ilovechopin is so right. It's very important that they not read by the finger numbers through position playing. I don't teach much with an interval approach, but we do a lot of reading.
Flashcards are my greatest blessing in teaching! One teacher once taught me "Cut C" for the middle c, "Dangling D" for the d above, and "Even E" for the e. I've expanded a little to "First Space F" and "Ginny G." (We call the G Clef "Ginny G Clef.")
For the left hand in middle C position, we have "Left-Hand C," "Bubbling B," "Top Line A," "Under Ground G," and "Freddie F." (We call the F Clef "Freddie F Clef.")
I use "Very First Piano Book: Story of Tony" by Elizabeth Quaille. This book, however, is slow-going for those that don't practice much. If that's the case, then they don't learn much! So I usually add "me and my piano: very first lessons for the young beginner" by Waterman-Harewood. Although it uses English (as in British) terminology, it's proven to be extremely successful in teaching students to read.
I then go into Diller-Quaile's "25 First Grade Piano Pieces." and "Me and my piano:part 2, Piano Technique." The first is not as easy as the title, and the second is not really a book of technique. It's just the second level book of learning to play the piano.
After that, we go into repertoire books like Gretchaninov, Kabalevsky, and Bach.
What's nice about these books is that they're "teacher-dependent." Unlike some method books which spoon feed everything to the student, these books need a teacher. I find that when I teach out of books like that, I'm more likely to think of what a student needs to learn, then find a piece to match.
In method books, it's easy to fall into the trap of just turning the page and assigning everything in order.
But ilovechopin said it simply and correctly. Avoiding the position and fingering heavy books is important!