Imagine that you're given the opportunity to do an extensive evaluation of undergraduate teaching and learning on campus with the idea that the data collected from such an effort would be used as the basis for subsequent changes on faculty development, curriculum reform, and oversight of instruction. What sort of framework would you use to drive the evaluation?
I know what I'd do. I'd survey instructors, then their department heads (perhaps also including on the department head's recommendation any and all other faculty who don't teach the course but who are knowledgeable about the course content, which is what I mean when I refer to department heads below), and then finally the students on these two rather straightforward questions:
(1) How important should memorization be for students to get a firm understanding of the subject matter in the course?
(2) In practice, how much of student study time is devoted to memorization in the course as a fraction of total study time?
I would expect such a study to show the following:
(a) There are some courses where all three groups: instructors, department heads, and students agree that the course demands a large amount of memorization. However, as a share of total course offerings, this possibility represents a small fraction of what occurs.
(b) There are some other courses where all three groups agree that little to no memorization is required but, as in (a), this possibility also represents a small fraction of what occurs.
(c) The bulk of the courses are in this category, where there is substantial disagreement across the groups with students saying the amount of memorization is high, department heads saying it should be low, and instructors somewhere in between.
I say this based on my own recent teaching experience, talking about the issues with my students and thereby learning about their experiences in other classes, and having some sense of what is happening elsewhere on campus, especially the adjunct-ification in the teaching of the large general education classes and the large classes that are the gateways to popular majors, even if those classes are not gen ed.
The hypothesis, not particularly novel or really much of a surprise but I've never seen it expressed quite this way, is that The Disengagement Compact, George Kuh's aptly put but discouraging label for the unholy implicit contract between students and instructor, where no party is burdened much at all while all parties get to reside in a virtual Lake Woebegone, is manifest in a very particular way. If the Disengagement Compact is the Devil making himself known in undergraduate education, then memorization is the Devil's disciple, an artifice for claiming both that learning is happening and that substantial effort in the name of learning is occurring. Hardly anybody, after all, wants to be labeled a slacker. Further, students want to resist the damning evidence of low grades. So students somehow feel that they've been tasked by their instructors to memorize course content. Many instructors indeed do task their students this way so as to satisfy student expectations and thereby avoid their enmity. Other instructors combat this pressure, but then are more likely to garner angry course evaluations from the student's after which they might change their tune about how to teach, in order to satisfy student expectations. This is the operating hypothesis that explains alternative (c).
Let me address a couple of criticisms about this approach before moving onto how the issues may be addressed in a way that is more than merely cosmetic. In each of (a) - (c) I'm taking the department head's view (or their delegated expert) as offering the norm for good behavior, in which case substantial deviations from the norm should be a matter of concern. In many areas, however, there is a powerful argument to be made on behalf of the learner to the effect that the learner should drive his or her own learning, with the so-called experts view on the matter playing at most a subsidiary role. When considering myself as a learner I subscribe to this view. On occasion I want the expert opinion of others to guide my thinking, but mainly I'm driven by my own explorations and what I garner from them. If as a learner I feel one way, how can I credibly argue for the opposite way in writing this piece?
The resolution of this apparent contradiction can be found by focusing solely on memorization and whether it is at the heart of the learning or not. On that question I believe the expert view can be trusted. The microeconomics that I teach, for example, is not learned by memorizing the textbook or the Excel homeworks that I assign. Students must work through the models. Indeed it is because I understand myself as a learner of microeconomics and how I went about internalizing it in a way to become expert that I can assert that memorization provides a false path. So, too, I believe it reasonable that other experts in their own fields reflecting on their paths can with high accuracy provide a view about the role memorization should play. I want to be clear here. Memorization is quite a distinct concept from memory. Any immersive learning experience will create objects that are committed to memory, but that happens en passant and is not the emphasis in the immersion. One may have committed a wealth of information to memory without the aid of any memorization whatsoever. Also, I don't want to deny the importance of the ability to retrieve facts from memory. In my present circumstance where I encounter health care professionals quite often, I'm asked to provide my date of birth and/or my home address with regularity. This is done, presumably, as a method of identification, though inadvertently seems a test of whether Alzheimer's is in the offing, one I fear I will fail in the not too distant future. My point here is not to confound identification with identity. My essence cannot be found in my birthday or my home address. So too it is with the college subjects students study, where the issue is whether the students penetrate the surface. I'm arguing that all too often they do not. They can retrieve what they have memorized only in a very limited setting, the one where the information was presented to them. Deeper penetration of the subject requires the ability to retrieve the appropriate information as the context dictates. It is a much higher order of understanding and places much greater demands on the students.
The other issue concerns demographics and where the Disengagement Compact is likely to manifest. One can vertically differentiate students, for example standardized test performance imperfectly does this, and then make the case that memorization is the path followed by the middle group of students. Students in the top group find their own way to make an immersive learning experience for themselves and learn from that. This gives them both confidence and a sense of independence. Students in the middle group have not yet figured out how to create their own path, so opt for memorization in its stead. This way of considering things also means there is a third group of students, who do neither. Either they have better things to do with their time than their schoolwork, or they are simply immature and have not yet found a sensible balance between having fun and doing their schoolwork, or they are alienated by the way instruction occurs and have opted out in a kind of silent protest. The focus in this piece is with the middle group. Improving their situation and their own capacities to self-teach may have indirect benefit on the third group, as it may encourage some of them to join the middle. It might also sharpen what can be done otherwise to help them out. I'm afraid that on the immaturity issue the best I can offer is an admonition to hurry and grow up, yet not really mean it because I'm jealous of their youth.
There is also a horizontal way to differentiate students, by the nature of the subject they study and how that subject tends to task the students with work. A student in the fine arts or one in computer programming has to produce a product, one of his or her own making, or give a performance, or a combination of these two. This type of tasking encourages placing efforts elsewhere. Memorization doesn't play a primary role here, though it probably still is part of the mix. There are other subjects however, where the primary product that the student makes is a conceptual understanding of the subject matter for himself or herself. Even when there is a concrete intermediary product - a problem set to complete, a paper to write - the final product may seem abstract and elusive. In this case students are more prone to memorize as they go about their work because, in effect, they task themselves and they haven't found a superior alternative method to go about doing this.
My friend Lisa, with whom I had a conversation earlier this week, points out my academic character flaw. I'm a liberal arts college kind of guy in a research university setting, meaning I suppose, that I like intelligent argument as an end in itself and prefer it to the advancement of knowledge within a discipline. That is definitely true. But there is an additional meaning as it applies to public research universities, such as Illinois. Though the College of Liberal Arts and Sciences has roughly half the students on campus, it is nonetheless the weak sister of other colleges, notably Engineering and Business, especially when considered from the perspective of the vertical differentiation of the students. The standardized test scores are lower, and LAS is a college that absorbs many transfer students, both within campus transfers and external transfers; so getting into LAS has some of the feel of a consolation prize. Further, on the horizontal differentiation front, it has more subjects that are, like economics, fundamentally conceptual in what they ask of the students. The effect is something of a double whammy at play in what I see in the students I teach.
We humans, as a species, tend to confound what we know based on our own experience with all that is possible to know by including potential experiences that are yet outside our scope. Daniel Kahneman in his book Thinking Fast and Slow refers to this phenomenon and What You See Is All There Is (WYSIATI). I mention it here because it is quite possible that I'm guilty of WYSIATI in giving my analysis above and the picture one would get from looking at the full set of evidence is different from what I paint. This is one reason why I'd actually like to do the hypothetical study I described at the outset of this piece. It would be good to know what the real picture looks like. Absent that information let me give some support for why what I argue is not too far off.
First, there is the work of others. In addition to Kuh, there is the Declining By Degrees documentary and complementary book and there is the more recent Academically Adrift, which advance much the same hypothesis, although memorization is not given such a primary role in these other works. They tend to represent matters as overt shirking from instruction and learning. I think this point matters, because I believe the students in the middle group don't consider themselves as shirkers and their instructors probably don't see themselves as complicit in the matter. What might be recommended as cure depends on the diagnosis of the illness. To my knowledge none of these authors have recommended a direct assault on memorization, though to me that is required. The second half of this piece outlines what such an assault might look like.
