SACRAMENTO -- After proposing a bold new education-funding plan in January aimed at helping schools better educate disadvantaged students, then facing push-back from his own party, Gov. Jerry Brown stuck to his guns in his May budget revision released Tuesday.

"I think most Democrats -- in our heart of hearts -- want to help those whom life has not given the same opportunities to enjoy," he said as he unveiled his revised budget.

Brown said all K-12 schools would get more funding than they received in 2011-12, but that those with higher concentrations of low-income students, English language learners and foster youth would get more. All districts with students in these categories would receive 35 percent supplemental grants for each unduplicated student, according to the plan.

Those school districts in which more than half of students are disadvantaged would receive additional "concentration grants," which Brown said would amount to only 4 cents for every dollar being spent on education. Senate Democrats recently unveiled their own proposal, which would eliminate concentration grants and spread them to all districts to increase the base amounts for every student.

But Brown said that would end up diluting the concentration grants to the point that they would barely be felt. State Senate President pro Tempore Darrell Steinberg, D-Sacramento, said in a prepared statement that he supports the policy direction of the governor's education funding proposal, but still has serious concerns about how to accomplish its goals.

"The concentration grants treat thousands of disadvantaged students unequally," he said. "(The proposal) also fails to expand the proven success of career pathway programs which can reduce dropout rates and improve our kids' readiness for the workforce by combining rigorous curriculum that's also relevant to students' career goals."

Currently, programs such as career technical education receive "categorical" money that is earmarked specifically for them. Under the governor's proposal, districts would receive "base grants" that could be used to fund programs with more local control.

State lawmakers will almost certainly come back with another proposal, said Assemblywoman Susan Bonilla, D-Concord, who heads the budget subcommittee on education finance.

Still, she said, "I believe it will be an alternative that will reflect the spirit and the principles the governor has put forward."

Although Brown didn't budge on funding, he did compromise with some critics, who said his proposal needed to build in more accountability to ensure that districts that receive extra dollars for disadvantaged students will actually spend the money on them. Districts would be required to create plans showing how the money would be used and would be expected to show academic growth for low-income, English learner and foster youth students.

Brown also built in about $1 billion to help school districts implement the state's new Common Core Curriculum Standards, which will require all testing to be done on computers. The money could be spent on professional development, technology or curriculum materials.

Bonilla praised the inclusion of money to help schools transition to new teaching methods and testing.

"Our students deserve this opportunity to be challenged by standards that require analytical thinking," she said in a statement, "and this targeted use of one-time money provides educators with the tools to advance instruction and integrate technology into the learning environment."

Brown also devoted more money toward paying back money owed to districts from past budgets, known as "deferrals." In addition, his plan accelerates the rate at which his new funding formula would be phased in, giving more money to districts next year than originally anticipated.

While the specter of more dollars from Sacramento elates educators, uncertainty about whether the Legislature will adopt the governor's plan is throwing a wrench into sticky contract talks between unions and some school districts.

"That's slowing down negotiations," said Superintendent Dennis Byas of the San Lorenzo Unified School District.

Because his district includes a high percentage of English learners and low-income students, Byas said San Lorenzo would get more money if the Legislature adopts Brown's plan.

"I like the governor's proposal better," he said. "It gives us the opportunity to really support our teachers."

Even though his suburban district doesn't stand to gain greatly by the governor's revamped school funding formula, Superintendent Mark Barmore of the Moreland elementary district in San Jose was happy after taking a preliminary glance at the revised budget.

"I very much believe in what the governor is attempting to do," he said. "I'm also very happy that there will be more money for all schools."

He appreciates the proposal to repay districts more of what the state owes them, and to allocated funds for preparing for Common Core tests and curriculum.

"This is a particular issue that has made everybody very anxious," he said. "Getting some support from the state is very critical."

Raul Parungao, Fremont Unified's assistant superintendent of business services, was also pleased about the additional money for implementing the standards.

"There are no guidelines as of yet," he said. "But it's very promising."

Newark Unified's assistant superintendent Tim Erwin called the governor's plans "a major overhaul in the way that California funds schools."

"There are a lot of details still out there that will have to be explored," he said. "But I'm cautiously optimistic that we're turning the corner in California in spending for education."

Next week, lawmakers expect to hear from school officials from around the state about the governor's plan and what it would mean to implement it in the coming school year, as he proposes.

"This is the critical week," Bonilla said, "when we need to find out: Is the governor's time line a possibility or not?"

Brown's budget summary is available by visiting www.ebudget.ca.gov/FullBudgetSummary.pdf. Revised district funding estimates should be available in the next few weeks on the Department of Finance website.

Staff writers Katy Murphy, Sharon Noguchi and Chris De Benedetti contributed to this report. Theresa Harrington covers education. Reach her at 925-945-4764 or tharrington@bayareanewsgroup.com. Follow her at Twitter.com/tunedtotheresa.