Thursday, December 20, 2007

Learning Blockages, Doing Math Online, And the Failure of the LMS

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.
- Martin Gardner

I may be teaching intermediate microeconomics again in the not too distant future, this time to adult learners in some professional program offered here, quite possibly in a totally online or blended format. So I’ve been thinking a bit about how I might do that effectively. Intermediate micro requires math. In my view the appropriate content soft pedals calculus ideas in favor of making the basic economics points in a discrete choice setting. But graphs, the kind one did in analytic geometry in high school, are appropriate, even essential. There is much economic intuition in the construction and proper interpretation of these graphs. Indeed, some instructors who teach this stuff think of this course as essentially applied math. My view is otherwise, there is also much economic intuition in considering real world issues that demand an economic analysis and in applying an appropriate economic framework to that real context. So I favor a balanced approach where one does both, some math but also some interpretation of real situations.

When I was teaching this course to 18-22 year old undergraduates, the course was taught by a wide variety of instructors. It had a poor reputation among many of the students, the majority of whom were majors in the College of Business. Their perception was both that it was difficult and that it wasn’t particularly relevant. The former, I believe, was because of the math, although all the students had taken Calculus (or placed out of it) ahead of time. The latter because they didn’t perceive the economic ideas to be foundational for what they might learn in their other Business courses. This may be an example of the broader problem that students fail to see the forest for the trees with respect to their studies and hence typically adopt an extreme instrumental approach to what they learn. Ironically, the economics metaphor can be extremely helpful for students in enhancing their soft skills, since as I’ve argued elsewhere it is much easier to communicate ideas if those are cast within a simple framework and the economics metaphor is precisely that. The math emphasis, with its seeming focus on technical detail, (the instructor intent is to supply needed rigor to the analysis) obscures the simplicity and elegance of the metaphor. So, unfortunately, mostly the students don’t get the economics to which they are exposed.

Whether I could now do a better job with this undergraduate audience will remain an open question for me. Given what I’ve gained from the learning technology job and some successful experiments I tried when teaching Principles to Campus Honors students, I have more experience with which to address the issue how to tap into the basic motivation of students taking the Intermediate course. For now my focus will be on adult learners. While there still are questions about providing motivation with that audience, I believe those students will not be quite as impatient nor will they be prone to cheat or to take their preparation lightly. And these students will almost certainly have a richer set of real word experiences that we can tap into to add flavor to what we will study. So I hope to avoid some of the pitfall I experienced teaching Intermediate in the past. Sometimes I felt there was a kind of Gresham’s Law at work. So, for example, I got into designing assessments with random numbers in large part to discourage cheating – each student would get an individualized version of the questions. But those were harder to write and so effort put forth in that dimension meant less effort to design assessments that would be broadly educative.

As I am writing this post, there was a very favorable piece in this afternoon’s Chronicle Update about the UTeach Program at the University of Texas-Austin College of Education, which shows that others have been thinking hard about related questions – are the skills for doing effective teaching of this sort transferable and what mechanisms promote that transfer? Their Publications Page appears to have many interesting resources to aid in thinking about these questions. I will work through some of those as I go through designing the intermediate microeconomics site after the New Year. But I’ve got a more immediate reason for writing now.

* * * * *

It’s now Thursday and my kids are on Holiday till after the New Years. Last week my younger son, an eighth grader and now somewhat of a history buff, bombed on an algebra exam. Many of his classmates did likewise, so the instructor sent home the graded exam as a practice test for a makeup that was given yesterday. I spent several evenings trying to coach my son into better understanding the math. It was an anxious time for both of us. I’m going to try to take some lessons from that experience and then circle back on the subject of this post.

Both my kids, like their entire generation, have been heavily into fantasy stories - Star Wars, Lord of the Rings, Harry Potter, Halo, etc. They have access to these stories in multiple media – DVD, Xbox, computer games, etc. The joy from these narratives led to other computer games that are historic fiction, not pure fantasy – Age of Empires, Civilization. The younger one, especially, learned a huge amount of historic detail as he encountered the narrative and challenges of playing these games. This is the benefit of immersive gaming environments that so many others have talked about. Interestingly, at least to me, the games have created a taste for historic narrative itself, whether that comes through a game or otherwise. The younger one is now an avid fan of the History Channel. It feeds on the learning need that the computer games created. And there are beginning to be signs that books will do likewise. Indeed, while the books are obviously slower to get through, they have that much more detail and a more intricate story. In other words, what was set in place as playful diversion with computer games has been transformed into learning via intrinsic motivation through a habit developed outside of school. After inwardly moaning that the games were a complete waste of time for several years, I’m very pleased with this more recent development.

