The state's Education Department won't send student data to inBloom's online portal.
A proposal to ease overcrowding at P.S. 11 in Woodside would make it worse, parents said.
Parents charge through schools for time slots "like the running of the bulls," one PTA member said.
Educators laud the assessments that could draw attention to subjects other than English and Math.
Class sizes rose across the city this year, the Department of Education said.
A total of 670 schools have overcrowded classes this fall, the United Federation of Teachers said.
Queens had 155 of the city's 357 trailers during the 2011-12 school year.
The city has nearly 1,000 more overcrowded classrooms this year than last year, the United Federation of Teachers said.
Schools Chancellor Joel Klein stepped down Tuesday and will be replaced by Hearst magazines executive Cathie Black.
More than 700 elementary and middle schools received lower grades this year compared to last year.
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