Second, there is the matter of the transition from high school to college and whether students successfully get over that hump. Colleges have been sensitized to the issue, witness the university 101 movement. As with the first argument, there is the issue of the appropriate cure. Now students do get some coaching about time management skills. There is little to nothing said, however, about what students should be doing intellectually when they do study. So the memorization issue is largely ignored. Let me mention a related question for which I'm unsure of the answer, though it certainly would be good to know what is going on. One possibility is that memorization was the primary approach in high school and by the time college happens the students' intellectual habits are locked into that approach. The hump in this case results because college calls for a different approach, but the students are unwilling or unable to make the switch. Another possibility is that students are not so locked into memorization at the outset, but college material is much more difficult than high school material and that comes as a shock to students. They take their first set of exams and get slammed by those. Their ego is bruised and there is an immediate concern about creating permanent damage to the GPA. So they seek to self-protect against further bad grades and find memorization as the form of self-protection. These two possibilities are not mutually exclusive, though it is important to observe that the more important one is than the other would impact how best to address the issues.
Third, this generation of college students had the bulk of their K-12 education under No Child Is Left Behind and the excessive testing that the "accountability movement" has imposed. The socialization of the students that has resulted from years and years of this approach is to put an even greater emphasis on good grades as the object that students should pursue and indirectly has lessened encouragement for the alternative view that learning is an end in itself. To a parent who is not an educator, it might seem these two goals are one and the same. In an ideal world, they should be. But in practice they are different. The more risk averse among the crowd opt for the paper chase. This motive serves as impetus for any purely instrumental method that purports to provide good grades as the outcome. It's what elevates memorization for these students into contexts where memorization would otherwise seem inappropriate.
Let me close this section with the following observation. Focusing on the subject matter only, it probably makes sense for gen ed courses and introductory courses in the major to temporally precede the more advanced courses in the major. Lay the foundation first. Then build additional structure on top of that. If, however, we think of the issue not from the content perspective but rather from the vantage of student intellectual habit formation, we are getting things backward. Students should be moving away from memorization during their first year in college but in the current system many are inadvertently being pushed toward it. So the entire system must change. The issue cannot be handled with cosmetic change made around the edges.
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Below are a set of four "recommendations." Some really are concrete suggestions for implementation. Others are more a discussion of the underlying issues with suggestions for implementation still to be determined. The ordering in which they precede is from easiest to hardest, from assessment of performance to how teaching and learning should take place, and from where my expertise both as an economic theorist who understands incentives and as an administrator with first hand experience of what the recommendation entails to where I'm merely an enlightened amateur and others with more expertise should weigh in on how how the recommendation should be suitably modified and implementation should occur. Taken together I think these recommendations give a reasonable first pass at what an assault on memorization looks like, though I would welcome additional suggestions of what might be done to improve the impact from the recommendations working in concert. It is also possible to consider each recommendation implemented on its own, with possible other benefit emerging. I will do so explicitly for the first recommendation. I leave it to the reader to do so for the other recommendations.
Recommendation 1: Eliminate grade inflation by moving to a system of standardized ranking.
Let's first explain what standardized ranking means, then discuss some of the implications of the approach, some probable criticisms of standardized ranking that would likely arise, the implications of standardized ranking for the Disengagement Compact, and then other possible benefits of standardized ranking.
Suppose a class has n students. Those students can be ranked by their performance and let's call that the ordinary rank. Note that instructors who keep a grade book almost certainly have the information in it to produce an ordinary rank - say by adding up the points on the various assessments in the class and then ordering the students by their total points. So one thing to note here is that the proposal is not asking the instructors to generate any information that they don't already have. It merely changes what information they do have which gets reported. Then, standardized rank = (ordinary rank)/(n + 1). In actual grade reporting instructors could report ordinary rank and the recording software could then convert that to standardized rank, which is what the students see and what is recorded on the transcript.
A critical issue for such a system is whether ties would be allowed. In my view, yes that would be an important feature of the system. Then for the set of students who are tied, each receives the average rank of the group. For example, if students ranked 1 through 9 were tied, they'd each receive a ranking of 5 in their ordinary ranking. The use of ties is a way to introduce some cardinality within cohorts. For example, if the student ranked 10th is not tied with the first 9 students, then the student ranked 10th would see a drop off in ranking of 5 between him and the students who are ranked above him; this as distinct from the drop off of only 1 that would happen if students ranked 1 through nine were not tied. An ordinary ranking scheme that didn't allow for ties might very well encourage more competition across students to come out ahead of their peers. A system with ties need not promote any additional student competition.
The average standardized rank across all students in the class must be 0.5. This is how grade inflation is ruled out. There is no Lake Woebegone effect. Everyone can't be above average in a standardized ranking scheme. Standardized ranking eliminates the possibility of recording across cohort effects in the grading scheme, e.g., this was a very good class so all the students get A's, while this other incarnation of the course had students who didn't perform so well so some got B's and C's. In other words, standardized ranking takes discretion away from the instructor. As such, faculty might not like it at all. The argument to persuade faculty to think otherwise is that the system with discretion produces grade inflation as an equilibrium phenomenon; to eliminate that some concession on their part is necessary. Further, standardized ranking likely would lessen students haggling over grades with the instructor, because then bettering one student's ranking comes at the costs of lessening some other student's ranking, while in the current setup bumping up one student's grade appears as a victimless activity. Still one additional way to mollify instructors would be to allow both the standardized ranking and a letter grade to be recorded, likely a necessary step during the transition from the current system. Even after the transition was over the new solution would still have to require the instructor to report where the F line is because the standardized ranking doesn't itself reveal that.
If students were told their standardized rank going into the final exam, which is when course evaluations are typically administered, then the use of high grades by the instructor to bribe students to bias the course evaluations would be eliminated as a a possibility. The course evaluations themselves would become a more trusted instrument as a consequence. Further, one can do a backward induction on the way instruction is carried out to show that there is no benefit to the instructor in dumbing down a course to boost the student grades so to get a better evaluation. Therefore, there is apt to be an indirect effect from moving to such a grading system that makes the course difficulty level closer to what the instructor really believes it should be. (There remains a question here of whether students have a preference over course difficulty when abstracting from the implications of difficulty on the grades they receive. We might conjecture that they prefer to learn something substantial to nothing whatsoever, so their ideal difficulty level is somewhere in the middle, though the precise location might vary from student to student based on their prior preparation and aptitude for the subject.)
At present, when outsiders see a student's GPA or a grade in a particular course on the transcript, they have no context in which to evaluate that grade information. Getting an A in a class means something quite different when only 10% of the class gets an A as compared to the case where 100% of the class gets an A, but the way we currently do things an outsider is not able to discriminate between these two cases. An interested outsider really wants to see where the particular student fits in the grade distribution. So it would be quite informative if course grade distribution were reported. In the present system, instructors might resist that as it would reveal whether they are an easy grader or not. Standardized ranking eliminates easy grading or hard grading and therefore should enable the reporting of the course grade distribution, which means outsiders would get a more informed view of student performance.
Recommendation 2: In addition to course evaluations require that adjunct instructors get real and substantial evaluation from someone in the department with subject matter expertise.
Let me note at the outset that this is costly. Therefore current faculty likely will object at having such a burden imposed on them - they have enough on their plate as it is. The response to that criticism is as follows. On the economics of it, the cost of undergraduate education has been rising in real terms and the share of that cost that is covered by tuition also has been rising. For students in the top group, that is not a big concern. A college degree is a great deal. They should be more than willing to pay. For those in the middle group, who may become increasingly aware that they are not getting much in the way of human capital value add that should come along with the degree, they may therefore become increasingly reluctant to pay that tuition. When some threshold on reluctance is crossed enrollment might very well drop precipitously as a consequence. A faculty retort to that which would not be unreasonable would focus on current enrollments. Is there any evidence of decline there or even evidence of deterioration in the quality of incoming students? (My guess about the answer to this question is that if focused only on domestic students then there is evidence of both effects but if international students, particularly from South Korea and China, are included then there is no current evidence.) If there isn't much in the way of current evidence, why not let this go for now till more hard evidence on the economic front becomes available? At the appropriate time, this responsibility can be taken up.
