At the beginning of a descent, I would put him in the big ring. Enough speed here, and the small hills no longer required pedal strokes at all. That momentum could even bring him halfway up the steeper hills.
Just before the crest of a hill I would have him shift into a harder gear so that he could get a few full strokes going into the downhill. This prevented the necessity for drastic gear changes. Additionally, being in a larger gear meant that pedal strokes on the flat and rolling parts of the downhill provided speed, rather than useless spinning and grabbing for bigger gears.
So be prepared for the terrain by choosing gears ahead of time, and you will increase your efficiency as well as stay on the bike more. Just remember when floating through the technical spots to stand in the pedals with your weight over the back wheel. And pack a first-aid kit.
