There are 3 kinds of scans I try to improve:
The following diagram is quite well suited to explain how the exercise works.
In the problemset of Chess Tempo there are a lot of mates. I consider a mate to be a special instance of a trap. You trap the king. A mate like below took me quite some time since there are a few initial moves which look promising but which are not.
White to move.
You don't know beforehand that this is a mate, but it isn't likely that you can win a piece.
Solution [1.Qxg7+ Kxg7 2.Rf7+ Kg8 3.Rxe7+ Kf8 4.Ng6#]
It isn't important to spend much time to find the solution but it doesn't hurt either. There is no objection to look it up. The exercise starts when the solution is known.
The input is the position at hand.
The output is the endposition with the mate.
The narrative describes in words how you arrive at the mate starting from this position.
How the white pieces work together to box in the black king. In this kind of mates typically the six squares f8, g8, h8, f7, g7, h7 must be covered. Imagine from the startposition which white piece will be responsible for which of those 6 squares.
The goal is to see the characteristics from the endposition in the startposition.
You must ask yourself the question, what characteristics do I need to notice to be sure that I recognize the solution immediately the next time I get to see this position?
It is not so much about visualising the move sequence, but to relate the input to the output simultaneously.
For this post no mice were hurt.