Three links (OK, four) on teaching math

I came across this NPR post today via a post on Facebook. This led me to remember this one and that one, from a recent post and an older post I made myself on FB. The last one of these three links leads to a great discussion of how becoming good at math is a path open to everyone, but it takes hard work. Older people in a position to advise / teach younger ones should be keenly aware of the last one, and help their students/children/tutees adopt a growth mindset.

Give students more autonomy and responsibility for their learning

Today’s post: a warning about how the US society is not treating young students well, from a star SAT-preparation person. I’m including one snippet, but the whole post is very well worth reading.

American students have become far too reliant on everyone and everything but themselves. When our children don’t excel, we sign them up for classes, hire tutors, and, if all that fails, administer them amphetamines like M&Ms. Plummeting SAT scores stand as a blaring testament to the fact that this approach isn’t working.

Ideas for reforming college in the U.S.

The Brookings Institution has collected eight ideas for reforming college, to help promote social mobility, here. I tend to think #3 is the best of these, although I would not want to make higher education totally tuition free for all students, especially those who have the means to pay.

The US News College Rankings Scam

Henry on Crooked Timber (I just had to repost the whole thing):

The US News College Rankings Scam:


Stephen Budiansky, via Cosma Shalizi’s Pinboard feed.

Back in ancient times when I worked at esteemed weekly newsmagazine U.S. News & World Report, I always loathed the annual college rankings report. Like all cash cows, however, the college guide was a sacred cow, so I just shut up about its obvious statistical absurdities and inherent mendacity. As a lesson in the evils of our times, it is perhaps inevitable that the college guide is now the only thing left of U.S. News.

A story in today’s New York Times reports that Claremont McKenna college has now been caught red handed submitting phony data to the college guide to boost its rankings. But the real scandal, as usual, is not the occasional flagrant instance of outright dishonesty but the routine corruption that is shot through the whole thing. … To increase selectivity (one of the statistics that go into U.S. News’s secret mumbo-jumbo formula to produce an overall ranking), many colleges deliberately encourage applications from students who don’t have a prayer of getting in. To increase average SAT scores, colleges offer huge scholarships to un-needy but high scoring applicants to lure them to attend their institution. (The Times story mentioned that other colleges have been offering payments to admitted students to retake the test to increase the school average.)

… One of my favorite bits of absurdity was what a friend on the faculty at Case Law School told me they were doing a few years ago: because one of the U.S. News data points was the percentage of graduates employed in their field, the law school simply hired any recent graduate who could not get a job at a law firm and put him to work in the library. Their other tactic was pure genius: the law school hired as adjunct professors local alumni who already had lucrative careers (thereby increasing the faculty-student ratio, a key U.S. News statistic used in determining ranking), paid them exorbitant salaries they did not need (thereby increasing average faculty salary, another U.S. News data point), then made it understood that since they did not really need all that money they were expected to donate it all back to the school (thereby increasing the alumni giving rate, another U.S. News data point): three birds with one stone! (I gather the new Case law dean has put an end to these shenanigans.)

Worth reading the whole thing (even though Budiansky’s site has one of those annoying and anti-social ‘if you cut and paste text from my site, you will get unasked for cruft about how you ought to click on the original link added to your pasted text’ installations).


(Via Crooked Timber)

Academic textbooks and healthcare incentives compared – Boing Boing

The always interesting Boing Boing blog has a long post on the market for academic textbooks and makes explicit comparisons of the incentives in this market and in the U.S. healthcare system. I won’t quote from the article, as it is good enough for me to recommend you to read it in whole, along with the comments, several of which are good also. I will say that I am making some progress in this area, having for the first time given students several weeks’ notice about the textbooks I am going to use in the upcoming spring semester. Next year, I will try to substitute some creative commons sources for textbooks, but it will be hard, and very hard for my graduate courses.

How do we reform university teaching?

The procrastination is over. This site is designed and almost all its pages are pathetically blank as of now, with only place-holding text to keep the blank page fear away. But it is time to start one the blog, and I can hope to flesh out the rest of the site, as well as enrich the blog with frequent posts and get a regular blog-posting rhythm, before the Fall semester is upon me.

I thought I would start the blog with a discussion of a provocative suggestion for the reform of university teaching by Philip Greenspun. It has to do with incentives and with a fine desire to improve undergraduate teaching. Greenspun’s site, from which the link above comes, has more information on him and the course he teaches at MIT. I want to discuss here only his proposals for reforming teaching, and not his rather unquestioned taking of Clark’s book A Farewell to Alms as offering the one and only explanation for economic growth.

