A Freedom of Information request revealed there were 634 reports in the 2015-16 financial year, compared with 316 the year before.
Police said the rise could have been caused by changes over which incidents schools can deal with internally.
An education expert called the figures "worrying" and said police needed to identify the reason for the increases.
John Howson, who is also a former teacher, said: "I'm extremely worried about these figures - the doubling of the violence against a person, whatever source it is or however minor."
Thames Valley Police said more incidents were now included in their figures after the Home Office clarified a policy about what must be investigated.
It added: "Recorded violent crime went up in the Thames Valley overall last year by 30% so we would anticipate an increase in violence in schools as well.
"All schools in Thames Valley have contact with police through either dedicated schools officers or neighbourhood policing teams.
"Their approach is one of preventing young people from entering the criminal justice system rather than criminalising them."
In January a survey by the Association of Teachers and Lecturers showed that, nationally, 43% of teachers four out of 10 teachers had to deal with physical violence in the past year.

The British Medical Association in Scotland makes the proposal in its manifesto for the Scottish Parliament elections in May next year.
It says the measure could help children form the habits of a lifetime.
The Scottish government said it had worked for a decace to ensure health promotion was "at the heart of a school's activities".
The BMA represents around 16,000 doctors in Scotland.
School meals are now free for children in the first three years of primary education, but the BMA says its survey of local authorities suggests they have cut back on the amount of fruit and vegetables offered for free outside school meals.
Last year 16 out of Scotland's 32 councils provided free fruit and vegetables but by this year, this had fallen to just 11.
None of the councils provided fruit and veg to children above P3, and none provides it more than three days a week.
The BMA says the NHS is facing rising demand for its services and promoting healthy behaviour is essential to reduce demand.
BMA Scotland council chairman Peter Bennie said: "Providing primary school pupils with free fruit or vegetables means that they are less likely to eat unhealthy snacks between meals and helps to build positive habits that can last throughout their lives.
"Investing in children's health in this way can help them to lead healthier lives and reduce the burden on the NHS in the long-term.
"It is concerning that several local authorities have actually scrapped the provision of free fruit and vegetables in schools in recent years.
"Action is needed to address this variation and ensure that primary school pupils in all parts of the country benefit equally from free fruit and vegetables."
In September the Scottish government-funded Scottish Health Survey suggested that children eat even fewer portions of fruit and vegetables than adults.
Scottish adults ate an average of 3.1 portions a day whereas children aged 2-15 ate an average of 2.8.
Only 14% of children were getting the recommended five portions a day.
The BMA says its survey of 2000 parents of school-aged children in the UK suggests that 8 out of 10 (79%) support the idea of free fruit and vegetables for all primary school children.
Health Secretary Shona Robison said: "Under this government, 129,000 children in primary one to three now have access to a healthy, free school meal - a policy which benefits children and their families alike. In total, almost 260,000 pupils are now registered for free school meals.
"The Scottish government is committed to a whole school approach to healthy eating and have worked for the past decade to ensure that health promotion is at the heart of a school's activities. The delivery of this approach rests with local authorities as part of school food provision."
The number of violent incidents in schools reported to Thames Valley Police more than doubled last year.
[NEXT_CONCEPT]
Doctors' leaders want all primary school children to get a free portion of fruit or vegetables every day.