A pilot scheme is to examine whether "all or nothing" national school tests in England should be replaced by more frequent assessments.
Children could take tests when teachers think they are ready
Instead of fixed tests taken by pupils at 11 and 14, tests will be taken when teachers think children are ready.
Schools will also be offered financial rewards for raising the achievement of pupils who have been struggling.
"I want a relentless focus on the progress of each individual," said Education Secretary Alan Johnson.
The proposal to introduce a more flexible approach - which would mean tests in English and maths up to twice a year - will be piloted for two years in 10 local authority areas.
It is intended to allow schools and parents to monitor children's progress more regularly - rather than depending on the national tests at the end of key stages, when pupils are 11 and 14 years old.
Mr Johnson, speaking at a press briefing, said this could provide a more "transparent" form of testing, highlighting when children needed to be given extra support to catch up or given harder work to stretch them.
"I want it to be possible for pupils to take an externally-marked test, whenever the pupil is ready, rather than only at the end of a long key stage," he said.
"Parents will know how well their child is doing in moving through the different levels," said Mr Johnson.
And Sue Hackman, the education department's chief adviser on school standards, promised that all parents would be told when their children were to take these tests.
This will not mean scrapping the current national tests - as the pilot scheme will continue in parallel with the present testing system.
But Mr Johnson ruled out any suggestions that this would mean the end of exam league tables - saying that would be a "disaster".
The proposals also include "progression premiums" which will give extra payments to schools which substantially raise their pupils' performance - with financial rewards up to 10% extra in per pupil funding.
Alan Johnson wants to focus on individual pupils
It is aimed at rewarding schools which have made a difference with struggling pupils - rather than "coasting" schools which are making little extra progress with an intake of high achievers.
"One of the current criticisms has been that you might have a low-attaining pupil who has done remarkably well, coming up from two levels behind, but who is still not reaching the threshold - so is not considered a success for the school or teacher.
"One the other hand, you might have a high-attaining pupil who is coasting and could go further. But the system at present doesn't recognise that in the way it should," said Mr Johnson.
The pilot scheme's changes to testing are particularly targeted at those pupils who are failing to reach the expected standard for their age group.
Among 14 year olds, there are about 26% of pupils who have not reached the expected level - and the revised testing and proposals for individual tuition are designed to identify and support these struggling pupils.
This would also mean that the current cap on primary school achievement would be lifted, so that potentially even young pupils could hit levels well above what is currently expected of 14-year-olds.
The arrangements set out in the pilot project would also be likely to bring new targets for schools. Mr Johnson says he wants a debate about how school performance should be measured, about which he had a "genuinely open mind".
"Should we look at schools in terms of the overall numbers of pupils making progress at each stage?
"Should we move over time to a system where all pupils are expected to progress by at least two levels, say, in each key stage in reading, writing and maths?"
In response, the Shadow Education Secretary, David Willetts, said that it is "worthwhile piloting more in-year assessment, but school children need an authoritative statement of what they have achieved as they move from primary to secondary school".
NUT leader Steve Sinnott approved of testing children "when they're ready", but he warned that "another layer of testing will impact badly on our education service and indeed I think will impact badly on the, on youngsters - some will feel failures".