This is how I approached poor kicking with cyclists and runners.
What stood out is that they often kicked in the water like they ran and cycled because of muscle memory OR they had compensating kicks in an attempt to get themselves back in balance.
To stop these patterns, I flipped them over to their back where they were to do two things: flutter kick and engage their lower abdominal muscles. As a dry land exercise they would flutter kick on their backs from the pool deck, bed or floor. Once they could flutter kick on their backs efficiently, it was time to flip them over.
A gauge for measuring if they were level on their backs were their hands on their front thighs. If the hands while on their thighs were on the surface feeling air, their hips were up and their core engaged properly. Too often people “sit” in the water while on their backs kicking.
Their new flutter kick and lower abdominal strength was basically to build them up for a 2 beat kick, unless they were able to do a 6 beat kick rather naturally. From my experience and theirs, it seemed better to take just two average kicks rather than six average kicks. Most triathletes who lack ankle flexibility and have a hard time maintaining a toe point without their foot cramping want to save their legs for the bike and run.
For swimming, the main focus was on fixing breathing, comfort/confidence in the water, ability to roll up and down, body position and stroke, catch, pull. While power and drive for swimming comes from the front not the back, neutralizing a poor kick and creating a 2 beat pattern was necessary for a consistent body position in order to build a consistent stroke.
When improving an adult swimmer, everything doesn’t improve at the same time, it’s picking your battles and then going back later to improve further.