Greenspun observes that universities are still operating on the model established in 1088 with the opening of the university of Bologna. Lecturing was an efficient way to reach many people at once, back then. Students had no IM/Facebook/Limewire/Hulu/Twitter to keep them distracted, no video game consoles at home, and the lecture hall was more comfortable than their living quarters. But since then we have seen the arrival of so many technologies that upset the logic of lecturing that we should step back and reconsider our inertia in changing how we teach students.

I skip over the entertaining skewering of the video of some lectures at Yale. Suffice it to say that they show that a big-name professor at a big-name university can use classroom time inefficiently. So let me discuss Greenspun’s concrete proposals.

“Stop grading your own students.” I may be woefully uninformed here, but I am surprised that it is not a mechanism design theorist who came up with this suggestion first, but Greenspun, an engineer. For many courses taught at universities this makes excellent sense. Professors should grade others’ students’ exams, anonymously. This eliminates with one stroke the ego-boo bias that makes professors unwilling to give F grades as often as necessary, because their teaching can’t be so bad as to allow so many students to come out of their classes unenlightened. At the same time, student anonymity eliminates gender, racial and other biases in grading. I recall Steve Landsburg arguing that, on the basis of the famous Groves incentive schemes, that municipalities should have their populations pay each other’s taxes, which is an even more radical proposal than this one.

The biggest problem I can see with this grading-swap approach across universities is that it would encourage a cookie-cutter approach that would over-homogenize the course content. For some fields (many?), this would stifle creativity and innovation. Suppose I want to teach microeconomics by emphasizing game theory and using simulations on the computer to illustrate big points. I would have less time to teach the standard stuff I would be expected to teach (never mind that perhaps we should not be teaching the same stuff as Alfred Marshall did in 1890). Meanwhile, the grader is convinced that microeconomics is completely the study of competitive markets and game theory is a waste of time. Who sets the grading standards? And what about grading in subjects such as music? I can see grading a video of a soprano’s senior recital being graded remotely, but that will miss the way it sounded in the room, the way the soprano built (or failed to build) rapport with her audience, and, heaven forbid that the remote grader does not like her interpretation of the songs (maybe the grader never really liked Schubert, either, but she’s doing a lot of Schubert songs that she loves).

Another problem would be the stratification necessary to avoid introducing name-brand bias in grading. You would not want a professor at Boondocks College grading MIT students, and vice versa, as it may lead to the MIT students getting overly low grades out of pure spite. But if you try to escape this bias by stratifying universities and allowing, say, only professors from top-20 schools to grade students at top-20 schools, then what do you do about the incentive to make the other school look bad by giving its students bad grades? Perhaps this proposal can best be adopted within an institution, but then staffing levels can severely limit the number of courses in which the grading-swap can be used.

Yet there is meat in the grading-swap and I would argue in favor of its serious consideration in higher education, with whatever refinements will be necessary to address the points I raise here and others that I surely have missed.

“Stop lecturing.” OK, the human attention span is not much longer than 20 minutes at a stretch. More interaction among students in the classroom is essential. I cannot find anything to criticize here, except my own teaching practices, which I need to reform. There are good reasons when teaching something heavily technical to lecture at length, but such lecturing can always be interleaved with classroom activities to break monotony and reinforce points.

“Build open offices for students.” The idea here is that students study in close proximity to other students so they can get help from them as well as motivation. All of the student work for the day should be accomplished on campus, there should be no homework. Greenspun discusses well the implication that the semester system would need to be abandoned for this idea to succeed. He does not discuss the cost of the idea, however: at many universities space is at a premium and changing classrooms and labs to accommodate this approach would not come cheap. It may well be that this idea is good enough to overcome the cost, but we should have an idea of the latter before we can tell.

“Modest Change: Provide detailed review of all work; grade students on their ability to assist other students.”
This sounds excellent, but again the cost in time for the faculty would be very high. It contributes to the feeling I get from reading Greenspun’s suggestions that they would work best at universities that are devoted to good teaching rather than research. At the least, if a university does not properly compensate professors for this level of feedback (and does not monitor its quality somehow), not much good reviewing will be done. If the game is publish-or-perish, who will spend hours upon hours giving real, in-depth reviews of student work? To be fair, Greenspun anticipates the cost objection and proposes peer review of students and reviews by outside graders.

Greenspun’s essay continues with suggestions to improve the teaching of engineering. They seem workable and effective, but they would have less wide applicabiilty than the suggestions I have chosen to discuss here. Nevertheless, Greenspun’s essay is well worth a read. I may well be wrong in not seeing some excellent ways to adopt even his engineering-specific suggestions in the teaching of my field, economics, and if I think of such ways, I will post another discussion here. For now, though, this post has grown to gigantic proportions and it is time to call it a day. No, let me call it the first full-blown blog post in this site, instead. I promise many more to come (and, yes, to fill out these embarrassingly empty pages listed in the top navigation bar).