I liked Bill Keller's column today, a snip of which is below. There is a sort of Gresham's Law for economists in the Internet era. The bad drives out the good. It's definitely true and an important point.
Yet paying attention only to the good economists is not enough. There are questions about the economic morass that economists normally don't dwell on too much. One is about fairness. Another is about obligation. Should we take Thoreau as a model? When we consult our consciences they may suggest that is the right path. But truthfully, if I can use myself as a case in point, I don't want to live in the woods and I don't think I'm capable of that.
Even with that admission, however, there's probably a lot more my family can do without, some of which we pay for directly out of our pockets. So I, for one, wouldn't mind if the Bush tax cuts expire for people in my tax bracket. Our marginal rate is 28%. If it were the year 2000 regarding tax brackets for everyone, but our income was as it is in 2011, our marginal rate would be 36%. We would need to adjust to that, but we could. (I did a quick calculation of the difference in tax owed under this scenario assuming an AGI of $180,000. I don't know what our AGI is, but I'm guessing we're in that ballpark. In that calculation the taxes increase by almost $7,000.)
I had thought that if there were enough like-minded people at around the same level of income that making that known would shame those at higher income levels to also be willing to contribute that much more. I still wish that to be true. It is why there is this Facebook group, For a More Compassionate and Saner America. But that group didn't grow like weeds, as I originally hoped. Occupy Wall Street has been infinitely better at capturing people's attention and raising the issues of unfairness and income inequality in our society.
So in this post I would like to show solidarity with that movement. And beyond that I'd like to suggest resolution of the big economic issues, as they make sense to me, where the economic issues are tied to the ethical issues, the increase in the income tax for people who can afford it an example of what I have in mind.
Debt Forgiveness
The Right is captivated by the magnitude of the National Debt and the fear that it will bury us, or bury our children, or bury our children's children. There is some basis for that fear, but not in the way it is depicted by the Right. However, there is another problem that has been well aired over the last several months, which we in the ten percent can do something about more immediately. This regards privately held debt, particularly with respect to housing and in student loans. Some fraction of the principal needs to be absorbed by the taxpayer, as long as the loan satisfies certain criteria. The economist Ken Rogoff has recommended a general inflation to address the problem (inflation reduces the value of the debt in real terms), because he doesn't believe a more direct solution is politically feasible. We should go for that direct solution and recognize that those who can fund it will shoulder a good chunk of the burden.
In the case of housing, the criteria should include: fraction that the house is under water, number of periods that the mortgage has been delinquent, past and current income of the debtor. The most troubled loans, those nearest to foreclosure, should be targeted first, provided the occupants do have a decent source of income. The aim of the program is that after forgiveness and a refinancing of the mortgage to current low rates, the occupants should be able to stay in the home and make future payments. It makes no sense to forgive debt only to then have subsequent default, as I wrote here.
In many cases the income requirement won't be met. What then? There has been a fair amount of discussion that many of these current borrowers should in the future become renters and leave the issue of paying off the mortgage to the landlord. I would like to see the arithmetic on this regarding how the likely rents compare to current mortgage payments. And I would like to know: what will keep the rents modest over time? So I have my doubts that a move to a rental model alone solves the problem. Maybe it does, but I'd like to see the analysis. At the link I provided there is an analysis from the perspective of investors who purchase underwater mortgages and convert those units to rental properties. We need an analysis from the perspective of the current occupants.
I should point out here that this is why a jobs program is so important. The jobs issue and the housing debt issue are tied at the hip. It's why I can't understand not attempting a latter day version of the WPA. In turn, there seems to be some consensus for a Federal Investment Bank, which would oversee and provide financing for such projects. Sure, making private sector jobs would be a good thing. But, clearly, that's not happening fast enough. Let's make public sector jobs in the meantime, as many as we can, and keep doing so till until the economy recovers.
It also needs to be admitted, up front, that a debt forgiveness program will not preclude foreclosures entirely. That shouldn't be the aim of such a program. Rather the aim should be twofold. First, the goal is to keep as many current occupants in their home as is possible. Second, troubled assets on bank balance sheets need to be resolved. In some cases the resolution will be by some forgiveness financed by taxpayers and new smaller loans replacing the trouble loans that should be healthy. In other cases there will be foreclosure and mortgage holders will have to write down the value of those assets. Clearing up the bank balance sheets should loosen credit for small business and those seeking mortgages in the future. The tightness of the credit market for such borrowers has been a major impediment to economic growth.
Turning to students loans, for those covering tuition and fees at accredited not-for-profit institutions, a partial forgiveness program is in order. The program should be targeted at students of modest income and, if below age 26, those whose parents are also of modest income. This would be a near term solution to the hyperinflation in tuition issue that as a result means high quality education is no longer accessible by students of modest means. It would serve as a prelude to a longer term solution, that needs to keep costs in check while keeping quality of education high, at least for qualified students of modest income. As health care reform was the target of the first Obama administration, higher education reform surely will be the target of future administrations. There is not a quick and dirty solution to this. Elsewhere I suggested that a salary cap system might be in order. But nobody else seems to be talking about that so it is not in the offing.
Loans should not be forgiven at all for people who could have self-financed their education but took the loans simply because payments could be deferred till after graduation. So the means testing on such a program is important.
A different but related issue regards predatory practices of some for-profit higher education institutions that admit unqualified students who are eligible for federally sponsored student loans and grants. There is a piece in Wednesday's Chronicle of Higher Education on the issue. That piece refers to this GAO report. Even if the students are the victims of these predatory practices, having their hopes raised only to eventually drop out or get a diploma mill degree that has no value on the job market, loan forgiveness is not the right solution here. That would be like pouring fuel on a fire. Better to go after these institutions hard, force them to pay heavy fines and/or rebate tuition they have already received. The predation needs to come to an end. As much as we might feel sympathy for the victims, our remedies should not prolong the problem.
Entitlement Reform
There are two distinct issues at root that need to be addressed. The first is the increase in life expectancy, especially for those who've done white collar work. This means that current beneficiaries receive their benefits over a longer period of time than beneficiaries 70 years ago. The system needs to be recalibrated as a consequence. The second is that there is confusion on whether the primary purpose of these programs is as insurance against low income when people retire or if it is meant as a payback for contributions made while working, irrespective of the person's income. There is a third concern that is more of an accounting matter, but I raise it here because it has influenced discussion of the programs in the political arena. The issue is whether each program must balance receipts and expenditures or if balance needs to happen only overall, i.e., a balanced federal budget but where individual programs may run surplus or be in deficit.
Social Security and Medicare are actually quite different on these fronts. Social Security is near to in balance and does act like an income insurance program. Depending on when the individual retires, there is an income limit where if income exceeds the limit social security benefits are reduced on a fractional basis for each additional dollar earned. This is precisely how an income insurance program should work.
There are three possible controls to adjust in the recalibration process on Social Security. (I'm assuming no adjustments are made to benefits.) First is the tax rate; second is the maximum income subject to taxation; and third is the retirement age. Because of the income insurance aspect of Social Security, if you work sufficiently while above the retirement age, you will receive no Social Security benefit. For this reason I favor leaving the retirement age as is, with the following caveat. The applicable income limit currently applies to wage income. Dividends and capital gains are not included in the calculation. They should be.
The Social Security tax is a flat tax - up to the limit. The rate applies to employees and then again to employers. Self-employed individuals pay both the employee and employer shares. Raising the rates would put a hardship on lower income earners. That is a bad idea.
A better adjustment, in my view, would be to raise the income limit rather substantially. If high income earners do live longer, they should contribute more. This type of adjustment would do that. It also is in accord with the idea that those who can afford it do pay more in taxes to help out those who are less well to do. So this is also a matter of fairness.
Medicare is a different animal, in large part because while working most people get their health insurance through their employer. Not discussed very often, but something that is frightening about Republican proposals on Medicare reform, particularly the Ryan proposal, is that both employer provided health care and Medicare as it is currently constituted is not experience rated according to the health history of the insured. Premiums that are collected from employers as well as the employee contribution are tied only to the average health risk of all those insured. Likewise, this is true for Medicare. Contributions depend on income, but not on health history.
A private market, however, will price health insurance based on perceived risk, and the individual's health history clearly matters for this. This makes health insurance unaffordable for those who've been in bad health. It is why single payer, something we should have but don't, is preferred. One of the unfortunate aspects about the political rhetoric in the time immediately before the Affordable Care Act was enacted, is this Market for Lemons aspect of health insurance was not brought to light. Alas, we won't have single payer and in what I write in the next few paragraphs, I assume single payer is not possible to address the issues.
Medicare is much more out of balance than Social Security. With Medicare, the hyperinflation of health care costs exacerbates the issues created by longer life expectancy. So much of the solution will rest on controlling health care expenditure, particularly near end of life. It will also be about controlling income of health care service providers. Both of those issues have been discussed elsewhere, so I won't repeat that discussion here. Instead I will discuss something that hasn't gotten any attention but should. The revenues needed to support Medicare are inadequate. Those revenues need to be enhanced.
Unlike Social Security, there is no income limit on the Medicare component of FICA. But the Medicare tax rate is less than one quarter of the Social Security tax rate. Either Medicare rates must go up or additional taxes must be raised for Medicare from a different source. The question is how to do this without over burdening people with modest incomes.
I favor two different ideas to address the the revenue shortfall issue. First, working people who do get employer provided health insurance, even if they make a direct contribution to that heath insurance, should be required to treat the employer contribution as income for tax purposes and pay income taxes on it that are returned to the Medicare trust fund. There are several reasons for this. Employees may be less than fully aware even of their own contribution to health insurance because that is something that is withheld from their paycheck at first. They never receive the income and don't explicitly write a check to cover their own contribution. Employees have no obvious way of learning the magnitude of the employer contribution. One clear way to do this would be to have that amount reported on W-2 forms. Further, employees would become sensitized to the full cost of their health insurance, by paying income taxes on the employer contribution. Then there is the fact that currently the Medicare tax is a flat tax, but this way the employer contribution would be taxed differently depending on the individual's marginal tax bracket. This idea will raise eyebrows. It may seem like a step back from the social contract. But given the imbalance, it is necessary.
Second, historically there has been a separation between payroll taxes and income taxes, with only the former used to finance Medicare. The first idea is beginning to eliminate that separation. It is not sufficient in itself. The second idea is to further use the income tax to help finance Medicare, perhaps raising marginal tax rates beyond the Clinton rates, if necessary. In this way adequate revenue can be raised to pay for Medicare. It also means, in particular, that senior citizens who generate sizable income will continue to pay for Medicare, well after they have "retired." It may mean that we stop using the word "entitlement," which I believe has taken on a pernicious connotation, as if there is a right to health care without having to pay for it. In our society as a whole, we have to own up to the fact that the benefits need to be paid for.
Means Testing
There are three points I'd like to make here. First, the extended family needs to provide some self-insurance for family members. An example, currently being discussed, is that many college grads who have been unable to find a job have gone back home to live with mom and dad. As a partial explanation for why the economy is not growing faster, this is of course bad news. The demand for housing, in particular, is less as a consequence. But from a social insurance perspective, this is very good news. When things are bad family members should take care of each other, if they can. This means that when government benefits are means tested it is really income of the extended family that should be measured. When one generation is well to do while another is not, the source of social insurance should be from within the extended family, not from the government.
Second, there needs to be self-insurance by individuals done over time. The traditional vehicle for doing this is via personal savings. The low saving rate in our society makes people particularly vulnerable to hard luck. A higher saving rate should be encouraged. One way to do this would be to instead of using current income only as a measure of means, use a 5-year moving average of income as a preferred measure, as I suggested here. When incomes are rising, this means the person's taxes rise less quickly than income, so there is an ability to save the residual. It also means, however, when incomes are falling the person is on the hook for obligations and can anticipate that, even as income falls. This provides a motive for the precautionary savings.
Third, means testing may very well become a two-sided concept in the future, where if income inequality persists to the extent it does now, then those above a certain income threshold find themselves facing an imposed obligation that the rest of us don't face. This obligation would be something like a charitable contribution, but with the difference that the giver doesn't get to specify the use. Here I'm thinking in particular of funding public schools, where the property tax mechanism almost guarantees there won't be decent schools for all, so that too many low income students are denied a decent education. This fact itself is eroding the notion we call the American Dream. Why have this sort of means testing rather than make the income tax system more progressive? The answer is that the current arrangement has tax collection severed from how tax revenues are spent, with Congress responsible for the latter. There are very few of us who believe Congress has acted responsibility with respect to its spending authority. And the current process is fraught with problems due to lobbying, so the rich get to manipulate how tax revenues are spent for their own benefit. The proposed solution then is to carve out some areas of spending, public education is a very good place to start, and obligate those who are above the income threshold to help make the system better and more equal.
Conclusion
I would like to see more mainstream economists make their policy recommendation based on a mixture of economics orthodoxy and ethical considerations. Whether left or right, I believe this would bring us closer to consensus on what we should be doing. There is a tendency for economists to eschew the ethical issues - that's not their department. The biggest lesson we can learn from Occupy Wall Street is that we must deal with the ethical issues squarely, as we look for economic solutions.
Monday, November 28, 2011
Saturday, November 19, 2011
Math as a gateway to creativity
The operative questions in this post are two. First, can we teach all students math in the way we teach elite students math? Second, if we can, why don't we?
Math can be about intuition and the spark from an idea that has potential. Math can also be drudge, slugging through a lot of notation that is not enlightening, perhaps learning algorithmic procedures with no other motivation to do so other than that it will be on the test. One might think there is a clear division between the two, though I believe otherwise. While on occasion results may appear immediately to the bright student, verification is a staged procedure and one needs to work through the steps. More often, even the bright student discovers the result only after working through several preliminary results. The intuition is at hand at the beginning, to suggest this is a good path to try. Or the intuition may appear only after some faulty alternatives have been attempted. Elite students learn this linking between spark and process and develop intellectual confidence this way. If it is well learned it becomes enjoyable to do and the student wants to continue to employ the approach even in non-math pursuits. One reason I like to write blog posts is that the exploration of ideas that appear as I compose, Donald Murray calls it writing to learn, feels like working a math problem, as does the pre-writing I do before getting to the keyboard.
In the nature/nurture debate about what drives individual performance, I don't want to rule out the nature component entirely, but here I do want to focus on the nurture bits. I was an elite math student and I will use my recollections to illustrate, both how that came about and the advantages that education conferred. Much of this happened outside of regular math classes, either in entirely social situations or in academic situations that were available only to elite students.
The earliest memories are from grade school and I have two distinct ones that come to mind. Students who bought the hot lunch ate in the cafeteria. Students who brought their lunch ate in the auditorium. I don't recall which grade this was but I sat together with a few classmates in the auditorium and one of them would quiz the rest of us as follows. x plus y equals some number. x minus y equals some other (smaller) number. What are x and y? We did these for the fun of it only, at least as far as I could tell. And I was definitely a follower here. I don't remember what got me to sit with these boys, nor what drove the leader to ask these questions. But what is obvious to me now is that this social interaction was early preparation for algebra, which I take makes for a stumbling block for many kids. For me it was a breeze.
The other memory is of my sister getting tutoring at home. She is five years older than I am and so was many grades ahead of me. The way our house was set up, the logical place for the tutoring session was in the dining room, which we otherwise didn't use too often. Sometimes I would sit in the living room and listen to the tutoring. For a while this was science tutoring. Later it was math tutoring done by a different tutor. I don't remember specific math I picked up this way, but it was again early exposure to things I would see later.
Perhaps the bigger deal is that the math tutor was Mrs. Joffe, who would become my eighth grade math teacher. When I was in her class she remembered me from earlier and was insightful enough and kind enough to suggest I join the math team. I wouldn't have done this on my own. At the time I thought of myself as a social studies guy. (My dad was a lawyer.) The school had some current events magazine that I did join myself as an extracurricular activity. Some of the other kids on the math team had done it in seventh grade too (and I recall them eventually going to Bronx High School of Science, even though it was a schlep from where we lived in Bayside).
The math team was a world unto itself, with a culture of its own and a linkage to people who were a year ahead of me in school. (My school was converting from a junior high school to an intermediate school. So I graduated from there after eighth grade. The other school we had our math meets with was still a junior high school at the time.) This exposure to bright kids a year ahead indirectly is like getting a big gold star. It really conveys a sense that you belong there and creates an expectation that you should follow a similar path to what these people were doing. Also, the math team established for me a connection between doing math and playing chess, which would become important in high school.
I next did math team in eleventh grade, with the coach my ninth grade math teacher, Mr. Conrad. Ultimately, I took two other classes from him, analytic geometry and trig, which most college bound students take, and math team workshop, a specialty class aimed at preparing us for the competitions and for working exotic problems. Near the end of one marking period, I recall playing him a game of Twixt for my course grade in the math team workshop. I'd get a 90 if I won but only a 75 if I lost. Not that long ago I found this Math League Web site. My teacher was one of the co-founders of Math League. So I contacted him via that site and asked if he recalled the Twixt game. He did and said he didn't pull any punches in playing me. He was a tournament bridge player and quite competitive about these sort of games. By the way, I did get a 90 in the class.
Prior to and during math team there was another activity that was similar, but not done in a timed way, called the Problem of the Week. A non-typical algebra or geometry problem was posted on the bulletin board outside the Math Department office. Students were invited to submit their proposed solution. This was done for the fun of it, not for the credential. Doing these, in my view, is similar to working a very hard Sudoku. The procedure to solve the problem is not automatic. One has to discover it. My favorite one of these that I recall is the modified donkey theorem. Two triangles are congruent if angle, side, side, equals angle, side, side as long as angle is the largest angle of the triangle.
How does one go about proving such a result? There is a trick, of sorts. Someone on the math team is apt to figure this out on his own but many other students would not, because it simply wouldn't occur to them to do this. The trick is to draw the triangles adjacent and sharing a common side (one of the sides that are equal). It turns out that using the side that is opposite that largest angle is what you want. That's not a full construction, but it is enough that a bright student should be able to figure out the rest. I've written a chapter of my book Guessing Games entitled Guessing in Math that argues students should be taught to work such problems. Many people should be able to do so. Alas, those who see math only as a drudge would view such a goal as outside their capabilities or as a painful thing to do, rather than a reward in itself, which it rightfully is.
I suppose many people hit a wall with math. They find themselves in a class that seems over their head and don't feel comfortable about working through their difficulties, with no confidence that they can put in sufficient effort to overcome their lack of understanding. I first experienced this sort of thing at the HCCSIM, the Hampshire College summer program in math. I was a member of their very first cohort, forty years ago. I took a class in number theory/abstract algebra done in an intuitive way sans textbook. The program was for six weeks. For the first two weeks or so I was doing fine in this class and keeping up with the daily homework. But by week three I started to find it difficult and didn't know what to do about it, so floundered thereafter. I don't believe I was alone in this. There were three or 4 geniuses in the class and a few others who were keeping up even at the end, but the rest of us were not treading water. During the last two weeks of the program I took a class on probability, which was more do-able.
Looking back at the time I think there were two things going on that explain the trouble. First, abstract algebra for me was not as much fun as geometry, because with the algebra I didn't yet have the mental equivalent of drawing pictures, so we were taught some structure without much intuition. There was some intuition - doing arithmetic modulo a prime number gives an example of a non-ordered field - but in other cases there wasn't. I don't know if I first heard this at Hampshire or only later in college taking abstract algebra, but there was encouragement to not rely on the examples because they might include features that don't generalize. That proved hard for me. I wanted the examples. Previously I had found most math fairly immediate. This was the first instance where I didn't.
The other thing was how the day was scheduled and not putting in enough time to make up for my shortcomings. Mornings were filled with class. In the afternoon you could do your homework. But it was good to get some physical activity and I often played tennis in the afternoon and there was a very popular volleyball game after dinner. Later in college I learned that figuring things out takes as long as it takes. Sometimes that can be quite a while. Hitting a wall may make you less inclined to put in the time, though I think in my case then I simply didn't understand it was necessary.
Nonetheless there were some very large positives from the Hampshire experience. It gave a much better sense of what would be next academically, much more so than high school ever could. One of my college roommates at MIT, Neil, also was in the Hampshire program. (Our other roommate was from Jamaica High School, where my mother taught; she introduced us.) It's much easier going away to college already knowing some people there before you start.
Each of us had some math inclination. We took a few classes together. MIT at the time offered some special topics courses for freshmen that were for half the credit of a regular course. We took one on Calculus Theory, taught by A.P. Mattuck, which developed our intuitions about infinite series. At the start of this class Neil was ahead of me in figuring out things. I believe that by the end of the course I had caught up. It was the first time taking a class where I was aware of my own growth in understanding things at a deeper level, the first class where my intuition noticeably improved. We took another course from Mattuck the next semester - linear differential equations. This is Mattuck 33 years later giving the first lecture in the regular differential equations class. He was a wonderful and dedicated teacher.
I started to have some emotional problems sophomore year and in the math classes I took then - abstract algebra and analysis - I found myself in a situation similar to what I had experienced in Hampshire. I had a strong feeling of needing to get into a different environment, one where there was more diversity of interest. At MIT I was too much like everyone else. I ended up transferring to Cornell for the second semester. I still was a math major there, but math occupied a smaller part of my life.
