Tasmanian State School Parents and Friends president Jenny Eddington said yesterday there would be many issues to work through before it could be rolled out.

''If they did it right now I think many schools would actually fall apart,'' Ms Eddington said.

Students are likely to take their literacy and numeracy tests online from 2016 after the nation's education ministers yesterday agreed there was a ''strong rationale'' for the change.

Students in years three, five, seven and nine sit tests in literacy and numeracy in May but receive their results five months later. 

Federal Schools Minister Peter Garrett said moving the tests online would mean results could be given out quicker. 

''Using online testing is also more accessible for many students with disability, compared to a paper test,'' Mr Garrett said after the ministerial council meeting in Canberra. 

However, Ms Eddington said that in Tasmania very few schools would have enough computers for each year three, five, seven and nine student at their school.

The other problem would be access to the online testing website and likelihood that it would crash with about one million students across the nation using it at once.

Ms Eddington said that she understood students with disabilities, particularly those who had difficulty writing, would be the first to do the test on a computer, but not online.

The state ministers also endorsed a national senior secondary curriculum for English, maths, science and history yesterday. 

The Australian Curriculum, Assessment and Reporting Authority will spend 2013 looking at how this can be integrated into the different state courses and when.