A leaked government document appears to confirm an expected £4bn boost in funding for schools in England.
Details of the cash injection for education, revealed by the BBC at the weekend, have been published by the Guardian newspaper.
It follows warnings by heads and teachers of a worsening funding crisis in schools and colleges.
In the Conservative leadership campaign, Boris Johnson had promised to reverse cuts to school budgets.
Head teachers' leader Geoff Barton said school leaders would "need some convincing that any funding commitment really does address the crisis and isn't simply part of a strategy for a forthcoming general election".
Higher starting pay
It is understood that the leaked document published by the Guardian shows the education department's bid for funding, rather than a final outcome.
It includes proposals for how extra funding would be spent, such as higher starting salaries for teachers to tackle a staffing shortage.
There are also suggestions of measures to improve discipline, such as ensuring that teachers are able to use "reasonable force" in restraining pupils and to ban mobile phones.
And there would be a further commitment to open more free schools.
But it is understood that these have been ideas put forward during negotiations for more funding - and that the final deal will reflect Mr Johnson's pledge to put £4.6bn extra per year into schools by 2022.
A one-year settlement would be seen as a stepping stone towards that amount.
The Guardian's leak breaks down potential increases - including £2.8bn for primary and secondary schools up to the age of 16, including £800m for children with special educational needs and disabilities.
A further £800m could be for two areas which have faced particular funding problems - sixth form and further education.
Letters to parents
Putting more money into cash-strapped schools is likely to be seen as a popular grassroots measure ahead of a possible autumn general election.
There has been a long-running campaign by school leaders protesting about inadequate funding.
This was backed by analysis from the Institute for Fiscal Studies that suggested schools had suffered budget reductions of 8% since 2010.
The Department for Education had rejected such accusations, saying that schools were receiving record levels of funding.
But teachers' unions and head teachers' campaign groups have maintained a constant challenge - writing directly to millions of parents about the financial difficulties facing schools.
Further protests by head teachers are expected in the autumn term - and school leaders will want to check the detail of any promises.
Jules White, the West Sussex head teacher who has organised a funding campaign involving thousands of schools, says there is a "strong sentiment" among heads that there must be a "guaranteed long-term settlement" and there is transparency in the detail of what is being promised.
"Once we see the details we will tell parents the accurate truth again," said Mr White.
"If the news is good we will say it but we will not be fobbed off by any election-driven gimmicks."
Geoff Barton, leader of the ASCL head teachers' union, said schools would welcome any increase in funding.
But he warned that: "Any extra money must be allocated immediately and it needs to be part of a longer-term commitment to reverse the education cuts because the sums of money being discussed are not enough to achieve that objective on their own."
Labour's shadow education secretary, Angela Rayner, said: "Time after time Boris Johnson has backed Tory cuts to school budgets that created the crisis in our classrooms, while slashing taxes for the richest.
"Johnson shows no sign of taking the action needed to undo that damage, and isn't even proposing to reverse the Conservatives' cuts to schools since 2010."