This elementary school was probably founded in 1848 and in 1870 there were 43 children attending the school. In 1871 a site for a new school was given by T.J. Heathcote and money was raised to provide a new building. The government gave a grant of £166, the promoters of the school provided £179 and local people subscibed £507. The school was completed in 1874 and the former school was given by its owner, Mrs Hume, to provide a house for the teacher of the new school. This school could accommodate 97 children and had an average attendance,in 1878, of 76. By 1893 the attendance had risen to 100 and by 1899 there was accommodation for 119 and an attendance of 107. The school was enlarged in 1907 and again in 1911. In 1938 there was accommodation for 110 boys and girls to the age of 14 and for 46 infants. The average attendance was 93. In 1953 Shurnhold Secondary Modern School opened in Melksham and pupils over the age of 11 were transferred there. The school thus became a primary school, was granted voluntary controlled status and was known as Shaw Church of England Voluntary Controlled Primary School.
In 1973 the school was extended to create considerably more space and later two mobile classrooms were added. The school used the Victorian building for Reception children and one other class while all other classes were housed in prefabricated buildings on the site. In 2003 two 30 year old mobiles were replaced with a two classroom extension with toilets, cloakroom area and group room. A new sports hall is being built in 2009 at a cost of £450,000 of which the school has raised £200,000. In 1997 there were 203 children on the school roll in 7 classes with an average size of 28. In 2002 there were 217 children aged from 4 to 11 years while in 2008 there were 180 children on the school register..