"I think we really need a Prime Minister that cares about and represents all of Aotearoa's children, not just the ones in the high deciles," she said.
Key appeared to have "a slim grasp on what poverty actually means", she said - following his comments on the difficulties around measuring poverty last week - and visiting low deciles schools would help address that.
"Actually going and visiting some of the low decile schools and listening to teachers and principals about the issues in their communities around housing and around feeding kids and transience etc would be helpful, because it's really important that he as the Prime Minister understands what all children are going through," Delahunty added.
"I've got nothing against the schools he has visited, I'm sure they've all got a great contribution and a really interesting story that he needs to hear, but so too do these other schools."
It was a conscious decision by the Prime Minister, she said, because "he's a very busy person, so where he puts his time is always carefully thought about".
A spokeswoman for the Prime Minister said he was invited to visit a number of the 27 schools, others "simply occurred because they were located in area he was visiting".
"The Prime Minister spends a lot of time in the regions, where he meets a diverse range of New Zealanders.
"During these visits the Prime Minister talked to students, parents, teachers, principals and board of trustees members, from a range of socio economic backgrounds.
"On top of these visits, from time to time school groups visit the Prime Minister at the Beehive, and he talks to schools via Skype."
Key's contact with the education sector was much wider that the list of 27 schools, she said. The Prime Minister also hosts Education Excellence Awards each year where he engages with a number of schools from across the decile system.
More children were participating in early childhood education and more students were achieving NCEA Level 2 than ever before.
"Maori achievement had risen from 44.6 to 72.3 per cent, and Pasifika from 51.3 to 79.1 per cent."
David Hodge, principal of Rangitoto College, a decile 10 school on Auckland's North Shore, said Key spoke to senior and international students at the school during a visit to the East Coast Bays electorate with local MP Murray McCully.
He suggested the discrepancy was due to the National Party's representation in high decile communities.
"Given that, I'm guessing that school visits might well be attuned to visits to the local electorate."
Neil Watson, principal of Otahuhu College, decile 1, said the Prime Minister had accepted an invitation to open the school's new $7 million science block in April.
"We were pretty honoured to have him open that building," he said, adding that Key took the time to tour the school and speak to a large number of students - even winning over a number of pupils who he described as coming from "pretty strong Labour families".
Asked why he thought the college was the only decile 1 school on the list, he said: "We had a pretty significant building, I guess it fits in well with our priorities and the Government's priorities of getting more students science literate."
Schools visited by John Key between January 1 and September 12, 2016:
Decile 1
Otahuhu College, Auckland: April 8, opens new $7m science block.
Decile 2
Hastings Boys' High School, Hastings: July 7, invited by local MP Craig Foss to visit Hawke's Bay.
Rata Street School, Naenae: August 31, visit to Hutt Valley with local MP Chris Bishop.
Decile 3
Blomfield Special School and Resource Centre, Whangarei: March 2, visit with local MP Dr Shane Reti.
Decile 4
Avondale College, Auckland: August 11, official opening of final stage of the school's multi-million dollar rebuilding programme.
Beach Haven School, Auckland: June 30, visit to North Shore with local MP Jonathan Coleman.
Decile 5
Rosehill College, Auckland: April 8
Halfmoon Bay School, Stewart Island: April 15, during visit to Stewart Island.
Decile 6
Campion College, Gisborne: September 1, during visit to Gisborne.
Mt Maunganui Intermediate School, Tauranga: June 22, invited by local MP Todd Muller to visit western Bay of Plenty.
Marlborough Boys' College, Blenheim:
Decile 7
Mt Albert Grammar School, Auckland: June 2, during visit to Mt Albert and Grey Lynn with local MP Melissa Lee.
Inglewood High School, Taranaki: June 3, during visit to Taranaki with former PM Jim Bolger and Minister of Parliament Barbara Kuriger.
Marlborough Girls' College, Blenheim:
Decile 8
Palmerston North Girls' High School, Palmerston North: March 3, during a visit to the area.
Dunstan High School, Alexandra: August 29, during visit to Alexandra, becoming first PM to visit the school.
Waitakere School, Auckland: September 2
Cobham Intermediate, Christchurch: August 31, accepted invitation from Year 8 pupil to visit the school.
Decile 9
Huapai District School, Auckland:
Riverhead School, Auckland:
Havelock North Primary School, Havelock North: July 7, invited by local MP Craig Foss to visit Hawke's Bay.
Te Horo School (Otaki), Kapiti Coast: March 30, during visit to Horowhenua and Kapiti with local MP Nathan Guy.
St Matthew's Collegiate, Masterton: February 11
Decile 10
Rangitoto College, Auckland: March 24, visit to East Coast Bays electorate with local MP Murray McCully.
Samuel Marsden Collegiate School, Wellington: May 11, official opening of new building.
The Cathedral Grammar School, Christchurch: July 27, opens new building.
Pinehurst School, Auckland:
