More than half a million 11-year-olds sit Sats in England
The Conservatives have announced proposals to scrap all Sats taken by 11-year-olds in England at the end of their primary schooling.
The Tories want pupils to sit national tests in the first year of secondary school, marked by their teachers.
Shadow schools secretary Michael Gove told the BBC they would better serve children's interests.
But Schools Minister Vernon Coaker said the proposals would be a "huge step backwards for school accountability".
Teaching unions who plan to boycott next year's Sats welcomed the plans.
What effectively [the Tories] are doing is to remove all public accountability from primary schools
Former schools minister Lord Adonis
But the NASUWT, which does not support the boycott, said the Tories' announcement would have "appalling" implications for teachers.
Mr Gove told the BBC's Andrew Marr Show that last year's Sats system "went into meltdown" and the Tories want testing and assessment which "actually serves the interest of the children".
He said testing at the end of primary school "completely narrows teaching" and all the focus is on "drilling" children just for those tests.
Testing pupils at the beginning of secondary school - and using teachers to mark exams instead of external examiners - would free the final year of primary school for "teaching in a broader sense", he said.
It would also provide a "more rigorous, more transparent" indication of how well children were taught at primary school, he added.
He said the best comprehensive schools had told the Tories that they "do not completely trust Sats tests" and ran their own tests to check literacy and competence levels.
"If the very best secondary schools are running their own tests and the primary school tests are becoming increasingly discredited, why don't we move to one simple unified system of testing at the beginning of secondary school?" he said.
Schools Minister Vernon Coaker said Mr Gove needed to "urgently clarify his position" and re-think "half-baked proposals".
"If Michael Gove is proposing to push the tests back to Year 7 in secondary school and not publish the results for each primary school, this will be a huge step backwards for school accountability and will deny parents information we know they find valuable," he said.
Michael Gove said the Conservatives plan to scrap Sats for 11-year-olds
Publishing the results for each primary school, but having the tests done and marked by teachers in secondary school, will be "less reliable, less accurate and less effective", Mr Coaker added.
The government was already making changes to the national curriculum and moving Sats from May to June, he said.
Transport Secretary and former schools minister Lord Adonis said he was "amazed" by the proposals.
"What effectively they are doing is to remove all public accountability from primary schools," he said.
The internally assessed tests would not be credible to the public, he added.
Teaching unions are currently split on the Sats issue, with the National Association of Head Teachers and the NUT arguing the current tests damage children and schools.
They say Sats narrow the curriculum as schools are forced to "teach to the test".
The two unions also object to the publication of the results for 11-year-olds in league tables, but the Conservatives do not plan to change this.
While NUT head of education John Bangs said he welcomed the "imaginative" Conservative proposals, he stressed the Tories needed to explain whether they were proposing "compulsory" tests for every child secondary school - and whether these would be fed into school performance tables.
He said he would like to hear Mr Gove say the Conservatives were opposed to the use of results to compare schools against each other.
However NASUWT general secretary Chris Keates warned that even if Sats were abolished, what he termed "divisive performance league tables" would remain.
She said: "Now the primary school rankings will be based on the results of tests internally administered and marked by secondary schools.
"The implications for primary and secondary school teachers are appalling."
Miss Keates said teachers would face a new system of testing, and all the extra work that involved.
Last October, Schools Secretary Ed Balls scrapped Sats for 14-year-olds in England after the fiasco over the marking of exam papers, but the tests remain for seven and 11-year-olds.
The government says the tests are important to parents and that a boycott would be "irresponsible".
However, ministers have agreed to recommendations from a group of experts, which include scrapping science Sats taken by 10 and 11-year-olds from next year.
Instead, teachers will assess pupils, but English and maths tests stay.
The tests will be moved back next year from May to June.
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