The Chadderton Coat-of-Arms and Turton High School Badge

I had been looking at the various crosses and shields associated with the medieval knightly orders, which I'd become interested in after going to Santiago de Compostella in Spain.  I noticed a cross symbol on my old school badge (Turton High School), which I hadn't paid any attention to before.  I wondered where it had originated from.

Turton High School Badge