I did eventually did learn how to break through the wall in a topology class taught by George Cooke. One factor in this breakthrough clearly was his teaching and the high motivation he provided. I found his problem sets very intriguing. He didn't use a textbook at all and in class he encouraged us to talk our way through the abstract concepts, our imprecision with language a demonstration that we did not yet fully understand what we were being taught. Another factor was that I did this course entirely on my own, not knowing the other students in the class ahead of time and doing the problem sets in isolation. A third factor was that I was not overwhelmed by other school work so over the weekend I could put in a full day of thinking through the homework and doing only that. And a fourth factor was the prior experience. I believe the earlier failure was fully necessary for this later success.
When I went to graduate school at Northwestern in economics, after having very little economics at Cornell, I felt an enormous deficiency in background relative to my classmates. I was determined to make that up and worked harder than I had ever done previously during that first quarter at NU. Spending most evenings in the reserve room of the Library till at least 9 pm, I did learn I was capable of making such an intensive commitment. Yet I soon became aware that I was better prepared than most of my classmates. I could think about the economics deeply, because that's how I had been trained to think about the math.
Indeed it is because math thinking is such good preparation for other thinking that I believe we should make effective math thinking a primary goal in our education system. I'm not talking about how well students do on the math SAT or other standardized tests they take earlier in their school careers. I'm talking about whether students can creatively find the right path to solve a complex math problem. Because the SAT is essentially a speed test it can't possibly measure the ability to find a path that will only be uncovered after hours of thought. At best it can test whether a path can be found in under a minute. Certainly that is better than not finding the path at all, but this notion that path finding is always a quick hitter activity is pernicious. It is much better to know whether the student will persist till the path is found. The SAT doesn't measure persistence at all.
In teaching the student we should be encouraging that sort of effort. Elite students receive that encouragement, in a variety of different ways. Can't we find at least some ways to offer it to the rest?
Math can be about intuition and the spark from an idea that has potential. Math can also be drudge, slugging through a lot of notation that is not enlightening, perhaps learning algorithmic procedures with no other motivation to do so other than that it will be on the test. One might think there is a clear division between the two, though I believe otherwise. While on occasion results may appear immediately to the bright student, verification is a staged procedure and one needs to work through the steps. More often, even the bright student discovers the result only after working through several preliminary results. The intuition is at hand at the beginning, to suggest this is a good path to try. Or the intuition may appear only after some faulty alternatives have been attempted. Elite students learn this linking between spark and process and develop intellectual confidence this way. If it is well learned it becomes enjoyable to do and the student wants to continue to employ the approach even in non-math pursuits. One reason I like to write blog posts is that the exploration of ideas that appear as I compose, Donald Murray calls it writing to learn, feels like working a math problem, as does the pre-writing I do before getting to the keyboard.
In the nature/nurture debate about what drives individual performance, I don't want to rule out the nature component entirely, but here I do want to focus on the nurture bits. I was an elite math student and I will use my recollections to illustrate, both how that came about and the advantages that education conferred. Much of this happened outside of regular math classes, either in entirely social situations or in academic situations that were available only to elite students.
The earliest memories are from grade school and I have two distinct ones that come to mind. Students who bought the hot lunch ate in the cafeteria. Students who brought their lunch ate in the auditorium. I don't recall which grade this was but I sat together with a few classmates in the auditorium and one of them would quiz the rest of us as follows. x plus y equals some number. x minus y equals some other (smaller) number. What are x and y? We did these for the fun of it only, at least as far as I could tell. And I was definitely a follower here. I don't remember what got me to sit with these boys, nor what drove the leader to ask these questions. But what is obvious to me now is that this social interaction was early preparation for algebra, which I take makes for a stumbling block for many kids. For me it was a breeze.
The other memory is of my sister getting tutoring at home. She is five years older than I am and so was many grades ahead of me. The way our house was set up, the logical place for the tutoring session was in the dining room, which we otherwise didn't use too often. Sometimes I would sit in the living room and listen to the tutoring. For a while this was science tutoring. Later it was math tutoring done by a different tutor. I don't remember specific math I picked up this way, but it was again early exposure to things I would see later.
Perhaps the bigger deal is that the math tutor was Mrs. Joffe, who would become my eighth grade math teacher. When I was in her class she remembered me from earlier and was insightful enough and kind enough to suggest I join the math team. I wouldn't have done this on my own. At the time I thought of myself as a social studies guy. (My dad was a lawyer.) The school had some current events magazine that I did join myself as an extracurricular activity. Some of the other kids on the math team had done it in seventh grade too (and I recall them eventually going to Bronx High School of Science, even though it was a schlep from where we lived in Bayside).
The math team was a world unto itself, with a culture of its own and a linkage to people who were a year ahead of me in school. (My school was converting from a junior high school to an intermediate school. So I graduated from there after eighth grade. The other school we had our math meets with was still a junior high school at the time.) This exposure to bright kids a year ahead indirectly is like getting a big gold star. It really conveys a sense that you belong there and creates an expectation that you should follow a similar path to what these people were doing. Also, the math team established for me a connection between doing math and playing chess, which would become important in high school.
I next did math team in eleventh grade, with the coach my ninth grade math teacher, Mr. Conrad. Ultimately, I took two other classes from him, analytic geometry and trig, which most college bound students take, and math team workshop, a specialty class aimed at preparing us for the competitions and for working exotic problems. Near the end of one marking period, I recall playing him a game of Twixt for my course grade in the math team workshop. I'd get a 90 if I won but only a 75 if I lost. Not that long ago I found this Math League Web site. My teacher was one of the co-founders of Math League. So I contacted him via that site and asked if he recalled the Twixt game. He did and said he didn't pull any punches in playing me. He was a tournament bridge player and quite competitive about these sort of games. By the way, I did get a 90 in the class.
Prior to and during math team there was another activity that was similar, but not done in a timed way, called the Problem of the Week. A non-typical algebra or geometry problem was posted on the bulletin board outside the Math Department office. Students were invited to submit their proposed solution. This was done for the fun of it, not for the credential. Doing these, in my view, is similar to working a very hard Sudoku. The procedure to solve the problem is not automatic. One has to discover it. My favorite one of these that I recall is the modified donkey theorem. Two triangles are congruent if angle, side, side, equals angle, side, side as long as angle is the largest angle of the triangle.
How does one go about proving such a result? There is a trick, of sorts. Someone on the math team is apt to figure this out on his own but many other students would not, because it simply wouldn't occur to them to do this. The trick is to draw the triangles adjacent and sharing a common side (one of the sides that are equal). It turns out that using the side that is opposite that largest angle is what you want. That's not a full construction, but it is enough that a bright student should be able to figure out the rest. I've written a chapter of my book Guessing Games entitled Guessing in Math that argues students should be taught to work such problems. Many people should be able to do so. Alas, those who see math only as a drudge would view such a goal as outside their capabilities or as a painful thing to do, rather than a reward in itself, which it rightfully is.
I suppose many people hit a wall with math. They find themselves in a class that seems over their head and don't feel comfortable about working through their difficulties, with no confidence that they can put in sufficient effort to overcome their lack of understanding. I first experienced this sort of thing at the HCCSIM, the Hampshire College summer program in math. I was a member of their very first cohort, forty years ago. I took a class in number theory/abstract algebra done in an intuitive way sans textbook. The program was for six weeks. For the first two weeks or so I was doing fine in this class and keeping up with the daily homework. But by week three I started to find it difficult and didn't know what to do about it, so floundered thereafter. I don't believe I was alone in this. There were three or 4 geniuses in the class and a few others who were keeping up even at the end, but the rest of us were not treading water. During the last two weeks of the program I took a class on probability, which was more do-able.
Looking back at the time I think there were two things going on that explain the trouble. First, abstract algebra for me was not as much fun as geometry, because with the algebra I didn't yet have the mental equivalent of drawing pictures, so we were taught some structure without much intuition. There was some intuition - doing arithmetic modulo a prime number gives an example of a non-ordered field - but in other cases there wasn't. I don't know if I first heard this at Hampshire or only later in college taking abstract algebra, but there was encouragement to not rely on the examples because they might include features that don't generalize. That proved hard for me. I wanted the examples. Previously I had found most math fairly immediate. This was the first instance where I didn't.
The other thing was how the day was scheduled and not putting in enough time to make up for my shortcomings. Mornings were filled with class. In the afternoon you could do your homework. But it was good to get some physical activity and I often played tennis in the afternoon and there was a very popular volleyball game after dinner. Later in college I learned that figuring things out takes as long as it takes. Sometimes that can be quite a while. Hitting a wall may make you less inclined to put in the time, though I think in my case then I simply didn't understand it was necessary.
Nonetheless there were some very large positives from the Hampshire experience. It gave a much better sense of what would be next academically, much more so than high school ever could. One of my college roommates at MIT, Neil, also was in the Hampshire program. (Our other roommate was from Jamaica High School, where my mother taught; she introduced us.) It's much easier going away to college already knowing some people there before you start.
Each of us had some math inclination. We took a few classes together. MIT at the time offered some special topics courses for freshmen that were for half the credit of a regular course. We took one on Calculus Theory, taught by A.P. Mattuck, which developed our intuitions about infinite series. At the start of this class Neil was ahead of me in figuring out things. I believe that by the end of the course I had caught up. It was the first time taking a class where I was aware of my own growth in understanding things at a deeper level, the first class where my intuition noticeably improved. We took another course from Mattuck the next semester - linear differential equations. This is Mattuck 33 years later giving the first lecture in the regular differential equations class. He was a wonderful and dedicated teacher.
I started to have some emotional problems sophomore year and in the math classes I took then - abstract algebra and analysis - I found myself in a situation similar to what I had experienced in Hampshire. I had a strong feeling of needing to get into a different environment, one where there was more diversity of interest. At MIT I was too much like everyone else. I ended up transferring to Cornell for the second semester. I still was a math major there, but math occupied a smaller part of my life.
I did eventually did learn how to break through the wall in a topology class taught by George Cooke. One factor in this breakthrough clearly was his teaching and the high motivation he provided. I found his problem sets very intriguing. He didn't use a textbook at all and in class he encouraged us to talk our way through the abstract concepts, our imprecision with language a demonstration that we did not yet fully understand what we were being taught. Another factor was that I did this course entirely on my own, not knowing the other students in the class ahead of time and doing the problem sets in isolation. A third factor was that I was not overwhelmed by other school work so over the weekend I could put in a full day of thinking through the homework and doing only that. And a fourth factor was the prior experience. I believe the earlier failure was fully necessary for this later success.