Once one has what seems to be a good algorithm for learning one wants to try to learn everything that same way. Further, if the learning seems effortless and happens en passant, the learner develops an expectation that can continue to happen regardless of context. It makes it hard to admit that a subject is difficult and even harder when there aren’t coping skills in place to manage the learning more effectively. Math, particularly the algebra my son is being taught now, is quite different from history. There is no narrative into which to weave the various facts and procedures. There is only abstraction and the seeming arbitrariness of the various rules. These eight grade kids have experienced what appear to be arbitrary rules before (“i” before “e” except after “c” or when sounding like “a” as in weigh or neighbor). So there is a tendency to want to learn the math the same way they learned to spell – through rote. But that is wrongheaded. The problem is there is nothing else to ready them for a better approach. (My kids did some computer programs in the very early grades to learn spelling and arithmetic (perhaps those were in the Reader Rabbit series), but those apps were not nearly as compelling as the games they played later.)

The fundamental value of the math – something that will serve the kids big time later in life if they get it during Middle School and High School – is that there are multiple ways to represent the same idea. A big part of what we call critical thinking is to find a convenient representation, reason through it, and then translate the results back to some other representation that motivated the inquiry at first. But to an eighth grader who has yet to see the value of multiple abstract representations for his own thinking, the math just seems like an obstacle, one that might limit his GPA and thereby thwart some ambition for yet unknown down-the-road achievements. That induces stress qua performance anxiety that exacerbates the problem.

There is a further complication, one that I’ve witnessed repeatedly in my intermediate microeconomics teaching, that the math currently being taught rests on a foundation, one where the student’s understanding is shaky and vague. For my son, the critical conceptual base is arithmetic with negative numbers. If done slowly and patiently, he can reason through it well enough. But he has nowhere near the fluidity with such arithmetic as compared to his mastery of the historical facts about battles in the Civil War. This lack of comfort with the basics contributes to missing the forest for the trees and feeds into the desire to want to learn the math by rote.

Also, it appears nobody has coached him previously on the recording and record keeping of his thinking through the algebra. He writes an equation down and then immediately manipulates that. It doesn’t occur to him to write the equation again and manipulate the reproduction, keeping the original pristine. This matters not if the thinking is correct all the way through. But it matters a great deal if errors are made and one has to back track to find the error. If the steps are rendered distinctly, then each can be checked for correctness. I believe that learning how to spot errors and correct them is an additional crucial skill, one that doing math well encourages. Even very bright folks who can keep a lot of information in their heads can benefit on occasion from clear record keeping of the intermediate steps. Doing that lessens the cognitive load and allows for quicker recognition of the source of the error. It is a must for a student who is struggling with the concepts.

Now I want to switch gears slightly and recall a presentation that Julie Evans made at the annual ELI Conference last January, where she reported on the technology habits and desires of then current High School students. My recollection is that she found: (a) the students were alienated from the curriculum in general, (b) the students would like to see more technology used in their classes because it would better match their informal learning outside of school, and (c) Math, in particular, was the subject matter they thought would benefit the most from being taught with computers. I had the thought of Julie’s presentation in the back of my mind as I was trying to help my son.

So, as is my passion even though I knew timing-wise this effort would not help my son in this particular instance, I made an interactive spreadsheet that is a tutorial on determining the equation of a line given the coordinates of two points on the line. It is by no means perfect; for example, it can’t deal with vertical lines, some of the formatting is only so-so (particularly the mixed fraction for the Y intercept), and in the method it uses where items are hidden till they are needed, in a few cases that is done imperfectly.

But there are certain parts of it that appeal to me nonetheless and I want to emphasize those here. For each coordinate of the points, students can choose integer values from -20 to +20. This gives them an ample set to practice with so they can try this until they feel comfortable that they understand. There is an attempt to make the various stages at the right coincide with the plotting of some component in the graph on the left. This is meant to capture the dual representations of the same idea. To compute the run and the rise, there is enough information so students can actually count the answer. I believe that counting is more basic than arithmetic and allowing the students to count should help them feel comfortable about the calculations they make. Further, the data entry is by pushing a button rather than by typing in a number. They can hold down the button and watch the graph instead of the button, to see the consequence of their action. This gives them a qualitative sense of what is going on. Indeed the calculation of the Y intercept is deliberately done to encourage them to eyeball the graph. If they want to for the sake of their own understanding, they can in addition compute the Y intercept on a piece of paper to verify that they get the same answer either way.

