A "small-is-beautiful" approach to upgrading a beginning geophysics course

Considerable attention is now directed toward improving earth science curricula, as illustrated by both presentations at national scientific meetings and discussions in the literature. Much of the discussion addresses large-scale changes, such as the development of new degree programs [e.g., Stein, 1996]. Such reforms can be very successful, but require lengthy interactions with university bureaucracies.

A complementary approach is to upgrade individual courses or groups of them. This approach has the advantage of being doable by individual faculty, without bureaucracy, and on small (or zero) budgets. We have been taking such a "small is beautiful" [Schumacher, 1973] or "faster, cheaper, better" approach to upgrade our introductory geophysics course. In discussion with colleagues elsewhere, we have found interest in this effort, and so summarize it briefly in the hope of encouraging discussions of similar experiments elsewhere.

We have begun with a beginning geophysics course required of geology majors, and taken as a distribution course by engineering majors. It provides a relatively rigorous and homework-intensive overview of the structure and evolution of the Earth and terrestrial planets, at a level higher than a descriptive "Geology 1" class, but lower than the standard introduction to geophysics for seniors or first year graduate students. For example, in this class we typically present without proof results such as Snell's law, which will be derived in later courses.

Although the course is highly rated, we wanted to make it livelier and to make the concepts more memorable. We decided to do this primarily (though not exclusively) with class demonstrations and experiments, rather than follow current trends and use computer simulations, for two reasons. First, computer simulations "work" even if the basic principle is wrong. For example, an experiment with light beams demonstrates Snell's law (the sine of the incidence angle divided by the velocity (sin i / v) remains constant when a ray passes from one medium to another), but a program can produce equally convincing graphics assuming i/v is constant. Second, many of today's students have not conducted or even seen (or, equivalently, have seen and forgotten) the once-standard experiments demonstrating many basic ideas of classical physics used in geophysics [e.g. Ehrlich, 1990].

We needed demonstrations that were inexpensive, easy to set up and take down, and which could be conducted in a standard classroom not set up for laboratory experiments. Fortunately, many suitable demonstrations are available at low cost from educational materials suppliers. We have also developed others using inexpensive homemade apparatus. This provided an inventory large enough to illustrate key concepts physically as they arise in class.

Our present repertoire includes:

Gross Earth and solar system structure:
We find Earth's mass from the acceleration of gravity by two methods: a ball drop using a commercial timer and photogate system, and timing several swings of a pendulum. (The pendulum method, which was pioneered by Gallileo, works as well or better than the more modern electronic method.) Racing a hoop and disk of the same mass down an inclined plane motivates the concept of moment of inertia, and leads to the idea of using a planet's moment of inertia to learn about its core density. When discussing solar system formation, we demonstrate conservation of angular momentum using a string connecting two balls threaded through a hole in the base of a cup. We set the upper ball swinging, so as the lower one slides down, the radius of the top one's orbit decreases and it speeds up.

Seismology:
We demonstrate aspects of seismic wave propagation using largely standard means. A block of foam rubber with a grid is used to illustrate the bulk and shear moduli. Light beams in a tank with a protractor back, whose upper and lower parts contain air and water, display both Snell's law (from the angles the beams make) and the angle dependence of the reflection coefficient (from the beams' brightness). We do a number of the standard wave (ripple) tank demonstrations for basic wave propagation, and local variants including using the disk (from the moment of inertia demonstration) as a "core" about which diffractions can be seen. P- and S-wave particle motions are illustrated with the classic "Slinky"and by rubber bands stretched over the open side of a plastic box. The latter demonstration is particularly useful because it shows how the wave speed depends on the tension (adjusted by stretching the string) and density (adjusted by attaching paperclips to the band). The idea of using travel times to infer structure is demonstrated using an inexpensive electronic (acoustic) distance measurement device to find the room's size.

We also use some computer simulations which reinforce concepts, showing features more clearly than we have been able to do with demonstrations. We illustrate a number of wave propagation ideas, including the effect of multiple reflections and transmissions, via a normal-mode simulation of waves on a string with an internal boundary [Geller and Stein, 1978]. We show a video simulation of seismic waves in a realistic Earth model, which demonstrates the relation between the seismic wave field and specific wave phases (e.g., ScS) [Wysession and Shore, 1994].

