The Three Finger Positions on the Cello
Janos Starker, in his interview posted at the Internet Cello Society, said that cellists tend to get lost in the three finger positions. In my experience this is often the case.
The “four finger positions" are half position through 4th position in which we use our 1st through 4th fingers in half steps.
The "three finger positions" are the 5th through 7th positions on the cello in which the cellist uses the 1st, 2nd and 3rd fingers and ceases to use the fourth finger (hence the name). Generally, the thumb stays back for the three finger positions or, for small hands, can be on the side of the base of the neck.
Thumb position comes after the three finger positions.
There are some excellent resources for our cello students to help them learn the three finger positions. The book that I like to use in my teaching of pre-college aged students is the Position Pieces for Cello, Book Two by Rick Mooney. The book is quite systematic and organized according to finger patterns from 5th through 7th positions. It is also a great book for teaching tenor clef.
For my college and some high school students I use the three finger position serial control exercises in An Organized Method of String Playing, Violoncello Exercises for the Left Hand by Janos Starker. "Serial control exercises" are finger or note patterns that one learns in multiple positions. The patterns rise and fall by half steps. You can also write out your own three finger serial control exercises for your students or, better yet, the students can write out their own.