I strongly believe that kids should be taught to improvise shortly after they can play chords with no problem. I can’t remember being taught any improvisational teaching, even though I had a knack and drive to do so when I first started accompanying my high school choir. I want to make sure none of my students who have been with me for a while never go without dabbling in the art of improvisation at least a bit.
As you can see, it’s easy to come up with the chords underlying each measure to both of these works. Teachers should take advantage of this fact and tell Jingle Bells players to try playing quarter notes or something different from the simple, repetitive accompaniment given. And you can tell what ought to be done with Silent Night: