For my first post, I will share a thought on what most consider a basic element of vocal technique: breathing.
Thinking about breathing, you usually think about images of low breaths, the diaphragm, an attempt at defining "appoggio," and maybe a few props like books or elastic bands to help feel the abdominal and rib expansion. In the same way that a tennis player should know the basics of how to hold their racket, so too should the singer have a general idea about the mechanisms of inhalation and exhalation.
But, one of the principles of motor learning I have always remembered is that focusing on the mechanics of any motor task, athletic or vocal, is almost never as effective as focusing on the result of one's task. It is the difference between what is called internal vs. external focus of attention. External focus of attention results in better performance, retention and transfer, while internal focus does the opposite. In other words, if you try to micromanage your breathing muscles, you usually end up doing a poorer job of actually singing and your body will learn less.
The solution is to focus on the result of your breathing, i.e. the sound of your singing and the music (the obvious result of any singing task), or for breathing specifically, the breath flow. There are many exercises that singers and teachers are already familiar with that bring attention to the flow of breath: lip flutter and other similar raspberry noises, straws, blowing bubbles, noticing the flow of breath at the lips or through the mouth, the old method of singing into a candle, /s, /z/, /v/ etc. exercises.
In the end, it is the delicate balance of air pressure and air flow that will determine if the sound is properly supported, and there is no way that we can consciously direct all the muscle groups necessary for such a feat. Our bodies will find the balance needed if it knows what it is looking for and is given sufficient feedback and practice. Go ahead and teach students how to expand on the inhalation and support on the exhalation, we should not withhold information that can be easily presented, but be careful of drawing attention internally and encourage attention externally on the result: breath flow and the music they are making.