As the national Labour government prepares for an election later this year, the union has set out a stimulating argument for change in a new policy document, Creating an Education Nation.
The union represents 180,000 teachers and is a powerful political force nationally. It wants the federal government to become a full partner in the funding of schools and has called on it and the states to allocate another $2 billion (almost Pounds 1 billion) to schools by the end of the decade.
This would bring Australia up to the average level of spending on schools among countries that are members of the Organisation for Economic Co-operation and Development.
Although the federal government provides tied grants to the states, in which it specifies how the money is to be spent, state and territory governments make the major decisions and have long bitterly opposed federal intervention.
Yet, as AEU president Sharan Burrow pointed out at the launch of the policy document: "We have national policies on industry, employment, higher education and technical education and the training market. It is high time we developed a genuine national approach to schooling, based on planning, targets, co-ordinated policy and agreed responsibilities, accountability and funding stability."
The AEU has become increasingly concerned in recent years as newly-elected Conservative governments have slashed spending on education as part of their general cuts to the public sector. In Victoria, an economic rationalist government has eliminated 8,000 teacher jobs and closed more than 200 schools over the past two years.
The union has called for a Schools Advisory Council to act as a forum for federal-state negotiations, including national policies, funding allocations, and the reporting of outcomes.
Under the proposed system, all money for schools would be pooled in a "national bank" and allocated to the states and territories on the basis of advice from the council. Administration of government-run schools would remain a state responsibility, but the federal share of spending would rise to 50 per cent by 2000.
Ms Burrow said the single greatest impediment to education progress in Australia had been squabbling between states and the federal government over powers, responsibilities and money.
A unique aspect of the union's proposal is the creation of a national reporting system. Student achievement would be measured and the information obtained used to assess the performance of state systems. Planning and money would then be adjusted accordingly.
Ms Burrow said that the first step towards creating "an education nation" would be more money for Australia's primary schools. She described current spending as a national disgrace.
"The evidence is overwhelming that primary education, particularly early learning and literacy, is where the greatest educational gains are to be made," she said.