I’ve been using this series with some of my youngest students and I think it’s brilliant. Each book is divided into sections so students can focus on technique, note reading, theory and repertoire development equally. The series progresses in a step-by-step manner so yes, a student should be able to confidently play the repertoire and exercises in one book before going on to the next.
Adult beginning students who had some musical education as children often have gaping holes in their music theory knowledge or feel rusty on note reading. Look through each book in the series and find the one that suits your student’s current level. It’s not a bad idea to begin them in a book that is a little too easy so they can start off with confidence, fill any knowledge gaps and build from there. If you’re not near a harp store that carries these, check out the descriptions of each book at an on-line store such as http://www.harpconnection.com.