Wednesday, December 13, 2006

Coordination Problems and Large Class Redesign

When I used to teach intermediate microeconomics, the last time was over 5 years ago, near the end of the course I would give a lecture on bi-matrix games as a sequel to the more traditional oligopoly theory. Among these games are the Prisoners’ Dilemma, which has a dominant strategy equilibrium (both players cheat) that is a reasonable first pass at the problem faced by cartels. But apart from Prisoners’ Dilemma, I also spent some time on games of “pure coordination” where there are multiple equilibria and where each player agrees on which one is preferred. The issue at hand is whether the players naturally “find” the good equilibrium or if they can get stuck in the bad equilibrium. The following link represents this type of situation.

There are two different games depicted, each game symmetric for the two players. In both there are two equilibria, the blue one (Top, Left) is better for each player than the red one (Bottom, Right) and the payoffs in these equilibria are identical across the games. Yet even with these similarities, game theorists would predict different outcomes in the two games because of differences in strategic risk.

The Row Player’s payoff is the number to the left of the comma, the Column Player’s to the right. In the first game, Top gives the Row Player 300 if Left and 80 if Right, so 80 is the worst the Row Player can do by choosing Top. Bottom gives 20 if Left and 100 if Right, so it is not just that (Bottom, Right) is a bad equilibrium. It is also that by playing Bottom the Row Player can get really hammered (earning only 20) if an out of equilibrium outcome (Bottom, Left) is reached. Each of these factors reinforces the other and the consequence is for the Row Player to be inclined to choose Top and, since the game is symmetric, for the Column Player to be inclined to choose Left, so in this game the coordination problem is only a minor issue.

The situation is different in the second game. Now it is Bottom which is the safer strategy, since the minimum payment under it is 80. Top is riskier, with a minimum payment of 20. So while (Top, Left) is still the good equilibrium, risk averse players may very well find their way to (Bottom, Right), in which case we might characterize the situation as being stuck in a lower level equilibrium – there is definitely a better play to be had that if found is self-enforcing, but owing to both lack of pre-play communication and the caution of the players, they instead find the inefficient equilibrium. In this game the coordination problem is severe.

* * * * *

I think the second game, though too simple to completely describe the situation, provides an apt metaphor for how our campus manages many issues related to instruction, particularly as they pertain to large classes. I want to describe some of these but before I do so, I’d like to summarize the circumstances under which these issues became sufficiently prominent for me to connect them with the elementary game theory discussed above.

As part of the Campus Information Technology Advisory Board, I serve on the standing subcommittee for Learning Technology. We had a meeting yesterday to talk about the potential for a Campus Blended Learning Initiative. I thought it would be useful for the group to hear from Carol Twigg about the National Center for Academic Transformation and their new Redesign Alliance of which my campus is a member. So we had a teleconference with Carol, which I believe was helpful for the group and got a bunch of core issues on the table (thank you Carol), and then we had a fairly animated conversation afterwards mostly about the impediments to undertake such type of reforms on our own campus. Part of the action items from that discussion was for me to write up a list of bottlenecks that the group has identified and then to consider whether a Blended Learning Initiative might seriously address those issues or be constrained by them.

Here is a glimpse of some of the issues we discussed yesterday from as viewed from coordination failure perspective:

Grade Inflation/Measuring the Effectiveness of Reform/Disengagement Compact – I told the group a story of a conversation I had with the course instructor for our large intro to accounting class. She is an adjunct who enjoys the job and whom I know from a long time ago because when she was a doctoral student she took graduate microecon from me. I asked her about the grade distribution in her class and in particular whether she gave out a lot of C’s. She told me that she did when she first started but there were student complaints. She doesn’t grade so hard now. We know from Declining by Degrees, among other sources, that this is a ubiquitous issue, not at all unique to this particular instructor. The grades are high and the work requirements imposed on the students are low. There are few complaints about the course and in this way the instructor maintains a sense of job security. If other courses had harder grading and more demands placed on the students, then this instructor could do it too, indeed she might very well be so inclined. But doing so unilaterally is self-defeating.

Juxtapose this with the question Eric Meyer, our rep from the College of Communications and member of the Campus Gen Ed Board, posed. Eric said the Board was concerned about technology solutions that are replacing traditional approaches and in particular whether there was any way to know whether the reforms were really effective or not. Eric posed a question to Carol on that subject. Carol gave what I thought was a good response, emphasizing the importance of evaluation in reform and in establishing baselines with prior practice if possible via common exams and performance on those or common exam questions within exams that are otherwise differentiated if there is need to change tests over time (e.g., to deter cheating). And if such type of “objective” testing in the course didn’t make sense as a means to assess student understanding, then rely on a fully specified rubric for assessing students and demand that rubric be the same in the pre and post reform environments. In other words, take measurement seriously and then implement those measurements and learn from them.

