Five candidates for mayor debated education policy in New York City, and gave their views on topics such as how to better work with unions and how to ease the strains of co-locations.

Despite the public exchange of barbs and insults, the Bloomberg administration and teachers’ and principals’ unions said they are planning to meet this week to talk about teacher evaluations. One key issue on the table: how to provide meaningful training to principals and teachers in time to implement a new system by September.

The teachers’ union and the city walked away from a deal they both say was essentially hammered out. As a result, city schools face more budget cuts.

The Bloomberg administration plans to tell a state judge on Tuesday that an arbitrator exceeded his authority when he found the city must hire back thousands of teachers at 24 struggling schools. But with less than two months to go before school starts, the city’s decision to appeal means uncertainty and confusion among affected teachers and administrators.

Education officials say they will not make personnel decisions at 24 schools scheduled to be closed and reopened this summer, until a court hearing next week. Unions representing the city’s teachers and principals claim that the city’s plan to replace staff members at the schools violates their contracts, and they are seeking a restraining order so an arbitrator can have time to rule on their complaints.

Of the unions representing teachers and principals in New York City, the principals’ union had played a passive role in the charged and increasingly divisive dispute over an evaluation system to gauge the performance of teachers and principals in 33 struggling schools receiving federal grants to help improve their results. No longer. On Wednesday, the principals’ union president, Ernest A. Logan, sent a strongly worded letter to the state’s education commissioner, John B. King Jr., saying the city’s plan for those 33 schools was simply a ploy to shut out the unions.

An official of the principals’ union writes that when training expands in New York City, his members are likely to view the new teacher evaluation system as punitive to teachers and damaging to students, who would be far better off if the money being spent to develop new tests were invested in true classroom instruction.