The way I see it there are two competing benefits to the student: learning from the notes and practicing visualization.
Setting a position up on a board and playing through the variations can help the student see the moves and positions more clearly. So now all the effort can be spent on learning from the notes. Alternatively, using only a diagram the student must practice the essential skill of visualizing moves and future positions.
In general I'd say solve puzzles from a diagram because they'll be short and only one or two variations. Even when looking up the solutions, try to visualize them from the diagram.
In strategy books it's similarly useful to try to follow along using only the diagrams, but sometimes (likely all the time for a beginner) the variations are too long and the diagrams too few so it's not practical for the student. In those cases use a board, but don't completely stop visualizing. If there is a very short variation or small tactic, try to visualize it first before moving the pieces.
I wanted to ask experienced players or to professional teachers if it is better for a 7yrs old kid (my son) and in general for children to solve tactical problems directily on books or on the chessboard (which obviously takes lot of time to be set up).
I'm asking this because on some books it is suggested to do the exercise directily on the book while i have been told by other players (much stronger then me) to use the board.
thx in advance!