The problem is that we don't really know what real and substantial evaluation by subject matter experts looks like. So the reason to start sooner rather than latter is to allow for learning by doing and find mechanisms that might be appropriate. It seems obvious enough that this won't happen unless there is suitable administrative intervention to make it happen. Back to the economics, in an opportunity cost sense there may be other uses of faculty time on which the faculty themselves place high value but that are entirely orthogonal to any revenue generation by the university. Some of this time must then be reallocated to evaluation of adjunct instructors. For example, if the faculty member is not a big generator of outside grant funds it may then be necessary for the faculty member to reduce time on his own scholarship in order for him to spend time on the evaluation activity. That is the consequence of this recommendation.
Now let's consider the recommendation from other than a resource point of view and get to some of the things that the evaluation by the expert is supposed to accomplish. One big question up front is the extent to which the evaluation is monitoring versus the extent to which it is mentoring.
When I was an Associate Dean in the College of Business, I implicitly mentored several of the large course instructors (all whom were adjuncts) though on the use of technology in instruction issues rather than on subject matter concerns. Some of these people had taken graduate microeconomics from me fifteen years or so earlier. In one case I had played golf with the person several times while he was a graduate student and I was a younger faculty member. So I had some prior credibility with these people and they were more than happy to engage in conversation. As a group they were quite risk averse regarding implementing any changes I suggested. On the monitoring versus mentoring issue that is what I'm trying to get at. Who has the last word about what changes will be made in the course? If you think of this as an ongoing activity rather than a one and done, it may be that more mileage can be gotten from mentoring. But it also may be true that there needs to be some triangle between the instructor, the person doing the evaluation, and the department head who sets the instructor's salary and writes the instructor's performance review, so both carrots and sticks get utilized and in the right proportion.
Now let's talk about the various learning issues the evaluation is aimed at dealing with. As a research university, we pride ourselves in how how research impacts instruction. The same course will be taught differently when it is taught by a researcher than by a non-researcher and as a consequence there is further benefit to the student from having the researcher as the instructor, at least according to our usual propaganda. Some might counter the propaganda with considering effectiveness as an instructor that really counts, especially in these courses taken during the first year or two of college. In this thinking, it is better for a student to have an effective teacher who is an adjunct than to have a researcher who is a mediocre teacher. Here I want to resolve this in a way I believe is appropriate given that the goal is to move students away from memorization. The necessary ability in the teacher is to have a view of the subject matter that can be well articulated entirely independent of the textbook. Some adjuncts may have that ability so I don't want to confound the ability with the job classification. But I believe many adjuncts don't have this ability or it is not something they pursue vigorously. It is more likely to be found with research faculty.
On the other hand, many research faculty have no experience at all teaching a large class. There is no doubt that large class instruction poses its own set of challenges and it may be that in addressing those challenges a research faculty member would tend to teach just like the adjunct, because the management issues in the large class setting trump other considerations. If that is really true, then this expert evaluation is largely a waste of time and energy (and I wouldn't have posited Recommendation 2). So it should be apparent that I don't believe it to be case, but I want to hold out the possibility because others might disagree with me.
Let me return to the role of the textbook in this setting and see how that matters. I've expressed some reasonably strong opinions about this in a post I wrote a couple of years ago called Excise The Textbook. But I recognize that because of the management issues I mentioned above, the current fascination with eTexts, and a traditional view of how college classes should be taught, textbooks aren't going away any time soon. So to get at my concerns lets consider the opposite extreme, where the instructor adheres quite closely to the textbook during lecture, possibly using PowerPoints supplied as ancillary materials in lecture, and using test bank questions for the online homework, with the exams closely mimicking that. In a lot of courses this is what students have come to expect regarding how instruction occurs.
In my view, in this approach the instructor has become the unwitting agent of the textbook authors, who are cast as the ultimate authority on the subject. The students, a few more rungs down on the totem pole, have been told implicitly that the textbook is the bible for the course and that they should know their bible. This approach, in other words, indirectly promotes memorization. If we are going to make an assault on memorization we need to move away from the approach. That is the primary aim of the expert evaluator.
There is a further related issue. Many of the adjuncts teach one very large course, over and over again. While each offering may pose unique challenges, there is a tendency for these courses to become very static and over time it may be that the instructor lectures by the numbers, bored because there is no remaining novelty in the approach.
The solution to both of these issues is for the instructor to view herself more like a peer of the textbook authors and take on some of the authoring activity herself - whether in the presentations, the homework, or the exams. Further this authoring must not be done as aping the textbook but rather in the instructor's own style and approach to the material. This won't happen all at once. It is a too daunting task for that. But over time the instructor can insert herself more into command of role of equal partner with the textbook authors and the evaluator can encourage that ongoing development.
Let me take on two other issues here. The first regards the psychology of students who are challenged in their learning and their reluctance to seek help because doing so appears to them a stigma. Hence the usual pattern is to shun help until times get desperate and then ask for help as a last resort. Our classes are not well designed this way in that office hours are optional and hence are lightly attended, especially early in the semester. This is why in describing the problem I repeatedly used the expression "how students are tasked." The key, it seems to me, is to embed the help in the tasking so that it is required of all students and hence there is no stigma attached to it and therefore is heavily accessed. In recommendation 4 there is further elaboration on this point.
The other issue regards the likely outcomes when the assessments in the class move away from rewarding memorization. It is reasonable to expect that raw scores on the assessments will decline. (The memorization had been masking the lack of actual learning and now we're eliminating the mask.) Students may take comfort from higher raw scores and that in itself might impact the course evaluations. In this case the evaluator must run interference on behalf of the instructor and argue that the instructor should be rewarded for making the changes. The transition to a more intellectually healthful approach might be quite painful and it might take several iterations of the course before the instructor is confident that the course is better than it was before the changes were put in place. It is very important during this interim that the instructor hear a voice counter to the complaining voices of the students, to keep at it. The evaluator provides that counter voice.
Let me also note that to the extent that this sort of change is happening in other courses the students are taking, they are less likely to be resistant, because their expectations are changing and they are learning to move away from memorization as their habit in approaching their studies.
Recommendation 3: Establish a campus research project about memorization as the line of defense by students in large classes. Get all staff in support of instruction on campus, regardless of the unit in which they reside, to be involved in this project. In other words, make the project the strategic focus of the campus with regard to undergraduate instruction. Build a community of practice among the various adjunct instructors across their disciplines, so they have people with whom to share their teaching ideas who are similarly situated as themselves. Let much of the the faculty development activity that the support providers offer aim at these adjunct instructors and let it be informed by the research results of this campus project.
In the present world adjunct instructors have very little standing and get comparatively little support, especially if looked at by the number of IUs (enrollments times credit hours) that these instructors generate. More support is aimed at tenured and tenure track faculty, who have greater standing and, in particular, at helping assistant professors prepare their teaching portfolio so they are ready for the promotion and tenure process. I don't want to diminish the importance of that, however one must ask from a utilitarian view focused on undergraduate education whether that use of support resources is the most effective, measured by how much improved learning it engenders. It would seem that steering support resource toward the adjunct instructors would create a bigger bang and further that by moving support resources in this direction it would signify to the adjuncts the importance of taking on this challenge and as a consequence offer them encouragement to do so. Absent such a campus project, it would become the expert evaluator's job to secure the appropriate support resource and there is no reason to expect that the evaluator has the inclination or the wherewithal to do that.
In my experience, evaluation projects tend to follow funding, to go strong when funding is strong and to fade away when the money does likewise. Further, while the evaluation results may be publicly available for anyone to read, the results nonetheless lose their impact on current practice in instruction when the funding has worn out. If that is taken seriously as a guideline with regard to how this project should be designed, either the target must be that most large courses have gone through a metamorphosis in approach during the time the project is ongoing or the funding for the project itself must be sustained for quite a while to enable later entering courses and instructors to benefit.
My sense of how best to do this is to have two phases, pilot and full scale. To make matters concrete, the pilot phase lasts three years (this can be tweaked to make it more sensible) and offers via a competitive process grants to units that are fairly sizable, to get volunteer instructors and incentivized expert evaluators to participate in the process outlined above and to be willing to become the subjects of intense observation so the mistakes can be learned and the fruits of the effort be found and so that those who follow will have an easier way of it. The pilot phase also offers the possibility that if each pilot project fairs miserably, then phase two can be scrapped. Assuming that did not happen, in phase two the intent is to convert all other large courses that are taught by adjuncts. The various department heads need to be behind such a plan up front and mean it when they lend their support. They may very well have to move around departmental resources during phase two to get it accomplished when the project funds themselves prove inadequate for the task.
