School principals have published alternative proposals for next summer's exams amid serious concerns about how changes will affect pupils.
The National Association of Head Teachers (NAHT) is seeking a formal meeting with the education minister to discuss its document.
Young people are due to sit A-level, AS-level and GCSE exams next summer, although will take fewer papers.
Students, teachers and principals have all voiced objections.
For those taking GCSEs, the number of exams will be reduced significantly.
Pupils will be assessed in all written units of English and maths, but speaking and listening in English language will be scrapped.
There will also be no speaking components in Irish, French, German and Spanish.
AS-level grades awarded in the summer will not form part of the A-levels in 2021.
NAHT said the reduction of the burden of assessment for the speaking and listening components of English, whilst beneficial for teacher workload, "has huge potential to disadvantage those learners within the special educational needs and/or lower attainment
brackets that can communicate more effectively through the spoken word".
It recommended that GCSE English should have an assessed grade awarded for the speaking and listening component.
Exams that currently have a 50/50 split in their assessment of units, the union said, should have half removed and a replacement 10 per cent controlled assessment task added.
This would ensure equality with other GCSE subjects.
In addition, it said all schools should maintain a record of ongoing assessments that may be used in the awarding of a future predicted grades.