Almost 90% of school staff in England want to tailor the curriculum to suit pupils' needs, a survey suggests.
The ATL argues that the curriculum is too restrictive
The Association of Teachers and Lecturers (ATL) asked 628 teachers and support staff about the issue.
ATL leader Mary Bousted said the system was failing to engage children and should be replaced by a skills-based curriculum drawing on local knowledge.
But the government says the national curriculum is broad and balanced, with scope for flexibility and innovation.
Dr Bousted said: "We believe giving teachers greater freedom to set the curriculum would help raise results and keep more children engaged in learning so that fewer leave school at 16 feeling failures, having been failed by the system."
She said the current emphasis on "teaching to the test", with a focus on literacy skills, was turning many off learning.
It was undoubtedly a cause of increased truancy, and the reason so many left the education system as soon as they could at the age of 16.
"Children naturally want to learn but far too much of our curriculum stops them learning," she told BBC News.
Paradoxically the government's focus on functional maths and English skills was not the way to raise standards in reading and writing.
Instead young people needed to be shown the connections between things, through integrated subjects and lessons that related to their local environments.
"We say first look at the skills, then at the knowledge constructs you need on which they can be developed," she said.
"The nature of thought is to connect - and we don't enable our children to connect."
The ATL is holding a fringe meeting on the subject at the Labour Party Conference in Manchester on Wednesday.
In its survey, the other key finding was that 78% said pupils with special educational needs were particularly disadvantaged by being taught according to the current national curriculum.
A member of staff from a primary school said: "Children are also being encouraged to be academically competitive at a much younger age and therefore aware of being less able and this turns some of them off trying. I think this particularly affects SEN children and some boys."
A secondary school member said: "The very bright are limited by it. They get heavily penalised for careless errors in writing in English, but their reading age and skills are much higher and this is not recognised."
Another said: "We are in a socially deprived area and recently started to cheat the league tables by allowing pupils more time on favourite subjects and less on others.
"Pupils' response was excellent and the discipline problems in year 11 reduced substantially."
A spokesperson for the Department for Education and Skills said the national curriculum ensured that schools provided a broad and balanced education for all of their pupils.
It still allowed them considerable flexibility to develop their own courses of study to meet the needs of their pupils and introduce new approaches to teaching and learning.
"This ensures that teachers are able to take account of pupils' diverse learning needs and allows them to progress and show what they can achieve at their own pace and to their own level."