* * * * *

Of course, since I’m writing this post quite soon after I completed the spreadsheet I’ve not tested this content on students and this being the holiday I doubt very much I’ll get my son to try it. So what I say next is pure conjecture. It doesn’t have use data to back it up. Nonetheless, I believe this is the type of content that the students Julie Evans surveyed would regard as useful and engaging for learning math. And what I want to argue here is that we should be authoring more of this type of content (and then get the students themselves to author even more of it both to aid their own learning and to help others). Unfortunately, we don’t see much content of this sort. What we do see is flatter, less interactive content, a lot of multiple choice questions, stuff that may be ok to assess the student’s understanding, but is much less useful in helping the students gain that understanding. This puts the technology in the role of the stick. We need more carrots, but we’re not getting them. Here’s my argument for what this the case.

I put in somewhere between 12 and 20 hours to author this tutorial. And for a similar tutorial on Long Division I made a couple of years ago, I spent the better part of a weekend in the construction. This is not because I was ignorant of the math or of the design issues. It is simply because there is a need to conceptualize in the construction – the layout and sequencing of the presentation matter as does the math and one has to see those pieces interplay well. I did this free form starting from a blank Workbook in Excel. I don’t believe there are too many people with the wherewithal to make content of this sort in this manner. They might be many others with an interest to author stuff of this sort, but they would need to rely on templates so they can focus on the content. Unfortunately, to my knowledge there are few if any templates of this sort for content creation. (The software our Physics department uses for student homework has some of this type of capability but it requires authors to submit Perl scripts. That works in Physics but is too much of an entry barrier to be more broadly applicable.)

We are now more than 12 years after I got started with learning technology and back in 1995 there was the promise to deliver on what I’m talking about right here on my campus with CyberProf and Mallard; the CAPA system from Michigan State was another good possibility. The more recent commercial course management systems and even most of the newer open source alternatives have delivered less in this dimension than might have been hoped. Part of that is because they’ve not yet integrated current technologies (Ajax) into the assessment tools, so you can’t yet do what I’ve got in my Excel tutorials – students do data entry that shows up in the graphs, which are rendered dynamically.

But another part of this is conceptually and I believe even the early assessment engines made this mistake, a mistake which parallels a conceptual error we’ve seen in the Banner student system, where the basic element is the section. That approach goes against the culture here where the basic unit is really the course – we have many multi-section courses as well as courses taught in a single section but that are cross listed.. We spent a good part of the first year after Banner was implemented here reconciling our ordinary business processes concerning instruction with the peccadilloes of how Banner manages these things. (For example, the professor may have had access only to the lecture section, not to the discussion section, but it was the latter where the grades were to be entered.) The same sort of issues occurs with how the LMS deals with assessments.

There the basic element is the question, with question one essentially unrelated to question two except in the order in which they are presented to the students. In my tutorial each stage of the process coincides approximately to a question. That all the stages can be rendered in one unified view (I designed the tutorial with that goal in mind) is a huge benefit compared to where one must scroll to see subsequent or prior questions. Most of the learning management systems don’t even allow a numerical parameter to be passed between questions. Instead, with each subsequent question the parameters are set anew. And, most definitely, students can’t set the parameters themselves so they can practice. The notion of practice is in the number of attempts that are allowed, but not otherwise found in the quiz tool. Further most of these assessment engines don’t allow the provision of instant feedback in quiz mode (meaning the assessment is for credit) but rather only allow it for self-assessment. Instructors are apt, however, to design quizzes because they know students will do those to receive course credit. (Although it is also true that many students “do” the quizzes in a manner aimed at circumventing the intent. For example, with multiple choice that can be submitted many times, they simply try the various letter alternatives till the get the thing correct.)

All of this is unfortunate. The question is what to do about it. One possibility is to extend the argument I made about 18 months ago and add this to the wish list for what we need in an LMS. But now I’m less inclined to think that is the best answer. My sense is that we need to bring the discussion of what is educative content outside of any container that might deliver it. And I’d like to engage all my friends and colleagues who embrace a Constructivist approach toward learning to reflect and comment on this question, particularly as it pertains to the teaching of math content, especially when that math is used in a College level setting, such as the Intermediate Micro course that is my focus. To aid in that, I will close with a critique of my own approach.