When I went to graduate school at Northwestern in economics, after having very little economics at Cornell, I felt an enormous deficiency in background relative to my classmates. I was determined to make that up and worked harder than I had ever done previously during that first quarter at NU. Spending most evenings in the reserve room of the Library till at least 9 pm, I did learn I was capable of making such an intensive commitment. Yet I soon became aware that I was better prepared than most of my classmates. I could think about the economics deeply, because that's how I had been trained to think about the math.
Indeed it is because math thinking is such good preparation for other thinking that I believe we should make effective math thinking a primary goal in our education system. I'm not talking about how well students do on the math SAT or other standardized tests they take earlier in their school careers. I'm talking about whether students can creatively find the right path to solve a complex math problem. Because the SAT is essentially a speed test it can't possibly measure the ability to find a path that will only be uncovered after hours of thought. At best it can test whether a path can be found in under a minute. Certainly that is better than not finding the path at all, but this notion that path finding is always a quick hitter activity is pernicious. It is much better to know whether the student will persist till the path is found. The SAT doesn't measure persistence at all.
In teaching the student we should be encouraging that sort of effort. Elite students receive that encouragement, in a variety of different ways. Can't we find at least some ways to offer it to the rest?
Thursday, November 17, 2011
Myths and their propogation
The following is from a piece in September when a Republican, Bob Turner, won the Congressional seat vacated by Anthony Weiner. Since the seat is in a heavily Democratic district, it was viewed as a stunner. One of the issues that mattered was Israel.
Ehud Barak was on Charlie Rose a couple of nights ago. Barak currently is the Israeli Defense Minister. He had previously been Prime Minister. After the beginning of the conversation which dealt with Iran, eventually (at around the 13:00 minute mark) the discussion turns to Israeli-Palestinian issues. Barak makes a point of offering very strong support for the Obama administration on security issues. How can that be, given the perception that Obama is soft on Israel? A couple of weeks after that Congressional election Ed Koch changes his mind and supports Obama. But the myth of Obama being soft on Israel persists. Gossip travels fast. Presidential candidates from the other party benefit from the myth being believed. Here's a comment about this from Mitt Romney and one from Rick Perry.
* * * * *
I suppose because Penn State has been in the news so much it occurred to me to watch That Championship Season, a Pulitzer Prize winning play that I saw in New York in the 1970s, but where much of the specifics of the story I had forgotten. I downloaded the 1999 made for TV version. Paul Sorvino plays the retired coach who is dying from cancer. He also directed the movie. Apparently, he has quite a connection to the play, having been in the original stage version as well as an earlier movie version where Robert Mitchum played the coach. The other main characters are four out of the starting five that won the Pennsylvania High School Basketball Championship twenty years earlier. The fifth starter, who is mentioned in name only, has made none of the reunions since. The viewer finds out why only near the end of the movie.
The movie is not uplifting but it makes a powerful point. Clinging to myth when one knows it to be untrue is destructive. Each of the main characters lives in a world of denial, misperceiveing reality, filled with emotional pain, trying to pretend things are better than they actually are. They are strangely dependent on each other, the basketball championship supposedly form a deep and everlasting bond. But they are also antagonistic to each other. Scranton is a small enough town that three of the four former players continue to have ongoing business and social relationships that are a source of tension. Much of the truth comes out as they betray each other during the reunion at the coaches house. The fourth player is a brother of one of the other three and a lush, presumably drink the only refuge he could take given the truth of the past. It his cynicism and demand that myth not triumph by which we ultimately learn that they won the Championship over the much favored team by deliberately injuring their best player. Unlike in the Karate Kid, where Daniel Larusso ultimately wins the tournament even after he has been severely injured because one of his nemeses has "swept his leg," in a deliberate attempt to hurt Daniel, in That Championship Season the cheaters prosper insofar as they win the championship. They suffer, however, for the rest of their lives.
I wonder if it would be helpful for the Penn State faithful to watch this movie. When one believes in myth very strongly and for a long period of time and then one is confronted with facts that put the lie to those beliefs, there is a tendency to ignore the facts. It is painful to have to change one's world view to accommodate the truth. But it is more painful to live a lie, particularly when it is not possible to bury the issue. Today the Times has a long piece about a possible coverup and CNN also has long piece, this one focusing on the mother of one of the alleged victims, who fears that Sandusky may get off. This story won't go away for quite a while.
* * * * *
There is a huge myth about big government and high taxes being a block to economic growth. Tom Friedman's column earlier this week, which is mainly about the situation in India, and the insufficient degree of public works and infrastructure, is meant as an object lesson for our own economy. Yet the Tea Party types live in their own universe and choose to cling to their myth. In today's Washington Post, there is a tragic-comic piece about millionaires lobbying Congress to raise the taxes of anyone making over $1 million, finding it difficult to get an audience for this message but ultimately having several such conversations, including one with Grover Norquist.
As a result of this myth we can't get to a sensible place by negotiating our way there. E.J. Dionne argues today that the best we can hope for now is to do nothing - have the automatic spending cuts triggered by the August agreement and then next year let the Bush Tax Cuts expire on their. His analysis may be correct. But it is disheartening how we are blocked from doing better than that by so many who cling to their myth.
I suppose because Penn State has been in the news so much it occurred to me to watch That Championship Season, a Pulitzer Prize winning play that I saw in New York in the 1970s, but where much of the specifics of the story I had forgotten. I downloaded the 1999 made for TV version. Paul Sorvino plays the retired coach who is dying from cancer. He also directed the movie. Apparently, he has quite a connection to the play, having been in the original stage version as well as an earlier movie version where Robert Mitchum played the coach. The other main characters are four out of the starting five that won the Pennsylvania High School Basketball Championship twenty years earlier. The fifth starter, who is mentioned in name only, has made none of the reunions since. The viewer finds out why only near the end of the movie.
The movie is not uplifting but it makes a powerful point. Clinging to myth when one knows it to be untrue is destructive. Each of the main characters lives in a world of denial, misperceiveing reality, filled with emotional pain, trying to pretend things are better than they actually are. They are strangely dependent on each other, the basketball championship supposedly form a deep and everlasting bond. But they are also antagonistic to each other. Scranton is a small enough town that three of the four former players continue to have ongoing business and social relationships that are a source of tension. Much of the truth comes out as they betray each other during the reunion at the coaches house. The fourth player is a brother of one of the other three and a lush, presumably drink the only refuge he could take given the truth of the past. It his cynicism and demand that myth not triumph by which we ultimately learn that they won the Championship over the much favored team by deliberately injuring their best player. Unlike in the Karate Kid, where Daniel Larusso ultimately wins the tournament even after he has been severely injured because one of his nemeses has "swept his leg," in a deliberate attempt to hurt Daniel, in That Championship Season the cheaters prosper insofar as they win the championship. They suffer, however, for the rest of their lives.
I wonder if it would be helpful for the Penn State faithful to watch this movie. When one believes in myth very strongly and for a long period of time and then one is confronted with facts that put the lie to those beliefs, there is a tendency to ignore the facts. It is painful to have to change one's world view to accommodate the truth. But it is more painful to live a lie, particularly when it is not possible to bury the issue. Today the Times has a long piece about a possible coverup and CNN also has long piece, this one focusing on the mother of one of the alleged victims, who fears that Sandusky may get off. This story won't go away for quite a while.
* * * * *
There is a huge myth about big government and high taxes being a block to economic growth. Tom Friedman's column earlier this week, which is mainly about the situation in India, and the insufficient degree of public works and infrastructure, is meant as an object lesson for our own economy. Yet the Tea Party types live in their own universe and choose to cling to their myth. In today's Washington Post, there is a tragic-comic piece about millionaires lobbying Congress to raise the taxes of anyone making over $1 million, finding it difficult to get an audience for this message but ultimately having several such conversations, including one with Grover Norquist.
As a result of this myth we can't get to a sensible place by negotiating our way there. E.J. Dionne argues today that the best we can hope for now is to do nothing - have the automatic spending cuts triggered by the August agreement and then next year let the Bush Tax Cuts expire on their. His analysis may be correct. But it is disheartening how we are blocked from doing better than that by so many who cling to their myth.
Monday, November 14, 2011
Missed The Boat
In the Sunday book review Henry Kissinger wrote the lead piece - a belated eulogy to George Kennan on the occasion of a new biography about him by John Lewis Gaddis. Kennan was a strategic policy genius, the originator of "Containment," which though it saw blunders on our side, particularly Vietnam, ultimately did lead to the demise of the Soviet Union. In other words, Containment did what it was supposed to do.
This leads to the following question about history and driving forces. How much of America's military presence globally is simply a consequence that we filled a void left by the demise of Europe and Japan after World War II and how much of it was a necessary piece of the puzzle that Kennan had us solve? (Kissinger's piece talks about treaty organizations, NATO and SEATO in particular, as a different piece of the puzzle, and other forms of soft competition as also very important.) I don't know and I consider myself a reasonably well educated American. How many fellow citizens actually have a decent understanding of the role the American military presence has played since 1991? What about the role it should play in the future? Our political rhetoric seems so low level as to be incapable of taking on this question. But the question needs to be asked.
America has been the World's policeman for the past 65 years, but there is nothing written in stone that it should continue in the role. Perhaps some will argue that an updated Containment is still necessary, with the primary object of the policy now China and the secondary object rogue states like North Korea. But I could see a different argument made as well, that the police function must shift from a unilateral to a shared governance approach with China a strategic partner in that. This same debate existed at the end of World War II, with some viewing the Soviet intentions as benign at the time.
My own view on the issue is that while China is still authoritarian to a larger degree than we'd like to admit, none of the Chinese leaders are near as brutal as Stalin and further that trade, which has meant enormous progress for China, acts as a liberalizing force. If, as Kennan insisted, slow and steady wins the race, then it seems to me we should make a deliberate if gradual switchover to a shared governance approach in this police function. Our politics might not like that conclusion. But is there really a tenable alternative long term solution?
At present, military spending seems broadly tied to fiscal policy. In Europe, with austerity the buzzword for the time being, it is hard to imagine an immediate increase in the Euro contribution to the police function. When the global economy does return to a normalcy that feels healthy, that Euro contribution should increase. In the meantime, where does the slack get made up? Does the U.S. maintain the status quo or invite other partners while beginning to reduce its presence?
This gets me to the piece linked below, about the size of our Navy and how to manage the budget issues entailed in supporting it. The piece takes for granted that the legacy remains a future obligation and then makes the case for innovation as the way to address the issues. As someone who normally doesn't focus on military matters, reading the paragraph below it sure seemed to me we have a lot of big hardware.
Is all that hardware necessary? And if it is, would it matter if some of it sailed under different flags? How would Kennan answer these questions?
