Not entirely true.. it depends with the particular school district and with the teacher as an individual
They can decide to have a portion of their no weekly wage put aside to pay them over the summer holiday but that is entirely a personal choice... those who choose to get paid their full salary then go on EI regular benefits.
And some school districts have repetitive 10 month contracts for teachers making eligible for EI regular benefits during the non teaching period till the beginning of the next school year when the new contract for the year is signed...
Also makes them ineligible for extended healthcare benefits, etc during the summer. Guess in my province you are only on contract if you don't have a permanent teaching position.