'Accurate picture'
For example, pupils were expected to reach at least Level 2 by the end of Year 2 - when they had completed Key Stage 1 or infant school.
There were also three sub-levels within each level, designed to inform teachers how close children were to reaching the level.
But some say these confused parents, and the levels have not been updated for the new national curriculum.
Instead, ministers have left it up to schools to decide what system to use.
Teaching unions have expressed concerns about schools using a range of different assessment levels and the fact that the details of the national tests for 11-year-olds - when they have completed Key Stage 2 or junior school - due to be introduced in 2016, are not yet available.
School Reform Minister Nick Gibb said: "Ensuring pupil assessment provides an accurate picture of a pupil's attainment and progress without placing a bureaucratic burden on teachers is a key part of the government's plan for education