The overture is being watched with hope, but also wariness.

On a cool, February morning in Scottsdale, Ariz., last year, 250 teachers gathered in a hotel ballroom at the biggest conference for teachers the Bill & Melinda Gates Foundation had likely ever held.

A few principals and superintendents were in the room, too, along with people from advocacy groups, but the vast majority were classroom teachers, mostly from Tampa, Pittsburgh, Memphis, and other school districts with big Gates grants.

Many felt a little out of place in such a fancy hotel, with its 10 swimming pools and a seven-acre lake, and every meal amply provided. It felt good, they said, to be treated like other, more highly paid professionals, even if it was a little intimidating to be the guest of one of the richest men in the world.

Irvin Scott, a then-new Gates Foundation official and former high-school teacher, stepped to the front of the stage and counted backward, slowly, from 10—a teacher trick for quieting a room.

He didn’t talk much about any of the foundation’s initiatives. He didn’t even mention the one that’s alienated teachers the most—the test-score measures of teacher performance the foundation has pushed in the second phase of its richly financed mission to overhaul America’s public schools.

Instead, Scott told a heartfelt story about how his high-school English teacher, Ms. Scritchfield, taught him to love poetry, setting him on a path to becoming a teacher. He talked about the importance of teaching, how much the foundation values teachers and wants to help them raise the prestige of their profession.

Though widely viewed as a critic of teachers and their unions, the world’s largest foundation has begun reaching out to them in new ways, sending the message it wants to be their friend—and their champion.

“We’re trying to start a movement,” Scott told the teachers in Scottsdale. “A movement started by you. A movement you’re leading.”

The overture is being watched with hope, but also wariness, with questions about whether the foundation truly wants teachers to help shape its agenda, or just to advance it.