Here's a lesson they don't usually teach in school: New York City teachers won't give up parking privileges without a fight. The teachers union yesterday filed a grievance against the city to head off a plan to cut the school system's 63,390 parking placards by at least 20 percent. The cuts aren't supposed to be instituted until September - four months after 68 other city agencies surrendered 32 percent of their 80,770 permits as part of a citywide reduction ordered by Mayor Bloomberg. But the United Federation of Teachers isn't waiting to engage in battle. UFT president Randi Weingarten was traveling yesterday and unreachable. However, in a Jan. 4 letter to Bloomberg and Deputy Mayor Ed Skyler, she stressed that the permits are only valid during school hours and only around schools, most of which are outside central business districts. "Teachers do not clog areas such as lower Manhattan," Weingarten wrote. "Teachers are not abusers of parking permits, and to suggest that they are is deeply troubling." City officials say they're confident they have the right to restrict parking under the terms of the city's contract with the union. "Teachers will be asked to do what police officers, firefighters and what all other city workers have already done," said mayoral spokesman Jason Post.

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