Signaling a preference for a much smaller role for the federal government in public schooling, Senator Lamar Alexander, Republican of Tennessee, is introducing legislation on Thursday to revise No Child Left Behind, the Bush-era education law, The New York Times reports. Coming two days after Senator Tom Harkin, Democrat of Iowa and chairman of the Senate education committee, released a 1,150-page education bill, the bill by Mr. Alexander, who is the ranking Republican on the committee, will compete with it…