This leads to the following question about history and driving forces. How much of America's military presence globally is simply a consequence that we filled a void left by the demise of Europe and Japan after World War II and how much of it was a necessary piece of the puzzle that Kennan had us solve? (Kissinger's piece talks about treaty organizations, NATO and SEATO in particular, as a different piece of the puzzle, and other forms of soft competition as also very important.) I don't know and I consider myself a reasonably well educated American. How many fellow citizens actually have a decent understanding of the role the American military presence has played since 1991? What about the role it should play in the future? Our political rhetoric seems so low level as to be incapable of taking on this question. But the question needs to be asked.
America has been the World's policeman for the past 65 years, but there is nothing written in stone that it should continue in the role. Perhaps some will argue that an updated Containment is still necessary, with the primary object of the policy now China and the secondary object rogue states like North Korea. But I could see a different argument made as well, that the police function must shift from a unilateral to a shared governance approach with China a strategic partner in that. This same debate existed at the end of World War II, with some viewing the Soviet intentions as benign at the time.
My own view on the issue is that while China is still authoritarian to a larger degree than we'd like to admit, none of the Chinese leaders are near as brutal as Stalin and further that trade, which has meant enormous progress for China, acts as a liberalizing force. If, as Kennan insisted, slow and steady wins the race, then it seems to me we should make a deliberate if gradual switchover to a shared governance approach in this police function. Our politics might not like that conclusion. But is there really a tenable alternative long term solution?
At present, military spending seems broadly tied to fiscal policy. In Europe, with austerity the buzzword for the time being, it is hard to imagine an immediate increase in the Euro contribution to the police function. When the global economy does return to a normalcy that feels healthy, that Euro contribution should increase. In the meantime, where does the slack get made up? Does the U.S. maintain the status quo or invite other partners while beginning to reduce its presence?
This gets me to the piece linked below, about the size of our Navy and how to manage the budget issues entailed in supporting it. The piece takes for granted that the legacy remains a future obligation and then makes the case for innovation as the way to address the issues. As someone who normally doesn't focus on military matters, reading the paragraph below it sure seemed to me we have a lot of big hardware.
Is all that hardware necessary? And if it is, would it matter if some of it sailed under different flags? How would Kennan answer these questions?
Thursday, November 10, 2011
Lira Kill
Capital flow
Needs to slow.
Sovereign debt
The worst not yet,
The Euro structure,
About to rupture,
It's the creditors,
Who are the predators.
Needs to slow.
Sovereign debt
The worst not yet,
The Euro structure,
About to rupture,
It's the creditors,
Who are the predators.
Wednesday, November 09, 2011
Living Up To (Or Down To) One's Own Image
Some odd coincidences led up to this post. I subscribe to the ESPN Classic Network on TV because I like the show Sports Century, which features biographies of many of our sports heroes from the previous century. In 1999 ESPN did a countdown of the top 100 athletes of the twentieth century, with a show on each of them. As a result of the popularity of the series they made other shows of great athletes who hadn't made the original list, as well as shows about coaches, and celebrated sports events. I have the DVR set to record the show - all new episodes. And I watch them with some regularity. I like to watch biography on TV. In addition to the excellence the athlete has achieved, invariably the person went through a struggle on some sort. This duality of struggle and excellence makes for good viewing.
On Halloween there was supposed to be a show about Carl Yastrzemski. A couple of nights ago I got set to watch it, but the show wasn't there. In its place was a Dick Schaap One On One Interview with Joe Paterno, for a half hour, followed by another show, this one a special with Paterno and Coach K from Duke. I watched these shows instead, having an eerie feeling throughout the viewing. It didn't occur to me till afterward that these shows were on because Paterno had just broken the career wins record by beating the team I root for, Illinois. In that game I thought the refs did a bit of a homer job on us and that we'd have won the game otherwise. But it didn't feel it was a conspiracy, just the usual home team advantage.
With all the press now about the situation at Penn State, one could not watch this programming (I believe the Dick Schaap interview was from 2003) wondering whether the particular coverup of Jerry Sandusky's sexual predation was part of a larger pattern. In her column this morning, Maureen Dowd in her column this morning wrote:
Dowd has written many previous columns about the Catholic Church's coverup of abuse committed by Priests, so I suppose she felt obligated to write a similar piece on Penn State. But I'd want to know if this is part of a larger pattern before arriving at this conclusion. If I had a very close friend do a heinous thing, I don't know how I'd resolve that. I'm not saying that Dowd is wrong in her conclusion. I am saying that this "insular world" comment requires additional evidence for support. I wonder if now there will be a search for this additional evidence, looking for other sorts of indiscretion if not overt wrong doing.
In the Schaap interview Paterno talked about visiting Green Bay after the Hula Bowl, to have a chat about the head coaching job there. Paterno said he didn't really want the job and so was cagey and not forthcoming about his own preferences. It's a completely different context, for sure, and may sound innocent for the situation that he described. But that Paterno by self admission can be cagey and not forthcoming suggests to me there should be a further look at his broader record. It was also clear in the Schaap interview, where they discussed the Paterno Library, that Paterno was very prideful and concerned about his image. That itself is not a sin. The vast majority of us are egotistical, perhaps to a fault. But if other sins were committed it might explain why. It is now being reported that support for Paterno on Penn State's Board of Trustees is drying up. Yet many students appear to be extremely loyal to Paterno. It may be too early to ask how the Penn State community heals itself. From where I sit, that can only happen by having a rather full picture of what was going on.
The Board has presumably also lost confidence in Penn State's President, Graham Spanier. For most of us he is far less visible than the football coach, so have even less of a basis on which to offer a judgment. I have one experience, most of you will think it is comparatively minor, on which to make a surmisal. Penn State was one of the campuses RIAA went after about illegal file sharing. An agreement was reached to resolve the issue. Part of that agreement was a promotional video to warn students about the evils of downloading copyrighted music without paying for it. Graham Spanier appears in that video. That upset me at the time and I wrote a long post about it. In that post there is a link to the Web site RIAA sponsored. (I'm unsure whether the video that is there now is the same one that I railed about five years ago. I watched it this morning and it seemed milder than what I remembered.)
My conclusion is this. We want people with substantial authority to act ethically, but for their own survival and the survival of the institutions where they work, rather than ethical behavior the operational rule is to respond to political pressure when it is potent but to not respond otherwise. Penn State will get its comeuppance because it put on a veneer that it was above those survival behaviors. The rest of us might learn to not lionize important people, in the sports world or elsewhere. That intense admiration sews the seeds of betrayal and coverup.
On Halloween there was supposed to be a show about Carl Yastrzemski. A couple of nights ago I got set to watch it, but the show wasn't there. In its place was a Dick Schaap One On One Interview with Joe Paterno, for a half hour, followed by another show, this one a special with Paterno and Coach K from Duke. I watched these shows instead, having an eerie feeling throughout the viewing. It didn't occur to me till afterward that these shows were on because Paterno had just broken the career wins record by beating the team I root for, Illinois. In that game I thought the refs did a bit of a homer job on us and that we'd have won the game otherwise. But it didn't feel it was a conspiracy, just the usual home team advantage.
With all the press now about the situation at Penn State, one could not watch this programming (I believe the Dick Schaap interview was from 2003) wondering whether the particular coverup of Jerry Sandusky's sexual predation was part of a larger pattern. In her column this morning, Maureen Dowd in her column this morning wrote:
Like the Roman Catholic Church, Penn State is an arrogant institution hiding behind its mystique. And sports, as my former fellow sports columnist at The Washington Star, David Israel says, is “an insular world that protects its own, and operates outside of societal norms as long as victories and cash continue to flow bountifully.” Penn State rakes in $70 million a year from its football program.
Dowd has written many previous columns about the Catholic Church's coverup of abuse committed by Priests, so I suppose she felt obligated to write a similar piece on Penn State. But I'd want to know if this is part of a larger pattern before arriving at this conclusion. If I had a very close friend do a heinous thing, I don't know how I'd resolve that. I'm not saying that Dowd is wrong in her conclusion. I am saying that this "insular world" comment requires additional evidence for support. I wonder if now there will be a search for this additional evidence, looking for other sorts of indiscretion if not overt wrong doing.
In the Schaap interview Paterno talked about visiting Green Bay after the Hula Bowl, to have a chat about the head coaching job there. Paterno said he didn't really want the job and so was cagey and not forthcoming about his own preferences. It's a completely different context, for sure, and may sound innocent for the situation that he described. But that Paterno by self admission can be cagey and not forthcoming suggests to me there should be a further look at his broader record. It was also clear in the Schaap interview, where they discussed the Paterno Library, that Paterno was very prideful and concerned about his image. That itself is not a sin. The vast majority of us are egotistical, perhaps to a fault. But if other sins were committed it might explain why. It is now being reported that support for Paterno on Penn State's Board of Trustees is drying up. Yet many students appear to be extremely loyal to Paterno. It may be too early to ask how the Penn State community heals itself. From where I sit, that can only happen by having a rather full picture of what was going on.
The Board has presumably also lost confidence in Penn State's President, Graham Spanier. For most of us he is far less visible than the football coach, so have even less of a basis on which to offer a judgment. I have one experience, most of you will think it is comparatively minor, on which to make a surmisal. Penn State was one of the campuses RIAA went after about illegal file sharing. An agreement was reached to resolve the issue. Part of that agreement was a promotional video to warn students about the evils of downloading copyrighted music without paying for it. Graham Spanier appears in that video. That upset me at the time and I wrote a long post about it. In that post there is a link to the Web site RIAA sponsored. (I'm unsure whether the video that is there now is the same one that I railed about five years ago. I watched it this morning and it seemed milder than what I remembered.)
My conclusion is this. We want people with substantial authority to act ethically, but for their own survival and the survival of the institutions where they work, rather than ethical behavior the operational rule is to respond to political pressure when it is potent but to not respond otherwise. Penn State will get its comeuppance because it put on a veneer that it was above those survival behaviors. The rest of us might learn to not lionize important people, in the sports world or elsewhere. That intense admiration sews the seeds of betrayal and coverup.
Tuesday, November 08, 2011
Where Are Plato's Children?
In some respects this is a sequel to an earlier post, Some regrets about learning management systems. When you have a bug of an idea in your head it is hard to let go. So I'm writing another one. But unlike that post my focus here will be all technology where "presentation content" is rendered. For example, there is now something of a craze about eReaders and the possibilities they engender. Many other learning technologists see with that technology the glass currently half full, with a possibility of a full glass in the not too distant future. In contrast, I see it as less than half full, with little chance of that changing. Here's why.
For narrative content eReaders are great. I've greatly enjoyed the ones I've used - the original Kindle and the first iPad. This is for reading done in a comfortable lounge chair, where the reading becomes a totality into itself. I know a year or two ago I read a review somewhere about eReaders used for instruction but sorry, I don't have the reference at the ready, so the gist of that piece will be given by recall only. In that review the students wanted to provide annotations for what they read, and the input capabilities of the eReaders were quite limited, so the students gave the eReaders low marks as a result. I thought at the time that the students really wanted a laptop and do their reading on that. To modify that conjecture a bit, perhaps what they want is laptop functionality but with a wireless keyboard and touchscreen capability, so they can use it in "slate" form while in the lounge chair and then use it in usual laptop mode when inputting the annotations.
