Aero -- I'm sorry but the students are not going to be plotting a C of L curve for any of the wings they are going to be flying.
For aerodynamicists it is important for them to understand how their wing as a whole responds to the use of high lift devices and ailerons, they need a reference chord line to plot the graph -- for a student trying to understand the concept of washout, or why deflecting an aileron down in an incipient spin is bad, a C of L curve for the whole wing doesn't tell them jack.
They need to know that the
outboard section of the wing is more stalled than it was before they added the aileron -- you said it yourself: Deflecting it causes more flow separation. Well what causes that flow separation???? The answer is that particular section of the wing is now flying further BEYOND its critical angle, because they moved the aileron down. In effect, they have increased the Angle of Attack on that section of the wing. These are terms they can understand. If you can't see the benefit in being able to explain it that way, instead of stubbornly clingling to conventions more appropriate for a course in aerodynamics, then we will never see eye-to-eye.
YES, they have also changed the camber, and the coefficient of lift for that section, and indeed the entire wing as well. But they are not aerodynamicists, and the 14 year old you are trying to get PGI before your training flight would be much better served by an instructor that can teach it in whichever way he most readily absorbs it.
you may not see the reason why you should be learning that AoA doesn't change based on aileron deflection and you may still get the same understanding of the result of control deflections on the handling characteristics of the airplane, but the end doesn't justify the means and I believe it applies in this case. There is absolutely no reason to teach something incorrectly in my opinion. Pilots only require a simple explanation and basic understanding of how the control deflections affect aircraft handling and that can be achieved. However, I won't lie to a student.
I'm sorry man, there's a difference between "incorrect" and "different". You are arguing for convention; one specific way of teaching -- I have no problem teaching students either way. I'm sure many aerodynamicists can happily discuss what may be happening at a specific section of an airfoil -- by deflecting an aileron or deploying a flap, you are changing the shape of that airfoil section, it is no longer the same and if your aircraft is still moving in the same direction, that section is no longer generating the same lift, it no longer has the same camber, it no longer has the same chord, it no longer has the same angle of incidence, it no longer has the same angle of attack!
The question we've been debating is whether or not it is appropriate to examine that isolated section of wing on its own. You are insisting we can't, and have to view the changes in the context of the wing as a whole -- but a simple C of L curve doesn't tell you anything about how the wing changes along its span. Sometimes this information is important to get across to the student! Not only that, but sometimes by breaking the wing down into sections it becomes more intuitive for them to learn!