Adrienne Allen
NB: I wrote this over the week without much attempt at coherence; as a result, it's even more random than usual...sorry! Feel free to ask/email/tell me to write a few connecting sentences if it's really unclear.
There seemed to be little intersection between the topic of the talk and the content of it. I suppose the point
of closest approach is the idea that by making math less a process of learning by rote, and more a process of
learning to consider the world from a particular (i.e., quantitative) point of view, students become more
involved in it, and even despite a heavy workload, seem to enjoy it. I was reminded of the semester
I tutored a woman from Lyons, who was employed as a teacher's aide, in basic math. While the text
seemed very formal, abstract and distant, her teacher made an effort to relate the work to the real world.
How do you use this information to convert recipes? Calculate tax? Understand a graph in the newspaper? She
was so interested in learning these things and being able to apply them, it was actually inspiring to me;
it was clearly opening up a whole new world for her.
One wonders if perhaps this personal involvement
is much of the attraction of humanities courses- perhaps it is not their ease or their mythical lack of a
correct answer, but rather the way in which one is able to personally contribute to the class, instead of
having it always be something abstract and external (which is how many math and science classes are).
You can argue whether or not the author is referring to the Ulysses story here, and usually come to
a conclusion, but if what you're supposed to learn is that the charge to mass ratio for an electron is...
Where is the personal input in that? Which doesn't mean that one can't present science and math subjects
in a more interactive way. ("What are the relevant length scales here?" and "When is
the Wigner-Eckart theoem useful?", for instance, encourage discussion in ways that "What is the
value of the magnetic force at x=3.5cm?" or "Does the proportionality constant in the Wigner-Eckart
theorem depend on geometric properties?" do not.)
Not-so-random anecdote #2: While in Costa Rica, I took an "Introduction to Meteorology" course for non-science majors. In addition to learning to read weather maps and classify hurricanes and do some of the usual intro to meteorology type things, everyone in the class had to do a project whose topic was "How meteorology relates to my major", and present it in class. While this was kind of a bummer of a topic for me (how does meteorology NOT relate to a physics major?), it was really interesting to see what artists, education majors, literature majors and economists came up with. It also really involved them in the course, and they were very excited to talk about something they knew (relatively) well, much more excited I think than they would have been if the topics had been more traditional: "What we know about tornados" etc. And given the nature of the class, I think that was a much more useful exercise than having them present something on a topic they were not scientifically or mathematically prepared to understand fully. While in a large class these presentations would be impractical to say the least, I think the projects wouldn't be. Students often complain about doing something "like, totally unrelated to my major". I really you to find a major which is totally unrelated to astronomy....totally unrelated to the Chandresekhar mass, sure, but totally unrelated to astronomy? Unlikely.
In some of the introductory physics classes which I've TA'd here, one encounters the problem that Jim Dove mentioned - not so much math anxiety as abstract-concept anxiety. Prevalent in a lot of the engineering students I've encountered, concept anxiety (or concept loathing, at times) is evidenced by a resistance to formulating problems or devising solutions with little reliance on canned formulae. I wonder if such a problem is a result of the ideas that students have about science as a consequence of their early science classes, i.e., that it is simply a big ole mound o' facts. While I don't know this, and didn't experience it as an astronomy tutor (with my grand sample of 6 students!), I suspect that this is also evident in introductory astronomy courses. (I'm reminded for instance of the comment Kelsey received on her FCQs once: "There was too much of an emphasis on thinking in this class." And presumably too little emphasis on remembering the names of the constellations and one small, witty historical fact about them...)
Just for the record, the only classes I had which I spent at least 5-6 hours per week on were literature classes. (At least until graduate mechanics...) And yes, they were still often my favorite classes. My physics and math classes were often really boring: sitting and taking notes. And the exams tended to be on the material covered in class or in the text; sure, you had to understand it well enough to do problems, but you didn't have to come up with anything original. You do a substitution, and oh, look, it's the Bernoulli equation, and (big surprise) you write down the solution. Physics was pretty much the same, except you usually had to come up with the equation first. (Lab courses naturally were different.) But in general, there was nothing unexpected. Not so my literature classes, where exams could involve texts you'd never seen before and certainly involved essay questions not discussed in class. Exams aside, literature classes were much more fun to be in - no one ever got into discussions in physics or math classes, unless the professor made people guess how to work a problem. Even then the discourse was not among students but between student and professor, so it was more like a question-and-answer session than a discussion. So it was very hard for me to relate to the humanities-bashing that Jeff Bennett (and to a certain extent, David Griffiths) seemed so fond of.
One wonders if one of the reasons that physicists and astronomers have such a poor opinion of humanities majors might be that they took the English department's equivalent of "Physics for Poets" or took "French I and II" and think that that's what English majors and French majors do for four years. (My evidence for this assertion comes from the physicists that I know, admittedly a limited pool, and from my observations of physics profs from CU in the "Basic Humanities for Ignorant Scientists" colloquium series that was presented last year, also more anecdotal than statistical.) In a related anecdote, I once had a math major tell me that "physics majors don't understand much math". I asked why he thought this, fully expecting some reference to our referring to a "delta function" when it isn't really a function, or to our using mathematical properties which only hold for compact sets without first checking if the set we're using is compact. Imagine my surprise when the best example he could come up with (he had only taken intro physics) was "Well, they use an expansion for sin(x) that's only valid for small x, and the picture of the pendulum clearly shows x is pretty large; see, they don't even understand the idea of a power series expansion". As the saying goes, a little knowledge can be a dangerous thing.
Recently while browsing in the bookstore I stumbled across a book called "Second language learning and use"
which addressed various issues relating to second language learning and second language use. In the
first chapter (as far as I got before research-guilt set in), the author discusses several learning
styles, discusses what happens when there is a mismatch between the learners' preferred learning style
and a teacher's preferred instructional style, and what one can do about it, as well as specific learning
strategies. Of course, this discussion rests on the numerous studies which have been done on how people
learn second languages, as well as on the many studies conducted to determine which teaching techniques
are useful.
Are there such studies done in physics and astronomy? If not, why not? I find it
somewhat disturbing that these disciplines, which pride themselves on being "hard (not soft)
sciences," seem to rely primarily on anecdotal evidence and intuition, with all the biases
inherent therein, when developing teaching techniques.