I have a wireless keyboard for the iPad. I rarely use it however. Mostly, I use the built in keyboard and do hunt and peck input with that. I never use it to make annotations. I use it to send email. I have on occasion written a draft of a blog post in it and then emailed that to Blogger. But it is difficult, if not impossible, to put in hyperlinks to other online content that way. So it is limited for this function.
Perhaps the eReaders will improve for how they process the narrative content. I said there is little chance for improvement, but there is some, and this is what I was referring to. Here there is a question of how much the larger eReader market, which I take will continue to grow, wants this sort of functionality. It is hard for academic use to generate functionality it wants if the larger market doesn't care. We should learn from prior experiences that there are substantial benefits in using technology that appeals much more broadly, even if it means the technology must be taken "as is."
* * * * *
I want to make a distinction between the narrative content I've described above and the analytic content, which is my focus here and was the focus of my previous post. The correct way to read analytic content is quite different. Prior to the personal computer, the place to read analytic content required a table or other flat surface as well as a chair. A pencil and a pad of ruled paper were needed to accompany the readings. At regular junctures, the student would draw diagrams on the paper or write down and solve equations. This written work would come out of the readings. The activity with pencil and paper was there as a way for the student to gain understanding of what they were reading. In this sense it was different than writing notes about the reading, which were intended to be looked at later, perhaps when preparing for an exam. The diagrams and the equations were for the present, then and there. You don't learn analytic results simply by reading them as you would read a narrative. You learn them by reproducing the results from first principles. If you can reproduce the results, then you know them. The pencil and paper are there for reproducing the results.
Over the years as students would come to me in office hours not understanding the economics, I came to learn that many also didn't understand this about processing analytic content. They would try to process it as if it were narrative content. Their tool of choice was the yellow highlighter. Their textbooks would be highly marked up and they seemed to approach the subject by trying to memorize it. They didn't know how, or didn't think to try, to process the results by reproducing them. So they couldn't work problems that required such processing. For analytic content, I believe the eReaders are somewhat pernicious in that they have a built in highlighter tool and that encourages the students to treat the content as narrative, whether doing so is appropriate or not.
For the learning technologist, then, there is this question with analytic content: Should the student still rely on pencil and paper and develop learning to learn habits from that sort of processing or, instead, should the experience be done totally within the communications and computing device? I can see arguments for this both ways, but to make the point simply I will distinguish work done in the major from work done to satisfy general education or distribution requirements. In the major, I believe some pencil and paper skills are necessary, even if there is sophisticated computing software that professionals in the field use to solve the problems. Sometimes it is still important for deep understanding to draw diagrams or write down equations. Professionals need to have that ability. Non-professionals, in my view, don't require those skills and if their major field doesn't emphasize them then they needn't develop that set of skills at all. But they still need to be able to process the content in those required courses. And since their pencil and paper skills are not so well honed, it really would be better for them to experience the processing part of the subject while working at their computers.
This notion that computers should aid students by helping them with the processing of the content has a long and honored tradition. It goes by the name - computer assisted instruction. The people who work in this field are called computer assisted instruction specialists. When I ran the campus Center for Educational Technologies, many of my staff held the title CAIS. Yet it now is a title that seems dated, with a preferred alternative title, eLearning specialist. Instead of incorporating computer assisted instruction into our bag of tricks, relying on it where appropriate, we seem to be ignoring our history entirely, except in a few dark outposts.
That history may have been strongest at Illinois, where the Plato system was initially developed. I never used Plato myself. In the 1980s there were some bargaining experiments that relied on Plato. While I was quite friendly with the authors, I never got involved directly with those. I learned the little I know about Plato via a different route.
When I succeeded Burks Oakley in running the SCALE project, there were then some programmers working for the central campus computing organization who had previously worked on Plato. From them I heard complaints about using the Internet for instruction - it wasn't nearly as good as Plato. The interactions were too slow. On the World Wide Web full screen refreshes were necessary and that took a while, especially given the bandwidth and processing limitations of the time. Plato could refresh only small parts of the screen leaving the rest intact. It was built with interaction in mind.
I learned much more about Plato from conversations with Stan Smith, a Professor of Chemistry, and an early leader on campus in the effective use of computer assisted instruction. At the time I met him Stan was engaged in a multiyear project do deliver via the Web what he was previously able to deliver in Plato. He eventually achieved a tolerable integration of his own created content with WebCT. In my earlier post on learning management systems, I discussed random number generators in assessment questions. It was Stan who got Murray Goldberg to put a random number generator into an early version of WebCT. But Stan wasn't just about technical functionality of the software. He had very strong ideas regarding pedagogic practice. I picked up many of those and have since written about them in a piece praising some of my forerunners with learning technology, entitled Homage to Jerry Uhl. (See pages 12 - 16 for the bit about Stan.)
At various conferences I've had several old time learning technology folks not at Illinois, but who knew about the Plato system and had some experience with it, tell me what a wonderful system it was. So the knowledge of Plato was diffuse and perhaps still is diffuse. Yet Plato's influence on the present seems very weak, at best. It may be that the teaching of analytic content in the way I'm discussing here is more a job for K-12 than it is for Higher Ed, though there are college courses such as intermediate microeconomics, where the subject still has a substantial analytic component. If this is right, then what we seem to be experiencing is a problem that's fallen through the cracks. Effective use of technology to help students process analytic content would first develop at the college level and then filter down to the high schools, and maybe further down than that. But I don't think that's happening and if it is happening, it's invisible to me. My second son is a high school senior. For math and science homework he's been assigned throughout high school, it's all been out of a textbook or a xerox copy of and assignment from another source. Ditto for my older son, who graduated a couple of years ago.
The students themselves seem to understand that technology should be used this way and are disappointed that it isn't happening. Not quite five years ago, in January 2007, I wrote a blog post that reviewed the ELI conference. The segment quoted below is from that post. It confirms the need.
Authors who learn about their audience tend to write differently from those authors who write only for themselves. Invariably when online instructional content is created and its deployment is evaluated, the evaluators will ask about stumbling blocks for the students in using the content to learn. The evaluation will reveal whether the students process the content effectively and if not will unearth the impediments that block doing so. The conscientious content author who participates in the evaluation will then become sensitized to the question: what makes students process effectively? Answering that question becomes the driver in further content creation. With much of the analytic content we use there is only narrow authorship. Most instructors divorce themselves from online content creation. And what they do create, still mainly PowerPoint presentations, don't really facilitate student processing at all. All of us who teach analytic subject matter should be an offspring of the Plato system.
I wish I knew how to get there from here.
For narrative content eReaders are great. I've greatly enjoyed the ones I've used - the original Kindle and the first iPad. This is for reading done in a comfortable lounge chair, where the reading becomes a totality into itself. I know a year or two ago I read a review somewhere about eReaders used for instruction but sorry, I don't have the reference at the ready, so the gist of that piece will be given by recall only. In that review the students wanted to provide annotations for what they read, and the input capabilities of the eReaders were quite limited, so the students gave the eReaders low marks as a result. I thought at the time that the students really wanted a laptop and do their reading on that. To modify that conjecture a bit, perhaps what they want is laptop functionality but with a wireless keyboard and touchscreen capability, so they can use it in "slate" form while in the lounge chair and then use it in usual laptop mode when inputting the annotations.
I have a wireless keyboard for the iPad. I rarely use it however. Mostly, I use the built in keyboard and do hunt and peck input with that. I never use it to make annotations. I use it to send email. I have on occasion written a draft of a blog post in it and then emailed that to Blogger. But it is difficult, if not impossible, to put in hyperlinks to other online content that way. So it is limited for this function.
Perhaps the eReaders will improve for how they process the narrative content. I said there is little chance for improvement, but there is some, and this is what I was referring to. Here there is a question of how much the larger eReader market, which I take will continue to grow, wants this sort of functionality. It is hard for academic use to generate functionality it wants if the larger market doesn't care. We should learn from prior experiences that there are substantial benefits in using technology that appeals much more broadly, even if it means the technology must be taken "as is."
* * * * *
I want to make a distinction between the narrative content I've described above and the analytic content, which is my focus here and was the focus of my previous post. The correct way to read analytic content is quite different. Prior to the personal computer, the place to read analytic content required a table or other flat surface as well as a chair. A pencil and a pad of ruled paper were needed to accompany the readings. At regular junctures, the student would draw diagrams on the paper or write down and solve equations. This written work would come out of the readings. The activity with pencil and paper was there as a way for the student to gain understanding of what they were reading. In this sense it was different than writing notes about the reading, which were intended to be looked at later, perhaps when preparing for an exam. The diagrams and the equations were for the present, then and there. You don't learn analytic results simply by reading them as you would read a narrative. You learn them by reproducing the results from first principles. If you can reproduce the results, then you know them. The pencil and paper are there for reproducing the results.
Over the years as students would come to me in office hours not understanding the economics, I came to learn that many also didn't understand this about processing analytic content. They would try to process it as if it were narrative content. Their tool of choice was the yellow highlighter. Their textbooks would be highly marked up and they seemed to approach the subject by trying to memorize it. They didn't know how, or didn't think to try, to process the results by reproducing them. So they couldn't work problems that required such processing. For analytic content, I believe the eReaders are somewhat pernicious in that they have a built in highlighter tool and that encourages the students to treat the content as narrative, whether doing so is appropriate or not.
For the learning technologist, then, there is this question with analytic content: Should the student still rely on pencil and paper and develop learning to learn habits from that sort of processing or, instead, should the experience be done totally within the communications and computing device? I can see arguments for this both ways, but to make the point simply I will distinguish work done in the major from work done to satisfy general education or distribution requirements. In the major, I believe some pencil and paper skills are necessary, even if there is sophisticated computing software that professionals in the field use to solve the problems. Sometimes it is still important for deep understanding to draw diagrams or write down equations. Professionals need to have that ability. Non-professionals, in my view, don't require those skills and if their major field doesn't emphasize them then they needn't develop that set of skills at all. But they still need to be able to process the content in those required courses. And since their pencil and paper skills are not so well honed, it really would be better for them to experience the processing part of the subject while working at their computers.
This notion that computers should aid students by helping them with the processing of the content has a long and honored tradition. It goes by the name - computer assisted instruction. The people who work in this field are called computer assisted instruction specialists. When I ran the campus Center for Educational Technologies, many of my staff held the title CAIS. Yet it now is a title that seems dated, with a preferred alternative title, eLearning specialist. Instead of incorporating computer assisted instruction into our bag of tricks, relying on it where appropriate, we seem to be ignoring our history entirely, except in a few dark outposts.
