Actually, I would like to see if where they are in their reading, even if the check off may not always be an accurate representation, if you know what I mean.
I know it's not much help for you today but if I remember correctly this kind of feature will be included in moodle 2.0 where any activity in moodle can be ticked off as done by students as part of the conditional activities feature.
Perhaps somebody else knows how to achieve this with the current version of moodle?
Or Forum. Make a topic for each assigned reading. Student replies to the first post in each topic with "done." Fiddle around w/ ratings/gradings and maybe you can get it into the gradebook?
A forum is interesting... if you did a separate entry for each reading. You can turn on the tracking feature. If students don't click onto the reading entry until they have completed the reading, they could track where they are.
Are these readings resources in the Moodle or in a book?