Two dozen Virginia elementary schools, including one in Alexandria, have applied for waivers from the state Board of Education to free schools from mandatory state testing requirements in science and social studies for third-graders so they have more time to develop reading skills.

The new flexibility was proposed by Gov. Robert F. McDonnell (R) and approved by the General Assembly this year as a way to help all students shore up their reading skills in time for what educators call a key academic turning point.

“Third-grade reading is a good gatekeeper for academic success,” said Javaid Siddiqi, deputy education secretary in Virginia. “We want to make sure the young people who get beyond the gate are reading on grade level.”

Experts say that third grade is when students stop learning to read and begin reading to learn in other subjects. Up to half the printed curriculum in fourth grade is inaccessible to students who read below the third-grade level, according to the Children’s Reading Foundation.

Students who have fallen behind by third grade struggle increasingly over time and are more likely to drop out, studies show.

Politicians nationwide have responded to such research in recent years with a spate of legislation.

Fifteen states have adopted laws requiring schools to identify struggling readers in third grade or earlier and to intervene, according to the Foundation for Excellence in Education, a Florida-based advocacy group. Six states require schools to retain students who are not reading on grade level by fourth grade.

Virginia invested in early reading intervention 15 years ago by requiring schools to screen students in kindergarten or first grade for reading difficulties and to give them extra help. The initiative was expanded in 2000 to serve students through third grade.

Last year, the General Assembly increased funding so that all eligible students get some sort of reading intervention before fourth grade.

This year, lawmakers passed the waivers to give schools more testing flexibility. The law, which expires in 2015, is a kind of a pilot program, Siddiqi said. He said that schools with low reading pass rates often have low pass rates in social studies and science because the two are connected. “It’s not about what they know,” Siddiqi said.

“They are struggling with comprehension.”

Under the law, any school with a schoolwide pass rate of less than 75 percent on the Standards of Learning reading assessments can apply for a waiver for one or two years and for either science or social studies or both.

Nearly 40 schools were eligible, according to a list released by the Virginia Department of Education. So far, 24 schools in17 school districts have applied, including three schools in Manassas City — Jennie Dean Elementary, Baldwin Elementary and Richard C. Haydon Elementary.

Three schools in Loudoun and three in Prince William could have sought the extra flexibility and funding but chose not to. A Loudoun official said the conditions of the waiver were too restrictive.

Schools that are granted a waiver still have to provide at least 30 minutes of instruction daily in science and also in social studies, and they still have to test in those subjects and publish the results.

But they can use an alternative to the SOL assessment, and the scores will not be used against them in accreditation decisions.

The State Board of Education is scheduled to approve qualified applications in late June. Schools that are granted waivers will get extra state funding to help pay for a full-time reading specialist to work with struggling students.

John Adams Elementary in Alexandria, which had a schoolwide reading pass rate of 73 percent in the 2011-2012 school year, was one of a handful of schools in Northern Virginia to apply.

Its application said the reading specialist would provide one-on-one or small-group tutoring to third-graders who are six or more months behind in their skills. The 20- to 30-minute sessions would supplement the 90-minute reading blocks that all students get each day.

Two other schools, Patrick Henry Elementary and Jefferson-Houston, were eligible but did not apply. Gwen Carol Holmes, chief academic officer for Alexandria schools, said the other schools decided to invest in literacy coaches who could help train teachers to bolster reading instruction for everyone.

John Adams, she said, already has a literacy coach for teachers. The extra reading specialist will work with students, many of whom come from other countries.

“There are a lot of new arrivals at the elementary school who have a steep curve to get up to where they need to be,” she said.