That history may have been strongest at Illinois, where the Plato system was initially developed. I never used Plato myself. In the 1980s there were some bargaining experiments that relied on Plato. While I was quite friendly with the authors, I never got involved directly with those. I learned the little I know about Plato via a different route.
When I succeeded Burks Oakley in running the SCALE project, there were then some programmers working for the central campus computing organization who had previously worked on Plato. From them I heard complaints about using the Internet for instruction - it wasn't nearly as good as Plato. The interactions were too slow. On the World Wide Web full screen refreshes were necessary and that took a while, especially given the bandwidth and processing limitations of the time. Plato could refresh only small parts of the screen leaving the rest intact. It was built with interaction in mind.
I learned much more about Plato from conversations with Stan Smith, a Professor of Chemistry, and an early leader on campus in the effective use of computer assisted instruction. At the time I met him Stan was engaged in a multiyear project do deliver via the Web what he was previously able to deliver in Plato. He eventually achieved a tolerable integration of his own created content with WebCT. In my earlier post on learning management systems, I discussed random number generators in assessment questions. It was Stan who got Murray Goldberg to put a random number generator into an early version of WebCT. But Stan wasn't just about technical functionality of the software. He had very strong ideas regarding pedagogic practice. I picked up many of those and have since written about them in a piece praising some of my forerunners with learning technology, entitled Homage to Jerry Uhl. (See pages 12 - 16 for the bit about Stan.)
At various conferences I've had several old time learning technology folks not at Illinois, but who knew about the Plato system and had some experience with it, tell me what a wonderful system it was. So the knowledge of Plato was diffuse and perhaps still is diffuse. Yet Plato's influence on the present seems very weak, at best. It may be that the teaching of analytic content in the way I'm discussing here is more a job for K-12 than it is for Higher Ed, though there are college courses such as intermediate microeconomics, where the subject still has a substantial analytic component. If this is right, then what we seem to be experiencing is a problem that's fallen through the cracks. Effective use of technology to help students process analytic content would first develop at the college level and then filter down to the high schools, and maybe further down than that. But I don't think that's happening and if it is happening, it's invisible to me. My second son is a high school senior. For math and science homework he's been assigned throughout high school, it's all been out of a textbook or a xerox copy of and assignment from another source. Ditto for my older son, who graduated a couple of years ago.
The students themselves seem to understand that technology should be used this way and are disappointed that it isn't happening. Not quite five years ago, in January 2007, I wrote a blog post that reviewed the ELI conference. The segment quoted below is from that post. It confirms the need.
Let me switch gears. I attended two presentations where students were the presenters and a third presentation, the opening plenary, where the technology behavior of students was the object of study. The opening plenary was given by Julie Evans who presented evidence about K-12 student technology use and needs. It was a very good talk and I’m sure others will comment about it more extensively. So here I want to pick on only one point that came out of the presentation. Students want to see their course content use more technology --- particularly in math. I agree with the students. This should be done.As I mentioned, there are outposts where Plato's legacy can be seen even if the users are not aware of the connection. A partial list includes the Online Learning Initiative from Carnegie Mellon, LON-CAPA, and some publisher run systems also blend interactive simulation, presentation, and assessment. Some of these, however, are too cookbook. Plato provided a framework where the student had substantial freedom in exploring, while having a clear goal to attain. There is a huge design difference between the Plato approach and a cookbook approach, although much of that difference must also be attributed to the authors of the lessons, which brings me to my conclusion.
Authors who learn about their audience tend to write differently from those authors who write only for themselves. Invariably when online instructional content is created and its deployment is evaluated, the evaluators will ask about stumbling blocks for the students in using the content to learn. The evaluation will reveal whether the students process the content effectively and if not will unearth the impediments that block doing so. The conscientious content author who participates in the evaluation will then become sensitized to the question: what makes students process effectively? Answering that question becomes the driver in further content creation. With much of the analytic content we use there is only narrow authorship. Most instructors divorce themselves from online content creation. And what they do create, still mainly PowerPoint presentations, don't really facilitate student processing at all. All of us who teach analytic subject matter should be an offspring of the Plato system.
I wish I knew how to get there from here.
Monday, November 07, 2011
The Blue Screen of Death
Death by the blue screen,
Far worse than obscene,
What does it all mean?
Tricked by Halloween?
Hard disk, time to clean?
No virus yet seen.
My face turning green,
Need to vent my spleen,
Or find another scene.
Far worse than obscene,
What does it all mean?
Tricked by Halloween?
Hard disk, time to clean?
No virus yet seen.
My face turning green,
Need to vent my spleen,
Or find another scene.
Sunday, November 06, 2011
Some regrets about learning management systems
A traditional approach to education has learning preceding assessment, with the assessment activity itself distinct from the learning and typically where the assessment doesn't produce additional learning. Here I'm not referring to the incentive effects the assessment might generate - students do study for an exam. What I'm talking about is that while taking the exam, might the students learn something new then and there? If my experience as a teacher is any indicator of that, the expectation of the students is that this shouldn't happen. They want to be tested on what they already know.
As a reaction to the stress that high stakes assessment generates, the student reaction is sensible. They'd like to reduce uncertainty and have confidence of the grade they will earn, based on the preparations they've already made. This, however, doesn't mean students feel the same way when in a low stakes environment, such as doing homework online. And if you focus on that environment, it is much more natural to have an iterative approach between learning and assessment. Put a different way, learning is mainly by doing and in the doing there is assessment at each step, a check on whether that which just preceded makes sense and if the learner is ready to proceed to the next step.
Those with strong learning-to-learn skills develop methods of self-assessment entirely on their own and use those methods to master new material and internalize that material into their own world view. One big goal of college is to help students develop their learning-to-learn skills when those skills are no so well developed, as is the case for many students. Homework should be part and parcel of that. Unfortunately, the mechanism by which students develop the learning-to-learn skills remains opaque. When homework was done on paper, the assessment had to occur subsequently to when the student turned in the assignment. The technology of the time enforced the notion that assessment follows learning. Textbook chapters had problems at the end for students to work. Within a chapter there might be illustrative examples, but they are fully worked through. Throughout my years of teaching I've had many students say, "I understand it when you it explain it, but I can't work a problem on my own." They don't realize that they don't understand it. They don't receive any helpful feedback after getting the example that tests their own understanding.
With online technology and automated assessment there is the possibility of doing things differently. Some years ago at the behest of my friend Steve Acker, I wrote this piece on Dialogic Learning Objects for Campus Technology Magazine. As example, I talked about "content surveys" that asked questions at various junctures of the presentation. The students were expected to provide a written response to each question, after which a suggested response was provided. The students could back up and rewrite their responses after having seen the suggested response. The iterative aspect was definitely in the content surveys, but the automated assessment at each juncture was not. I downloaded the student responses, put them into a spreadsheet, and discussed some of the more interesting and revealing ones in class.
I don't know how many other disciplines can be described this way, but economics certainly can be divided into models and their understanding, on the one hand, and story telling about real world economic applications, on the other. It's the story telling part that I was getting at with the content surveys. The model part perhaps can be done with automated assessment, in whole or part.
Here are two examples of model-type dialogic objects done in Excel. The first is on the elements of supply and demand, developed in a particular way to tie individual behavior to what happens in the market overall. (You have to download the Excel file to do this. You can't do it in Google Docs, which here is used simply as an open repository for the content.) The second develops the buyer side notion of reservation price, the analogous seller side notion of opportunity cost, and talks about substitutes and complements in the market. These examples do the dialogic part quite well and do have automated assessment. I have recently rewritten them taking out all macros and activex controls so they should work on Mac as well as on PC, as long as you have a recent version of Excel.
You can't do in the LMS what I've done with Excel. Indeed you can't even come close. The question is why. Let me give two different reasons. One is that browsers are more limited than applications. The second is that there's been a lack of imagination in developing the LMS, so the limits with what can be done in that environment result because the assessment engines remain unsophisticated. I'll illustrate some instances of each. My further remarks are meant for all LMS, but I don't know all the systems well. So I will make reference explicitly only to the ones I know a little.
The old WebCT Vista and the current Blackboard Learn has a self-test function. When writing a self-test the designer has the option of providing feedback either immediately, as soon as the student has answered the particular question, or deferring all feedback till the student finishes the self test. (Moodle 1.9, I believe, doesn't have that function. You can give practice quizzes worth zero points, but you can't provide immediate feedback in those.) Feedback immediately after a question is answered is consistent with the dialogic approach. However, there was no way for the instructor to track whether the students did the the self test. Such tracking (a participation credit, if you will) is a necessary component of an effective system. Many students will do the work if they get credit for it, but not otherwise. Why isn't there a self test with tracking option? I attribute this to lack of imagination, since all the component functionality exists in other forms of assessment in these systems.
The WebCT and Blackboard systems have a random number question type. It allows a single answer only. What I want, however, is to have random numbers for a problem, with a graph, where there are multiple questions pertaining to the same problem and where the realization of the random numbers stay fixed from one question to the next. The LMS does allow randomized questions within an assessment, but you can't correlate the realizations of those across questions. The upshot is that if you want to have a bunch of questions in the LMS that refer to the same scenario, you then have to give up on having randomization in parameter values. I should note here that Moodle does offer a Cloze question type that does allow for multiple questions within a question. Presumably, you could write multiple versions of the same Cloze question, with each version representing a particular realization of the random values. It is possible but clunky. And it doesn't address the immediate feedback issue. Here too I attribute the limitation to a lack of imagination.
The LMS allows for third party hosted assessment done as a SCORM module, so you might have thought the issue could be outsourced to other content tools, such as Adobe Presenter, which does allow quiz questions with immediate feedback to be interspersed in a presentation. My experience with that is the questions must be simple (multiple choice or matching) and the responses can't be tied to any random variables. Scorm modules may be good and useful for other things. But I don't believe they solve this set of issues.
There is a further issue with Economics in particular, but perhaps exists in other disciplines as well. Since the subject is so graphical in nature, when random numbers are used it would be good for those numbers to appear in the graphs as well. By 1997, if I recall correctly, Mallard could do that. The designer had to specify not just the random number but the (x,y) coordinates of where that random number should appear in the graph. I believe this was done with Javascript that produced an overlay on the original image. The random number was in the overlay. Generating the right (x,y) coordinates was a pain, but it was possible. It is a snap to do this in Excel. Much of it is done automatically. This one I attribute to limitations with browser functionality.
