After all, the Catholic education system educates 20 per cent of Australian students - that's 725,000 children in more than 1700 Catholic schools supported by a hefty $5 billion per year in public funding.

The next chapter in this debate is about to be written with the government to shortly announce its response to the Gonski review on the future of school funding. If the government can maintain the courage of its convictions then significant reform will rightly follow to address two major shortcomings with the current Catholic school funding arrangements.

The first is the lack of transparency around the funding decisions of Catholic education authorities. The second is the 2005 funding deal that delivers many wealthy Catholic schools up to three times the funding of other equivalent private schools.

To follow this debate, a bit of background policy is needed. In very crude terms, state schools have a direct funding relationship with the state government. Private schools that operate independently of any particular school system (sometimes referred to as independent schools) have a direct funding relationship with the Commonwealth and state government. Most Catholic schools do not have a direct funding relationship with government. Instead, public funds are allocated to centralised state Catholic education authorities, which then distribute the funding to their member schools using their own methods and formulas.

The Gonski review finds the arrangements for funding private schools ''complex, confusing, opaque and inconsistent among jurisdictions, and obscure educational goals and accountability''. In the case of Catholic schools, the Commonwealth Auditor-General went even further in a 2009 report, saying there was a lack of information on the formulae used by Catholic education authorities to distribute funds. Worse still, he found that schools serving poorer communities received less funding from their local Catholic education authority than if they were funded directly by government.

The Catholic education authorities responded to these findings by highlighting the widely acknowledged shortcomings in the SES model used by government to distribute funds to private schools. This model takes into account the socio-economic status of students' parents. The Catholic education authorities prefer to use their own definition of ''need'' and include other factors for deciding a school's funding, such as its size and whether it is growing.

The second major issue with Catholic school funding stems from what is known as the ''funding maintained'' arrangement. As the name suggests, public funding for what are effectively elite Catholic schools is maintained even if a school would not be entitled to as much under the SES funding model that applies to other private schools. The Gonski review strongly criticises these arrangements.

The Catholic education authorities have responded to these concerns in the past by committing to redirect funds from their elite schools to disadvantaged schools.

But a recent review of these elite Catholic schools by former Productivity Commission economist and public education advocate Trevor Cobbold found the claims by the Catholic education authorities were ''misleading and untrue''. He compared the funding rates for elite Catholic schools obtained through Senate estimates with the figures for federal government funding reported on the My School website. His conclusion is that elite Catholic schools in New South Wales and the Australian Capital Territory appear to retain all their funding, while elite Catholic schools in Victoria, Queensland, South Australia and Western Australia appear to distribute about 40 per cent of their funding. As a result many elite Catholic schools receive and retain more than twice the public funding they would be entitled to if they were funded under the broader school funding model that takes account of the socio-economic status of students' parents.

The Catholic education authorities argue that on average Catholic students receive 20 per cent less public funding than government school students and when fees from parents are included, Catholic schools operate on about 90 per cent of the cost of a government school.

But this argument ignores the fact that Catholic schools are able to charge fees to help fund their operation. It is also the case that state school enrolments carry a much higher proportion of all disadvantaged students and these students cost more to educate.

The central recommendation of the Gonski review is that we need to improve the performance of disadvantaged schools. One way to achieve this could be to let the elite Catholic schools operate like other elite private schools - cut their public funding and let them charge higher fees.

The remaining Catholic schools could become part of the public system with the schools serving poorer communities to get a substantial funding increase.

Catholic schools are part of the public system in New Zealand, Canada and elsewhere and have successfully managed to retain their identity and autonomy. But the hard politics of school reform means this is simply not going to happen in Australia. So the best realistic option is to go for the ''full Gonski''.

This would mean school systems, run by state government and Catholic education authorities, would continue to play a valuable role in the detailed allocation of funding. But a condition of future public funding for the Catholic education authorities should be that they publish the formula they use to fund their member schools so they are publicly accountable in the same way other education authorities are.

And all schools must be funded according to an agreed and consistent definition of need - with funding for disadvantaged schools, including Catholic schools in poor areas, to be substantially increased.

Nicholas Reece is a public policy fellow at Melbourne University's Centre for Public Policy and a former senior adviser to Prime Minister Julia Gillard and premiers Steve Bracks and John Brumby.