Tenant at my property wishes to leave

Tenancy Deposits

Hi, I have a house that I have been letting to students. I arranged the contracts in a manner that is probably incorrect, as I provided assured shorthold tenancy agreements for each tenant individually, naming the room for which each agreed to take as the "Property" for the purposes of their contract in each case. The term of the contract was for "52 weeks" but I stipulated the rental period as "monthly".
The students all agreed that it would make life easier for all parties if they actually paid me for the term when they got their grants through.(This was not put in the contract, (rent remained stated as £341.92 per month in the contract).
One of my tenants has decided he wants to leave, and has given me 4 weeks written notice. I have told him that the notice is fine, but as the rental period is monthly (to be paid on 26th of each month), he can leave on 25th of the following month, at the end of the rental period, and I will refund any rent already paid that extends beyond this date. He says that as it is a 52 week contract that he only has to give 4 weeks notice and I have to pay everything else back. Can you tell me what the situation actually IS in law please, thanks.