Finally let me say here from what I've observed of the support community the past few years that they are aching to have such a campus level project so they can see a greater purpose to the activities they are performing. Consequently, on the principle of doing this I'd expect to hear a great deal of enthusiasm from them, though on how the implementation is done and who has control of what, there are likely to be lots of stumbling blocks. I don't believe those stumbling blocks are insurmountable, but people need to have their eyes open at the outset so that progress is not blocked altogether.
Recommendation 4: Students need to be provided with a venue where they express their own thinking about course content on a regular basis and where they are encouraged to reason through things when they get stuck, though also in this venue share tips and tricks for getting unstuck.
There is an issue whether class time should be used for this purpose, or if it happens out of class (meaning mainly during the evening). There is a second issue tied to the first regarding the people with whom the students share their thoughts. I've written something on this issue in a post entitled Rethinking Office Hours. I believe small cohorts of classmates (4 or 5 in total) along with an experienced peer mentor (a student who has taken the class previously) offers an ideal setting for having such discussions - about how to do the homework, how to prepare for an exam, what something in lecture meant that the students didn't understand, etc. The discussion section is supposed to manage these functions, but some of the large courses don't have discussion sections and in others the section size is fairly large and/or the TA opts to lecture rather than facilitate discussion. So it doesn't work. There needs to be a functional solution where students feel their learning needs are being addressed. In a large class setting that burden can't fall entirely on the instructor, even a very energetic one.
If there are both graduate TAs and undergraduate peer mentors in a course utilized at the scale I suggest, that can get pretty costly unless some other modifications are made to enable the activity - either giving the mentors course credit or some other perq that makes them willing to perform the activity even if much of it ends up as volunteer work. Deanna Raineri and I have advocated for quite some time that this sort of mentoring activity exemplifies what we mean by leadership, so the mentoring could be the practicum of a leadership course that the students take. But to pull this off successfully one would have to manage well the triangle between the leadership course instructor, the subject matter instructors, and the student mentors. Also, students who have previously taken the mentoring course and already served as mentors likely require some other form of compensation. How that would work offers a challenge, one I'm convinced has a solution that if found would make the rest of the proposal fall into place.
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This piece, already quite long up to this point, shows how I vent about something I care a great deal. When I see my students memorize in my course, it hurts me at my core because I know it's the wrong thing to do. When I hear it is a learned behavior because that's how they've gotten through the other courses they've taken, it impels me to change the system, though unlike Archimedes, I will never get a long enough lever to makes those changes on my own.
So I hope this piece actually gets read by a few folks, long though it is, folks at Illinois and my friends in learning technology from around the country. It offers a different vision of what sort of change is needed in Higher Ed than what we read about daily in the Chronicle and elsewhere, how the next generation of online learning is where the train is headed, and might be of value simply for providing a counterpoint to that view. But I hope it is more than that because it is grounded in where we are now, while the futurists who argue for the online vision ignore the status quo other than to note that like print journalism, the current model is broken. Let's not try to fix that. Instead, let's just move to the new thing. I say, instead, before moving on let's bust a gut to fix what we already have, especially since it seems quite fixable to me.
I close by noting that my campus has announced a new position - Vice Provost for Undergraduate Education and Innovation. Ten years ago I would have aspired for that position for myself, so I'm a bit chagrined it has taken so long in the coming. Nonetheless, I'm happy to see it and I hope we get a very good person to fill it. Perhaps that person will read this piece. Perhaps then we'll get a chance to have a coffee and chat about it. That would be delightful.
Friday, October 26, 2012
Friday, October 19, 2012
The Diffeq From Hell
As I sit here composing the morning schtick, ungraded midterm exams quietly beckon to reveal their hidden truth. Today I prefer ignorance. The truth may be too much to bear. Instead I cling to the belief that with clever use of Excel to exposit the math models and let the students get their fingers dirty with them, students can learn some interesting economics, stuff that 20 years ago we'd only teach to graduate students and then only in a formal way.
The current topic is bargaining, not unlike what you do at a flea market or when buying or selling a house. The buyer knows her value. The seller knows his cost. Each is uncertain about the player on the other side of the table. The operative questions are: (1) will they end up walking away or reaching a deal, and (2) if they do reach a deal, at what price?
Last time when I taught the course I was perfectly content to cover the model about bargaining as it is done in textbook. In that setup there are two types of potential buyers, high value and low value, and there are two types of potential sellers, low cost and high cost. In other words, on each side of the market there is a good type and a bad type. The interesting economics happen when the parameters are set so good types should always reach a deal but bad types should only reach a deal when their counterpart is a good type. Further, the setup should be symmetric so as not to confer bargaining power on one side or the other.
Considered in isolation, the 2x2 model is fine to illustrate the ideas. But this time around in looking at it I find it clunky. We've already done a model of insurance (that I did not cover last semester) where each potential insured is one of two types, high risk or low risk. In that model it is reasonable to assume that the insurance providers know the probability distribution across types, as that comes from population averages and insurance companies are in the business of knowing what the population averages look like. In the bargaining context, however, it is far less clear from where beliefs over the counterpart's type emerges. Yet those beliefs are a critical determinant of the outcome, which starts to make the model look like a house of cards. There is a further issue that in the insurance model the insureds are risk averse, but in the bargaining model the players are assumed risk neutral. One might want to respond that risk neutrality is assumed to keep the model tractable but, really, the math is not much harder under risk aversion. The real reason is that one does not want differences in risk attitudes to confer bargaining power, yet risk aversion typically varies with circumstance, so that one side or the other has an idiosyncratic bargaining advantage seems unavoidable. To eliminate the bargaining power issue, each player should have the same risk aversion, independent of circumstance. Risk neutrality is then a reasonable approach in the modeling to achieve that end.
So I start to ask myself whether I can do a more elegant version of the model than the textbook authors provide. This might seem like hubris on my part. The authors, Paul Milgrom and John Roberts, are very good and well known economists. In that dimension, I couldn't carry their jockstraps. But their textbook doesn't have the insurance model I mentioned above, so building a bridge between the two models is not an issue they confront. Further, they are explicating in the traditional way while I have Excel at my disposal. The development of an alternative model puts me in the mindset I had as an assistant professor when I was doing econ theory research --- if for whatever reason you don't like how a model is designed, then build an alternative model more toward your liking. (You can take the boy out of economics....) But I fear this going back to a research perspective is deleterious to the teaching, because this urge toward a better model is driven by an aesthetic that is transparent to me but is likely opaque to the students. The students want some intuition that helps them penetrate the ideas. Beyond that the details of the model are extra baggage they could do without.
Let me get to the economics punchline (though not yet to the punchline of the story). At the 60,000 foot level, the message is that to get the incentives right (meaning that the choice the individual makes reveals the type of the individual in a way anticipated by the mechanism), it is necessary to produce some inefficiency relative to the case where the individual's type is known by others ahead of time. Further, the inefficiency manifests in a particular form - quality deterioration for low end customers. In the insurance example the result is that low risk individuals face very high deductibles or find no insurance available whatsoever. This is so high risk types don't pretend to be low risk. The insurance example is an instance of Akerlof's Market for Lemons or what economist's have termed adverse selection. The same underlying economics is afoot when talking about why when flying on an airplane coach is so often such a crappy experience or why in purchasing a new cable tv package the basic coverage offers such a limited variety of channels. Having modeled this once in the insurance case to show how the mechanism separates the types, one does not need to model it again and again as the context changes. The other contexts can be discussed without the aid of a model. Doing so helps to emphasize the underlying principle in operation.
This brings me back to bargaining and two sided asymmetric information. The operative pedagogic question is whether this represents a significant enough change to justify doing a new model from scratch and what lessons are to be learned from it that aren't in the single sided asymmetric information model. I believe that, yes, doing the bargaining model from scratch is justified and that the main lesson from it is that the inefficiency - parties walk away from a deal when there are actually gains from trade to be had - disproportionately impacts middling types.
