As most states have moved to new standardized tests based on the Common Core during the past two years, many also have switched from administering those tests the old-fashioned way — with paper and No. 2 pencils — to delivering them online using computers, laptops and tablets.

The transition aims to harness the power of technology to move beyond simplistic multiple-choice questions, using interactive questions and adaptive techniques to measure students’ critical thinking and problem-solving skills.

But the shift to computer-based testing has been riddled with technical glitches that have spanned many testing companies and states, including those that have adopted Common Core and those using other new academic standards.

Stressed-out students have found they sometimes can’t log on to their exams or are left to panic when their answers suddenly disappear. Frustrated teachers have had to come up with last-minute lesson plans when testing fails. Some school systems — and even entire states — have had to abandon testing altogether because of Internet hiccups thousands of miles away.

Some states — including California, with the nation’s largest student enrollment — have been pleased, calling their shift to online testing surprisingly smooth and effective. But the balky tests in numerous other states raise a broader question: Can the exams — which are supposed to offer an objective view of student achievement — produce the kind of valid, reliable results that are necessary for a fair judgment of the performance of schools, teachers and students?

“When the testing administration system is dysfunctional, the results are suspect, if not useless,” said Bob Schaeffer, the public education director at FairTest, a nonprofit organization that serves as a national watchdog on and frequent critic of K-12 testing. Malfunctions have disrupted computerized testing in more than 30 states since 2013, according to media reports compiled by FairTest — including more than a dozen states last year and three this spring, during a testing season that is still underway.

“The theory of standardized testing is that students are given equivalent questions in the same format and the same way,” Schaeffer said. “When you have some kids having a smooth testing experience and others having repeated disruptions, it’s no longer standardized.”

Tennessee scrapped its computerized exams in February, returning to the paper-and-pencil version when schools recorded a number of problems on the first day of testing.

Then in March, the state education chief in Texas called that state’s testing experience “simply unacceptable” after technical hiccups appeared to erase students’ answers on more than 14,000 exams.

And Alaska officials this month canceled all K-12 standardized testing for the year, citing “chaos” in schools because of repeated testing disruptions. The state was the victim of a freak accident: Someone operating a backhoe inadvertently severed a fiber-optic cable in Kansas, cutting the Last Frontier’s connection to its test vendor, the Achievement and Assessment Institute at the University of Kansas.

[Alaska cancels all K-12 standardized testing for the year, citing technical problems]

The same backhoe incident interrupted testing for students across Kansas and for students with disabilities in more than a dozen other states. Marianne Perie, director of the Center for Educational Testing and Evaluation at the University of Kansas, said the test vendor is working on plans for backup servers that could function in the case of another emergency — such as a tornado.

Frederick M. Hess, a resident scholar and the director of education policy studies at the American Enterprise Institute, blamed the widespread testing problems in part on federal pressure to quickly introduce new assessments based on the Common Core State Standards in many states, and other new college and career-ready standards in others. He likened the technical failures to the disastrous rollout of online health-insurance enrollment for President Obama’s Affordable Care Act.

“There were all these existing challenges, but the Common Core assessments were set to be rolled out on a political timetable,” Hess said. “The consequence is kind of predictable.”

U.S. Education Secretary John B. King Jr. acknowledged the widespread problems with computerized tests and attributed them to many causes that he said states are working to address. Those causes, he said, include limited bandwidth, particularly in rural schools; aging computers with inconsistent technical support; and even electrical problems in old school buildings that limit the number of computers that can be plugged in at the same time.

Companies that provide the tests also bear some of the blame, King said. “I think certainly some of the vendors underestimated what it would take to execute on the scale required,” he said in a meeting with reporters Wednesday.

In Nevada last year, officials accused test vendor Measured Progress of breach of contract after a massive meltdown in the state’s new computer-based test. Students had trouble logging on and were repeatedly booted off the system; state officials allowed districts to stop testing via computer after two sincere attempts, and ultimately, just 30 percent of students completed their exams.

Steve Canavero, Nevada’s superintendent of public instruction, said he does not know exactly what went wrong, saying the cause of the problem could have been a problematic piece of code, a lack of server capacity or something else. But the problem came from Measured Progress, he said, not from schools or districts, which had been testing IT infrastructure for months.

“We’re not smart enough to know what failed where, but we know our test experience was not what we paid for,” Canavero said.

Two other clients of New Hampshire-based Measured Progress, North Dakota and Montana, also experienced widespread technical problems last year. A spokesman for Measured Progress declined to comment.

Nevada ultimately reached a $1.3 million settlement with Measured Progress and this year chose a new vendor, Data Recognition Corp. Testing has been smooth so far in Nevada this spring, Canavero said. But last year’s problems mean that the state was not able to measure student performance in a meaningful way.

Canavero said it is puzzling that hundreds of thousands, or millions, of people could purchase something from an online store and have no problem, “yet we can’t produce a testing experience in K-12 that’s efficient and productive for our teachers, our students and our schools.”

Testing for students in Virginia was disrupted last year because a server reached its storage capacity, according to Pearson, the multinational publishing company that is Virginia’s test vendor.

Minnesota, another client of Pearson’s, saw widespread delays and problems last year because of what Pearson said was a denial-of-service attack, a deliberate action by hackers seeking to overload servers and slow their performance.

Spokeswoman Laura Howe said Pearson administered 50 million tests last year, the vast majority of which were completed with no disruptions. But the company has made changes and upgrades to defend against hacker attacks and to forestall server problems.

“We understand the frustration around this issue and continue to work proactively to make sure students have a good testing experience,” Howe said.

Test vendors and officials in some states said the real story is not one of disruption but of remarkable success, given the magnitude of many’s states’ rapid switch to online assessments.

And defenders of the Common Core say that technical issues with the tests are unrelated to the strength of the standards themselves. “Regardless of whether a test is aligned to Common Core, technical issues are just that; they are not issues with the content or implementation of the Common Core State Standards in the classroom,” said Blair Mann, spokeswoman for the Collaborative for Student Success, a pro-Common Core advocacy group. “What’s important is that students take assessments aligned to their state standards so that parents and teachers received valuable and honest information about their academic performance.”

Officials with the American Institutes of Research said their clients last year included more than a dozen states where testing went smoothly. California was one state where officials said they were happy with the results of last year’s switch to online testing. More than 3 million students were tested online, most of them without notable problems.

“That’s not to say there weren’t some glitches – but they were relatively minor compared to other states, especially given our size and the fact that our system was never actually down,” said Peter Tira of the California Department of Education.

Officials in many states that have had technical problems still think the shift to computer-based testing is and should be inevitable: The technology allows for adaptive tests that can more accurately home in on students’ academic abilities by presenting more difficult problems to students who are answering questions correctly, and serving up easier problems to those who are struggling. Supporters say online testing also allows for interactive questions and for quicker results than paper tests, which can take months to score.

Even in Nevada, where the testing system failed so spectacularly last year, the state education chief is bullish. “We are a state that believes in the new forms of assessment,” Canavero said. “We think it’s the right direction to go.”

But not everyone is so optimistic. Tennessee officials have not decided whether they will try online testing again next year.

Candice McQueen, Tennessee’s commissioner of education, was in a classroom on the morning that testing began in February. She saw problem after problem crop up on students’ screens — “nothing was working,” she said — and she watched the teacher scramble to come up with a backup activity.

She said she did not want to risk wasting students’ and teachers’ time on faltering online tests: “We couldn’t have kids just continuing to go into and out of a computer lab and hoping this thing actually works.”

This article has been updated.