What for which
Well we all agree that Power plus attitude = performance, I'm sure.
The primary effect of the elevator is pitch. Changes of pitch will always result in a change of speed. Changes in power (thrust) will result in a change in pitch, however the further effect of pitch from power changes will result in a change of height with the trimmed speed remaining pretty much the same. Power for height could be claimed. So in the ab-initio demo this can be easily demonstrated.
The students dilemna is to how to relate the two. So, we teach them a particular power setting that they will use and also a particular attitude relative to the horizon for each phaze of flight. Climbing, level flight and descending etc. The setting of the power is reasonably straight forward with reference to the tacho but the attitude is more complex to set with an ever changing horizon. With the correct power set they may have to adjust in pitch a number of times to discover the correct attitude relative to the horizon.
It is possible to make it simple for the student to confirm the correct attitude by reference to the ASI. If an attempt to maintain height is undertaken by using only the elevator then speed will be lost and the aircraft becomes set on a poor drag curve at a constant height or descent but at a lower speed or higher speed and out of trim. With many of the early low powered trainers this over simplified explanation worked well. It dosn't in the modern less draggy more powerful trainers being flown today, well under max weight.
Point and power is effective on the approach when a fixed visual reference (always the same) - the runway, is available. If height is lost on approach it will be owing to a loss of speed. the pilot then lowers the nose (keeping the constant picture) to maintain speed and also adds power. Speed is recovered and the aircraft maintains the glide path. If the speed increases the aircaft will go above the glide path, once again the pilot lowers the nose (keeping a constant picture) but reduces power maintaining the glide path. Note that in this method the student is unlikely to pitch up closer to the stall. The angle of attack does not always remain constant using the point and power technique as some claim. However the technique works well in my view although mis-understood and I also teach it. As with all methods there are of course downsides.