A senior House Republican on education issues challenged the Obama administration’s plan to use executive authority to ease some punitive provisions of federal education law for states that are taking steps to improve schools.

In a letter to Education Secretary Arne Duncan, Rep. John Kline (R-Minn) questioned his legal authority to grant waivers “in exchange for reforms not authorized by Congress.”

Kline, chairman of the Education and the Workforce Committtee, said lawmakers are making progress on an overhaul of the 2002 No Child Left Behind law.

“Despite what you’ve heard about nothing moving, we are moving,” he told a roomful of reporters Thursday.

While Obama had called for a rewritten federal law by the start of the next school year, Kline predicted that legislation would pass through the House by the fall.

Rather than rewriting a large bill, his strategy has been to break the law into pieces. The approach would make the law more understandable and transparent to most Americans, he said.

Kline envisioned five parts.

Two bills have already cleared the House committee: one would eliminate some federal programs; another would make it easier for states to create new charter schools. A third, which would give states more flexibility to spend federal funding according to their needs, should clear the committee this summer, he said.

The last two bills will be the most complicated and controversial, and will address the evaluation systems for teachers and the accountability provisions of the law. He predicted a lot of debate on those two, but said there was agreement that the law should not place such high stakes on the results of a single test.