The Ethiopian mother of four is raising her children alone in the Wellington Street housing commission tower in Collingwood.

She wants to send her kids to one of the best local schools in town, the prestigious Clifton Hill Primary School, a fifteen minute walk from her home.

But try as she might - she's been trying for five years - the school won't accept her kids.

"You have to be a lawyer or a doctor to get in there, and I'm none of them … you need to have a posh life to get in," she said.

Tigist believes she has been shut out of a class-based state school system.

She says over-subscribed state schools are cherry-picking middle class kids, shutting out students they deem too challenging, too disadvantaged, or not sufficiently academic.

The Wellington Street flats are just a couple of streets outside of the school zone and Tigist has been rejected on that basis. She now pays to send her kids to a local Catholic school, St John's Primary.

Yet she knows several other families living outside of the zone who have secured enrolments.

Megan Smith, co-principal of Clifton Hill Primary, said the school follows education department policy, and accepts "occasional enrolments from outside our neighbourhood boundary where we have the room".

It is "absolutely incorrect to suggest that we enrol students based on class," she said.

But Clifton Hill admits on its website that it is the closest school for just 65 per cent of students, while "the remaining 35 per cent being drawn mainly from neighbouring middle class inner suburban areas. A minority of students are drawn from public housing."

It goes on: "The school's strong academic reputation attracts students from outside the area and waiting lists apply at all levels".

Under the current rules, oversubscribed state schools can accommodate additional enrolments from outside their zone on specific curriculum grounds.

This means that a student outside of the zone can enrol in a school if they excel in a particular area - music, sport, or a second language.

But the process lacks transparency, and Melbourne University's Senior Lecturer in Education Policy and Politics, Dr Glenn Savage said principals are prioritising affluent and academic students.

"I think it's unconscionable that principals choose students based on socio-economic backgrounds, and there is evidence to suggest that this is happening at the moment."

Dr Savage said there is very little accountability around enrolment decisions, and this has led families to feel they have been unfairly rejected.

"I'm not suggesting that we shouldn't have out-of-zone entries, but it's the haziness and lack of clarity of the process that is driving a lot of these problems."

The Greens – who represent thousands of inner-city voters in areas where there is marked segregation along race and class in schools  – said the real issue was parents' "unfair assumptions" about the education delivered at some schools.

"The main issue is that there are unfair assumptions about schools that principals are trying to change," Greens Melbourne MP Ellen Sandell said.

She said many inner-city schools were stretched – and extra funding would make them more attractive to all families.

Deputy Greens leader and federal Melbourne MP Adam Bandt said schools should reflect the diversity of their local community.

"When making the big decision about where to send their children, I'd encourage parents to pay a couple of visits to their closest public school before deciding," he said.

Architect and town planner Damien Bonnice said popular state schools should not be allowed to select desirable students outside of their zone, as this robs neighbouring schools of enrolments.

An analysis by Mr Bonnice, a former Clifton Hill Primary School council president and treasurer, showed that between 2009 and 2015, prep enrolments at Clifton Hill Primary increased by 115 per cent, while Fitzroy Primary School's dropped by 32 per cent and North Fitzroy Primary School's fell by 22 per cent.

"The system is chaotic," he said. "The education department is not exercising its authority to impose caps on popular schools … it needs to force students to go to their local primary school."

Education Minister James Merlino said Victorian schools did not segregate students along racial lines, and every student should have access to a quality education.

"The Department of Education proactively and constantly monitors enrolment policies to ensure families have a place at their local school," he said.

An education department spokesman said some schools were allowed to enrol students on curriculum-specific grounds to extend them in certain subjects, "however these programs must not adversely impact the enrolment of students at their designated neighbourhood school".

They said from next year, Clifton Hill Primary would limit the students it accepted from outside its zone who did not already have a sibling attending the school.

"In previous years the school was able to enrol students from outside its enrolment boundary, however due to significant local population growth it is now at capacity," he said.

The co-principal said she would be "happy to meet with Tigist to discuss her situation".

She also said it was common for schools to state their demographics.

When asked why the school thought it necessary to publish that its families came from middle class areas, she replied "it is a statement of fact."

Do you know more? timna.jacks@fairfaxmedia.com.au