The accident took place Friday evening on a motorway in Chonburi province as the teachers and other school staff travelled back to Bangkok from a seminar in Rayong province.
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"The van's tyre burst and it turned over before catching on fire," an official from Thailand's Disaster Prevention and Mitigation Department told AFP.
Photos published in local media showed the toppled vehicle engulfed in flames on the side of the road.
The passengers were from a small private elementary school in eastern Bangkok.
Four survived the accident with injuries, the disaster official said.
A school employee told AFP the school's director was driving the vehicle and was among the injured.
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Despite relatively good infrastructure, Thailand has the second most dangerous roads in the world in terms of per capita deaths, according to data collected by the World Health Organization (WHO) in a 2015 report.
The WHO estimates about 24,000 people die each year in traffic accidents on Thailand's roads.
Only Libya records a greater number of fatalities per capita.
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