With these limitations, the assessment engines in the LMS are kind of dull. As a result, the content that is written for them also tends to be dull. The real issue here is not any one particular functionality but rather that we've not seen a broad culture develop to produce rich content with interesting assessment. And we've certainly not seen the hope I articulated in that Campus Technology piece, that we'd begin to see students producing these sort of learning modules as part of their coursework, to be redeployed in future offerings of the course, so that having produced some rich content, a suitable volume of content would be produced.
As I've been writing this piece, I read Why Science Majors Change Their Minds. My son, who is a sophomore in Industrial Engineering here, sent it to my wife. She forwarded the link to me. There is a big argument in this piece that we need project oriented STEM education. I agree. But I suspect there still will be basic courses taught more traditionally. In those basic courses, one might have hoped 15 years ago that the LMS would improve the instruction in them. Alas, the LMS has not lived up to that potential.
As a reaction to the stress that high stakes assessment generates, the student reaction is sensible. They'd like to reduce uncertainty and have confidence of the grade they will earn, based on the preparations they've already made. This, however, doesn't mean students feel the same way when in a low stakes environment, such as doing homework online. And if you focus on that environment, it is much more natural to have an iterative approach between learning and assessment. Put a different way, learning is mainly by doing and in the doing there is assessment at each step, a check on whether that which just preceded makes sense and if the learner is ready to proceed to the next step.
Those with strong learning-to-learn skills develop methods of self-assessment entirely on their own and use those methods to master new material and internalize that material into their own world view. One big goal of college is to help students develop their learning-to-learn skills when those skills are no so well developed, as is the case for many students. Homework should be part and parcel of that. Unfortunately, the mechanism by which students develop the learning-to-learn skills remains opaque. When homework was done on paper, the assessment had to occur subsequently to when the student turned in the assignment. The technology of the time enforced the notion that assessment follows learning. Textbook chapters had problems at the end for students to work. Within a chapter there might be illustrative examples, but they are fully worked through. Throughout my years of teaching I've had many students say, "I understand it when you it explain it, but I can't work a problem on my own." They don't realize that they don't understand it. They don't receive any helpful feedback after getting the example that tests their own understanding.
With online technology and automated assessment there is the possibility of doing things differently. Some years ago at the behest of my friend Steve Acker, I wrote this piece on Dialogic Learning Objects for Campus Technology Magazine. As example, I talked about "content surveys" that asked questions at various junctures of the presentation. The students were expected to provide a written response to each question, after which a suggested response was provided. The students could back up and rewrite their responses after having seen the suggested response. The iterative aspect was definitely in the content surveys, but the automated assessment at each juncture was not. I downloaded the student responses, put them into a spreadsheet, and discussed some of the more interesting and revealing ones in class.
I don't know how many other disciplines can be described this way, but economics certainly can be divided into models and their understanding, on the one hand, and story telling about real world economic applications, on the other. It's the story telling part that I was getting at with the content surveys. The model part perhaps can be done with automated assessment, in whole or part.
Here are two examples of model-type dialogic objects done in Excel. The first is on the elements of supply and demand, developed in a particular way to tie individual behavior to what happens in the market overall. (You have to download the Excel file to do this. You can't do it in Google Docs, which here is used simply as an open repository for the content.) The second develops the buyer side notion of reservation price, the analogous seller side notion of opportunity cost, and talks about substitutes and complements in the market. These examples do the dialogic part quite well and do have automated assessment. I have recently rewritten them taking out all macros and activex controls so they should work on Mac as well as on PC, as long as you have a recent version of Excel.
You can't do in the LMS what I've done with Excel. Indeed you can't even come close. The question is why. Let me give two different reasons. One is that browsers are more limited than applications. The second is that there's been a lack of imagination in developing the LMS, so the limits with what can be done in that environment result because the assessment engines remain unsophisticated. I'll illustrate some instances of each. My further remarks are meant for all LMS, but I don't know all the systems well. So I will make reference explicitly only to the ones I know a little.
The old WebCT Vista and the current Blackboard Learn has a self-test function. When writing a self-test the designer has the option of providing feedback either immediately, as soon as the student has answered the particular question, or deferring all feedback till the student finishes the self test. (Moodle 1.9, I believe, doesn't have that function. You can give practice quizzes worth zero points, but you can't provide immediate feedback in those.) Feedback immediately after a question is answered is consistent with the dialogic approach. However, there was no way for the instructor to track whether the students did the the self test. Such tracking (a participation credit, if you will) is a necessary component of an effective system. Many students will do the work if they get credit for it, but not otherwise. Why isn't there a self test with tracking option? I attribute this to lack of imagination, since all the component functionality exists in other forms of assessment in these systems.
The WebCT and Blackboard systems have a random number question type. It allows a single answer only. What I want, however, is to have random numbers for a problem, with a graph, where there are multiple questions pertaining to the same problem and where the realization of the random numbers stay fixed from one question to the next. The LMS does allow randomized questions within an assessment, but you can't correlate the realizations of those across questions. The upshot is that if you want to have a bunch of questions in the LMS that refer to the same scenario, you then have to give up on having randomization in parameter values. I should note here that Moodle does offer a Cloze question type that does allow for multiple questions within a question. Presumably, you could write multiple versions of the same Cloze question, with each version representing a particular realization of the random values. It is possible but clunky. And it doesn't address the immediate feedback issue. Here too I attribute the limitation to a lack of imagination.
The LMS allows for third party hosted assessment done as a SCORM module, so you might have thought the issue could be outsourced to other content tools, such as Adobe Presenter, which does allow quiz questions with immediate feedback to be interspersed in a presentation. My experience with that is the questions must be simple (multiple choice or matching) and the responses can't be tied to any random variables. Scorm modules may be good and useful for other things. But I don't believe they solve this set of issues.
There is a further issue with Economics in particular, but perhaps exists in other disciplines as well. Since the subject is so graphical in nature, when random numbers are used it would be good for those numbers to appear in the graphs as well. By 1997, if I recall correctly, Mallard could do that. The designer had to specify not just the random number but the (x,y) coordinates of where that random number should appear in the graph. I believe this was done with Javascript that produced an overlay on the original image. The random number was in the overlay. Generating the right (x,y) coordinates was a pain, but it was possible. It is a snap to do this in Excel. Much of it is done automatically. This one I attribute to limitations with browser functionality.
With these limitations, the assessment engines in the LMS are kind of dull. As a result, the content that is written for them also tends to be dull. The real issue here is not any one particular functionality but rather that we've not seen a broad culture develop to produce rich content with interesting assessment. And we've certainly not seen the hope I articulated in that Campus Technology piece, that we'd begin to see students producing these sort of learning modules as part of their coursework, to be redeployed in future offerings of the course, so that having produced some rich content, a suitable volume of content would be produced.
As I've been writing this piece, I read Why Science Majors Change Their Minds. My son, who is a sophomore in Industrial Engineering here, sent it to my wife. She forwarded the link to me. There is a big argument in this piece that we need project oriented STEM education. I agree. But I suspect there still will be basic courses taught more traditionally. In those basic courses, one might have hoped 15 years ago that the LMS would improve the instruction in them. Alas, the LMS has not lived up to that potential.
Meritocracy is good but requires humility
I found myself agreeing with this Ross Douthat column. I would add the following, however. Some people are taken with themselves pretty early on. For them there is probably no hope. Others who are quite talented are nonetheless modest, simply out of disposition, or because of a humble background, or that although prodigious in some areas, struggle mightily in others. I believe there is a tendency for these people to either entirely lose this modesty or let it submerge under an external veneer that develops as a defense mechanism, by the time the person has become a senior executive. So maintaining humility is a stern requirement, one that may be near impossible to fill if it is accompanied by a history of genuine accomplishment.
By the way, Corzine was an alum of the Economics Department here. He was the featured speaker at the 100th anniversary of the department, when Corzine was still at Goldman-Sachs. I was told the fund raisers were all over him to make a big gift. I don't believe he gave one at the time. I wonder if they'll invite him back now.
By the way, Corzine was an alum of the Economics Department here. He was the featured speaker at the 100th anniversary of the department, when Corzine was still at Goldman-Sachs. I was told the fund raisers were all over him to make a big gift. I don't believe he gave one at the time. I wonder if they'll invite him back now.
Thursday, November 03, 2011
Chinese Undergraduate Students - Issues and Opportunities
In the Behavioral Econ course I taught last spring I confronted some of the issues discussed in this article. There was a high turnover at the beginning of the semester, I believe because the course was writing intensive and some of the international students found that intimidating, so they dropped. Another issue emerged regarding in class discussion. I've always tried to promote a form of Socratic dialog. I think it is the natural way to teach economics. Sometimes it doesn't work because students won't participate and I don't like calling on students who do not raise their hands. But last spring I had a different issue. Some students were eager to participate but when I called on them I could not understand what they were saying. It wasn't the economic content of what they were saying. It was their spoken English. I didn't resolve that issue well.
The snip below is from the end of this quite interesting article, a collaboration between The Chronicle of Higher Ed and The New York Times. Of course, the money is a big part of this. At Illinois out-of-state tuition is three times the in-state level. But even with those low-to-the-ground reasons for enrolling so many Chinese students, there are some more elevated reasons as well. Higher Education is an export product and in this case should ultimately reduce the friction between China and the U.S.
So I think we should be talking about the low to the ground issues more and developing coping strategies. I've only heard this discussed in one context - the Writer's Workshop on campus has been overrun by international students. The issue is broader than that and it deserves a broader set of responses.
The snip below is from the end of this quite interesting article, a collaboration between The Chronicle of Higher Ed and The New York Times. Of course, the money is a big part of this. At Illinois out-of-state tuition is three times the in-state level. But even with those low-to-the-ground reasons for enrolling so many Chinese students, there are some more elevated reasons as well. Higher Education is an export product and in this case should ultimately reduce the friction between China and the U.S.
So I think we should be talking about the low to the ground issues more and developing coping strategies. I've only heard this discussed in one context - the Writer's Workshop on campus has been overrun by international students. The issue is broader than that and it deserves a broader set of responses.
Tuesday, November 01, 2011
Extremely Interesting Interview
This is the first of 11 video segments of an interview with Bill Gates and Steve Jobs from 2007. They are interviewed by Kara Swisher and Walt Mossberg of the Wall Street Journal. The interview is fascinating in many respects, not the least because we now know the future to which they are speculating about in the conversation. It is also great to hear them talk about their personal motivations and what they regard as the strength in the other. And both of them refer to changes in business models to support technical innovation. Without saying it this way, Apple had a huge win with the iPod and iTunes because the music companies screwed up when Napster appeared and because Sony didn't know how to write software for the Walkman, either of which would have preempted the iPod/iTunes bundle.
BTW, to find segment 9 I had to go to segment 10 first. Then segment 9 appeared in the right sidebar.
BTW, to find segment 9 I had to go to segment 10 first. Then segment 9 appeared in the right sidebar.