Bent arm action is Not necessary to a fast freestyle!
Yep you heard it.
There are some top level swimmers today that use a straight arm action. How they do it I don't know because it must be exhausting. Never-the-less that is the case. Needles to say they must have enormous upper body strength to be able to carry it off without injury.
Having said that for most of us a bent arm action out of the water is the best form of arm recovery you can have.
Bent arm recovery by it's nature is faster and requires less energy.
You need proof?
A straight arm action out of the water requires the arm to travel in a circle.
A bent arm action is essentially a straight line from exiting the water and entry into the water. The shortest distance between two points is always a straight line. Therefore a bent arm recovery must use less energy and be a faster arm recovery.
If a student comes to you and the teacher has only taught them freestyle using a kickboard - yes there are still some around - you won't have to do anything because they will already have a bent arm action out of the water. You will almost certainly, have to get them to finish their stroke underwater. (Teaching with a kickboard does have some advantages).
What do I mean by finish their stroke?
Well when a swim student has learned with or kickboard or other technique that has not picked up on this, you can end up with a stroke that does not end with a full extension of the students arms before they leave the water.
Whether you teach bent arm action to a swim student first or a straight arm action first (my personal preference) if a swim student is not finishing their freestyle stroke in my opinion the best way to correct it is to get them to drill with a straight arm action (above) out of the water for a while.
I prefer to teach a straight arm action to a beginner before I teach them a bent arm action because I find it easier to teach a student to bend their arm than to get it straight. Particularly to those who have been doing a bent arm for a long time like adults.
Once a student has learned to finish their stroke, if they haven't already learn they need to learn a bent arm action out of the water.
There are a number of ways to teach a bent arm action out of the water:
1. Try getting them to run their thumb up their side in the arm recovery phase.
This has some significant disadvantages. New swimmers usually drag their hand through the water as they do this, but it does get their elbow bent. Remember this is an exaggerated swimming movement so keep it to a short term drill, otherwise the disadvantage becomes a fault that you have to fix (usually using catch up stroke with straight arm recovery out of the water).
2. Get them to alter their pitch on their hand . this is by far the easiest way but does not always achieve the results. Children in particular are really good a contortions that a body does not usually do.
4. Using a kickboard held with one hand, do a one arm drill where the hand has to enter the water under the kickboard. That is the swimmer does one arm for one lap and the other arm for another lap. You must only do this with one arm at a time or it introduces faults that you have to fix (usually fixed using catch up stroke with straight arm recovery out of the water).
All of these are good drill for introducing a bent arm out of the water action which is the most efficient method of freestyle arm recovery. But I can't emphasis enough, you must only do this with one arm at a time or it introduces faults that you have to fix.