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Education officials are refusing to name four schools last year investigated for alleged breaches of NCEA assessment regulations.
Waverley High School in South Taranaki had its ability to internally assess students suspended in December after an investigation found teachers gave out answers to tests, marked work as "correct" when wrong and gave credits for work they knew was plagiarised.
Four other schools were also investigated last year, bringing the total number to 10 schools over three years.
National Party education spokeswoman Katherine Rich called on Education Minister Steve Maharey to name the schools and said parents needed to be told if their child's school was under investigation.
"If NZQA has deep concerns about a school's ability to do internal assessment for NCEA, then it is taking a huge risk with the education of every one of those students unknowingly working within that school's faulty system."
A spokeswoman for Mr Maharey said he would not identify the schools because it was an "operational issue" and referred questions to the New Zealand Qualifications Authority, which is in charge of the investigations.
NZQA deputy chief executive, qualifications, Bali Haque said schools would not be named.
The public could apply to see a school's Managing National Assessment report but he would not identify which schools were the subject of supplementary reports, ordered when the NZQA felt issues needed addressing.
Mr Haque said: "The qualifications authority has a priority of working with schools to address issues.
"Naming schools could be counterproductive to this normal operational process."
Two of the five schools with a supplementary report had acted on recommendations and would return to the normal reporting cycle, he said.
The NZQA continued work with the remaining schools to develop work plans, such as improving documentation and providing better material to moderate internal assessment.