BOSTON — Charter school advocates applauded a new attempt by House lawmakers to salvage a bill allowing for the expansion of charter schools in struggling urban school districts.

The bill was introduced Wednesday by state Rep. Alice Peisch, the House chairwoman of the Legislature’s education committee, one day after the panel failed to reach agreement before a deadline for acting on previously-filed legislation.

The House proposal would gradually raise the existing cap on charter school spending in Boston and 28 other low-performing school districts. The cap, already slated to rise from 15 percent to 18 percent by 2018, would further rise to 23 percent by 2022 under the bill.

Charter schools are public schools that operate independently from local districts. Supporters say they are laboratories for educational innovation, but critics say they drain financial resources from conventional public schools and often provide fewer opportunities for special education students.

The measure would also create a new category of “challenge schools” that would be required to implement two-year turnaround plans.

The bill “renews the hopes and dreams of parents and children across the Commonwealth who are seeking high-quality educational opportunities for their children – whether they are in charter public or district public schools,” said Marc Kenen, executive director of the Massachusetts Charter Public School Association.

The House proposal does not link charter school expansion to a requirement that the state fully meet its commitments to reimburse districts when students move from traditional schools to charter schools.

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