Red Hill principal Kathy Irvine says poverty struck her most last winter when many pupils came to school in thin shirts and shorts without shoes or sweaters.
Others come in dirty uniforms because their parents are on pre-paid electricity cards and can't afford to top them up to do the washing.
"What I have noticed over the last few years is that there is more and more of that happening. The students are quite literally coming to school with less and less support."
Nationally, the gap between the top and bottom quarters of students on the PISA index of socio-economic status is still slightly less than the PISA average, although wider than in Australia.
The index measures home educational resources, cultural possessions and the parents' educational levels as well as their occupations and wealth.
But the gap in children's reading levels between the top and bottom quarters is slightly wider than average, so the effect of socio-economic status is more amplified in New Zealand than in any of 38 other countries.
Professor Stuart McNaughton, the acting head of Auckland University's Starpath project aiming to cut socio-economic gaps in education, says some Auckland schools are doing better.
Wymondley Rd School, a decile 1 primary in Otara, has lifted its pupils' literacy levels to the national average by monitoring pupils' achievement and changing its approach when required.
"Their data told them two or three years ago that boys, particularly Tongan boys in years 5 and 6, had low reading comprehension. So they deliberately restructured the year 5 and 6 programme to capture the Tongan boys' interest and engagement," Professor McNaughton says.
Massey High School in West Auckland lifted students' pass rates in national exams by regular one-on-one student meetings with deans to discuss their goals and progress, setting targets for all students and groups, and holding in-depth meetings for parents and children with their form teachers.
A Starpath report says the change in parent-teacher meetings raised parents' attendance from 13 per cent or less in previous years to 76 per cent, and transformed some teachers' views.
One teacher said: "I had one girl that said to me, 'Mum doesn't care about stuff like that.' And when I spoke to the Mum, I realised the Mum just completely cared. So it made me aware of misconceptions I had about the parents."
Professor McNaughton says the Auckland Council could help projects such as the Manaiakalani Trust, which is helping parents at seven Tamaki schools to buy laptops which the children use for homework and to communicate with their teachers.
Wymondley Rd School also encouraged its children to read books over the summer by parking the mobile library outside the gate. "I would increase the libraries' capacity for outreach to communities, particularly the low-decile areas."
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www.starpath.ac.nz