A new "rigorous, engaging and tough" national curriculum is critical to Britain's future economic success, David Cameron said.
The Prime Minister described the changes - being detailed by Education Secretary Michael Gove on Monday - as a "revolution in education".
School leaders warned though that the timeframe and lack of resources to prepare for the significant shake-up, at the same time as exams and assessment are being overhauled, would end in classroom "chaos".
The new subject structure for primary and secondary schools in England is due to be introduced in September 2014.
History as well as design and technology (D&T) are undergoing the biggest rewrites after experts and education leaders raised concerns about the draft syllabuses of these subjects.
Ministers want pupils to learn a complete chronological history of Britain, though primary pupils are expected only to have to learn about events up to 1066 after criticisms going further would stretch young minds too far.
Changes to the D&T syllabus follow claims it focused more on "life skills" like cookery, bike maintenance and gardening than science-based subjects like engineering which are required by industry.
It has been reported that climate change is now set to feature explicitly in the geography curriculum, after a campaign raising concerns that it was not specifically referenced in the syllabus garnered widespread support.
Hailing the changes, Cameron said: "We are determined to give all children in this country the very best education for their future and for our country's future.
"New national curriculum is a vital part of that.
"The curriculum marks a new chapter in British education. From advanced fractions to computer coding to some of the greatest works of literature in the English language, this is a curriculum that is rigorous engaging and tough.
"As a parent this is exactly the kind of thing I want my children to be learning and as Prime Minister I know this revolution in education is critical for British prosperity in the decades to come.
"This is a curriculum to inspire a generation-and it will educate the great British engineers scientists writers and thinkers of the future."
Brian Lightman, general secretary of the Association of School and College Leaders (ASCL) said he understood that ministers had listened to points raised by the union and others about these subjects, and that he hoped to see revised programmes that are "more relevant to the skills and knowledge needed in the 21st century."
"Our biggest concern is with the timeframe and the lack of resources to prepare for such a major change," he said.
"Pupils and teachers in 2014 are going to have to cope with new GCSEs, new A-levels, new vocational qualifications, new ways of tracking pupil progress once levels are abolished, on top of new curriculum content in all subjects. This is a massive change.
"So that the reforms don't disadvantage pupils, we need the Government to publish a fully developed implementation plan of how it is going to support schools to achieve all of this in 12 months. Our young people shouldn't be treated as guinea pigs in an educational laboratory."
Dr Mary Bousted, general secretary of the Association of Teachers and Lecturers said there was a "complete disconnect" in Gove's thinking.
"He fails to understand that curriculum changes and exams need to be considered together as they are interlinked. Yet we still have no details of how the primary curriculum will be assessed and the Government is carrying out separate consultations on how young people should be assessed at ages 16 and 18.
"Michael Gove is risking total chaos in September, with schools unclear about what they need to be planning for."
Shadow education secretary Stephen Twigg said: "This is now Michael Gove's third attempt to rewrite the curriculum.
"He should listen to the experts and not try to write it himself based on his personal prejudices. We need a broad and balanced curriculum that prepares young people for the modern world and gives teachers in all schools the freedom to innovate."
Gove told ITV's Daybreak the curriculum changes "can't come quickly enough".
He said: "I want my children, who are in primary school at the moment, to have the sort of curriculum that children in other countries have, which are doing better than our own.
"Because, when my son and daughter graduate from school and then either go on to university or into the workplace, they're competing for college places and jobs with folk from across the globe, and I want my children to receive an education as rigorous as any country's."
Asked if the changes could leave behind less bright children at a young age, the Education Secretary said: "I think the most important thing is to make sure that we understand when children arrive in school how well they're performing so that we can then ensure that those children who are bright are really stretched, but also those children who may arrive at school not perhaps with all the preparations in place for them to enjoy their learning are helped to enjoy their learning so that children of all abilities can succeed.
"One of the things I've found is that children actually enjoy being set a challenge, and as soon as you ensure that you understand the level at which children are working, then you are able to set an appropriate challenge because all of us thrive when we are set a challenge that's just a wee bit beyond what we're comfortable with, but within our grasp."
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