Saturday, March 10, 2007

Style, pedagogy, and Purcell

This is not an idea yet. But I've been thinking lately about the relationship of curriculum development and teaching effectiveness to issues of pure style and aesthetics. Coming from the physics education perspective, I have been accustomed to thinking of curriculum development as a science. And I do think this is the best way to frame it. We need to know what works, and there are facts about this, in the way that there are facts about which therapies work for illnesses. And the main innovations in my teaching of Newton's Laws (well, at least I'd call them that) have come from the hard work of gathering data over a span of years. I might have done it more formally, made the data more quantitative, but the fact is that I asked, and asked, and asked, and listened, and changed my methods radically, and noted the results and changed my methods again.

But then again it might not be so accurate, this picture of me in a classroom with a white coat and a clipboard. The way it usually happened was in a sunny office with big windows, and two people with trust and warm feelings for each other. One of them maybe even beautiful, and one of them unintimidating and perhaps not so ugly either. (I guess if I was really serious about the aesthetic, I'd go back and correct that Bogart-esque rhythm.) In thinking about teaching and curriculum, we overlook questions of personalities and the personal for good reasons. But when you have a subject like physics that is so terrifying to people, I wonder if effectiveness might depend significantly on emotional and psychological factors. At any rate, I feel that my own effectiveness depends in part on these things.

I first thought of this general topic when I read the responses to a questionnaire that I gave to my students after we'd used a draft of the book as our primary text in physics class. One of the students wrote, "I'll always remember the sentence 'Forces are evanescent things.'" At first I skimmed past this, and then it sank in: he wasn't saying he'd remember the fact that forces are evanescent things, but rather the sentence that told him this. It struck me that something interesting had happened here: in crafting a successful sentence, I may have actually accomplished something concrete on the pedagogical front. (And of course the rhythm of the surrounding writing must also have contributed somewhat towards making this key sentence "pop.")

Students complain about the "dry" writing in the standard physics texts; can lively writing and a discernible authorial voice contribute significantly to learning outcomes? I think it is possible, perhaps especially with respect to a deep idea like the Laws of Motion. A friend wrote in response to this post, "From your comments below, I wonder if part of the distinction you're
making is a personal relationship you can have to the ideas in Newton's
Laws - the way you can to Hamlet - as opposed to the prosaic
relationship with the lenses. So in the right book about Newton's Laws
we'll want to hear the author's voice."

There are some other loose associations between "purely aesthetic" considerations and "purely intellectual" ones - such as the way certain qualities of verse make poetry amazingly easy to remember, or even the fact that in a published study (available here), professors' teaching evaluations were significantly dependent on the physical attractiveness of the professor. (See especially Figure 1 on page 23 of the PDF; every scientific paper should have a graph whose horizontal axis reads "Percentile of Beauty.") The authors are careful in stating their conclusions, but they do entertain the notion that the results may have been less about discrimination than about effectiveness. (p. 14 of the PDF) I wonder if, when you disaggregate their data by teaching department, subjects like physics get a "terror bump" in the strength of the effect.

I remember the sensual pleasure I felt during my undergraduate years when I regarded the proportions, the layout, the illustrations, and even the smell of Purcell's masterpiece Electricity and Magnetism. Didn't all these pleasures have something to do with how eager I was to apply myself to this difficult text? (Click the link, and notice that fifteen years after I graduated from college, this book is still sold in the same hardcover format, with its peculiarly square height-width ratio.)

Here is the first Amazon review of Purcell's book, by Professor Henrique Fleming of Sao Paolo, Brazil. The emotion is unmistakable, the book and the reviewer virtually characters in a romance:

"This book must have been a work of love. The reader of it who fails to fall in love with electromagnetism would better change his direction of study, as he will not find anything better, including the marvellous Feynman's "Lectures on Physics". Following a more-or-less historical approach, except for the early use of relativity, the author strives to get the results from a full understanding of the physical situation. This is obtained by the use of very clever intuitive models. After that comes the mathematics, rendered natural and welcome. An outstanding example is the treatment of polarization of a dielectric sphere, where most of the physics is derived from a drawing! Another feature, to be found only in books written by great physicists, is the ability of stretching the argument up to its limit, getting results we wouldn't think possible with so little formalism. Problems are extremely good and real. The drawings, done by the author himself (so I read some! where) are very beautiful and helpful. Some of the exercises are of numerical character, motivating the use of computers. After meeting this book I could never teach introductory electromagnetism from another text. The author, Edward Purcell, is a Nobel prize winner who discovered, among many other things, nuclear magnetic resonance."

It is instructive to compare this with the second review, by a Kevin Costello (perhaps this person?):

"This is a (very heavily mathematical) introduction to the physics of Electricity and Magnetism. Although it has some strong points (It takes the time to explain the math behind div, curl, etc. and some of the problems are rather neat), it also has its weaknesses. First and foremost, the problems are almost universally without solution, except for a select few whose numerical answer are written below the problem. Combine this with the almost total dearth of examples, and you have a pretty serious problem for anyone trying to learn the material on their own. The sections themselves are also sometimes rather poorly explained. Chapters 5(explaining magnetism as the relativistic effect of moving charge) and 10 (dielectrics) are both fairly confusing and hard to understand. At times I found myself begging Purcell to include one, just one little measly example that could possibly make more sense than his pages and pages of writing. Once or twice I found myself not noticing that I had a fundamental misunderstanding of a facet of the material, just because no example or solution in the book provided a counterexample to my way of thinking."

It will come as no surprise if I say I'm solidly with Henrique Fleming in this argument, but the second review does raise some interesting issues. I do actually remember Purcell's book as brutal when it came to the problem sets, and yes it was precisely because there were no example problems in the chapters. Purcell must have taken the view that the only way to learn these things is to struggle over them; it can't be shown, it must be discovered. This is actually not far from the currently accepted wisdom in some ways. I don't take it as far as Purcell did - my book has plenty of worked examples - but compared with contemporary texts, my book probably looks a lot more like Purcell than most of what's out there today does. Connell's last point is more interesting, to do with Purcell's failure to anticipate and prevent common misconceptions. Here physics education research has made leaps and bounds since Purcell's day.

It may after all be reasonable for Connell to ask for more in a text, but many students seem to want the impossible, which is for physics to be made effortless. And the publishers will certainly promise it to them. Not long ago I read the back cover of Physics Demystified, where it says it's going to make physics "fun, effective, and totally painless." I guess if you are talking about 'commodity physics' (haven't got a better way to characterize it yet), this is possible. But ask the most successful physics students if physics has been painless for them, and all you will get is bitter, bitter laughter.

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