Hey we have a chess reference from a major sports website
Here is the interesting part.
"Waitzkin's teacher, on the other hand, taught him through playing. Rather than play with a full chess board, they played with three pieces: two kings and a pawn to start. Once Waitzkin was comfortable with the movement, value and power of a pawn, his teacher changed the pawn to a bishop and a rook and so forth, until Waitzkin internalized the movement, value and power of each piece."
Perhaps this method might be used before doing the tactical exercises? Or perhaps the tactical exercises, ala the circles teaches us in the same manner the power of each and every piece. Anyway you look at it, learning something by starting to learn it from its most fundamental atomic value, in this case, learning what each of the pieces do is highly effective.
I remember when I was starting to play chess. My mind couldnt cope with the entire board. I would forget where a piece was played or worse couldnt see anything but a jumbled tangle of pawns. Like a maze I would get lost and only come out from out of it if enough peices were to be traded to reduce the number of things to juggle (Maybe this is why beginners so love to eat everything in sight?)
I actually wanted to do something like this during those times. Only there was no-one to play with me with "just" a few pieces. They want to play are real game, and so we did. But were it possible I would have done exactly what waitzkin did.