Topeka ? Legislative negotiators began work Tuesday on a compromise version of a bill to give public schools a $37.2 million increase aimed at boosting teacher salaries.

The increase would be for the 2009-2010 school year. The House passed the bill Tuesday by a 96-29 margin, but without support from most Johnson County legislators.

The Senate already had approved the increase as an attempt to add a fourth year to a three-year financing plan passed in 2006. That package was approved to satisfy a Kansas Supreme Court ruling that said the state wasn’t meeting its constitutional mandate to properly fund public schools.

Under the bill, school districts would receive an extra $59 per student for the 2009-2010 school year.

The House version also includes other changes in the finance law to encourage smaller districts to consolidate. Those changes would allow districts that consolidate to calculate their new combined budget as if they were separate districts for at least one year, giving them time to adjust their operations.

In addition, voters in the smaller of the two districts would have to approve the consolidation. Legislators were concerned that a larger district could impose its will in a merger.

The Johnson County delegation called the current formula “flawed” because small, rural districts receive a disproportionate amount of state aid compared with larger, suburban districts.