In the bargaining model it is necessary to focus on couplets, each comprised of a buyer and a seller, and make comparisons across them. For example, if when trade occurs the price was such as to split the difference between the buyer's value and the seller's cost, then holding the sum of value and cost fixed so that if trade occurs the price would remain unaltered, how does the likelihood of trade change as the difference between value and cost increases? Since that difference measures the gains from trade, one is apt to intuit that as the difference gets larger, trade gets more likely. That turns out to be true. If this were the main insight to be had from the bargaining model, it would hardly be worth doing.
What of this other comparison; holding the gains from trade fixed how does increasing the sum of cost plus value impact the likelihood of trade? One might intuit that it shouldn't matter, that only the gains from trade matter. It sounds good, but it is wrong. Something else happens. The parties are not symmetric in their contribution to the likelihood of trade. But to even begin to consider why, it is necessary to go beyond the simple two types model. There needs to be a type in the middle, preferably several types in the middle. Having made that concession, however, it really is better to go all the way to a continuum of types approach, since then one can use geometry in the representation to facilitate understanding of the issues and to rely on calculus techniques to perform the analysis when that is needed.
The model I had in mind has the cost realization, c, a draw from the uniform distribution on the interval [0,1] and the value realization, v, also a draw from the same distribution, with the distributions of the two random variables independent. Thus the pairs, (c,v), can be found in the unit square and under complete information the pairs where the players walk away from the deal are below and to the right of the main diagonal of the square, since for such pairs cost exceeds value.
In this model it is straightforward to consider the benchmark case where the seller can set a take it or leave it offer for the buyer. This translates to monopoly pricing under constant marginal cost and linear demand. In that model the monopoly price is midway between the marginal cost, c, and the demand intercept, 1. Hence buyers with v > (1 + c)/2 purchase at this price. Otherwise the buyers walk away. One can trace out the set where trade occurs as c varies. It too is a a triangle, one with half the area of the triangle where trade occurs under complete information.
This benchmark is useful, as is the analogous benchmark that arises when it is the buyer who can make a take it or leave it offer for the seller. Again the triangle where trade occurs has half the area of the triangle where trade occurs under complete information. What is unclear from these benchmark cases, however, is whether the underlying cause for the excessive amount of walking away from the deal is the asymmetric information itself or the price setting power. Getting at the answer to that issue motivates the remainder of the analysis, where neither party has a price setting advantage.
Mumbling about something called the Revelation Principle, which means that for whatever mechanism you might come up with to resolve the bargaining model there is an equivalent "direct revelation mechanism" where the buyer announces her value and the seller announces his cost and then based on that the mechanism specifies whether the players walk away or trade and if they do trade at what price, an economist teaching this would wave his hands and say we're going to model the bargaining as a direct revelation game. Non-economists who read this might prefer to personalize the concept called a mechanism in the form of an arbitrator whose word on the matter is final. The arbitrator makes this decision based on what is communicated by the buyer and seller about their circumstance. In turn, so the buyer and seller each know what message to send, the arbitrator lets both of them know how their joint message translates into the arbitrator's decision.
It is instructive to start out with a naive but hopeful arbitrator whose dual goals are to achieve the same efficiency in trade that occurs under complete information and do so with fair pricing. Letting cm denote the cost message the seller sends and vm the value message the buyer sends, the obvious rule for the arbitrator to come up with is trade only if vm > cm and when that is the case set the price, p, so that p = (cm + vm)/2. Under this rule would it be optimal for the buyer and the seller to tell the truth, which means cm = c and vm =v? Or would it be better for each of them individually, taking account of their own benefit only and ignoring the consequences for their counterpart, to "strategically misrepresent" their circumstance? When truth telling is optimal, the mechanism is said to be incentive compatible.
It turns out that the naive arbitrator's mechanism is not incentive compatible, but before explaining why a little aside. In a nation where every school child is taught that the Father of our Country and first President, George Washington, never told a lie shouldn't it be that telling the truth is its own reward and therefore that every possible mechanism is incentive compatible? Further, isn't economics as a discipline morally reprehensible for suggesting otherwise? The responses to these questions are as follows. In the model the message sent has no direct impact on the player's payoff. All that matters is the expected surplus generated for the player. If a message that is other than the truth yield's a higher expected payoff, then truth telling is not optimal. Shouldn't the model then be changed to reflect more preferred ethical behavior? The models purpose is positive, to predict what will be observed. The model is not normative. It should not be taken as a guide of behavior. The acid test of whether it is a good model, then, is whether the predictions of the model are in accord with experience. Anyone who observes when driving on the interstate that traffic slows down a cop car is in view implicitly knows that incentives matter, at least in certain settings. Without much effort, the reader likely can come up with several other scenarios where extrinsic rewards (or punishments) influence behavior in a predictable way. That is sufficient to justify the modeling approach.
Let's get back to the naive arbitrator's mechanism. We'll consider the choice problem of the seller under the assumption that buyers are truthful about the value they report in their message. Then sending a message of cm means the probability of trade is 1 - cm and the expected price at which trade occurs is (1 + 3cm)/4. In other words, the seller will treat the mechanism like a demand curve. For truth telling to be optimal, marginal revenue for this demand curve at cm = c must equal marginal cost, which is c. That doesn't happen here. Instead, marginal revenue is less than marginal cost at cm = c, which means the seller would prefer to sell less but at a higher price. Indeed, it is not hard to show that the optimal message is cm = (1 + 2c)/3.
What does an incentive compatible mechanism with split the difference pricing look like? From the discussion in the previous paragraph it must be that the implied marginal revenue when setting cm = c must equal the marginal cost, c, and that must be identically true for all c. Treating the mechanism from the seller's perspective, it specifies the minimum value at which trading occurs given the cost message of the seller. It is then not hard to derive that this function must satisfy:
This disarmingly simple looking equation is the diffeq from hell mentioned in the title of my post. So let me switch gears and leave the explanation of the model to give the little history from which the title emerged. Then I will close.
There is a practical aspect to teaching in more or less staying on track subject-wise and doing so at a reasonable pace for the students. On Sunday or Monday when I started to work on the alternative model, I implicitly told myself that I've got one day to solve this thing. If I do it, great. But if not I should fall back on the 2 types example and leave it at that. I'm more than a little rusty with differential equations, but I'm optimistic that once I get rid of the rust I'll get to a solution quickly. After one day nada, but I can't let go of solving this thing, so I don't honor my previous commitment but instead keep at trying to find a solution. Did I mention that this equation is not seperable? I know how to solve them when they are seperable. Sometime Wednesday morning it occurs to me that even if I can't find a closed form solution, I can do a numerical approximation in Excel. After working on that for a while it occurs to me that I'm confused about the boundary condition, v(0) = 0, which means for the lowest cost seller there is no walk away from buyers and for this one type (and the other extreme where v(1) =1) trade is at the efficient level. I somehow got it into my head that if the seller sets cm = 0 then the expected price would also be zero, but I was ignoring the contribution of the buyer's value in determining the expected price, which actually turns out to be .25, half the expected value. And here it is Friday and I'm still not done with the numerical approximation. It's close but the thing is off in some ways I'd like to fix. In particular, the area of the region where trade occurs should be greater than 1/4. I wasn't getting that initially. There are some other changes I'd like to make as well. For what it's worth, the graph of what I have at present is below. Now I think it's time to contemplate grading those exams.
The current topic is bargaining, not unlike what you do at a flea market or when buying or selling a house. The buyer knows her value. The seller knows his cost. Each is uncertain about the player on the other side of the table. The operative questions are: (1) will they end up walking away or reaching a deal, and (2) if they do reach a deal, at what price?
Last time when I taught the course I was perfectly content to cover the model about bargaining as it is done in textbook. In that setup there are two types of potential buyers, high value and low value, and there are two types of potential sellers, low cost and high cost. In other words, on each side of the market there is a good type and a bad type. The interesting economics happen when the parameters are set so good types should always reach a deal but bad types should only reach a deal when their counterpart is a good type. Further, the setup should be symmetric so as not to confer bargaining power on one side or the other.
