Former prime minister Tony Abbott has taken a swipe at Malcolm Turnbull’s schools plan, pointing out it did not go to the Coalition party oom and predicting it will be “pretty vigorously debated” there when parliament resumes next week.

In provocative comments on the government’s major attempt to neutralise Labor’s advantage on education, Abbott said it was a “a very big change of policy that the prime minister announced”.

The government on Tuesday committed to an extra A$18.6 billion in funding to Australian schools over the next decade, including more than $2.2 billion in this budget for the first four years.

“I note that at this stage it’s hard to see that any of this extra funding is specifically tied to better academic outcomes and better student performance,” Abbott said.

“I’ve always thought that the problem with our school system is not so much lack of funding, because there’s been very big increases in education funding over the last decade without a commensurate increase in outcomes.

"The problem is that we need better teachers not just more teachers.

"We need much more academic rigour in the curriculum, we need much more principal autonomy and we need much more parental involvement. That’s what we need in schools,” he said on 2GB.

Abbott did not mention the inquiry to be done by David Gonski – who prepared the 2011 report on which the funding commitments are based – into how the money can be invested to get better student outcomes. This review was announced as part of Tuesday’s plan. It is to report in December, and the government wants the recommended reforms tied to the states’ funding.

Under the government’s plan, a handful of wealthy non-government schools stand to lose some money. Asked whether he would be speaking up for two schools in his electorate that would go backwards, Abbott said he would not flag what may or may not be said in the partyroom.

“I just know that it’s been almost an article of faith in our party since the time of Menzies that we were the party that promoted parental choice in education, we were the party that promoted choice in health care, and I think it’s very important that we maintain our traditional position as the party which respects freedom of choice in both education and health,” he said.

The Greens on Wednesday signalled they are open to negotiations to pass the government’s schools package through the Senate.

As Labor, the states, and Catholic schools authorities attacked the plan, Greens leader Richard Di Natale said that while it was “early days”, the government’s announcement “puts the issue of needs-based funding firmly on the national agenda” and “we are open to a conversation about it”.

If the government got support from the Greens it would require just one additional vote in the Senate.

Nick Xenophon, who commands three Senate votes, said his team needed to get a full briefing. He said that in getting Gonski to give his imprimatur, the government had “pulled a rabbit out of the hat”.

The announcement was certainly an improvement on the government’s earlier position, Xenophon said. Gonski’s statements would carry “a fair degree of weight, but that’s not the only consideration”. “We will sit down constructively with the government and engage with other stakeholders,” he said.