Add Bronx Assemblywoman Vanessa Gibson to the growing list of legislators and school advocates criticizing Mayor Bloomberg’s appointment of media executive Cathleen Black as the city’s new Schools Chancellor.

Joel Klein resigned from the post to take a job with News Corp., which publishes the New York Post and Wall Street Journal.

In a letter to David M. Steiner, the commissioner of the New York State Education Department, Gibson said she “remain[s] troubled that Cathie Black would assume the role of Chancellor without neither substantial nor comprehensive educational or professional experience in teaching.”

State law requires that school chiefs hold certain qualifications, including a professional certificate in educational leadership. But the law also allows the commissioner to make exceptions. Klein was given a waiver when he was offered the job in 2002, and Gibson doesn’t want a repeat.

Leonie Haimson of the group Class Size Matters was happy to see Klein go and sees Black as more of the same. “As for Cathie Black, it is unfortunate that once again, the mayor has chosen someone with no educational experience,” Haimson said in a statement.

Meanwhile, Bloomberg heaped praise on Black in a statement last week. “Cathie Black is a superstar manager who has succeeded spectacularly in the private sector,” he said. “She is brilliant, she is innovative, she is driven — and there is virtually nobody who knows more about the needs of the 21st century workforce for which we need to prepare our kids.”

Black said she will build on Klein’s success.