Dr. Suzuki defined "ability" as "knowledge + 10,000 times." Remember that his guiding principle was that learning music should be like learning one's native language. In other words, the goal is to be able to play a piece with as much ease and comfort as we speak.
It is, therefore, very important to devote most of the practice time to review repertoire. Dr. Suzuki expected his students to play every piece they knew every day. That meant that a student working on Mozart concerti would still be practicing his Twinkles. That might sound silly, but imagine just how effortless it would be to play a piece if you've been playing it every day for ten years. Consider other activities that you've been doing every day for years: Driving, Walking, Speaking, Reading, Typing perhaps. Ideally, music should come just as naturally.
Most Suzuki teachers divide the pieces that a student knows (or is learning) into three categories.
1. The Working Piece is the newest piece - the student is just learning correct notes, rhythms and bowings, and working to play the piece in tune and with a beautiful tone and a steady tempo, appropriate articulations, and whatever technical point the teacher is asking for (e.g. tunnel fingers in Lightly Row).
2. Polishing Piece(s) - the student can play the piece at performance tempo, and apply musical concepts like phrasing, dynamics, etc., and is ready to play the piece in group class.
3. Review Piece (s) are pieces that the student has known for a while - these pieces should feel easy to play. The student can play the piece expressively, with beautiful tone, great intonation and great posture, with minimal effort. In my opinion a piece is not ready for a recital performance until it has reached the Review level, because the child will be much less likely to have memory slips or make nervous mistakes.
Review pieces are an incredibly important practice tool because they are where we develop cello playing skills. Most often, a technical point the teacher assigns you to work on at home will be too new or complex to address in the Working Piece. However, Review Pieces have become so effortless for the student that she can focus her attention on whatever skill you are working to develop.
The Suzuki repertoire is carefully scaffolded so that earlier pieces introduce skills that will be needed to learn latter pieces. Bowings and rhythms from the twinkle variations, for instance, appear in the Marcello Sonata in book 4. The rhythm and articulation in Humoresque in book 3 reappears in book 5's Goltermann Rondo, which in turn helps to prepare students for pieces like the Sammartini Sonata and the Haydn C Major Concerto. If a student continues to practice and refine her Review pieces, she will already be mastering the skills needed to learn those more advanced pieces.
As a teacher, I am not assessing a student's progress based on which new piece he's learning. Instead, I'm assessing his progress based on how well he plays his review pieces. Does a book 3 student play French Folk Song with a sophistication and maturity appropriate to his level? This student has gotten to Webster Scherzo after only two years of study. Great, but does she play in tune? Is her bow arm relaxed?