Mayor Thomas Menino was joined by charter school leaders to celebrate the signing of a compact that will lead to more collaboration between Boston charter and district schools.

As the city’s school department and teachers’ union squabble over a new contract, a report shows that charter schools are set for a significant expansion in Boston, with eight new sites possibly opening in the next two years, and the number of students who attend charters expected to increase by 55 percent over the next four years.

That could lead to the amount of tuition money the city pays to charters increasing to $90 million in fiscal year 2015, up from $55.1 million in fiscal year 2011.

“The rise in charter enrollment among Boston students comes at a cost to the City of Boston,” according to a report from the Boston Municipal Research Bureau, a business-backed nonprofit.

“State aid follows Boston students who attend charter schools,” the report notes. Over the past decade, as BPS enrollment has dropped by 6,380 students or 10.1 percent, the BPS has struggled to right-size the system in a timely manner. Challenges come from uneven enrollment losses across schools and the political difficulty of closing schools.”

Much of the prospective charter gains can be attributed to the “Race to the Top” law legislators passed in 2010 in a bid for a pot of federal education dollars. The law raised the state limit on charter spending in districts with underperforming schools and opened to the door for “innovative” public schools, such as the Roger Clap, an elementary school in Dorchster that was converted into an “innovation school” after parents successfully protested against its proposed closing.

Dorchester is home to a number of charter schools, including Neighborhood House, which focuses on high school prep; Boston Collegiate, which has a focus on college prep; Codman Academy and its focus on social justice and the arts; Smith Leadership Academy which emphasizes leadership development; and Dorchester Collegiate Academy, another college prep school.

State Sen. Sonia Chang-Diaz, a Jamaica Plain Democrat who represents some of Dorchester and co-chairs the Legislature’s Education Committee, said she didn’t want to “pre-judge” the outcome of the reforms. The committee is holding oversight hearings in late October on the law, and other education reform measures passed on Beacon Hill in recent years. “There’s no silver bullet in education,” she said. “Charter schools are one part of the puzzle.”

Chang-Diaz, a former teacher, said charters were more like “incubators for best practices” and not meant to be set up as “a parallel [education] system to district schools. They are independent and each school has a different governance model. You see there’s a real variation in the results we’re getting,” she said.

Mark Kenen, executive director of the Massachusetts Charter Public School Association, said that Chang-Diaz offers a narrow view of charter schools. “Charter schools first and foremost are providing public school choices for parents in Boston, especially those who might not otherwise have those choices,” he said. “By providing the choice to parents, it does force the district to change in order to keep the students in the district school.”

Both Kenen and Sam Tyler, the head of the Boston Municipal Research Bureau, said the figures in the report point to the district needing to make adjustments in the contract it has been hashing out with the teachers’ union over the last 17 months. “There’s a real urgency for this contract,” Tyler said.