But, getting back to my accounting professor friend and indeed my own experience with large class instruction, students here fully expect exams to have question that are only very minor variations on a theme to which they’ve already been drilled repeatedly and so testing in this way can measure familiarity with the material and discriminate against those students who are entirely unprepared, but it really does not do a good job of identifying those students with facility to use the material in interesting and creative ways from those who don’t have that capacity. Consequently, even if we do really want to measure the effectiveness of the reform and want to take that seriously, we strain to do so given that our pre-reform methods of assessment don’t discriminate across student performance in interesting way.

Facilities Scheduling and Course Reform – I think we could have talked about this issue for hours and hours. Everyone in the room had lots of stories to recount about the difficulty of scheduling large classes – there is a very high utilization rate for large classrooms exacerbated the last few years by exceptionally large entering classes – as well as the difficulty involved in finding technology classrooms when the class is not so large. We heard stories about how departments will opportunistically hoard the classrooms to which they have priority for scheduling even when they don’t have a class to put into the room immediately, for fear that by generously giving back the room for general assignment they will lose their priority in the future. Obviously, such opportunistic behavior makes the classroom scarcity problem seem all the more grim, for those looking to find a space to which they don’t have a priority assignment.

Related to scheduling we discussed the campuses Responsibility Centered Management (RCM) approach to compensating departments for teaching classes, where the revenue flows based on bums in seats, so there is an incentive to jam more seats into each classroom and indeed the scheduling/budgeting people in the departments communicate to the facilities folks needs to that effect. But in other conversations the department administrators and the faculty may argue the goal is to increase student critical thinking, while keeping that notion on an entirely abstract plane, outside the facilities dimension. It is interesting when the two are indeed put together. You will see the faculty argue for taking seats out of the classroom and encouraging more flex space. In my college where we have a new classroom facility currently under construction, precisely that discussion has occurred.

The RCM formulas are under assault for a different reason. Our implementation here strongly differentiates students in the major from those outside. Departments have a great incentive to attract students into the major and hence will offer a variety of perqs to students to compete in this manner. The competition for students between departments might and colleges might affect class size the other way. But for students outside the major, it is hard to see that encouraging high quality under the current formula and indeed it has been an impediment to encouraging interdisciplinary offerings, such as a new minor in Informatics, which sounds like a great idea but which can’t go forward because the costs of teaching the courses can’t be covered. So on the one hand our Campus Strategic Plan emphasizes the importance of such interdisciplinary activities, but on the other the RCM approach creates a disincentive. The RCM approach will be modified and that might address some of this issue. But as an economist let me point out that in the absence of heavily increasing tuition revenues overall, there is a zero sum aspect to any type of funding reform – if there are winners there will also be losers – and since I know we are struggling to make ends meet with our major in my College, we want to offer the students a truly outstanding business education but with largely in-state tuition rates even with the recent tuition differential it is hard to make the math work out correctly, we will be none to happy if the reform to RCM means a lower revenue stream from the majors.

Technology Support Adequate to Sustain Course Reform – My campus is known for its decentralized approach and this is seen clearly in the learning technology arena where some of the colleges have very substantial offerings that serve as a counterpart to what the campus does. This means what the campus provides must be very generic and it may not be suitable for some audiences or it may miss some requisite functionality that therefore gets provided by some college, or doesn’t get provided at all. The decentralization can be seen as a direct cause for diversity in approach and I (having worn the central provider hat for quite some time) would argue that we have too much diversity on campus (and my current student advisory committee in the College of Business has made it clear that they feel that way insofar as the issue is course logistics rather than important pedagogic function). But the issue is not just on the demand side. There is the question of wasteful duplication of function, duplication that is costly from the perspective of the institution as a whole. And the way this issue manifests to most is that many services which are provided are done so in a shoestring manner, often without adequate recurrent funding.

Large scale course redesign is likely to demand substantial up front technology support, quite possibly in areas that don’t represent current areas of production strength. In our discussion Carol, she made it quite clear to cost out any of the technology pieces that were fundamentally new as a consequence of the course reform. But, for example, in the case of online video to support instruction is the institution already headed down the path or is it going to dawdle unless pushed by course reform? And if it does move in this direction, what is the implication for other learning technology services?

Let me sum up. I will do so by appealing back to a post I made a while ago about whether technology is the problem or the cure. The coordination problem view of these issues is enlightening, I believe, because it does suggest that we can do better, but we likely won’t do so if we have a series of unilateral attempts at course reform rather than a concerted effort across the board. That’s why I’d like to see a campus initiative, one with some real teeth.

1 comment:

Lanny Arvan said...

Lisa Hinchliffe pointed out to me that while I did link to the Campus Strategic Plan I failed to mention that Blended Learning is explicitly encouraged in it (see page 27) and there are some funds proposed to be allocated for upper class undergrads to help/mentor other students enrolled in these blended courses.