The St. Paul Federation of Teachers, frustrated by the district’s move to take contract talks behind closed doors, returned to a public forum Tuesday to promote class size reductions and other goals.

Rebecca Wade, a union executive board member, appeared at Tuesday’s school board meeting to present petitions signed by nearly 4,000 people backing federation goals — one being a strengthening of class-size language negotiated during the previous round of bargaining.

The federation said in its most recent contract update that it had filed a grievance against the district alleging that class sizes in many parts of the city now exceeded goals set for 2013-14.

Earlier this year, the district established class-size targets for what it described as high-poverty and low-poverty schools, based on the percentage of students who receive free or reduced-price lunch. In kindergarten and first grade, for example, a high poverty school would aim for 24 students but accept a maximum of 28 students per classroom. For a low poverty school, the range would be 27 and 30.

District administrators have countered that more than 96 percent of classrooms were within acceptable class size ranges, and that a move to establish strict caps on class sizes would be costly and limit choices for students.

“I cannot agree more that class size matters,” but there is only so much that the district can afford to do, Superintendent Valeria Silva said Tuesday night.

Bargaining moved from public sessions to mediation after district negotiators walked out of a Sept. 19 session, claiming the talks were unproductive and the union’s “wish list” would bankrupt the district. The two sides since have negotiated twice behind closed doors and are scheduled to resume talks on Nov. 21.

The federation laid out its contract goals in a booklet, “The Schools St. Paul Children Deserve,” and followed it up in recent weeks with video testimonials on its website.

In a video about the class-size proposal, Laurel Berker, a fourth-grade teacher and union steward, spoke of teaching students whose reading abilities varied widely, and how she was fortunate to see the number of students in her classroom fall from 27 in 2012-13 to 24 this year.

“It doesn’t sound like a big difference. I’ve still got the huge range in ability,” Berker said. “But just three fewer bodies makes a significant difference in order to meet the needs of my students.”

In its petition, the union sought public support not only for smaller class sizes, but also for less testing and for preschool for all 4-year-olds.