NAPLAN first began a decade ago, testing students from years 3, 5, 7 and 9, using the traditional tools of paper and pencils.
Now, nearly 4,000 schools are currently taking part in the online trials.
The Australian Curriculum and Reporting Authority believes online testing will result in better assessments for individual schools and students.
CEO Robert Randall says the trials are trying determine if schools are capable to go online.
"School readiness testing is having a look at computers in the school, networks in the school, making sure teachers and students have the confidence to sit the test,” he told SBS World News.
“The improvements that we're going to realise through moving it online will address some of concerns that people have previously had - about the time it takes to get the tests back, about one test for all children, how we can make it adaptive."
But the education union wants the new format scrapped.
Deputy federal president Maurie Mulheron says it has received hundreds of complaints from teachers.
“NAPLAN online is a logistical and ethical disaster,” Mr Mulheron told SBS World News.
“Particularly in areas of social disadvantage, their kids are just not on a level playing field.
"We've also got a problem with the students from a language background other than English, where the technology is, again, not accessible."
Mr Mulheron says remote schools with poor internet and limited use of computers will be also be adversely affected.
"At the moment, schools are not yet ready for it,” he said.
“The system has not got the capacity to roll it out, and so we will need to ensure that the whole thing is put on hold until all the problems are worked out."
It will take two to three years before NAPLAN's digital transition is complete.
Mr Randall says schools not yet ready to go online should use that time to continue the trial, so they can identify and resolve all issues.
Edensor Park Public is one of 2900 schools in NSW to undertake the online trial. (SBS/Omar Dabbagh) Source: SBS/Omar Dabbagh
"If they have a doubt about their student's confidence or something, I’d encourage them not to take that step next year. Do another year or two of preparation,” he said.
“When we trial our items, we trial them with a whole range of young people. So we're confident with the English speakers, who only have English, and we're confident we trial them with those for whom English is a second or third language."
The paperless practice runs are mostly being conducted in New South Wales, which has never done such a digital trial.
Nearly 3,000 schools in NSW are participating in the digital trial, by far the most of any other state or territory since it has never done so before.
At Edensor Park Public in western Sydney, Year 5 student Dylan Luu told SBS World News he enjoyed doing the tests on his laptop.
"Yeah very easy on the computer, and much more better than on book and pencil,” said the 10-year-old.
“I'm more used to computers, and I like computers."
"It was pretty good. it was pretty easy,” agreed classmate Marilyn Karkeas.
“More efficient and possible."
But the education union believes many students will not be as happy about the tests.
