It is a FINGER!
And pianists must learn to use it that way!
As a college student, I had to unlearn years of bad habits in using my thumb. Why? I was using it like a thumb, the way it naturally works, and I was thumping keys when I should have been pushing them like the rest of my fingers were doing. Until I got to college, no one had worked with me on correcting this issue. For a while, I was obsessed with it, and as I listened to other pianists, I found I could tell, without looking, when they were using their thumb.
Don't let this happen to you (or your students)!
What to do?
As I start students on their 5 -finger warmups (covering every major key over a period of several months) we work on cupping the hand so there is an arch at the knuckles connecting the fingers to the hand. As they accomplish that position and learn to push into the keys from a 90 degree angle from their middle knuckles through their finger tips, we start to work on raising the thumb. The thumb cannot approach the keys from a 90 degree angle without disrupting the wrist movement, but neither is it most under control when it lies on the keys at 180 degrees. Keeping a high arch with the other fingers and pulling the tip of the thumb up close to where the tips of the other fingers are lying on the keys will raise the thumb slighty (about 30 degrees) and allow the pianist to use it like the other fingers in a pushing motion rather than a slapping/thumping motion. This will also help avoid the wrist motion some beginner or poorly- trained pianists use where the wrist pushes down fast and hard (almost a slamming motion) to get the thumb to play a key.
Raising and controlling the thumb means scales can now be played with a more even tone and wrist motion. Unintended accents will decrease in your pieces.
In piano, all ten fingers count! Remember the thumb is a finger. Use all your fingers well!