How you recognise a talented beginner?

I give every week chess lessons for beginners, and often players are very weak and do not show any especial talent in the game. But there are some interesting exceptions. For example, some players seem to have a natural feeling to where the figures belong. They will blunder a pawn or two, or sometimes even a figure, but they keep playing and give a lot of resistance, even threatening to checkmate you with the few figures they have. 

Other players seem to have strong skill in visualisation, and they usually will be able to reconstruct the position we are analysing much better than all other players and even me. 

I read once from  famous coach that you can recognise a talented young player through their ability to play blindfold chess almost from the beginning. I am extremely bad on this. If I try to play blindfold chess, then I say I will do this for a certain number of moves, usually 8 or 9, but afterwards I will play looking the board.

Do you have your own stories about recognising talented beginners? Did people tell you that you was talented when you began to play chess?