I have an adult beginner who has all the freestyle techniques OK and can put it together well. However, he has a problem with his shoulders lifting and rolling when kicking.
It is really pronounced. The shoulders lift and roll alternately to the leg kicks. ie, right leg kick lifts the left shoulder out of water. The faster he kicks, the more pronounced the roll. It's like he's dancing in the water!
However, the spine, arms, neck, and head appear to maintain their streamlined position (no noticeable movement other than a slight elevation of upper arms as the shoulder lifts/rolls). Any hints or ideas would be greatly appreciated.
The first thing that needs to be asked is what you are attempting to achieve from kicking with a kickboard.
If it is leg strength, stamina, or technique you are attempting to gain, then the fact that he moves his shoulders when he kicks is irrelevant. Especially if his leg kick technique is correct and he is covering some distance down the pool, he will gain what he needs from the exercise.
It is probably the case that he is only doing what comes naturally, and I suspect when he puts the arms and legs together for the full stroke, he kicks and pulls with the same rhythm and timing that he moves his shoulders when he kicks with the board.
If you really want to eradicate his shoulder movements, you could try getting him to kick without holding a kickboard, just keeping his hands together in front. The fact that he is not holding onto something may encourage him to keep his upper body still.
You could also try him with some fins. Sometimes the extra power generated from fins can add a new feeling and sensation in the water, meaning the swimmer gets a more enhanced feeling of movement through the water and therefore does not subconsciously look for extra help from other muscles.
Fins can also be a good way to enhance and develop leg kick strength, stamina, and technique.
Keep in mind that kicking front crawl legs while holding a kickboard can be a very demanding and energy-sapping exercise, even for well-established swimmers, let alone beginners. Therefore, it is very easy to recruit additional muscles and movements without consciously attempting to gain some extra momentum and movement.
This may well be exactly what your beginner is doing, and my suggestions above may help, but they may make things worse! I guess you will not know until you try them out.
I hope you find the information above useful and I wish you the best of luck.