The latest NAPLAN results reveal numeracy and reading skills need to be lifted across Australian classrooms, while cheating is an issue among students and teachers.
A teacher who changed student responses is among 42 breaches confirmed from the national literacy and numeracy test.
The Victorian teacher has been referred for disciplinary action in what was described as a serious cheating incident.
In five other cheating incidents, outlined in a report by the Australian Curriculum Assessment and Reporting Authority, inappropriate assistance was given to students during the NAPLAN test.
Other incidents included test materials not being kept secure, test books being copied and too much time being given for the test.
Another 11 incidents are still under investigation.
The report said about five million tests were taken by students nationally and the number of breaches was "very small".
Federal Education Minister Simon Birmingham said while there were fewer breaches than last year, any cheating was "disappointing and unacceptable".
The federal government was working with states and territories to move NAPLAN to an online test.
"I expect states, territories and non-government school authorities to swiftly deal with any incidents of cheating,"
Senator Birmingham said in a statement.
"The online delivery of NAPLAN should reduce this risk in the future."
Final NAPLAN results, released on Wednesday, showed Year 5, 7 and 9 outcomes had largely stagnated since national testing started in 2008, while Year 3 students had improved.
Senator Birmingham said literacy and numeracy skills needed to be lifted across all year levels.
"We can and must do better," he said.
NAPLAN TEST INCIDENTS
* Cheating: 6 substantiated; 6 under investigation
* Security: 9 substantiated; 1 under investigation
* General: 27 substantiated; 4 under investigation