In my view, the difference between what is construction “from scratch” and the reproduction of “spoon fed knowledge” has to be considered relative to the current understanding of the learner. In my tutorial the sequencing of the steps in built in, predetermined for the student’s point of view. In some cases there may be many different possible sequences that will produce the same result and in that case there is the possibility that such a tutorial creates the impression of a single correct approach. That would be unfortunate. In other cases the sequencing might matter more but it might be an important part of the construction for the learner to come up with the sequencing on his own. Then having it provided, as I’ve done in the tutorial, amounts to spoon feeding.

My retort is that tutorials of this sort represent early steps toward allowing the student to deal with complexity in the math. Students need to get past the approach in the tutorial onto harder stuff, but some students won’t be able to get there in one fell swoop. In any event, I hope we can separate out the question of what works for the students from the issue of whether we can generate this content given the limited free time of those who are likely to make it. For my part, I’ll try to make the more of this sort of stuff, targeted at microeconomics instead of eighth grade algebra and see how it works with my own students.

Happy Holidays

Monday, December 10, 2007

The “L” Word

Now, I'm liberal, but to a degree
I want ev'rybody to be free
But if you think that I'll let Barry Goldwater
Move in next door and marry my daughter
You must think I'm crazy!
I wouldn't let him do it for all the farms in Cuba.

Bob Dylan I Shall Be Free No.10

A week ago my wife had a colonoscopy. She passed with flying colors. My role was to chauffeur, to tote stuff to the car, and to hold my wife’s hand as she went from cloudy headed to groggy after the procedure was over and the anesthesia had done its thing. I knew there’d be some waiting till we could go home so I brought a book along. I was reading Paul Krugman’s latest, The Conscience of a Liberal. The nurse who was attending to my wife saw I had a book in my hand and asked what I reading. After I showed it to her she asked, “you’re not a liberal, are you?” as if that were a condition on a par with venereal disease. We then had about a five minute exchange about my job, how I dress (pretty traditional if you ask me but it was cold that day so I was wearing thermal socks that had some color to them), and my style of speech, all of which unmistakenly pigeon-holed me as a professor – one of those, which if it weren’t a college town, might be a cause for alarm. I could have done without the chit chat. At least she took good care of my wife.

But here I don’t want to ponder how the rest of the world views those of us in academe. I’m writing as one insider to another. What does it mean to be a Liberal in how we do our jobs and in those norms we’d like to see followed in Higher Ed? Does advocating for learning technology necessarily make one a liberal because implementing the technology requires change? Is there some tie between Liberal in the workplace and, for example, our attitudes toward the upcoming presidential primaries and our preferred candidates? Those are the questions I want to address. Recently I’ve had several instances where colleagues either referred to me as a liberal or where they referred to others as more conservative. When a group of others make a similar if not identical determination, it’s time to investigate the proposition more closely. That’s one of my work maxims.

Here are a couple of other axioms that guide me on the job. The first I call the traffic helicopter approach to management. There are a lot of bottlenecks in implementing learning technology, perhaps more on a big bureaucratic campus like mine than at smaller colleges and universities. The trick is to spot them early and once having identified a problem then to “reroute traffic” so to speak. I was able to do this reasonably well when I ran the small Sloan Center for Asynchronous Learning Environments (SCALE). It became harder to do as we got bigger and became the Center for Educational Technology (CET) and became still more difficult when CET merged with the big academic computing unit, then CCSO, to form CITES. I’m doing a bit more of it now in my new job, though we also have elements of gridlock that I associate with large bureaucracies.

The second I’ve mentioned before in other posts. It’s called “no surprises” and is a sound principle of IT management (really of all management. The Bush Administration would have fared much better with the public had they practiced it.) It means that when some information becomes known internally and that information will affect the decisions of others, get that information out now, even if those changed decisions are perceived as not desirable by you. No surprises makes sense as a long run approach to managing information flows. If you take your medicine early and often, you can limit the pernicious consequences of the negative information. It’s not that people will love you for getting the information out, but if you get a reputation of holding in bad news, nobody will trust you. That’s worse, much worse.

I’m now going to apply those principles in critique of Krugman’s book. I hope it to illustrate my approach more generally and to give the reader all the ammunition needed to make a determination of whether I’m liberal or not.

Krugman’s ideal society is a middle class world that he knew in his youth with little income inequality, a general sense of optimism, based on real opportunities for all. This is the world that the New Deal created, one that emerged after World War II and held together for about 30 years thereafter. FDR, as creator of the New Deal, is Krugman’s hero. Krugman would like to see a return to the principles that guided the New Deal, mainly that society should actively redistribute income to create more equality. This is a society with progressive taxation, a large fraction of the workforce unionized there by driving up the incomes of the working class members of society, and some substantial social stigma attached to CEOs and other high powered corporate executives receiving exorbitant compensation. In the main I agree with Krugman on this. Where I might disagree a tad, at least with how this was framed in Krugman’s book, is that there needs to be incentive to encourage innovation in society, the ‘70s were a period of no productivity growth and ultimately were marked by “Stagflation,” but we’ve swung way too far in that direction since the start of the Reagan Revolution.

