In my last entry, I touched on a rather difficult topic: how best to improve outcomes for women in college-level physical science courses. I don't think there are any simple answers to that question. Certainly the research being done on the topic has noble goals and the people working on it should be commended; they've done great work in finding ways to improve all students' learning, including women's. Nonetheless, I think the question itself is ill-formed. Before you read on, allow me to warn you that I have not done any research on the subject and am not in any way qualified to make authoritative statements about 50% of the human population of the planet; however, if you are interested in a 100% pure-opinion discussion of female students from the perspective of a female physical science student, please continue.

There is a reasonably large amount of relatively convincing evidence, as far as evidence in the social sciences goes, that when taken as large groups women and men are more alike than different. There do, of course, exist real differences. However, it is highly questionable whether generalized differences between large populations can be applied to tiny, self-selected subsets thereof. A difference between the populations of all males and all females which is statistically significant at the population level may not, and likely does not, have any predictive value for a sample of size 30 or 40, especially when that sample is self-selected for attributes that may very well correlate with the trait in question.

Therefore, I would urge anyone who is involved in teaching or curriculum development for college-level science courses to be very cautious with any statement of the form "Women are X" or even "Most women are X" or "Most women are more X than most men." It may be true. It may even be an accurate description of your wife, mother, daughter, self, or one or more memorable students. But there is no reason to believe that it will be true of any individual student and very little reason to expect it to be true of your students in general. The sizes of the differences between women and men in large-scale studies are tiny, and the individual differences among both men and women are far, far larger. Generalized ideas about men and women will not be helpful when working with individuals and small groups.

That is not to say that these generalized studies of gender differences are not relevant or useful. Certainly they can tell us some important things; the cohort studies in particular are interesting, as they help illuminate some mysterious elements of gender differences, telling us when - and occasionally why - girls diverge from boys in various aspects of psychology. However, to use a physical science analogy, studying overall gender differences in a population is like studying climate: you can make some useful predictions, but they only make sense on a large scale. A climate model can't tell me anything about the weather in my town tomorrow, in my county next week, or even in my state next month, and it will be shaky about next year - but it should be pretty good for my region over the next decade.

Keeping that in mind, I do have some constructive suggestions that I believe can have a positive effect on outcomes for traditionally-underperforming groups in physical science courses, including women and to some extent cultural minority groups.

1. Do not assume that your students know anything.

1a. Any required formal academic background for the class or major, including high school mathematics and science education, should be documented clearly in the course description; outlines of the content that should have been covered in high school classes should be freely available from the department. Prerequisites, including required high school preparation, should be enforced. Placement tests are not a bad idea - they have worked quite well for math departments.

1b. The expected informal/non-academic backgrounds for students entering your course/degree program should also be stated explicitly. This requires a certain amount of introspection; it is difficult to construct an explicit outline of the sorts of informal science and engineering experiences you expect your students to have come in contact with over the course of their lives. However, it will benefit both you and your students to make the effort. If you have a habit of using airplanes and bouncing balls as examples in your mechanics class, your students should know some basic ideas about airplanes and have played with a Superball at least a few times. If you can get together with other faculty members teaching introductory courses, you may even be able to put together a one- or two-credit preparatory course, or perhaps an optional seminar to parallel the introductory sequence, which focuses on these sorts of informal experiences with the physical world - building model airplanes, going to air shows, building or repairing simple electronics, stargazing, dissecting a telescope to see how it works. As a group, your female students are less likely to have had these experiences than your male students (although still more likely than the general population, since your class is self-selected for physical science interest) and are thus at a disadvantage in conceptual understanding.

2. Ensure that your students have a mix of both collaborative and non-collaborative out-of-class assignments and that not all collaborative assignments are done in exactly the same groups. Some students tend to dominate collaborative work, and others may be too timid to speak up or unaware of other students' subtle dominance (this may or may not break down along gender lines, and whether it does or not is completely unimportant). On the other hand, students often can genuinely learn from each other in collaborative assignments. If you encourage students to work together on homework, give a few low-stakes take-home tests or other independent assignments throughout the term to challenge your students and help them evaluate their own independent ability to solve problems. If you assign lab groups or project groups, ensure that you vary their composition. If you allow students to select their own groups, watch for subtle signs of problems (if a student's labs and homework show an excellent understanding of material but he/she appears lost on tests, that's a warning sign that he/she is relying too much on his/her group and should probably try working alone or with different people; the student may not realize this on his/her own, and it only takes a few seconds to write a quick note on a test or have a word with him/her after class).

3. Teach in a style with which you are comfortable. If you try new pedagogical techniques and discover that they take time away from presenting needed material or that they feel ridiculous, stop. The vast majority of your class will benefit most from you teaching in a way such that you feel comfortable and can muster as much enthusiasm as humanly possible for your subject. The fact that a study shows a technique to be effective does not mean that it will mesh well with your personality.

4. Try to avoid stereotyping and deal with your students as individuals. The young black woman in your class may be a future physics major who will exceed all your expectations and need a greater challenge, and the glasses-wearing kid who looks just like a younger version of you may be struggling desperately to pass the calculus-based physics class he selected because it would good on his law school application. Both will need support to reach their goals, but the support required will be of vastly different types and cannot be discerned from their gender or physical appearance.

5. Try to use inclusive examples of real-world applications of your physical science concepts. One excellent example that was used by my current physics professor was the application of rotational motion concepts to figure skaters. Most modern physics textbooks have an excellent selection of problems; take a look at your assignments and try to include a variety of problem types, making sure that not all of them involve guns, baseballs, slingshots, and rockets.

