Alright... you guys always help me out so let me try again with a home improvement question!

We are going to put slate tiles down in our sunroom. The sunroom (11ftX12ft) currently has disgusting brown tiles which are simply glued to the cement floor. Pain in the ass to get up.. and probably more harm than good to try and get it up. So what do we do??

Do we lay backerboard right on top of the old tiles? Is that okay to do? Or do we have to tear apart this floor and make the concrete uneven and then redo the concrete???

Thanks in advance!