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The Education Bill passed its second reading, on 15 October 2012.
The debate continued after Question Time.
Anna Lo of Alliance said her party had a number of reservations about the bill.
She was particularly critical of the composition of the ESA board, which would include as many as eight political representatives.
Ms Lo also criticised what she saw as the over-representation of the controlled and maintained sectors on the board.
The South Belfast MLA said her party supported the bill's advance to the committee stage.
Conall McDevitt of the SDLP said the bill failed to address the "two-speed" system in Northern Ireland's schools.
He said that according to parents' ability to earn, "their kids will nearly always end up in one class or the other".
Mr McDevitt compared the terms "academic excellence" and "educational excellence".
"That's the elephant in the room of this debate," he said.
The TUV's Jim Allister criticised the bill for allocating "totalitarian power" to the department since it controlled ESA.
He said the result was that the Sinn Fein minister emerged with "far more power" under the terms of the bill.
The motion was carried by 77 votes to 15 and the bill proceeded to the committee stage.