6. For those instructing physical science classes with students who will probably go on to take standardized tests in the field: Work with your department to arrange some sort of optional course or seminar that teaches standardized test-taking explicitly. Encourage your female students to take it. Many instructors include some multiple-choice questions as part of their regular tests, which is good, but one generalization that has proven true and significant among female physical science majors is that we tend to do worse on standardized tests than our male peers; evidently we are not absorbing the implicit teaching as currently implemented. Test-taking is a skill that can be taught, and your female students will go on to be more successful if they learn it.

Overall, I think most professors do an excellent job. As I noted in my previous post, the amount that a college professor can do about the "gender gap" is somewhat limited; students, both male and female, who come into a class with less will leave with less. But there are some few things you can do to help even the playing field for all of them.

## Thursday, December 4, 2008

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My first inkling about the importance of not making too many assumptions came when I was in grad school. My office-mate was having a hard time with a homework problem that was a simple (if you understood multivariate calculus -- which one does rather assume of graduate students in math-heavy sciences) matter of integrating terms that were given to us in the problem. Her comment "Just because I passed a class doesn't mean that I learned the material."

ReplyDeleteOn one hand, it rather

shouldmean exactly that. On the other, reality intervenes and even if a student has had a course that I as a teacher of some later class would think sufficient to understand my stuff, I really should not assume that it is the case.I had a more extensive introduction the last time I taught astronomy (100-level at a local community college). Though the class did have a math requirement, and my nominal expectations were well below that, I wound up giving my own in-class math placement test. I made a number of changes after discovering that few in the class could operate at a jr. high to high school pre-algebra level.

Next time I teach, whenever and whatever that is, I'll have some math and other in-class placement (or maybe I should call them warning?) tests in hand.

For the non-math sides, I've also started looking at the cultural assumptions. That, for instance, students will know what the path of a ball through air looks like. (I already know that this can't be assumed.) There are many such things. Some lend themselves to being labs (ok, go toss some balls, drop some and see how high they rebound, ...).

The problem I've seen a lot of is not so much what I'd call a math weakness, but a math applications weakness. Many math instructors and most math textbooks seem to try very, very hard to teach specific skills in sequence and in isolation. They are also generally very artificially consistent with notation, using the same letters for the same things almost every time. Applications problems in math classes are almost invariably a matter of "take the formula, theorem, or process you just used on the last 50 problems, figure out where the given information fits into it, and crank the problem out in exactly the same way."

ReplyDeleteThis does help students remember the processes well enough to progress in math courses, but it's not what's needed as preparation for science courses. When dealing with a science problem, one has to have one's math memories cross-referenced, not just sequentially ordered; one has to be able to reach back and pull out some techniques from pre-algebra, some from calculus, some from trigonometry, and some unique to science, and one has to be able to decide how to put them all together. In the process, one has to deal with scientists' peculiar notation habits and different variable names and moving coordinate systems, which tend to fail to "trigger" the correct process in students who have been well-conditioned by math departments.

Now, obviously this isn't the main problem for your students in intro astronomy courses who are barely functioning at a pre-algebra level. It may, however, have been an issue for your grad school office-mate.

I have to second your notion that too much math instruction falls into the "rote" mode of cranking out problem after problem with no real application attached.

ReplyDeleteHigher math is not my strong suit to begin with, but undergrad Calc II made no sense whatsoever to me until I took my first Graduate Physical Oceanography class, and we started doing motion equations for water parcels in differing sized basin. I still claim no math expertise as a result of that, but at least then I could see how it all came together. Perhaps we should have folks from non-math disciplines ( who are never the less trained in math) teach the calc I and II classes - if only so students don't get lost in the letters.

Much of math post-calculus level you simply lose if you don't use it enough. I'm sure a lot of scientists forgot many of the "integration techniques" such as trig. substituions, integration by parts, etc....the vital part is that they know what an integral means and why they or someone else should use it. "Solving for x" can be done with a calculator. I wonder what the recommended approach is for someone who forgot some of the stuff that is assumed in higher-level courses.

ReplyDeleteI think it depends on what's forgotten. If one has no idea what a derivative or an integral means, one should probably take calculus again. If one can't recall which trig substitution to use for e.g. int(sqrt(1+x^2)), one should do a few problems in the relevant section of a calculus text. If one doesn't recall the exact formulation of Green's Theorem, one can use the Google.

ReplyDeleteAs far as the actual doing of the math, most things (including symbolic differentiation and integration of anything that can be done comfortably by hand) can be done with a calculator. Virtually everything can be done by computer. The key though, in both of those, is that you have to know how to set up the problem, which requires a not-insignificant level of understanding and skill. Having learned how to do a decent amount of math by hand and by computer, I have to say it's actually

harder, in a lot of ways, to do calculus by computer if you're only doing it once (unless you're doing iterated integrals of nauseatingly complex multivariable expressions clearly never intended for human consumption). The main advantage is that if you want to run the same sort of procedure over and over using different functions or constants or whatever, or if you want to do relatively simple numerical computation on large quantities of data, the process is automated.I'd be distinctly surprised, in other words, to find out that a significant number of scientists whose field of work involves doing symbolic math on a regular basis have forgotten how to do it. Not only did most working scientists grow up before the technology to do this sort of stuff was widely available, but the technology in its current form just doesn't have any advantages for one-off problem-solving unless the problem involved is hideously complex. Of course, many modern scientists deal mostly with statistical analysis of large amounts of numerical data, but then even without computers their calculus skills might still get rusty without practice.