I am a Christian pastor and high school Religion teacher, and I'm currently using "The Story of the Qur'an" as part of a course for Juniors and Seniors on Islam. It's an excellent resource: deeply scholarly, but also user-friendly. It's technical, but absolutely approachable. Even those just beginning to learn about Islam and the Qur'an will be able to get it.
For teachers: Mattson's book occupies a niche that others don't cover. It explains "what's in the Qur'an," to be sure, but also questions including: "how did the Qur'an take shape?" and "what role(s) does it play within Muslim culture throughout history and today?" and "how have Muslims interpreted the Qur'an?" (Note: these are my summaries, not its chapter headings, per se.)
It's really the last three questions that set the book apart from other introductory texts. Most of these will tell you THAT the Qur'an is important, and many will tell you WHY, at least in a general way. But none I know offer the same nuanced view of HOW the text evolved and how its reception and interpretation have also evolved.
Why does that matter? Well, I've found that my students come to the Qur'an with a great deal of interest, but also suspicion. They are attracted to its emphasis on social justice and are often surprised by its beauty, but put off by its eschatology (which, in fairness, they have only just begun to learn). They struggle mightily to understand the authority of a text -- a struggle that is made harder by the general distrust of any authority that is typical of their age, but also compounded by the media treatments of Islam which are often all they know of the faith.
Mattson is brilliant in giving them ways to understand that authority as the product of revelation, but also history.
If you're serious about introducing students to the Qur'an as part of a course on Islam, this is an invaluable resource. Also good for helping students develop paper topics and bibliographies, as well as for developing a mental framework to understand the Qur'an on something closer to its own terms. It quotes a lot of Qur'anic material, so it might also be used as a reserve book or for the teacher to prep a unit for him/herself. Easy to use as a roadmap for teachers trying to decide which passages to teach and how to understand them.