To avoid confusion let me emphasize that I think it is pretty much mandatory for GSIs to make themselves available during the time leading up to the final to answer student questions and otherwise explain the material to students who ask. But the more I think about it the more it seems like offering a true review session, the sort of thing where you prepare specific problems for the students and have a spiel prepared for them is actually harmful (posting a list of practice problems to the web for all the students to try is a different matter and something I approve of).

Before we can even get a grip on this question we need to be clear about the goals of a class like this. Given that these students are fairly unlikely to ever use this material outside of this class three reasonable goals spring to mind.

1. Actually create real understanding in the students
2. Actually teach the students the skills of calculus.
3. Prepare the students for the second half of the year if this is the first semester.
4. Train the students to think quantitatively/formally (in a very weak sense)
5. Function as a hurdle passage of which indicates a certain level of work ethic, intelligence and ability to learn

No matter what we take the goal of the course to be we have two possibilities to face. Either review sessions are genuienly effective at improving student performance on the final or they are not. If offering genuine review sessions (as opposed to say office hours) doesn’t offer a substantial benefit over holding office hours then holding them is either a waste of time or some kind of dastardly trick played on the students (who are all clearly lead to believe the aim of the review session is to help them study) and in either case ought to be discouraged not celebrated . On the other hand if offering genuine review is substantially effective at raising exam scores we have to ask what makes these few hours have such a big impact.

From my experience I would conclude that what makes a review session effective at raising exam scores isn’t that it conveys more understanding than office hours, just the opposite in fact, but because it helps the students get the low hanging fruit. In particular it’s been my experience that the primary advantages review sessions have over office hours consists of helping the students avoid stupid errors like forgetting the +C in an integral, bootstrapping off the Ta’s implicit understanding of what sort of problems the professor is likely to ask, and seeing all the types of problems laid out at once letting the students build up a lookup table letting them infer what type of problem they are being asked using textual hints rather than real understanding. In short, to the extent review sessions are effective it isn’t because they make significant contributions to understanding.

Yet even if you think that having a real review session as opposed to just office hours has some benefit surely this is offset by the harm it does undermining the value of the test as an assessment. For starters since review sessions are offered outside normal class periods it is likely that some students will be unable to attend, or find it significantly more difficult to do so. With office hours the same TA will often have a range of options while with real review sessions there is often implicit (if not explicit) pressure not to attend another Ta’s review session and frequently only one or two Ta’s will offer full scale review sessions while the rest will offer something between office hours and review sessions.

Review sessions surely reduce the effectiveness of the exam in estimating work ethic or ability to learn independently as compared to office hours. To the extent that these math courses are simply hurdles to make sure that the students are smart and disciplined enough any kind of hand holding (as opposed to offering office hours for those who want to make use of it) is counterproductive. As many people don’t attend review sections because they judge it a poor trade off (need to study for other finals more) any ability review sessions have to improve grades without increasing understanding or future ability to apply the material undermines the ability of the exam to measure these attributes. Also more generally it seems like the more test taking strategies that students learn to use on the exam, e.g., learning to use textual clues to the type of problem, the worse the test will be at judging either actual understanding or ability to apply these skills in any context but this particular course.

In short it seems to me that the benefits of actual review sessions are quite small compared to those from office hours even though they may be quite effective at raising exam scores. On the other hand the harm done by review sessions to any reasonable conception of what course grades are supposed to track seems significant. Yet despite this holding actual review sessions seems to be uncritically regarded as a good thing for a TA to do and I’ve never heard of a professor banning them. At the very least professors should require that any TA who makes a review sheet available post it on the web to make it easily available by those without friends who attended the review section.

I’m well aware that most review sessions are offered with the best of intentions but that is my real complaint. During my 5 years of teaching I’ve seen a lot of strong attitudes about how teaching should be done and a whole host of other background assumptions about what makes for good teaching but virtually never heard any serious ground up analysis of what we are trying to achieve. At the very least it seems perfectly plausible that review sessions are actively harmful yet this sort of consideration doesn’t ever seem to come up. Perhaps doing so is too depressing and we need to pretend we aren’t inflicting totally useless material on students who won’t ever use it while making them hate math along the way but it seems we could be a lot more useful if we actually thought through what we were trying to do rather than taking for granted how we should teach and then trying to justify it.

For instance I think just having to draw a line between when it is acceptable to muck with grades to motivate students (allowing not turning in HW/low attendance to impact grades) and when it is not (seripticiously giving girls a 5% bonus in the class if we discovered this improved both sexes motivation) would be a huge improvement over the current situation.