I like to use a series originally published by ABRAM{I think} but now available in the US through Hal Leonard called Jazz Piano Pieces.Its not for beginning students but I like it for beginning jazz students.
I just ordered some of these books! They arrived yesterday and I was looking through them this morning. Actually they're published by ABRSM (Associated Board of the Royal Schools of Music), and as you said, available in the US through HL. The title of the HL books is "Jazz Piano The Complete Method." It includes the jazz pieces, aural tests, quick studies, jazz scales, and a CD, all for 12.95. These various components are in separate books as published originally by ABRSM, I believe. HL makes it a very economical package deal.
I am just recently trying to teach myself jazz, hoping to eventually teach some jazz improv to my students. My initial impression of these books is that I need some additional foundation to put under it. I only ordered levels 4 and 5, thinking that I surely wouldn't need the very beginning books (LOL). Actually I'm not sure if I need to get the first 3 levels to help me, or (what I'm leaning toward) Jazz from Scratch, which I believe correlates with "The Complete Method."
I think "The Complete Method" looks terrific, regarding its contents and thoroughness, but it does not seem to be self-instructional. I think it's designed for a teacher who already knows how to improvise to use with a student. (or else I just really stink at figuring this stuff out!)
I like how the book starts each piece with it fully notated (the "head"), then goes into an improv section, which has bass part written, chords written above the measures, and a set of RH notes from which to devise the improvisation. For me I just don't know enough yet to work out an interesting improv part, but for anyone who has spent much time listening to jazz and who has a good ear for it, it would probably be pretty easy.