Krugman argues that the more recent move toward inequality in income is not a consequence of globalization, as some others have argued. Rather, he asserts, it is a consequence of deliberate political acts. The welfare state of the New Deal and later the Great Society would have sustained if the Republican party had continued to be dominated with Eisenhower Republicans, who were moderate and not so different from their Democratic counterparts on the social agenda. (Did Ozzie and Harriet vote Democrat or Republican?) Krugman offers up Barry Goldwater as the father of “movement conservatism,” a different and more radical type of Republican; one who aimed to dismantle the welfare state. Goldwater failed miserably in 1964. But he sowed the seeds for what would come later. So far I’m still on board with Krugman.

The big issue for Krugman is how the radicalism of movement conservatism became so accepted, especially since much of the message was anti-populist, the very rich have benefitted enormously from the approach but the rest of us only a little and quite a few of us not at all. How can a rational electorate, the vast majority not in the very rich category, become enraptured by an approach to economics that does themselves a disservice? That is a puzzle which requires explanation.

Looking backward at history the path looks deterministic and there is a tendency to see things in terms of their primary cause. This partly explain why Krugman wrote the book he did. Further, Krugman is in an odd position writing this book, especially given his importance as a columnist for the New York Times. It’s as if much of the book is a primer for Democratic Presidential hopefuls, that they should press the points that Krugman argues for; to return to income redistribution policies that benefit the many. So he needs a winning rhetorical argument to win them over. As I’ve argued elsewhere, first here and then here, the best rhetorical argument comes from applying a very simple model in a consistent way and then just hammering on that over and over again. The model does all the work one needs to frame the issues. So the audience has no trouble understanding the points being made.

Western Europe (not so much the UK but certainly Scandinavia, France, Germany, etc.) has never abandoned the Welfare state; this in spite of globalization. Further, unions are much more prevalent there while CEOs are paid much more here. This makes the situation in the US look exceptional and so Krugman offers up an explanation that focuses on that. The coalition that Roosevelt forged for implementing the New Deal included the Dixiecrats in a crucial role. The south was poorer than the country as a whole and so it would benefit disproportionately from the redistribution policies of the New Deal. And the Roosevelt Administration more or less kept a blind eye to Jim Crow. Brown versus the Board of Education didn’t happen till Eisenhower was president.

But when it became clear that the Great Society aimed to improve the lot of Blacks in the country, something that Southern Whites were dead against at the time, there was now a reason for these same Southern Whites to vote against their own economic interests so they could put it to the Blacks. This was the essence of the movement conservative message and this is why it was a winning strategy, according to Krugman. First there were the Reagan Democrats. Then it became fashionable for Southern Whites to become Republican. That was the ballgame.

Krugman indeed hammers on racism and in my reading of the book he has two scapegoats – the Southern White racists and the politicians who have pandered to them. This scapegoat approach may be a good rhetorical device, but I quickly tired of it and then thought it limiting, even harmful. First, I believe it is not entirely accurate historically as the full explanation is more complex. Second, in terms of trying to implement redistribution policies, it is not sufficient to focus on the enemy who is them. One also needs to work through the enemy who is us. There is none of that till the chapter on Health Care reform, the penultimate chapter, the one chapter in the book I liked because unlike the rest of the book it got all the issues out on the table. But in all the prior chapters there is not this completeness in considering the issue. There is only the issue of racism, over and over again. Krugman must have written 5 times about Reagan announcing his candidacy for the Presidency in Philadelphia Mississippi, where the civil rights workers were killed. I get it. Keep it simple and stay on message. But as a reader I don’t have to like it. So let me take on the historical accuracy and enemy who is us issues in turn.

The ascendancy of movement conservatism was far from inevitable in my view. Many random events (random from the point of view of the story Krugman tells) ended up mutually supporting this outcome. None of them get a mention in Krugman’s book. I’ll focus on three of these.