Composition of the Earth:
We illustrate the effect of atmospheric pressure by having students attempt to pull a standard plunger off a desk, and then consider pressures thousands and millions of times greater. We pour water into a detergent bottle with holes drilled at various depths, so the obvious difference in water flow demonstrates the increase of hydrostatic pressure with depth. Half-frozen apple juice illustrates fractional crystallization, and the presumed partitioning of elements between the inner and outer cores, when the class tastes the difference in sugar concentration between the solid and (sweeter) liquid. A simple Geiger counter demonstration illustrates the concept of radioactivity, and is made memorable using a banana or sports drink such as Gatorade (which contain potassium sufficient for clear signal). The relation between cooling rate and crystal size is illustrated by heating crushed moth balls and crayons in test tubes until they melt, then cooling the tubes at different rates (placing one in an ice bath and one in the air).

Paleomagnetism and convection:
A dipole magnetic field is illustrated using a commercially available clear plastic box filled with iron filings in oil, into which a magnet is slid (this works nicely on a overhead projector). We then use a dip needle to illustrate Earth's field. To demonstrate convection simply, we put a clear beaker containing water and mica flakes (which make reusable tracers) on a hot plate, and let it heat up. With proper lecture pacing and some practice, convection begins just as the Rayleigh number discussion reaches the appropriate point.

Plate kinematics:
We demonstrate a number of ideas central to plate kinematics using paper cut-outs, following the spirit of Cox and Hart [1986]. The cutouts nicely explain the often tricky concept of transform faults, and the relation between relative plate motions, rotations about Euler poles, and plate boundary types. A cutout of the Pacific-North America plate boundary zone in a mercator projection about the rotation pole lets students watch the boundary evolve and see how this single boundary contains ridge, transform, and subduction portions. We also simulate triple junction evolution, and do simple past plate reconstructions. Absolute plate motions can also be demonstrated, using a pencil as a "mantle plume" and moving one piece of paper (simulating a plate) over a fixed one simulating the mantle [Stein, 1997]. An additional feature of paper cutouts is that they make great homework problems, and provide a sense of the history of plate tectonics.

Although this effort is just in its second year, we have some initial feedback about how well it is working. It makes the class much more fun to teach (and TA). Anecdotally, we hear it makes the class more fun to take. Whether it helps students learn more is difficult to assess but, we believe that it can be effective, based on results from relevant experiments [Renner, 1979; Ward and Herron, 1980; Hake, 1992].

We plan to continue these efforts. We have found that it is also useful to do these demonstrations in upper division classes (seismology, plate tectonics, etc.). Even when the concepts in question are derived rigorously, rather than simply presented, simple physical examples liven up the class and provide a break from a steady diet of equations. As a result, we will be adding additional demonstrations, some of which will feature field equipment (GPS receivers, seismometers, etc.)

We are also exploring simple demonstrations specifically for upper division classes. For example, in signal processing we insert an acrylic slab with metal bolts into a wave tank to show the concepts of Huygens' principle, point diffractors, exploding reflectors and focusing of energy by a synclinal structure. To illustrate the problem of undersampling, we watch the title sequence of "The War Wagon" (many other Westerns would work) on video, and note that as the stagecoach speeds up its wheels appear to rotate backwards!

An important question is whether these examples are better done as demonstrations or as class lab exercises. The answer is not obvious to us. Our goal is not to teach specific skills, but to liven up class. Hence, although a short demonstration during class can be fun, a longer version done in lab might be viewed as a tedious chore by many students. Moreover, it is not clear that everyone in class gains equally by doing all the experiments. Therefore, we draft a few students from our small (less than 25 students) class to roll the disk, time the pendulum, etc. while the others watch. We would be interested in hearing from other instructors (and students) on how they feel about the issue of demonstrations versus labs.

We suspect that some of the demonstrations might also work in distribution courses for non-majors ("rocks for jocks" or "moons for goons"). This requires a somewhat different approach, because students in our class have some introductory physics, chemistry, and math, and so can follow equations. Still, many of the concepts can be explained in words without equations.

In summary, we are finding that much can be done to make classes more fun to teach (and hopefully take) by individual instructors and TAs working with a limited budget. We suspect that this process also helps students visualize concepts and retain more, especially in geophysics classes which sometimes seem more abstract than many other earth science classes. Naturally, many other forms of simple class enhancements are possible in different courses. We have created a WWW page with information about these demonstrations, would enjoy hearing from others conducting similar efforts, and think such an interchange would help improve geophysics education.

REFERENCES:

Wysession, M. E., and P. J. Shore, Visualization of whole mantle propagation of seismic shear energy using normal mode summation, Pure Appl. Geophys., 142, 295-310, 1994.

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