As children across England take their SATs, campaigners have warned the tests are leaving youngsters "terrified of failing" and issued a fresh call for them to be scrapped.
The current system is "inhibiting children's learning", with revision classes "dominating the timetable", according to the More than a Score campaign.
Schools minister Nick Gibb said the Key Stage 2 tests "play a vital role" in ensuring children have a good grounding in reading, writing and maths, and the government "trusts schools not to put undue pressure on pupils".
School leaders said they shared many of parents' concerns about SATs tests, arguing test data is just "part of the picture" in judging how good a school is, or a pupil's success.
More than half a million 11-year-olds are taking national curriculum tests - known as SATs - this week in maths and English.
The results are used in holding primaries across the country to account.
But there are ongoing concerns about the use of the assessments, and the pressure put on pupils to achieve good results.
In addition, seven-year-olds, in the final year of infant school, will take Key Stage 1 tests in the two subjects this month.
The results of these tests - which the government has announced will be scrapped - are not reported to government or part of annual league tables but are used by schools to help with their assessments of pupils.
More than a Score spokeswoman, Madeleine Holt, said: "Surely learning is about more than getting a perfect score on a test? Children need a broad and rich curriculum that encourages them to be excited about learning, not terrified of failing at such a young age.
"With the status of a school and teachers' pay so linked to SATs results, it's no wonder so many are teaching to the test. The SATs regime is inhibiting children's learning as SATs revision begins to dominate the timetable.
"Our primary school children in England are already some of the most tested in the world. This results in stress and anxiety in children, narrows the curriculum and distracts teachers from doing their job: teaching."
A survey of over 500 parents of seven to 14-year-olds, commissioned by the campaign, found more than a third (37%) say their child has been anxious about SATs at some point, while 31% say they have not.
Nick Brook, deputy general secretary of the National Association of Head Teachers (NAHT), said: "Test data is only part of the picture when judging a school's effectiveness or a pupil's success.
"NAHT would like to see less testing in primary schools overall, leaving more time and space for a broad range of subjects and activities in the school day so that children's opportunities are not limited.
"School leaders share many of the concerns that parents have about SATs. Children have many interests and talents ranging from music to sports. They have acquired many life skills which will stand them in good stead for the future. They are not just numbers on a page."
He added: "It's certainly true that the assessment and accountability regime in primary schools is not working for parents, schools or children but we have made decent progress by working collaboratively with the Department for Education and there is more to come."
Mr Gibb said: "The Key Stage 2 tests play a vital role in ensuring that children have been taught, and have acquired a sound knowledge of, the fundamentals of reading, writing and mathematics.
"We trust schools not to put undue pressure on pupils when administering these assessments, and certainly not at the expense of their wellbeing.
"I wish pupils all the very best as they prepare to sit the key stage 2 tests and I look forward to celebrating their success in the summer."
:: The YouGov poll questioned 513 parents earlier this month.