I want to add something to what jasp said.
When you are giving your pre-new-terrain pep talk, do it well up the trail where the students can't see the steeper slope. Have them then ski the new slope without stopping to look at it.
This does several things. It limits the head games the students will play with themselves. They get to get moving on comfortable terrain rather than having to face the new stuff on their first turn. They're reviewing the movements they will need in a non-threatening situation, etc.
This, with the other things jasp wrote about, gives a success rate of almost 100% in moving to steeper terrain.
ps. It should be obvious, but the greater the increase in steepness the longer the time that must be spent getting ready for it on comfortable terrain.