After years of tense relations between teachers' unions and the growing charter school movement, unions are stepping up their efforts to organize educators at the independent public schools. So far, the results of the increased organizing activity-which stretches from Massachusetts and Pennsylvania to California appear modest. But it remains to be seen how much success the union efforts will achieve over time. The American Federation of Teachers, among the strongest critics of charters nationally, is directing increased energy and resources to helping its state and local affiliates with charter-unionizing efforts, Edward J. McElroy, the president of the 1.3 million-member union, said in an interview last week. The AFT's Massachusetts affiliate launched an effort last year to get charter teachers to sign up as associate members, but out of 2,000 teachers targeted, only a few dozen have decided to join. In Pennsylvania. although a few charters are unionized, staff members at one charter school opted last fall to server ties with the union, while teachers at a couple of other school have voted against unionizing efforts in recent years.