Starting with the final review session in Spring 2010-2011, I changed the format of my review sessions to be focused on solving error-spotting exercises (the link has more details on the general pros and cons of using error-spotting exercises as a diagnostic tool). You can access the error-spotting exercises I used in my review sessions under the “review sheet (advanced)” for the courses linked to from my teaching main page. An example is here (advanced review sheet for the final for Math 196, linear algebra).

Prior to this change in format, review sessions were mostly about me reiterating points from a review sheet (that students had access to in advance), quizzing students, as well as giving longer problems on the fly where I would check the desk work of students. With the error-spotting exercises format, the majority of review session time was devoted to students trying to spot errors in the items I had given them, with me coming around to them to see how far they had gotten, giving them more hints, and asking further exploratory questions of the ones who had discovered the main errors. I would sometimes round up the item with a discussion on the board. In some cases, I’d segue from the error-spotting exercise to a few practice questions.

Some observations:

• The change in tone and flavor of the sessions was significant. The review session felt a lot less like a classroom performance. At the same time, it was still a heavily guided and controlled experience (not a “students just come and ask questions” sort of experience).
• I believe that students’ sense of understanding and number of “aha!” moments increased significantly with the change in format, as they struggled more to interrogate their own conceptual understanding. I also think that students had a subjective sense of a similar sort.
• I believe that the change also improved student test performance, but hard evidence is difficult to adduce. (Student performance did increase somewhat after the change in format, but the student bodies weren’t identical, and it’s hard to isolate the effect of a particular change). One drawback of the new format was that it left less time for practice with routine problem types. I don’t believe the drawback is significant for students of the caliber I taught, since they were able to master routine problem types while the problem types were being taught and could review those problem types by themselves (I did try to integrate some routine problem practice in the discussion of the error-spotting exercises, but this was not a primary focus). For less elite student bodies, the balance would probably be in favor of fewer error-spotting exercises and more practice with routine problem types.