Considered in isolation, the 2x2 model is fine to illustrate the ideas. But this time around in looking at it I find it clunky. We've already done a model of insurance (that I did not cover last semester) where each potential insured is one of two types, high risk or low risk. In that model it is reasonable to assume that the insurance providers know the probability distribution across types, as that comes from population averages and insurance companies are in the business of knowing what the population averages look like. In the bargaining context, however, it is far less clear from where beliefs over the counterpart's type emerges. Yet those beliefs are a critical determinant of the outcome, which starts to make the model look like a house of cards. There is a further issue that in the insurance model the insureds are risk averse, but in the bargaining model the players are assumed risk neutral. One might want to respond that risk neutrality is assumed to keep the model tractable but, really, the math is not much harder under risk aversion. The real reason is that one does not want differences in risk attitudes to confer bargaining power, yet risk aversion typically varies with circumstance, so that one side or the other has an idiosyncratic bargaining advantage seems unavoidable. To eliminate the bargaining power issue, each player should have the same risk aversion, independent of circumstance. Risk neutrality is then a reasonable approach in the modeling to achieve that end.
So I start to ask myself whether I can do a more elegant version of the model than the textbook authors provide. This might seem like hubris on my part. The authors, Paul Milgrom and John Roberts, are very good and well known economists. In that dimension, I couldn't carry their jockstraps. But their textbook doesn't have the insurance model I mentioned above, so building a bridge between the two models is not an issue they confront. Further, they are explicating in the traditional way while I have Excel at my disposal. The development of an alternative model puts me in the mindset I had as an assistant professor when I was doing econ theory research --- if for whatever reason you don't like how a model is designed, then build an alternative model more toward your liking. (You can take the boy out of economics....) But I fear this going back to a research perspective is deleterious to the teaching, because this urge toward a better model is driven by an aesthetic that is transparent to me but is likely opaque to the students. The students want some intuition that helps them penetrate the ideas. Beyond that the details of the model are extra baggage they could do without.
Let me get to the economics punchline (though not yet to the punchline of the story). At the 60,000 foot level, the message is that to get the incentives right (meaning that the choice the individual makes reveals the type of the individual in a way anticipated by the mechanism), it is necessary to produce some inefficiency relative to the case where the individual's type is known by others ahead of time. Further, the inefficiency manifests in a particular form - quality deterioration for low end customers. In the insurance example the result is that low risk individuals face very high deductibles or find no insurance available whatsoever. This is so high risk types don't pretend to be low risk. The insurance example is an instance of Akerlof's Market for Lemons or what economist's have termed adverse selection. The same underlying economics is afoot when talking about why when flying on an airplane coach is so often such a crappy experience or why in purchasing a new cable tv package the basic coverage offers such a limited variety of channels. Having modeled this once in the insurance case to show how the mechanism separates the types, one does not need to model it again and again as the context changes. The other contexts can be discussed without the aid of a model. Doing so helps to emphasize the underlying principle in operation.
This brings me back to bargaining and two sided asymmetric information. The operative pedagogic question is whether this represents a significant enough change to justify doing a new model from scratch and what lessons are to be learned from it that aren't in the single sided asymmetric information model. I believe that, yes, doing the bargaining model from scratch is justified and that the main lesson from it is that the inefficiency - parties walk away from a deal when there are actually gains from trade to be had - disproportionately impacts middling types.
In the bargaining model it is necessary to focus on couplets, each comprised of a buyer and a seller, and make comparisons across them. For example, if when trade occurs the price was such as to split the difference between the buyer's value and the seller's cost, then holding the sum of value and cost fixed so that if trade occurs the price would remain unaltered, how does the likelihood of trade change as the difference between value and cost increases? Since that difference measures the gains from trade, one is apt to intuit that as the difference gets larger, trade gets more likely. That turns out to be true. If this were the main insight to be had from the bargaining model, it would hardly be worth doing.
What of this other comparison; holding the gains from trade fixed how does increasing the sum of cost plus value impact the likelihood of trade? One might intuit that it shouldn't matter, that only the gains from trade matter. It sounds good, but it is wrong. Something else happens. The parties are not symmetric in their contribution to the likelihood of trade. But to even begin to consider why, it is necessary to go beyond the simple two types model. There needs to be a type in the middle, preferably several types in the middle. Having made that concession, however, it really is better to go all the way to a continuum of types approach, since then one can use geometry in the representation to facilitate understanding of the issues and to rely on calculus techniques to perform the analysis when that is needed.
The model I had in mind has the cost realization, c, a draw from the uniform distribution on the interval [0,1] and the value realization, v, also a draw from the same distribution, with the distributions of the two random variables independent. Thus the pairs, (c,v), can be found in the unit square and under complete information the pairs where the players walk away from the deal are below and to the right of the main diagonal of the square, since for such pairs cost exceeds value.
In this model it is straightforward to consider the benchmark case where the seller can set a take it or leave it offer for the buyer. This translates to monopoly pricing under constant marginal cost and linear demand. In that model the monopoly price is midway between the marginal cost, c, and the demand intercept, 1. Hence buyers with v > (1 + c)/2 purchase at this price. Otherwise the buyers walk away. One can trace out the set where trade occurs as c varies. It too is a a triangle, one with half the area of the triangle where trade occurs under complete information.
This benchmark is useful, as is the analogous benchmark that arises when it is the buyer who can make a take it or leave it offer for the seller. Again the triangle where trade occurs has half the area of the triangle where trade occurs under complete information. What is unclear from these benchmark cases, however, is whether the underlying cause for the excessive amount of walking away from the deal is the asymmetric information itself or the price setting power. Getting at the answer to that issue motivates the remainder of the analysis, where neither party has a price setting advantage.
Mumbling about something called the Revelation Principle, which means that for whatever mechanism you might come up with to resolve the bargaining model there is an equivalent "direct revelation mechanism" where the buyer announces her value and the seller announces his cost and then based on that the mechanism specifies whether the players walk away or trade and if they do trade at what price, an economist teaching this would wave his hands and say we're going to model the bargaining as a direct revelation game. Non-economists who read this might prefer to personalize the concept called a mechanism in the form of an arbitrator whose word on the matter is final. The arbitrator makes this decision based on what is communicated by the buyer and seller about their circumstance. In turn, so the buyer and seller each know what message to send, the arbitrator lets both of them know how their joint message translates into the arbitrator's decision.
It is instructive to start out with a naive but hopeful arbitrator whose dual goals are to achieve the same efficiency in trade that occurs under complete information and do so with fair pricing. Letting cm denote the cost message the seller sends and vm the value message the buyer sends, the obvious rule for the arbitrator to come up with is trade only if vm > cm and when that is the case set the price, p, so that p = (cm + vm)/2. Under this rule would it be optimal for the buyer and the seller to tell the truth, which means cm = c and vm =v? Or would it be better for each of them individually, taking account of their own benefit only and ignoring the consequences for their counterpart, to "strategically misrepresent" their circumstance? When truth telling is optimal, the mechanism is said to be incentive compatible.
It turns out that the naive arbitrator's mechanism is not incentive compatible, but before explaining why a little aside. In a nation where every school child is taught that the Father of our Country and first President, George Washington, never told a lie shouldn't it be that telling the truth is its own reward and therefore that every possible mechanism is incentive compatible? Further, isn't economics as a discipline morally reprehensible for suggesting otherwise? The responses to these questions are as follows. In the model the message sent has no direct impact on the player's payoff. All that matters is the expected surplus generated for the player. If a message that is other than the truth yield's a higher expected payoff, then truth telling is not optimal. Shouldn't the model then be changed to reflect more preferred ethical behavior? The models purpose is positive, to predict what will be observed. The model is not normative. It should not be taken as a guide of behavior. The acid test of whether it is a good model, then, is whether the predictions of the model are in accord with experience. Anyone who observes when driving on the interstate that traffic slows down a cop car is in view implicitly knows that incentives matter, at least in certain settings. Without much effort, the reader likely can come up with several other scenarios where extrinsic rewards (or punishments) influence behavior in a predictable way. That is sufficient to justify the modeling approach.
Let's get back to the naive arbitrator's mechanism. We'll consider the choice problem of the seller under the assumption that buyers are truthful about the value they report in their message. Then sending a message of cm means the probability of trade is 1 - cm and the expected price at which trade occurs is (1 + 3cm)/4. In other words, the seller will treat the mechanism like a demand curve. For truth telling to be optimal, marginal revenue for this demand curve at cm = c must equal marginal cost, which is c. That doesn't happen here. Instead, marginal revenue is less than marginal cost at cm = c, which means the seller would prefer to sell less but at a higher price. Indeed, it is not hard to show that the optimal message is cm = (1 + 2c)/3.
