OLYMPIA — The Washington House passed a measure on Wednesday that would change the funding source of the state’s charter schools, which some lawmakers and advocates of the independent public schools say would ensure the future of the charter system.

The schools have been in limbo since September when the state Supreme Court ruled the charter school law approved by voters in 2012 is unconstitutional. The justices had a problem with the new schools getting state money set aside for traditional public schools but not being controlled by a voter-elected school board.

The proposal would re-establish a statewide charter authorizing commission and use lottery money to pay for the schools. But it would not give them access to local levy dollars.

Schoolchildren and parents have been parading through legislative offices and committee rooms all session, asking lawmakers to fix the law to satisfy the court. Passionate debate over how to satisfy the court — or whether to do so at all — reached the House floor on Wednesday, where lawmakers proposed about 20 amendments to Senate Bill 6194. The bill eventually passed on a 58-39 vote, and it now moves back to the Senate for a final vote. It is similar, but not identical, to the version of the bill passed by the Republican-led Senate earlier in the legislative session.

Rep. Chad Magendanz, R-Issaquah, said during floor debate that the bill was a “simple and elegant solution” that would satisfy the court.

“One size does not fit all when it comes to education,” he said in support of the charter system. “Children have different learning styles, and we need choices.”

Some Democrats said the bill was not really a fix because the proposal might be struck down by the high court. Many said charter schools would not have enough public oversight under the bill.

“It sets up a separate and unequal system of schools,” said Rep. Christine Kilduff, a Democrat from University Place. Democrats control the chamber, but only 10 voted for the measure.

Others argued the state should fix the way it pays for common schools and meet obligations of the state Supreme Court’s 2012 ruling known as the McCleary decision before addressing the relatively small number of students in the charter system.

The nine charter schools already opened in the state, plus three others approved to open next fall would be grandfathered into the system, if the measure passes the Senate and is signed by the governor.

“Let us fully fund our schools so that charter schools and public schools are in great shape going forward,” said Rep. Chris Reykdal, a Democrat from Tumwater who voted against the measure.

The bill passed Wednesday in the House did not include money to reimburse the open schools for the dollars they lost when the court order to shut down the system went into effect and the schools had to scramble for an alternative source of income. That was one of the provisions of previous versions of the measure.

One school — First Place Scholars in Seattle — turned back into a tuition-free private school. Most of the rest joined the Mary Walker School District in Stevens County school district under state guidelines for Alternative Learning Experiences and continued to receive state dollars. One remained an independent school supported with donations.

Many advocates of the measure said on the floor that the state can help kids in charter schools and common schools at the same time. Rep. Eric Pettigrew, D-Seattle, said passing the bill is “what we need to do,” even if there are more students in common schools.

“If it’s just one kid or 800 kids it doesn’t matter,” he said.