State education ministers have increased their calls for changes to Naplan after widespread failures in the rollout of the online version of the controversial test.

Connectivity issues have plagued the national rollout of online testing this week, with thousands of students across a number of states reporting difficulty accessing the test.

In Western Australia, the education minister Sue Ellery said this week that one-third of students doing the tests online could not complete them.

The Victorian minister, James Merlino, said of the 900 schools participating in the Naplan online tests, “dozens and dozens” had reported failures with connectivity.

About 50% of schools were due to complete the assessments online in 2019, compared with 15% last year.

The Australian Curriculum, Assessment and Reporting Authority, the body responsible for Naplan, said it was investigating the “connectivity issues” and had told schools they could revert to pen and paper if the online version of the test failed.

But issues with the rollout of the online test mark just the latest controversy with Naplan, and the latest failure has prompted both Ellery and Merlino to again question the value of the test.

Last year, state ministers called for a review of the test after it emerged that the scores of more than one million Australian students could be delayed due to concerns with comparing online and written results.

Merlino repeated those calls on Tuesday, saying that “Naplan online has failed again … The rollout and performance of Naplan online is simply not good enough, and Victorian students, parents and teachers deserve much better than this.

“Frankly I’m so fed up with Acara. We were given assurances … that they’d worked through all of the issues with Naplan online and that it would work. It simply did not.

“While we remain committed to a form of standardised testing, we need to be informed about where we need to make improvements.”

Ellery went further, saying it was a “live issue” whether WA would participate in the online test next year.

“This issue will not stop here … I will take this up with the next federal government, whoever that is,” she said.

In New South Wales, where one school principal reported 93% of students experienced at least one disruption during the test, the new education minister Sarah Mitchell said she has raised her concerns with Acara.

In a statement, Acara said more than 350,000 online tests were submitted successfully and any “inconvenience” completing the test was “regretted”.

“[A]nd if technical issues are experienced in the coming days, there are procedures in place to manage them and ensure that all students are able to take the tests,” it said in a statement.

“This includes taking the test on paper as a last resort.

“The technology and logistics of a national online project of this size are highly complex, involving national testing authorities, states and territories and schools, and the cooperation and assistance of all involved is appreciated.”

Other education ministers, including the Australian Capital Territory’s Yvette Berry, have been vocal critics of the “high-stakes” nature of the test.

The Australian Education Union, long critical of the test, said the failures had left “many students in tears after repeatedly losing work”.

“It is clearer than ever that Naplan is in no way fit for purpose, and that the farcical move to Naplan online has been hasty and ill-conceived,” the union’s federal president Correna Haythorpe said.

“After last year’s debacle with the delivery of Naplan online, federal education minister Dan Tehan had the opportunity to institute a full review of Naplan. However he failed to do so.”