Overview. This book is designed as a workbook because, in my experience, while undergraduates can learn both general relativity and tensor calculus but do much better if they "own the subject" by working through most of the ideas and math on their own. The workbook format prompts students to do this, and provides appropriate guidance to help them through the process. The format also makes it possible to spend class time efficiently by addressing students' actual difficulties (rather than in lectures that might miss the mark).
Making It Worth It. However, this design is effective only if (1) you as instructor emphasize the importance of this (and that you are counting on it) on the first day of class, and (2) the course structure makes it worthwhile for students to invest effort in filling out the text boxes before coming to class. This means that one must somehow make a students' grade depend (to some extent) on filling out those boxes.
Here is how I have done this in the past. At the end of every class session, I use some device to randomly select one to three students (depending on the class size), who hand me their books on the spot. After class, I grade the students' work in the boxes on a 10-point scale based on effort. The grade emphasizes the chapter discussed that day, but also assesses previous work done since I last graded each book. A selected student who is absen can earn up to 6 points by turning in the book later. At the end of the course, I drop each student's lowest grade, average the rest, and count the result as 12-15% of his or her course grade.
I have found that most of the time, students are good about doing this work ahead of time (particularly if on the first day of class I have helped them understand how important it is). The grade, however, rewards students for doing the work and provides a bit of extra incentive to do it even when inconvenient. In my course, students are tapped an average of about 6 times during the semester (though the statistics of small numbers means that some are tapped more and some less). Even so, using some device to make a truly random selection means (1) that any student may be "a winner" on on any day, and (2) that everyone recognizes the selection to be fair. The one dropped grade provides some automatic flexibility (so that I don't have to listen to excuses), and the fraction of the course grade that this option represents is large enough to be motivating but not so large as to be anxiety-provoking. Grading is quick and easy (particularly if the student was good); I am usually able to return the book to a spot where the student can pick it up within 15 minutes after the end of class.
One of my colleagues uses a more direct method. After deciding with the class which of the box exercises need the most attention, he assigns each student in a strict rotation (which includes the instructor) to go to the board to present the soltuion to whatever box falls to them. This strongly motivates students to come to class fully prepared. One might supplement this (if necessary) by making a portion of the course grade depend on the student's preparation, and/or allowing a certain number of "passes" without penalty.
These particular schemes may not work in your particular student culture, but I strongly urge that you find some way to hold students accountable and reward them. This is, I think, important for the course's success.
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Thomas A. Moore has been a professor in the Physics and Astronomy Department at Pomona College since 1987. He does theoretical research on detecting gravitational waves using LISA (now eLISA). Send him a message.