AUSTIN, Texas – The federal No Child Left Behind law was born in Texas, and billionaire Ross Perot first rallied big business to support tougher standardized testing and high school graduation standards here nearly three decades ago.

But the state now appears ready to step back from the strenuous accountability policies it has long been a national leader in championing, amid fears that youngsters are being forced to take too many high-stakes tests and that too many might drop out because of higher expectations. A number of other states are also considering pulling back.

The Texas House has approved 145-2 an education overhaul that cuts the number of high school standardized tests in core subjects from 15 to five. It also creates a base high school diploma that doesn’t require algebra II or high-level math and science courses. A similar bill is pending in the Senate.

“Parents, students, business groups, professional education administrators, school boards, everybody’s onboard with this,” said the House measure’s sponsor, Republican Jimmie Don Aycock, chairman of the chamber’s Public Education Committee.

In particular, algebra II should no longer be treated as the “holy grail” of education, said Republican Sen. Dan Patrick, chairman of the Senate Education Committee.

How to measure schools’ effectiveness and hold students accountable has become an almost unresolvable question in some states, coming up again and again for reconsideration. After rounds of raising standards and requiring tests, some legislatures are now swinging back in the other direction.

“Texas may be rolling backward too fast,” said Chester Finn, president of the Thomas B. Fordham Institute, a conservative education think tank in Washington. He fears many school districts will only offer enough courses to meet the new minimum degree standards, thus dropping high-level science and math.

“I am not worried about the kids in the fancy suburbs,” Finn said. “It’s kids in little, rural districts and the lesser schools in tough neighborhoods in big cities who are going to find that the school doesn’t offer the courses because they don’t really count.”

The qualms are being felt in both conservative states and progressive ones. But exacerbating matters are the Common Core standards, national benchmarks in reading and math promoted by the Obama administration and designed to enhance critical thinking. They have been adopted by 45 states.

Washington state’s superintendent of schools, Randy Dorn, has publicly worried that the testing has gone too far, with the class of 2015 now required to pass five high school exit exams. In North Carolina, legislators have scaled back the number of tests and the number of days students spend taking them.

Oklahoma’s Legislature was roiled when it was discovered that hundreds of students wouldn’t graduate because of their scores on the state’s new high school exit exam. Efforts to overturn the requirements failed after an emotional debate. Alabama is also fighting over its Common Core standards, with Gov. Robert Bentley and other top Republicans pushing for repeal while a key business lobby fights to keep them.

Michael Cohen, president of the Washington-based nonprofit Achieve, said that in Texas, though, “it appears to me that there is a more substantial retreat.”

“It’s not just a battle over the math and science,” said Cohen, whose group is dedicated to strengthening academic standards nationwide. “It’s between taking (standardized tests) at all now or not taking them.”

Texas first introduced a school accountability system in 1993, but the movement dates to 1984 when future presidential hopeful Perot headed a state Select Committee on Education that campaigned for tougher graduation standards. George W. Bush, as governor, made student performance on statewide tests a centerpiece of No Child Left Behind, which was passed into federal law in 2002 during his presidency.

But when the Obama administration began championing the Common Core standards, Texas lawmakers complained that their state requirements were already strenuous enough.