First off review the recovery from a normal stall (power on or off). Then introduce to the student what may happen when the stall recovery is not executed properly; ex. increase back pressure too rapidly before the airplane has a chance to gain airspeed. There really is no difference between a normal stall and secondary stall. However knowing the correct technique to recover from a secondary stall and preventing a secondary stall from occuring could save his/her life.
Show them the order in which your control surfaces will be ineffective during a stall.
During a stall your rudder is the last surface to become ineffective, instill that in your student so they which surface is going to give them the best performance and also so they can make a safer recovery. Hope this helps a little. Good Luck!!
Actually I meant AoA but after your response I did a little research (it's been awhile since I've had to teach these...).
As long as the discussion revolves around a 1g scenario then the AoA will remain the same as you point out.
But apparently some people consider these stalls to be 'accelerated stalls' (which I always associated with turning flight) but I suppose if you happen to pull more than 1g on the second recovery then the critical AoA will change.
I dunno, I am pretty sure that the critical AOA will not change at all. If you pull more that one G then the load factor will increase and the IAS (as well as the deck angle) at which the airfoil stalls will be higher but the critical AOA should not change at all.
However I could be wrong as I have been many times in the past.