What does an incentive compatible mechanism with split the difference pricing look like? From the discussion in the previous paragraph it must be that the implied marginal revenue when setting cm = c must equal the marginal cost, c, and that must be identically true for all c. Treating the mechanism from the seller's perspective, it specifies the minimum value at which trading occurs given the cost message of the seller. It is then not hard to derive that this function must satisfy:
dv/dc = (1 - v)/(v - c).
This disarmingly simple looking equation is the diffeq from hell mentioned in the title of my post. So let me switch gears and leave the explanation of the model to give the little history from which the title emerged. Then I will close.
There is a practical aspect to teaching in more or less staying on track subject-wise and doing so at a reasonable pace for the students. On Sunday or Monday when I started to work on the alternative model, I implicitly told myself that I've got one day to solve this thing. If I do it, great. But if not I should fall back on the 2 types example and leave it at that. I'm more than a little rusty with differential equations, but I'm optimistic that once I get rid of the rust I'll get to a solution quickly. After one day nada, but I can't let go of solving this thing, so I don't honor my previous commitment but instead keep at trying to find a solution. Did I mention that this equation is not seperable? I know how to solve them when they are seperable. Sometime Wednesday morning it occurs to me that even if I can't find a closed form solution, I can do a numerical approximation in Excel. After working on that for a while it occurs to me that I'm confused about the boundary condition, v(0) = 0, which means for the lowest cost seller there is no walk away from buyers and for this one type (and the other extreme where v(1) =1) trade is at the efficient level. I somehow got it into my head that if the seller sets cm = 0 then the expected price would also be zero, but I was ignoring the contribution of the buyer's value in determining the expected price, which actually turns out to be .25, half the expected value. And here it is Friday and I'm still not done with the numerical approximation. It's close but the thing is off in some ways I'd like to fix. In particular, the area of the region where trade occurs should be greater than 1/4. I wasn't getting that initially. There are some other changes I'd like to make as well. For what it's worth, the graph of what I have at present is below. Now I think it's time to contemplate grading those exams.
Sunday, October 14, 2012
Burdening A Shoulder
Later this afternoon they'll they will play game two of the ALCS between the Tigers and the Yankees. Had the experience in the last twenty four hours been the usual for playoff baseball, the announcers would be talking about the fact that the Yankees starter, Hiroki Kuroda, will be pitching on just three days rest instead of the usual four. But events have actually been freakish, particularly the play at shortstop in extra innings where Derek Jeter, the Yankees Captain, broke his ankle. Surely that will take center stage and everything else will become background noise. But, if the Yankees are to fare well under the circumstances, Kuroda will have to perform at a high level, the three days rest notwithstanding.
It is now more than three weeks since I had surgery to repair a torn rotator cuff in my right shoulder. With more than enough time to think about the heeling process, I have latched onto some sidebar issues. One of those is to marvel at the adhesiveness of the surgical tape. There are two pretty small incisions, one at the top of the shoulder, the other on my back but near the first one. The tape on the second one has been peeling off, but the tape on the first one is like new and for the last week or two I've been taking regular showers. I wish I had near as much stick-to-it-ness.
Another, perhaps this is a bit more than a sidebar, is to see how awkward and confused I am on the issue of accepting help when it's offered, maybe even asking for help, or doing it myself even if that entails a lot of fumbling around. The first week or so of post-op, I was extremely dependent on my wife to accomplish even the most mundane task. Yet she's been extraordinarily busy with her work, so I felt guilty about taking up too much of her time and I know I was feeling frustrated then because I did have some needs that required attention. As I've become more proficient doing ordinary tasks, much of the frustration has dissipated. Interacting with others, it's different. The help is a one-shot deal rather than a part of an ongoing relationship. Not accepting the help is from fear of showing weakness - deny the problem rather than deal with it. I will return to that point in a bit.
Another big concern is whether I should be winding down the pain meds. It is possible to develop a dependency on them. On the other hand, I think that as I make milestones in terms of improved functionality of the arm, that will come at the price of some pain, at least initially. I was very proud of myself after I finally was able to put on a long sleeve shirt myself. But it hurt doing so, no doubt about it. So there is the question of whether I can make further progress and yet still cool it on the meds. Physical therapy starts Tuesday. That's the main question I'll bring to the first session.
Now let me extend the metaphor beyond baseball and beyond my own physical situation and consider the students I'm teaching this semester. Compared to last spring or the year before that we are doing much better on students coming to class, though it was required in the spring and it is not required now. So that is a plus. But in a different dimension I'm still not satisfied. While some students have something on the ball too many seem to not be bringing enough to the table. Assuming that's right, the question is: what should be done about it?
I don't think it's an easy question to answer. It becomes even harder to answer when in some way the students themselves show they are aware of the predicament and then ask for help. Doing that they are more mature about their learning needs than I am about my physical needs, yet it doesn't seem to occur to them that the must burden themselves to find a way out. Perhaps we can end up teaching each other by sharing some of the burden.
It is now more than three weeks since I had surgery to repair a torn rotator cuff in my right shoulder. With more than enough time to think about the heeling process, I have latched onto some sidebar issues. One of those is to marvel at the adhesiveness of the surgical tape. There are two pretty small incisions, one at the top of the shoulder, the other on my back but near the first one. The tape on the second one has been peeling off, but the tape on the first one is like new and for the last week or two I've been taking regular showers. I wish I had near as much stick-to-it-ness.
Another, perhaps this is a bit more than a sidebar, is to see how awkward and confused I am on the issue of accepting help when it's offered, maybe even asking for help, or doing it myself even if that entails a lot of fumbling around. The first week or so of post-op, I was extremely dependent on my wife to accomplish even the most mundane task. Yet she's been extraordinarily busy with her work, so I felt guilty about taking up too much of her time and I know I was feeling frustrated then because I did have some needs that required attention. As I've become more proficient doing ordinary tasks, much of the frustration has dissipated. Interacting with others, it's different. The help is a one-shot deal rather than a part of an ongoing relationship. Not accepting the help is from fear of showing weakness - deny the problem rather than deal with it. I will return to that point in a bit.
Another big concern is whether I should be winding down the pain meds. It is possible to develop a dependency on them. On the other hand, I think that as I make milestones in terms of improved functionality of the arm, that will come at the price of some pain, at least initially. I was very proud of myself after I finally was able to put on a long sleeve shirt myself. But it hurt doing so, no doubt about it. So there is the question of whether I can make further progress and yet still cool it on the meds. Physical therapy starts Tuesday. That's the main question I'll bring to the first session.
Now let me extend the metaphor beyond baseball and beyond my own physical situation and consider the students I'm teaching this semester. Compared to last spring or the year before that we are doing much better on students coming to class, though it was required in the spring and it is not required now. So that is a plus. But in a different dimension I'm still not satisfied. While some students have something on the ball too many seem to not be bringing enough to the table. Assuming that's right, the question is: what should be done about it?
I don't think it's an easy question to answer. It becomes even harder to answer when in some way the students themselves show they are aware of the predicament and then ask for help. Doing that they are more mature about their learning needs than I am about my physical needs, yet it doesn't seem to occur to them that the must burden themselves to find a way out. Perhaps we can end up teaching each other by sharing some of the burden.
Thursday, October 04, 2012
Ask The Prof
This post is about an ongoing experiment regarding free online office hours for microeconomics available to any student on the Internet. Up to now the flow has been a trickle, so it is far too early to conclude that this is the next wave coming, or anything like that. But I think the general idea is interesting and worthy of some discussion. You can get a sense for how it works here. The About tab and The Reasons For This Site tab provide information on why the the experiment was initiated. Here I want to talk about some bigger picture ideas that might tie in even if the experiment is only modestly successful.
