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One consequence of this program fragment is that, if there is no force, velocity never changes. This is called Newton s first law, and it is counterintuitive. In everyone s experience, (earthly) motion always dies away. The representation makes no difference as far as this existence of the issue is concerned. A second typical problem is that, like Aristotle, many students feel the speed (magnitude of the velocity) of an object should be proportional to the force that you apply to it. A bigger engine makes a car go faster; in order to run faster, you have to do more work. But this would correspond to a law where velocity, not change in velocity, is proportional to force, change v F, rather than change v v + F. Again, the conceptual problem remains. For these two conceptual problems, the programming representation strips away a lot of complications, including units and limits (calculus), so that the core conceptual problems are exposed. For engaging those problems, students have the advantage of seeing exactly how different laws (F = v or F = v) correspond to different behaviors. They can make a simple edit to the program, and can see (or, perhaps better, run in their imagination to infer) the consequences. In net, the programming representation does not finesse the conceptual problems, it purifies so as to expose them more clearly, and it embeds them in a richer analytical/empirical set of experiences (which are, of course, dependent on the social practices engendered in the classroom). One sees the same pattern in learning again when forces and velocities become vectors. A principal conceptual problem is that when force is perpendicular to velocity, the speed (magnitude or length of velocity) does not change at all, but the velocity vector rotates. This is how it can be that 246
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New-Media Literacies objects orbit in a circle (roughly like the moon around the earth) at a constant speed, even as gravity is accelerating them toward the center of their orbit (accelerating the moon downward, toward the earth). Students in high school or freshman physics classes memorize in circular motion, the acceleration is toward the center of the circle, but they seldom understand it. The computational representation allows students to see exactly what happens to the vectors, one step at a time. With standard representations, seeing the consequences of a given force law involves a technically advanced task, solving a differential equation. Furthermore, with a simple program, students can play with the phenomenology. They can see how a force not-quite perpendicular to velocity speeds the object up or slows it down, while still re-aiming it (rotating the velocity). At the other extreme, a force aligned with velocity increases or decreases speed, but there is no change in direction. Forces not-quite aligned with velocity rotate it a little, in addition to changing speed. All together, these different experiences lend a fabric of sensibility to the initially counterintuitive fact that a force perpendicular to a velocity maintains speed, but rotates the velocity. Here, the contribution of the representational form is that simple experiments can be transparently notated, conceptualized (in seeing each step in the program), and experienced. Notes
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1 I want to make clear that I do not consider these fair and complete characterizations of Phase I researchers. They are rather homogenizing descriptions, closer to caricatures by critics. For my purposes, they are intended as backdrop oversimplifications that nonetheless provide a ground on which to position the points that follow. 2 I do not cite the individuals because I have reason to believe that both have moderated or changed their views since they spoke these words. 3 Surprisingly, however, many of our tasks seem to work as well for sixth- or seventh-grade students as for advanced high schoolers. 4 diSessa (1993) describes the nature of some intuitive knowledge that is virtually perceptual in form. A fair amount of work in experimental psychology has shown that modality of presentation (text, pictures, moving pictures) makes a difference in conceptualization. 5 The role of such representations in professional science is a critical complementary study. In short, we believe new media of exactly this type are revolutionizing science. That is, however, not a topic for this chapter. 6 This set of steps were reported to us by the teacher. Unfortunately, we did not video the first session. 7 For example, multimodality does not necessarily entail the level of abstraction, the precision, the degree of explicitness, the grain-size of articulation, the fit
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