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Fifty-nine per cent of voters polled in the TVNZ/Colmar Brunton survey believed Mr Key made the wrong decision by keeping Hekia Parata in the education portfolio in last month's Cabinet reshuffle.
This followed a torrid time during which she oversaw the class size backdown, the Novopay debacle and the breakdown in communications with Education Secretary Lesley Longstone and her subsequent departure.
Mr Key told TVOne's Breakfast programme this morning he was standing by his minister.
"She got some pretty bad press last year. She would admit herself there were some things that weren't well handled," he said.
"On the other side of the coin, there's been a lot of good news in education; we are lifting participation rates in early childhood, we are seeing more Maori boys being successful at school."
Ms Parata will today announce the Government's final decisions over the future of 31 Christchurch schools, with the prospect of a number of closures fuelling disapproval of her handling of the education portfolio.
Mr Key said there would be "some happy schools" and "some unhappy schools" as a result of the announcement, but Ms Parata had done what was necessary.
"We don't get up in the morning looking for ways to annoy Cantabrians. We ... have made those decisions and the minister has recommended those decisions because she believes, and I think rightfully so, those are the right decisions to be made."
The poll also had good news for National, with a 5 percentage point jump in support taking them to 49 per cent. Labour was on 33 per cent and the Greens 11 per cent. Mr Key also gained five points, according to the preferred prime minister measure, giving him 44 per cent, with Labour leader David Shearer on 15 per cent.