The words "enjoy" and "achieve" have been lumped together as a single aim for children as if they were naturally complementary aims.
But more than three-quarters of teachers believe that pupils' enjoyment of education is being damaged by the Government's methods for measuring and raising achievement - its tests and exams regime.
The finding comes from an exclusive TES survey of 2,109 teachers, conducted as part of our Big 5 series, looking into the five aims of Every Child Matters.
Four out of five teachers felt that the pressure to raise results conflicted with the broader goals of the programme, which aims to bring schools and other services together to give children better support.
In spite of the teachers' concerns, however, the vast majority of children appear to be happy at school.
Two of the detailed aims set for the "enjoy and achieve" target are that pupils should both "enjoy and attend school" and "achieve stretching national education standards".
However, many professionals believe that the testing side has dominated, marginalising pupil development. In particular, there is a widespread view that putting children through months of test preparation, with the aim of raising their achievement, can be boring for some and make others anxious.
One deputy head of a primary, who asked not to be named, said: "'Enjoy' and 'achieve' are not particularly happy bedfellows at the moment in schools, where standards are setting the agenda."
The head added that school leaders wondered whether every child really mattered when they looked at test results in June.
Steve Sanderson was head of St Joan of Arc Primary in Bootle, Merseyside, when a 2002 Ofsted report highlighted it as a school that managed to combine a rounded curriculum with good results.
He now heads All Saints Catholic Primary, a "super school" into which St Joan of Arc and another school have merged. "There is a conflict between enjoyment and achievement," he said.
"Ofsted says there are schools that can achieve both elements, and it is possible. But I think, if anything, the pressure has become even more intense on test results since the report was published.
"The message from many of us to our colleagues is that you should be making the curriculum as exciting as possible. But the unrelenting pressure of testing has meant that many schools have not done that.
"Despite the positive messages, teachers do not believe you when you say you can get good results by having a really exciting curriculum. They are frightened not to teach to the test because they think one bad set of results could be catastrophic: the head would lose his job and staff morale would plummet."
Lorraine Smith, head of Western CofE Primary School in Winchester, Hampshire, was so worried about the side effects of testing that she submitted evidence to a Parliamentary inquiry into assessment last year.
She wrote: "I feel the current situation puts staff, pupils and schools under enormous pressure and can be demotivating and demoralising.
"Of course headteachers should be accountable for pupil standards, but there is so much more to a school than Year 6 Sats results. By overemphasising this aspect, it seems to me that the system is taking the heart out of schools."
However, David Fann, head of Sherwood Primary in Nottingham, said that there was not necessarily a conflict, and that good schools were able to resist the pressures.
Several heads have told The TES that Ofsted prioritises test results above other aspects of school life, and that schools often receive poor overall inspection verdicts despite Ofsted saying pupils are happy.
Statistics appear to bear this out. Last month, The TES revealed that in the last academic year, 98 per cent of primaries received the same inspection judgement overall as they did on pupil achievement.
Now, we can reveal that the correlation between overall inspection judgements and those on pupil enjoyment is not nearly so strong.
Only 41 per cent of the 6,331 primaries visited received the same judgement overall from Ofsted as they did on pupil enjoyment.
Some 2,342 schools were rated "outstanding" at promoting pupils' enjoyment. But, of these, only 33 per cent were rated outstanding overall. By contrast, of the 758 rated outstanding on standards, 98 per cent received the top judgement overall.
Similarly, in secondaries, of the 290 schools rated outstanding on enjoyment, only 52 per cent got top rating overall. But 97 per cent of those that achieved an outstanding verdict on standards also received outstanding overall.
An analysis of research for the Primary Review also supports the idea of a conflict between enjoyment and achievement.
The analysis says: "The ECM agenda suggests that one of the purposes of schooling is to equip learners for life in the broadest sense.
"However, this ideal is not reflected in the current emphasis on target-setting and academic achievement in primaries. This imbalance needs to be addressed."
Last year, a Unicef survey placed the UK at the bottom of a league table for child wellbeing.
But there is also plenty of evidence that most children in England are happy. The Primary Review reported that primary schools are "largely happy places".
And Keele University's Centre for Successful Schools, which has surveyed 300,000 secondary pupils since the early 1990s, found that 88 per cent said they were happy at school last year - only a slight drop from 91 per cent in 1993, when data first became available.
This month, a British Council study suggested that pupils here were among the happiest at school in western Europe.
The correlation between enjoyment and achievement, it seems, is far from straightforward.
Aims for every child
Schools today are expected to nurture the whole child, not just their academic side. Nowhere is this clearer than in the five Every Child Matters "outcomes" they are meant to ensure for pupils.
The aims were introduced nearly five years ago, but their relevance is growing: schools are now judged against them, and they underpin the Children's Plan.
In this special six-part series, The TES examines what schools are doing, what they are missing and whether they can realistically make a difference.