Jerry Ford was a Republican in the Eisenhower tradition. Reagan tried to run for President in 1976. But Ford was the sitting President and he won the nomination. There is no way to know this, but I think it a likelihood that Ford would have won the election had it not been for the Pardon. After Watergate, most everyone hated Nixon, certainly Democrats and then many Republicans too. Ford explained that the Pardon was necessary for the country to heal. Maybe so. I’m not so sure. The Pardon was a huge assist to the Carter candidacy. Consider Ford as President from 1977- 1980, but imagine Ford facing the same Stagflation that Carter had to deal with and imagine the Shah falling and the hostage crisis in Iran happening anyway. Now when Reagan runs in 1980 it’s no slam dunk and quite possibly a Democrat wins that election as a reaction to the previous regime. But the Pardon set in motion the timing that we did observe. It’s not in Krugman’s book at all. It doesn’t help his case. But it clearly did set in motion a chain of events that contributed to Reagan winning in 1980.

Next consider that soon into Reagan’s term there was an assassination attempt on his life. This made Reagan a hero even to those voters who didn’t agree with him politically. (I wasn’t one of them. I never liked Reagan. That may be prima facie evidence that I am a liberal.) He was able to create a unity of purpose in the country that is relevant for the next point. This is the same type of support the Bush II received right after 9/11.

Paul Volker was appointed by Carter. There was a horrific inflationary expectation built into our economy when Volker took office. There was a lot of debate at the time of whether one could take inflation out of the economy and achieve a soft landing at the same time. Volker did the former but not the latter. He pursued a tight money policy that made credit hard to obtain. It induced a rather severe recession. The Reagan White House, for all the errors it made with Supply Side Economics, more or less let Volker have his way and did not impede him. Without Reagan’s popularity this wouldn’t have been possible, or at a minimum would have been much more difficult. So we endured the recession, wrested inflation out of the economy, and since then it has been much more under control. One of the unanticipated good consequences of the recession is that it encouraged the OPEC cartel strategy to unfold. The oil price drops made it much easier to keep inflation in check.

These macroeconomic wins happened under the Reagan watch. I think one can make a good case that Reagan policies did little to achieve them, other than, as I said, letting Volker stick with the tight money policy that was necessary at the time. This macroeconomic success allowed movement conservatism to grow more or less in an unfettered way. Again, none of that is in Krugman’s book.

Krugman also ignores two other factors I’d deem critical, not for his rhetorical argument but for implementing the redistribution policies he wants to see. The first is the graying of America and its effect as a political force. Krugman does say in his Health Care chapter that seniors consume health care disproportionately, but he doesn’t push on the political implications of that. Let me do that here. Quite a few of those Southern Whites who vote Republican, especially in states like Florida and Arizona, are formerly Northern Whites who have made the trek southward. Race may be a secondary issue for them but taxes are a big deal. They don’t like taxes. Especially taxes that are clearly redistributive in nature from old to young (think of funding for schools). When they were younger they may very well have been liberal in their political outlook. But a conservative point of view matches their current mindset. On the other hand, they treat Medicare benefits as an entitlement and would certainly not want to see those cut in any way, shape, or form. Indeed, they’d very much like to see the health benefits increase. They will consume those. This is simply an expression of self-interest, enlightened or not.

The other issue is the decline in the personal savings rate. My parents, who lived though the Great Depression, were voracious savers. It was habit for them. They lived frugally, if comfortably. They could have spent more on themselves but saved both as a form of self-protection for old age and so they could pay the college tuition for me and my sibs and also for the grandkids. My generation lives less frugally. The saving habit was not inculcated as severely. The perceived need was not so great. And in the next generation it is weaker still. Since by definition income minus savings is consumption, saving less means consuming more. Over consumption is like a more general form of over eating. At first it might actually be distasteful, but after a while it becomes addicting. We know it is very hard for addicts to get rid of their habits.

Those in society who are well off but not super rich, in other words those remaining members of the middle class, may very well dislike an income redistribution approach where they end up paying greater taxes without seeing any obvious concomitant increase in benefits, especially if their personal savings rate is low, because they’ll be forced to confront their consumption indulgence.

In other words, we’ve learned to be greedy and we’re used to it. Rising above personal greed is possible, first by making long term arguments about where we might end up, with society more healthy overall, and then also specifically in talking to seniors about what near term things can be done to assure them that changes put in place won’t be too drastic on them. But Krugman does none of that in the book. On the overconsumption, he writes a throw-away line to the effect that most of this spending is in housing and it happens as parents try to move to good school districts to get better education for their children. Of course there is an element of truth in this but it is not the whole story. Krugman ignores the rest of the story. In my view that is an error. Krugman wants to put a simple argument into the field. Simple arguments tend to win the rhetorical fights. But they are a bear when it comes time to implement policy.

