Have him take his hands off the controls on downwind then base then final. I bet it's lazy trimming. Students often think the traffic pattern is busy enough, so with with the addition of having to trim up for each reduction in power they may think its not worth doing.
Exactly.
Your student is just lacking a basic knowledge of what the trim is for and also needs a better understanding of how to "fly by the numbers" (proper power settings). Maintaining airspeed on climb-out is not the same as maintaining airspeed on final, they are practically opposite in my opinion. On climb-out, your student has full power applied and only has to pitch up or down to maintain his airspeed, which is why he is good at it. It's easy for him because his power setting is constant. On final, if you simply pitch for your airspeed, like you do during climb out, you are now deviating from the constant glide-path that is required while on final. When on final approach, it's power, not pitch, that is required to maintain a constant airspeed. Pitch is used to keep you on the glide-path.
Have you asked him why he slows down to the
final approach speed when he isn't on
final and doesn't have
final approach flaps selected yet? Make sure he understands that it is a backwards way of thinking. When he slows to 55 knots on the downwind, every time he adds flaps he also has to add power or pitch down to maintain his airspeed, which in effect is causing the major airspeed fluctuations he experiences (while he hunts for the pitch and/or power setting that he needs). What happens when one day he adds flaps but forgets to add the required power/pitch while already at his final approach speed? (He'll get slow!) It's not a good habit.
If you really want to get your student in the habit of flying a smooth approach, demonstrate and then have him practice flying the pattern with no pitch inputs (e.g "no hands"). When he feels it's time to turn base/final have him do it with two fingers, like he is holding a tea cup. If he's not configured properly with power and trim it won't be possible for him to fly a stable airspeed without changing pitch attitude.
In order for him to do this it's important that you have him fly the same airspeed on the downwind every time (90 knots). Just as always, abeam the touchdown point he pulls the power back to 1500RPM (estimate) and adds 10˚, after the plane is done ballooning (which he needs to get in the habit of counteracting) have him take his hands off of the controls (e.g. hands hovering next to the controls or using only two fingers). Then have him trim for an 80 knot descent. After this step he is practically DONE, and is stable. With two fingers, turn base, add 20˚ flaps, the plane will automatically slow to 70ish knots. Turn final, 30˚ flaps, the plane will slow down to 60ish (maybe 65ish?). Do not let him pitch throughout this whole process, just trim for the airspeed as needed and combat the ballooning when flaps are applied (palm the yolk to keep it from pushing back), that's it. Work on using the trim for the airspeed he wants, since the power is already set and not being messed with. If the trim is set properly in the beginning of the descent he won't have to touch it again for the rest of the approach (so long as power remains the same). This can all be demonstrated at altitude as well. Let him see and understand the drag factors of each flap setting and how it effects his airspeed when power and trim are relatively constant during a descent. The only real trick to all of this is making the turns at the correct time, and it's pretty intuitive after a couple tries.
If he initially trims for an 80 knot descent at 10˚ and is too fast when he has full flaps selected (say he is at 65 knots rather than the 60 he wanted with full flaps), try trimming out initially at 75 knots the next go around (you will consequently end up 5 knots slower in the end and be at that 60 knots you wanted).
Once you get the concept down that the power and airspeed (through the use of trim) should be constant the whole way down in order to maintain a constant airspeed and descent angle, then you can help him to better understand that when he is on final approach and below the glide-path, he simply pitches up to rejoin it, and when he is high, he simply pitches down. Subsequently, power is required to maintain the desired airspeed when he makes the pitch changes to get back on the glide-path. When he gets back on glide-path, he just returns the power back to the setting it was set to earlier when he trimmed it out abeam the numbers (1500RPM) letting the plane return to the airspeed he had it trimmed for in the first place.
This really is no different then the technique used for the power off (landing) stall; pull the power out to 1500 rpm, flaps 10˚, 20˚, 30˚, trim for 65 knots or whatever.