First, I am fascinated with the notion of students going outside the confines of the course they are in to search for freely available help online. I'm not talking about cheat sites here. I'm talking about students who do want to learn the subject matter in the course they are taking but for reasons we can only conjecture about want to go outside the confines of the course itself - by which I mean the instructor, the textbook, course materials provided in the LMS, etc. This going outside the course demand is modular and intermittent. Perhaps it emerges for a hard topic where both the lecture and the textbook are opaque and where going to the instructor's scheduled office hours is too daunting; showing one's ignorance in front of an authority figure is painful. These students are simultaneously motivated and yet constrained by their lack of understanding of the subject matter. They can be empowered by providing them with an alternative path, which is what the seem in search of.
Second, so much of what is done online today falls under the heading "Content Push" and is in some sense disappointing. Of course there is some very high quality content in this category and some that makes quite effective use of the technology. Alas, that remains the exception. Online office hours get far less attention and remain a relative novelty. My guess for why is that most instructors have no experience with online office hours so they don't perceive the possible benefit. Further, instructors who do have substantial experience with email queries by students may very well react by trying to block the activity rather than channel it to some other venue, for fear of being overwhelmed by the flow and lacking the resource to staff the channel by others.
In the the middle to late 1990s I had quite good success in my intermediate microeconomics class by using undergraduates who had taken the course from me previously and having them staff the online office hours, paying them as hourlies to deliver the service. Indeed, I continue to believe that this use undergrads was the most powerful innovation in instruction that the move online enabled, as it encouraged extensive use of office hours in a democratic fashion and thereby promoted student engagement. As I've written elsewhere, most recently in this post, one has to make changes in the course around how homework is done and evaluated in order to motivate students to utilize this alternative channel. My experience was that when these changes were put into place, the channel would be heavily utilized.
So in the late 1990s I developed an expectation that the approach with undergrads would diffuse broadly. Mainly that has not happened. Undergrads are used heavily in the various University 101 courses and in a handful of other courses. But they aren't utilized in the vast majority of courses that didn't previously have graduate student TAs, because that would be a cost add, and they also aren't utilized in those courses that do continue to have graduate student TAs. Further, those courses tend to deploy the gradate students in their own sections but not to use them in a pooled way over the course as a whole. So online office hours are not a prominent feature of these courses and I dare say that the traditional form are not used by most students.
Third, indeed you can use online office hours to pool across the different sections of a course, but the economies of scale by no means end there. You can also pool across the same course offered at many different universities, given the following. There is apt to be substantial idiosyncrasy in a how a course is taught going from one campus to the next, reflecting both individual instructor predilection and the composition of the student body taking the class on the particular campus. A person staffing online office hours done at full scale must be competent in dealing with the idiosyncrasy, both in answering the question as posed for the student posing it and in making the response intelligible and relevant for the student taking the course elsewhere. This requires both substantial subject matter expertise and enough teaching experience to have a sense where students are apt to struggle with the content.
The further implicit idea in the experiment is to rely on baby boomer faculty at or near retirement who do the work not for pay but rather as a give back activity to a younger generation. This is a high human capital group of people who are well heeled, if not in the absolute then at least compared to the population overall. My sense is that many in the group would be willing to participate on these terms if: (a) they themselves felt competent as the online TA and (b) they had a sense that the activity was socially useful to the students.
My limited experience with this experiment suggests this is possible. It offers some reason to continue with it and amass more evidence on this score.
Let me close with one other observation. At present, students find the Ask The Prof site via a mention and a link at my YouTube channel or from the descriptions of individual videos which have a similar mention or link. On the one hand, this allows the credibility of Ask The Prof to be determined in advance by the perceived quality of the video content. So perhaps bundling free content distribution with online office hours is sensible. On the other hand, given that the videos themselves attract only a limited set of eyeballs, the light flow at Ask The Prof is then not surprising. One almost certainly would want to try a more aggressive promotion of such a service to test whether there is substantial demand for it. That offers one reason why I hope others will take up the baton and push the idea fully through its paces.
First, I am fascinated with the notion of students going outside the confines of the course they are in to search for freely available help online. I'm not talking about cheat sites here. I'm talking about students who do want to learn the subject matter in the course they are taking but for reasons we can only conjecture about want to go outside the confines of the course itself - by which I mean the instructor, the textbook, course materials provided in the LMS, etc. This going outside the course demand is modular and intermittent. Perhaps it emerges for a hard topic where both the lecture and the textbook are opaque and where going to the instructor's scheduled office hours is too daunting; showing one's ignorance in front of an authority figure is painful. These students are simultaneously motivated and yet constrained by their lack of understanding of the subject matter. They can be empowered by providing them with an alternative path, which is what the seem in search of.
Second, so much of what is done online today falls under the heading "Content Push" and is in some sense disappointing. Of course there is some very high quality content in this category and some that makes quite effective use of the technology. Alas, that remains the exception. Online office hours get far less attention and remain a relative novelty. My guess for why is that most instructors have no experience with online office hours so they don't perceive the possible benefit. Further, instructors who do have substantial experience with email queries by students may very well react by trying to block the activity rather than channel it to some other venue, for fear of being overwhelmed by the flow and lacking the resource to staff the channel by others.
In the the middle to late 1990s I had quite good success in my intermediate microeconomics class by using undergraduates who had taken the course from me previously and having them staff the online office hours, paying them as hourlies to deliver the service. Indeed, I continue to believe that this use undergrads was the most powerful innovation in instruction that the move online enabled, as it encouraged extensive use of office hours in a democratic fashion and thereby promoted student engagement. As I've written elsewhere, most recently in this post, one has to make changes in the course around how homework is done and evaluated in order to motivate students to utilize this alternative channel. My experience was that when these changes were put into place, the channel would be heavily utilized.
So in the late 1990s I developed an expectation that the approach with undergrads would diffuse broadly. Mainly that has not happened. Undergrads are used heavily in the various University 101 courses and in a handful of other courses. But they aren't utilized in the vast majority of courses that didn't previously have graduate student TAs, because that would be a cost add, and they also aren't utilized in those courses that do continue to have graduate student TAs. Further, those courses tend to deploy the gradate students in their own sections but not to use them in a pooled way over the course as a whole. So online office hours are not a prominent feature of these courses and I dare say that the traditional form are not used by most students.
Third, indeed you can use online office hours to pool across the different sections of a course, but the economies of scale by no means end there. You can also pool across the same course offered at many different universities, given the following. There is apt to be substantial idiosyncrasy in a how a course is taught going from one campus to the next, reflecting both individual instructor predilection and the composition of the student body taking the class on the particular campus. A person staffing online office hours done at full scale must be competent in dealing with the idiosyncrasy, both in answering the question as posed for the student posing it and in making the response intelligible and relevant for the student taking the course elsewhere. This requires both substantial subject matter expertise and enough teaching experience to have a sense where students are apt to struggle with the content.
The further implicit idea in the experiment is to rely on baby boomer faculty at or near retirement who do the work not for pay but rather as a give back activity to a younger generation. This is a high human capital group of people who are well heeled, if not in the absolute then at least compared to the population overall. My sense is that many in the group would be willing to participate on these terms if: (a) they themselves felt competent as the online TA and (b) they had a sense that the activity was socially useful to the students.
My limited experience with this experiment suggests this is possible. It offers some reason to continue with it and amass more evidence on this score.
Let me close with one other observation. At present, students find the Ask The Prof site via a mention and a link at my YouTube channel or from the descriptions of individual videos which have a similar mention or link. On the one hand, this allows the credibility of Ask The Prof to be determined in advance by the perceived quality of the video content. So perhaps bundling free content distribution with online office hours is sensible. On the other hand, given that the videos themselves attract only a limited set of eyeballs, the light flow at Ask The Prof is then not surprising. One almost certainly would want to try a more aggressive promotion of such a service to test whether there is substantial demand for it. That offers one reason why I hope others will take up the baton and push the idea fully through its paces.
Onto the Playoffs
The American League has done much to amaze -
The first Triple Crown since Yaz, the Oakland A's.
The Yankees again are part of the show.
Leading the way for them is Robbie Cano.
Providing more evidence of this indisputable thing;
In Major League Baseball the Latin player is king.
So maybe we should reconsider immigration as a crime
Since it's done so well by the national pastime.
The first Triple Crown since Yaz, the Oakland A's.
The Yankees again are part of the show.
Leading the way for them is Robbie Cano.
Providing more evidence of this indisputable thing;
In Major League Baseball the Latin player is king.
So maybe we should reconsider immigration as a crime
Since it's done so well by the national pastime.