you should search for blocks/plugins like people, quickmail in the downloads section for your requirement.
or if you are using Moodle 1.9 ? If so you have a facility in the bulk user actions in site admin>users>accounts>bulk user actions
For all moodle activities, the best and easiest way to send a reminder message to all students who haven't yet completed an activity is as follows (for moodle 1.9).
Admin block -> Reports -> Participation report -> Activity module : Choose : select the quiz you want to get reports on -> Show only : Student -> Show Actions: all actions -> Go
In the results table, you can see the number of times that students have taken part in the activity. For the Quiz activity, the difference between the various actions mentioned in the Quiz Views: view, view all, report and Quiz Posts: attempt, editquestions, review, submit lists is pretty meaningless. Anyway, all it means it that those students who are marked No in the All actions column have not submitted their quiz. Click the Select all 'no' button at the bottom of the list, select in the drop-down list With selected users : Add/send message. (you don't need to click the OK button)
In the next screen, you will see the HTML editor to type your "reminder message" and you will see the list of students to which that message will be sent.
When I do this I see only 86 students marked "yes"; the other 310 students that have not participated in this quiz are not in the list (there are no entries marked "no"). What am I missing?
This is Moodle 1.9.2.
If you are a teacher, not an admin, is there a way to do this?
I'm editing to say that Quiz documentation handles this nicely. http://docs.moodle.org/en/Quiz_reports
And I should have remembered that.
What I'm really looking for is a way to respond to individual quizzes, not just questions, but the whole quiz. Is there a way to do that?
When I followed Joseph's steps carefully, I realized it is all in the classroom and it is all teacher action. You do not have to be an admin to do this.
Thank you, Joseph, a *really* useful post.