Krugman argues that Health Care is the issue for the 2008 Presidential Campaign. I agree. He would really like to see a single payer solution but doubting that is politically feasible he suggests some alternatives. These will require additional funding. He argues this is doable simply from rolling back the Bush tax cuts. Those cuts are due to expire in 2010. But Krugman also notes that Health Care is an area that has been hyperinflationary and that is because almost any innovation – a new procedure or a new drug – raises the cost of care. So either Health Care may very well require additional funds beyond the Bush Tax Cuts, or the new solution will have to ration care in some sensible way. Coming to a resolution on that will not be easy.

Krugman also argues that if Health Care Reform is successful, then it will create a taste for government solutions in other areas (for example to replace all the old roads and bridges so we don’t experience another debacle like the collapse of the bridge over the Mississippi River in Minneapolis). He argues that is another reason why movement conservatives are against health care reform. And in that he is probably right. But what of the Liberals who actually want to see such investment in America. Where do they see the funds for doing that? And for those of us in Higher Education who may be expecting a jolt from the Feds so that like universal health insurance everyone in the country has a guarantee to be able to get a college education, how are we going to pay for it?

If Krugman were to take a No Surprises approach to his argument, I think he’d be forced to say your taxes will go up. Everyone’s taxes will go up. We’ll make the system more progressive so they’ll go up disproportionately more on the rich, but everyone will have to pay. That’s how we’ll fund the other government spending Krugman talks about aside from health care.

But there is no discussion of that in the book. There is only the scapegoating regarding racism and pandering to it. In the eye for an eye world that is national politics, perhaps Krugman needs to write his book his way, to counter all the rhetoric from the conservatives who don’t want to see health care reform at all. But, if that’s the reason, I wouldn’t use the word “Conscience” in the title.

I’m kind of surprised he didn’t make any argument about the enemy who is us. If we were talking about environmental issues, there’d be no getting around it. Maybe he feels we’re still not ready for those type of arguments. But I, for one, feel that putting them off makes it harder to implement his reforms.

At this point in my life I’m confused about whether the term liberal applies to means or ends. I’m not that far from Krugman on the latter, but am quite uncomfortable in what he writes on the former. What does that make me?

