WASHINGTON  In a proposed change to the No Child Left Behind law, the Obama administration would require states to adopt new academic standards to qualify for federal money from a $14 billion program that concentrates on impoverished students, the White House said Sunday.

The proposal, part of the administration’s recommendations for a Congressional overhaul of the law, would require states to adopt “college- and career-ready standards” in reading and mathematics.

The current law, signed by President George W. Bush in 2002, requires states to adopt “challenging academic standards” in reading and math to receive federal money for poor students under the program known as Title I, but leaves it up to states to decide what qualifies as “challenging.”

The result was that states set their standards at widely varied levels, some as rigorous as those used in high-performing countries like Japan, but others at far lower levels that lay out at best, mediocre expectations for their students.