The Australian Curriculum, Assessment and Reporting Authority has issued its annual "test incidents" report for 2015, showing a slight downturn on the number of minor and serious breaches of the strict rules around NAPLAN tests.

The ACT's breaches were in the least serious "general breaches" category.

In May, about 5 million tests were sat by more than 1 million students across 9500 schools nationally.

Sixty-seven schools were affected by protocol breaches – down from an average of 75 last year.

Of these, six were the most serious cases of substantiated cheating.

Six were security breaches, and 27 were general breaches.

The three local incidents were relatively minor and related to test material not being kept secure in the school during the testing period, excess time given to four students in one class and the procedures for supervision not followed fully.

In each incident, the investigation revealed no evidence that data were compromised.

The schools were counselled on testing procedures.

Meanwhile, teachers faced more serious sanctions in South Australia, which posted the highest incidence of cheating and other investigations.

Three students in one school were provided with inappropriate assistance by one teacher – who was referred for disciplinary investigation.

Another teacher was referred for disciplinary investigation for assisting another student while two other teachers were found to have inappropriately helped students but were given verbal cautions.

In another South Australian school two students were prevented from participating in testing, and the school was warned.

In Victoria, 10 investigations took place including two serious cases in which NAPLAN booklets were copied for retention at the school. Copies were subsequently destroyed and the schools were formally warned.

Meanwhile, one school was found to have modified student results across two classes. That staff member has been referred for disciplinary action.

Of the security breaches reported in 2015, several involved the use of social media, which can also lead to other students' results being put at risk. Test administrators were increasingly aware of the challenges presented by social media and were being vigilant in ensuring phones and other devices prohibited by the protocols were not available to students during the tests.

A spokeswoman for ACARA said: "Currently, NAPLAN protocols include a two-week security window where all test materials are embargoed from release and we ask people to respect the embargo. When NAPLAN goes online [from 2017], security measures will include multiple prompts and a narrow test window which will limit the impact of social media postings."