Here's a bunch of things to do with a foot focus. Thanks for setting up the thread this way; it's been a fun list to compile. In all of these, the upper body does nothing; keep it "quiet."
1. Glide straight down the fall line on parallel flat skis. Do this on beginner slope so your student does not go too fast.
Slide one foot back, oh, about 3-5 inches while heading downhill. Do not allow the hip above it to move or rotate, just move the one foot.
Do not rotate the foot; no rotation, just a foot slide-back, or foot pull-back.
See what happens. (skis should turn together, no stemming)
Go do something with that revelation together on new terrain, you and your student, depending on what level they are skiing at. This can be morphed into a flat 180, then into a flat 360 if you've got enough time with the student.
2. Glide straight down the fall line on parallel skis. Do this on beginner slope so your student doesn't go too fast.
Slide one foot back, as above, keeping the hip above it stable, and at the same time point that knee outward to go bowlegged.
Try not to rotate the foot/ski, just move the knee outward as the foot slides back and keep skis parallel.
See what happens.
Go do something with that revelation together.... what depends on what level the student is skiing at, as above.
3. Same as 2, but this time allow the foot to rotate so that its tip points outward relative to the other ski. See what happens. (Works very well in dense glop.) Muse upon the perceived difference between 2 and 3. Go do something together with that observation on different terrain.
4. Glide straight down the fall line on beginner terrain. Hold hands together behind back, poles dragging. This will keep skier not-aft. Tip both feet onto left edges, then onto right edges, tipping at the ankles inside the boots. Do NOT rotate feet/skis. Try to not fall over. Keep at it until not falling over and not rotating feet/skis. Leave pencil-thin tracks in snow (RRtrx). Enjoy. If skier is intermediate, take this to next level of terrain and see how long the skier can keep hands together behind back, poles dragging. This can be built upon to generate round carved turns, but it takes time and the right terrain without traffic. Skiers used to pivoting skis at turn-start will have a very hard time deleting the pivot.
5. Glide straight down the fall line on beginner terrain. Lift the tail of one ski with the foot, keeping the ski's tip on the snow. See what happens. Vary how high the tail is lifted. Don't do anything else for a while to clarify the effect. (Stork turns, flamingo turns, ... etc.)
Add going bowlegged with that knee, without rotating the foot/ski. See what happens.
Add ankle-tipping that ski onto its little toe edge. See what happens.
Add pulling that ski back, oh, 3-5 inches. See what happens. (Whoah!)
Muse upon the different effects. Go mess around with this bunch of movements with your student, choosing terrain depending on the skier's level.
6. Side-slips to edge-sets, back to side-slips, to edge-sets, repeat. Progress to hockey-slows then to hockey-stops with a focus on foot rotation. Add hockey-stopping on a downhill target on the snow (shadow, leaf, divot), ending with a firm pole-plant. Take to new terrain for fun. Do slow gentle hockey-stops that don't wake up the snow, and fast hockey-stops that send snow-spray (to build tipping and rotating skills).
7. Falling leaf, side-slips to downhill targets, side-slip garlands with rotating feet to point ski tips downhill then back uphill. Side-slips with one-foot-pull-back to see what happens. Progress to very slow side-slippy turns down the hill.
8. Pivot slips, with a foot-only focus. Start with side-slips. Rotate flat skis, pulling/sliding one foot back uphill of the other, keeping feet on separate tracks. The foot-slide-back is essential, and builds on previous exercises above. Pay attention to the imaginary tracks and don't let the feet move left-right off those tracks. Upper body and hips face downhill. No pole plants.
9. Shuffle turns on beginner terrain, step-turns on beginner terrain, march! on beginner terrain, hop in between turns on any terrain (for centered stance).
10. Thumpers - lift tail of inside ski and THUMP! it down during turns. Start with thumping between turns, move to thumping through the entire turn (for outside ski balance).
11. Skate on flats using feet only, no poles, skate uphill, skate downhill on beginner terrain. Morph skating into turns (skate-to-shape).