and lived for half a year in temporary housing provided by the YWCA across the street from the East Cherry branch, then in another temporary location before moving into a place of their own. Home visitors from the branch follow families as they move around the area, working with about 45 families a year.

Leoul decided I needed a break from talking with his parents, so he flipped through a coloring book, pointing out cars to me. A coloring book can be a good way to learn at his age, and it’s one of the tools the program uses.

His parents said he counts and colors and can recognize lots of animals and can name body parts. “It helps for our kids to know so many things” before going off to school, Feyissa said. Preparing children for later education is a big part of the program’s mission. Children develop social skills and learn how to learn; parents are helped to do their job more effectively.

For two years a home visitor spends 30 minutes a day twice a week with a family. The visitor is usually someone who shares language or other cultural traits with the family. In this case, the visitor is Fahmia Ali, a young woman who graduated from the University of Washington in 2008. She has a sociology degree but also gained experience as a teacher in Dubai and Saudi Arabia after graduation. She wanted to explore the world, she told me, and she came back to the U.S. in 2012 with a desire to work with parents and children.

I spoke with the family before I met her, and they didn’t know that she was also from Ethiopia — she doesn’t speak their language — but they said it helps that she is familiar with African culture.

Ali said she likes working with a variety of families — Peruvian, African American, Caucasian and Syrian.

Feyissa said he and his wife learned from Ali better ways of teaching their children. He sometimes got impatient with Leoul’s high energy. “I get angry, but she has ways of getting him to sit and focus.” He said Ali also knew which teaching materials were best and where to find them.

Middle-class families and families that are fully adapted to American society may take for granted the foundations that children need to succeed in this country, but some families need a little help learning what those building blocks are and how to access them. Families in the program typically have fewer human resources and more challenges than the Feyissa family. Feyissa has a good job now as an accountant for Getty Images. But they, like other families, benefit from having doors opened early in their children’s lives.

The United Way sees the program as a way to address multiple problems at once with a proven strategy. Partner agencies served 750 families in 2012-2013, and the United Way is working to reach 1,200 a year. Children from low-income families who go through the program match the high-school-graduation rates of children from middle-class families, while nonparticipating peers fall far below.

The program fills a gap in assistance between early education programs and the Nurse-Family Partnership, in which a nurse visits a family from pregnancy through the child’s second birthday.

Closing gaps helps more children avoid falling into gaps later and we all benefit when they succeed. (Seattle is considering a plan for universal preschool that would close another gap.) Life trajectories are being raised every day and that’s worth its own celebration.

Jerry Large’s column appears Monday and Thursday. Reach him at 206-464-3346 or jlarge@seattletimes.com