After a number of years of experimentation and revision, this is the sequence of books and materials I use with my jazz saxophone students.
Essential Elements for Jazz by Mike Steinel*. This book provides an excellent transition from traditional music into jazz. It’s presented in typical method book format, with lots of short exercises and clear definitions of new concepts. Emphasis is on jazz articulation and swing style. It has some brief improvisation excercises, but not so much as to intimidate young players. There are brief biographies of important jazz players like Duke Ellington, Louis Armstrong, and Charlie Parker, and some discussion of different forms of jazz (swing, bebop, fusion, etc.).
Jazz Conception for Saxophone by Lennie Niehaus. This series of books is a great next step. The first section of each book is made up one-page exercises which help the student master jazz articulation, rhythm and phrasing. The second section of each book has 10 etudes which resemble bebop solo transcriptions. There is no explanatory material other than a brief preface, so a student would need a good jazz playing teacher to model the style.
How to Play Jazz and Improvise: Vol. 1 in Jamey Aebersold’s Play Along series. This is great entry level material with simple chord progressions and moderate tempos. Some improvisation teachers feel this material caters only to left brain thinkers and is overly academic in its approach. However, I’ve felt that a good teacher can balance that by keeping the lessons fun, with plenty of positive reinforcement.
Maiden Voyage: Vol. 54 in Jamey Aebersold’s Play Along series. A good next step for young improvisation students. I like that it uses real tunes, not artificial exercises. I’ve been playing the original recordings for my students to introduce them to the important jazz artists.
Charlie Parker Omnibook. Call me crazy, but it’s taken me a while to accept the fact that it’s pretty futile to attempt these solo transcriptions until until a sax student has had plenty of experience with easier material like the Niehaus books. Just be sure to buy only the Eb edition. The Bb edition might be okay for trumpet players, but it would be totally unrealistic to have a saxophonist play from the Bb edition.
*Mike Steinel was one of my professors at the University of North Texas, where he continues to teach. He has also written Building a Jazz Vocabulary which I would definitely recommend for experienced improvisation students who are capable of dealing with more advanced music theory concepts.