The UK has the highest rate of premature births in western Europe
More than half of children born before 26 weeks need extra help at mainstream schools, UK research suggests.
Maths and reading were the areas where they struggled the most, the EPICure study of 219 11-year-olds found.
Some 13% of the children, who were all born in 1995, needed full-time specialist education, the University College London-led team said.
Premature baby charity Bliss said there had been great improvements in neonatal care in the past 14 years.
Experts have suspected for some time that prematurity carries health consequences throughout life.
The EPICure study looked at 219 children born extremely premature - before 26 weeks - in 1995 in the UK.
Researchers analysed the IQ and academic ability of these children at age 11, the Archives of Diseases in Childhood, Fetal and Neonatal journal reported.
Their performance was compared with that of 153 classmates who had all been born after a normal length pregnancy.
One in three of the children born extremely prematurely found reading difficult, while 44% battled with maths.
These children also found it difficult to process lots of complex information at one time and scored lower on IQ than their contemporaries.
Twenty-nine of the children were at special schools.
The rest attended mainstream schools, where 57% had special educational needs, most of which required additional learning support such as one-to-one teaching.
This compared with one in 10 of their classmates who had some kind of academic or behavioural special needs.
Teachers rated the academic performance of half of their pupils who had been born extremely prematurely as below the average range expected for their age, compared with 5% of their other pupils.
Lead researcher Professor Neil Marlow said: "Extremely preterm birth places children at high risk for cognitive and learning deficits affecting schooling in middle childhood."
He also suggested parents of extremely premature children born in the summer may want to hold back their start dates a year to give them a chance to catch up.
He said there was some evidence from other work that if such children went into the next school year instead, they did not need so much support.
"Scarce educational support has to be directed towards these children who might be better served in the academic year below them," he said.
A Department for Children, Schools and Families spokeswoman said more money was being provided direct to schools to tackle the needs of such children.
"Improving the life chances of children with special educational needs and disabilities is an absolute priority for this government."
Bliss, the premature baby charity, said it was important those born extremely prematurely were given good support.
But a spokeswoman added: "Since the beginning of this study 14 years ago, there have been great improvements in neonatal care, better survival rates and better outcomes for premature babies.
"As this data is now 14 years old, new parents should interpret it in that context."