About 500,000 public school students in seven states “opted out” and refused to take federally required standardized tests in math and reading in the spring, according to a national group that wants to reduce the use of standardized tests.

The National Center for Fair and Open Testing and its affiliated groups surveyed school districts and monitored state government reports to come up with “opt-out” estimates for seven states. They are New York (240,000 students opted out), New Jersey (110,000), Colorado (100,000), Washington state (50,000), Oregon (20,000), Illinois (20,000) and New Mexico (10,000).

A spokeswoman for the U.S. Department of Education could not confirm those numbers, saying that states are not expected to report opt-out data to the federal government until December, and some have indicated they may not do so until February.

Test participation rates are important because the current federal education law, No Child Left Behind, requires every school to annually test at least 95 percent of its students in math and reading in grades 3 though 8 and once in high school.

Testing advocates say the public needs a clear annual measure of whether schools are educating all students, including those who have been historically underserved, and testing every student provides the best indication of school performance.

Critics say a test score does not fully measure what a student knows and blame the federal emphasis on math and reading tests to a narrowing of curriculum, an unhealthy focus on test preparation and an explosion in other tests designed to measure whether students are ready for the federally required exam.

Lawmakers in Oregon recently passed a law that allows families to opt out of state tests.

A study released last month found that the number of standardized tests U.S. public school students take has exploded in the past decade, with most schools requiring too many tests of dubious value. A typical student in a major U.S. school district takes 112 mandated standardized tests between pre-kindergarten classes and 12th grade, the study by the Council of the Great City Schools found. By contrast, most countries that outperform the United States on international exams test students three times during their school careers.

In October, President Obama offered a mea culpa of sorts, acknowledging that some of his administration’s policies, such as Race to the Top, a competitive grant program for states, have exacerbated overtesting. He vowed to help dial back the number of tests given in public schools.

Meanwhile, students and parents across the country have been pushing for the right to opt out of federally required tests. Some oppose the tests themselves, others object to overtesting and still others, including teachers unions, object to using test scores to measure the performance of schools and teachers.

Opt-out rates vary wildly among schools, and state averages can mask hot spots: Although the state participation rate for Oregon in the 2014-2015 school year was 96 percent, at Hood River Valley High School, just 30 percent of the junior class took the tests and 70 percent got their parents’ permission to opt out, giving the school the highest opt-out rate in the state.

Rhode Island officials reported this week that about 7,400 of their 82,613 students opted out of testing in the spring, pulling down the state’s participation rate to about 90 percent for reading and 91 percent for math, below the 95 percent federal requirement.

It is unclear whether states and schools will face penalties if fewer than 95 percent of students took the federally required tests.

Lawmakers on Capitol Hill who are meeting Wednesday to finalize a proposal to replace No Child Left Behind are considering a provision that would maintain the federal requirement that states test 95 percent of students but allow states to decide what to do about schools where participation drops to lower levels.

In Oregon, lawmakers recently passed legislation that allows families to opt out of state tests. Bob Schaeffer, education director of the National Center for Fair and Open Testing, said his group supports that change in federal law.

“It turns most decisions about testing and accountability back to the states,” he said. “Folks in the assessment reform movement know they’re going to have to ratchet up pressure on the states. When there is more power in the state, there will be more pressure on the state.”