Alistair B. Fraser


Comment: This document loads some objects. I have tried to reduce download time by presenting low resolution versions. But, some items may stream in slowly.



Preamble: towards a better metaphor

There is a simple commonality to the examples I show, and indeed all others I can imagine. It stems from the function of pedagogical modeling: to build a better metaphor. Anytime one presents a model of nature, one is offering a metaphor, be it one of words, diagrams, mathematics, or computer animation. And an object of good teaching it to make the metaphors as good as possible so the students will develop realistic mental models.

Sometimes the traditional tools such as words and diagrams are fully adequate to the task; often they are not. There are many examples where the metaphors offered by teachers are so bad as to fundamentally misrepresent realty, and others where the student's conjured mental model inevitably contains major flaws. I offer one example drawn from my essays on  Bad Science , in particular the one discussed in  Bad Clouds .

When discussing clouds, teachers regularly tell their charges that a cloud forms when air cools because cold air cannot hold as much water vapor as warm air. This explanation is categorically false; it is not even a simplification for it accords with no atmospheric process. A correct (but not very useful) statement is, the air sometimes behaves approximately as if cold air cannot hold as much water vapor as warm air. The first statement offered a literal, the second, merely a bad simile. The fact is that air does not have a holding capacity for water vapor (despite generations of teachers who have claimed it so), yet the system sometimes behaves approximately as if it did.

On mousetraps: If you build a better metaphor, students will beat a path to your door.

So, if the student is to understand the behavior of nature, what is the teacher to do in this case. First, do not pass garbage off as insight (holding capacity of air) merely so students have something to parrot on a test. Second, if you carefully state the situation as a simile (behaves approximately as if air...), little practical improvement is made for the simple reason that most students will fail to recognize it as a simile and interpret it as a literal anyway. Indeed, why wouldn't they, their teachers are generally equally inept on that count.

The problem here is that the constrained medium of communication being employed --- words, diagrams, etc. --- does not readily lend it self to mimicking the natural processes. One solution is to move to a medium with fewer constraints. And the most versatile medium we have at the moment for presenting a pedagogical model which captures the essence of a natural process is the computer. Then teacher and students can play with the model to gain physical insight. One such model is presented below (the bottom one).

This, then, is the task at hand: do not merely transfer old pedagogical metaphors to the computer; use the powerful new medium to build a better metaphor.

The fly: simple interactivity

Curiously, this first animation was not built to solve a pedagogical problem in communicating with conventional students. Rather, it was built to show other teachers that it is often very simple to build a visualization that does a tolerably good job of mimicking the natural world. The small amount of coding here merely specifies how the fly should react to a rollover of the cursor.

Stability: a case study

Meteorology students (well, science students in general) must master the concept of stability. It surfaces in many guises whenever one is dealing with an equilibrium state (a state in balance). Thus, any discussion of the hydrostatic equilibrium, the geostrophic wind, a satellite orbit, the formation of clouddrops, and on and on, eventually turns to the question of whether the equilibrium in question is stable or unstable. Alas, more than 90% of students misinterpret the idea of stability as applying to the case of a disequilibrium and so bandy misunderstand the physical processes.

Grab the ball and place it anywhere on the surface. If in equilibrium, test stability. Show forces by clicking on the ball and dragging down.

My solution is to present an interactive  (Shockwave)  case study, one that, if understood, characterizes the stability of a multitude of equilibria: a ball on a surface. One can pick up the ball and place it anywhere. If the ball is then in an equilibrium position, not being subject to a net force, it will not move. Now the stability of this equilibrim position (there are three of them: the places where the surface is horizontal) can be checked. A test of the stability of an equilibrium involves seeing how the system responds to a minute departure from that state.

The forces on the ball can be displayed by clicking on the ball and dragging below the surface; then move left or right to see the forces change as the ball moves over the surface. In this model, the ball can interact with the student and the surface. One can also use the button to label various states. The background image shows a cumulus cloud and pilius growing in an atmosphere in which the stability of the hydrostatic equilibrium changes with height. Of course, one could have illustrated these same concepts used physical props (a marble and bowl), but it is certainly more difficult to illustrate the forces in that case.

Coriolis force: improving the metaphor

An understanding of the Coriolis force is a prerequisite to the understanding of long-lived motion on the Earth. As such it is central to everything from meteorology and oceanography to ballistics. Often a phenomenological approach is used to teach it: the teacher merely asserts a behavior without explanation. But, because the Coriolis force depends upon the rotation of the Earth, and because that rotation can be modeled in class with a turntable, teachers often explain the force using that as a metaphor. In using a turntable, teachers do a tolerably good job. The table is spun slowly and a straight line is drawn radially; the path over the turning surface is seen to be bent as if the object is responding to a lateral force: the Coriolis force.

Dismiss Options (Done). Click to start an object moving. inertial coordinates   non-inertial coordinates

The difficulty with this approach arises from the difficulty in drawing the line in other than a radial direction when using a physical turntable; it is just too difficult to move one's hand in such a way that velocities are closely matched in anything other than in the radial direction. Consequently, many students believe that the Coriolis force only acts on objects travelling in a north-south direction (this is even asserted to be the case on some Web sites). Actually, the Coriolis force is independent of the direction of the motion, but the metaphor employed in the classroom is incapable of showing this and so students (not to mention, their teachers) do not understand it.

Again, the solution is to build a better metaphor with the help of the computer. One is shown here. One can start an object moving from anywhere and so easily produce either radial or tangential motion. Further, as various forces can be turned off and on (compensated for) a rich variety of other relevant behaviors can also be explored: in building a better metaphor for the Coriolis force, other problems in the communication of physical motion were solved as a collateral benefit. For futher sense and nonsense about the Coriolis force, see my  Bad Coriolis  page and its attendant FAQs.

Cloud formation: replacing nonsense with a good metaphor

The preamble, above, presented the problem faced by a teacher who wishes to explain the formation of clouds to students. Although presented in virtually all elementary textbooks, the standard explanation, which speaks of a temperature-dependent holding capacity of air, is categorically false. It was an eighteenth century speculation which, although disproved nearly two centuries ago, continues to be taught to this day as if it were science. It ranks right up there with astrology as a bankrupt idea. Yet, the superficial plausibility of the standard explanation is sufficiently seductive that (like astrology) it persists.

So, I faced a pedagogical problem with my own students: how do I build a better metaphor (or in this case, one which had a least a semblance of verisimilitude). My solution (well, Mark 3, and counting) is the visualization below. It simulates evaporation and condensation and the way in which one, the other or both depend upon the temperature, purity and shape of the boundary between the vapor and the condensed phase (liquid or ice). One can initiate evaporation and watch the evolution of vapor number in response to changes in the various parameters. As a joke, a click on the frame of the moisture container adds air to the system (or removes it). There is no consequence to such an addition (other than the a squishing sound), for air is irrelevant to the system (which is quite contrary to the line offered by the teachers who attribute the behavior entirely to some mystical property of the air).

The point of this discussion is not as much the details of my particular solution, but merely that one can create a vastly improved metaphor for students with the aid of a computer.

|  Web Visualization  >

|  Chronicle article  |  Temporal Models  |  2D Spacial Models  |  3D Spacial Models  | Parametric Models | Process Models