You guys are right. I have no idea how to fly my own airplane. It's amazing that I haven't ended up a smoking hole in the ground since I'm apparently using my controls incorrectly.
Just to be clear I am not saying your method is wrong, in fact as I already stated it works perfectly fine and is certainly a better method for precise aircraft control. However, we are discussing a primary student and what they should do. Plain and simple power for airspeed/pitch for altitude relationship can kill you because eventually you will run out of momentum and power for altitude/pitch for airspeed cannot because your thrust will be constant (not counting an engine failure). This basic understanding of physics is a must for a primary student to prevent them from making big holes in my back yard or yours.
I by no means am trying to accuse you of not knowing how to fly an aircraft. But you have to understand that while your procedures are different you are still acting within the bounds of physical law. We have to teach a student to operate within the bounds of physical law first and then we can fine tune their procedures or just let you guys do it when they get to jets.
Physical Rules: I will use AOA for pitch as it can be directly correlated with Lift = Speed + AOA (Practical application lift formula derived from L = 1/2 [p * V2 * A * (2 pi AOA)]
Power controls altitude always and does not ever control speed. When you increase power you climb, when you decrease it you descend. If you want to prevent the climb or descent from a power change then you change your AOA. If you change your AOA your speed must change to balance lift and weight. Speed changed because AOA was changed, not because power was changed.
AOA always controls airspeed because an increase or decrease in AOA will require a subsequent increase/decrease of speed to balance lift and weight.
Momentum can be factored in for changes in AOA, allowing AOA changes to be used for the purpose of a climb at the sacrifice of airspeed.
These are physical laws that cannot be argued even by the dumbest of pilots, they work every day in every environment and in every situation. They are as true as the law of gravity which causes one to fall on their face when they trip.
So why in the world would someone flying a jet not just fly by these simple rules you might wonder?
The answer is you are still operating your aircraft inside the bounds of these rules. Your jet procedures are the way they are because of other physical laws, those of momentum and inertia. Turbine spool up time also plays a roll as it takes longer for your engines to generate thrust equal to that of the power setting chosen.
Momentum = Velocity * Mass
Inertial = Mass (to keep it simple if mass goes up inertia goes up)
Inertia is an objects resistance to change.
If you take an large aircraft, say a 747, you will have a large amount of inertia and momentum. So if we want to make a small change in altitude in such an aircraft it would be more logical to use this incredibly large amount of momentum to make this small change. Where as increase power would certainly do the trick you have to wait for your turbines to spool up and then those engines have have to overcome a vastly larger amount of inertia than that of a smaller aircraft.
Inertia is also the reason you will never hear of a large commuter aircraft getting behind the power curve and surviving it. There is simply too much inertia for the engines to overcome once falling behind the power curve. This is also why stall recovery in such an aircraft takes such a large amount of altitude. All physical laws.
Like it or not and whether a pilot understands the laws or not they are laws. Until these laws of physics are proven wrong by someone much smarter than myself I will continue to follow them and teach my students accordingly.