Monday, December 03, 2007

Failure of Transitivity

Back in the ‘80s when I taught intermediate microeconomics, I would begin with the axiomatic approach to choice which goes as follows.
For a set of alternatives, A, suppose there is a relationship among its members, R, such that
Completeness: For all x, y in A either xRy or yRx. (In other words all pairs of alternatives can be ranked.)
Reflexivity: For all x in A, xRx.
Transitivity: For all x, y, z in A if xRy and yRz then xRz.
In this case R is called a preference ordering over A. To make some more sense of this, when xRy but not yRx, write xPy and say “x is preferred to y,” while if xRy and yRx, write xIy and say “x is indifferent to y.” Thus xRy can be read as “x is preferred or indifferent to y.”
When teaching my students, we’d discuss whether completeness makes sense. Are there cases where two alternatives can’t be ranked? We’d reduce this to situations where the decision maker didn’t have enough information. He or she could rank the alternatives after the fact, when the information was revealed. I’d say we can finesse that issue but for now let’s assume no uncertainty (this is how it is modeled theoretically). Reflexivity caused no trouble. It makes sense that an alternative is indifferent to itself. It would be a problem if it were preferred to itself. Students would invariably call Transitivity “being logical.” It made sense to them, though I’d let them know that upon occasion it failed in experiments where people were tested to see if they act according to their preferences. Mostly in those experiments those subjects where transitivity failed would report they had made a mistake.
When there is a preference ordering and the set of alternatives is finite, there is a choice point, x* defined by x*Ry for all y in A. In other words, x* is at least as good as any other available alternative according to the preferences. It weakly dominates all other alternatives and it itself is undominated. That is the entire theory in a nutshell.
Right now in college football, transitivity is being severely challenged. This season teams that were ranked number 2 routinely lost the following weak and then fell from their lofty perch. And several teams that were number 1, also lost to find their rankings dip. Among the various inconsistencies we’ve seen this season, I particularly like this cycle.
Michigan beat Illinois. Ohio State beat Michigan. But Illinois beat Ohio State.
This is a classic cycle. Based on head to head competition only, it is not possible to rank these three teams. That they are indeed ranked differently reflects their performance against others. This might seem a trifling but the ratings have been remarkably unstable this year because past performance has not been as strong as usual predictor of winning the next game. Contrast the Week 7 BCS and AP poll results where University of South Florida is ranked 2 in both polls and Illinois is out of the top 25 entirely, with the final results, where USF is ranked in the 20s and Illinois has moved quite a bit ahead of them. One might explain the anomaly of USF’s early high ranking by the fact that it was undefeated at the time, but Hawaii was undefeated for the entire season and they are ranked 10th. Hmmm.
For any situation with three alternatives, when there is a cycle there is no choice among them. Life goes on and a selection has to be made, true enough. But is the selection “rational” according to well established criteria? It can’t be. There is no rational selection. It doesn’t exist.
One sometimes hears the expression, “you have no choice.” But that really means there is one and only one available alternative. Similarly, there is a Hobson’s Choice, where there are two alternatives, the other being the status quo. We have language for those cases, even if the language doesn’t quite match up with axiomatic choice theory.
We don’t really have language for the case where there are cycles. We talk about “making the tough choice” but the issue is typically not that there are cycles, but rather that there are both upside and downside consequences in a binary choice setting.
The paucity of language to describe the situation notwithstanding, I think we face cycles in a lot of settings that are of concern to Learning Technologists. Consider this little scenario, cooked admittedly, but not without realism.
There are three alternatives:
x) Faculty Member uses online materials from Publisher via Publisher hosting and no contract with publisher.
y) Campus writes a contract with Publisher for Publisher hosted content on behalf of all faculty members on Campus.
z) Campus insists that all content possibly involving student grades must reside on Campus hosted Course Management System. Publisher content must be put there, if it is to be utilized.
And then, suppose there are three criteria by which to rank the alternatives:
  1. Security
  2. Academic Freedom
  3. New Partnerships Model
Further suppose that by each individual criterion alone the rankings are straightforward and are of the form:
1) First z, then y, and last x.
2) First x, then z, and last y.
3) First y, then x, and then last z.
Each criterion has a well established ordering of the alternatives but the different criteria disagree as to which is preferred. The question is how to aggregate the criteria. One might impose some further notion, such as fairness, so that none of the criteria are entirely abandoned. One possibility, would be to use Majority Rule. With the above one gets:
zMy, yMx, but xMz,
in other words, a cycle. Technically, there is nothing new here. It is well known that Majority Rule can produce cycles when there are 3 candidates and, indeed, this indirectly is an argument for a two party system. Further, Arrow’s Impossibility Theorem tells us Majority rule is not special this way. There is no rule that produces a satisfactory result for all possible rankings What may be new here, however, is to take this known result and apply to how we make decisions in an IT world.
Standard practice in doing an IT procurement is to first gather requirements prior to choice of product. Each requirement is analogous to the criterion in the above example. Then the various products under consideration are ranked separately by each requirement. Then somehow the results are tallied and aggregated and a choice is made. This can definitely produce cycles, particularly if there is not one product that shines above the rest.
Political scientists have understood the issues with cycles for some time. The power of a committee chair rest in large part from being able to set the agenda and thereby knock off some of the competition early on through preliminary votes. Sometimes we do something similar with IT procurement, where we make certain criteria mandatory. For example, back in late 2002 when we did the Campus RFP for a learning management system, we required the back end to be Unix/Oracle. We did get two bids, one from Blackboard and the other from WebCT. But a potential third bid from Angel was not forthcoming because they were Windows/SQL. At the time, nothing else in the Angel offering could offset that requirement, though in retrospect I think we should have looked at them more seriously, so our faculty and instructional designers could consider their functionality.
The problem with mandatory criteria is to rationalize why some items are in that category while others are only strongly preferred. As it turns out, we based our RFP in part on the RFP written by the Wisconsin System. Ironically, they ultimately went with Desire2Learn, a different Windows/SQL system. Obviously, at some point Wisconsin backed away from the mandatory nature of the Unix/Oracle requirement.
Cycles are becoming more prominent for me now, in my job in the College of Business. I’m confronting the following decision regularly. There is some category of software. That campus might very well provide a flavor in that genre. An alternative possibility is for my College to host a different flavor. A third possibility is to outsource the service. Among the criteria that are important for us in considering these options are Usability and Functionality for students and faculty, Budget, Security, and, for the within College hosting, whether we have the requisite expertise to support the service.
When there are cycles the status quo trumps new entrants. I think we see a lot of that on campus. It translates as inertia. We also see failure to communicate openly on issues of this sort. Is that because other folks recognize the lack of transitivity and are trying to keep the problem under wraps? I don’t know. It sure would be nice to find a Learning Technology initiative we all could embrace.