Question: How would you stop a pupil lifting their heel when using the pedal?
Albert's reply: To resolve this pedal problem you'll need to show your student that good piano pedal technique involves the toes as much as it does the ankle.
Pianists need to gain control over various muscles independently of one another, which involves the feet as well as the hands and arms. I'm guessing your student is using the pedal as a binary "on/off" switch and the solution is to explore the many degrees in between.
Tell the student that the heel is always glued to the floor. Have the student practice in socks, without shoes, and do three exercises:
First, the student should practice moving the foot from the ankle, not moving any other joints. The goal of this exercise is to keep the foot flat relative to itself.
The critical exercise is curling the toes without moving the ankle. Your student will realize that this allows for much finer control, and hence more subtlety, in pedaling.
Finally, have your student combine the first two exercises. This will form the basis of proper pedal technique and solve any interim piano pedal problems. Most importantly, it will make for more expressive playing!