Resigned in July for Term contract, now being asked to pay

I signed an "at will contract" in June of 2014 for the 2014-2015 school year. I was offered a better job in July, which I accepted. I sent a letter of resignation July 18th. Contract stated that if I resigned "after the Term of the contract has started, I would owe 10% of gross annual salary within 5 days of terminating contract". I received bill on Thursday for $3100 due within 15 days or they will "seek every reasonable means to collect the money". They are stating that I "broke my employment contract" and therefore need to pay the money.