Thinking and Deciding

22 WHAT IS THINKING?
We might be tempted to suppose that the valve theory is maintained by its functional
value in saving fuel rather than by the ready availability of analogies with other
valves (accelerators, faucets) and by its explanatory value. This conclusion does not
follow. To draw it, we would need to argue that the functional value of the valve
theory causes the theory to be maintained (Elster, 1979). Are people really sensitive
to the amount of fuel they use? People’s beliefs sometimes are for the best, but, as
McCloskey argues, sometimes they are not.
This example is a particularly good illustration of naive theories, because it seems
likely that the subjects have actually thought about how thermostats work. They
have had to face the issue in learning how to use them. In the previous examples
from college physics, it is not clear that the subjects really “had” any theories before
they were confronted with the problems given them by the experimenters. They may
simply have constructed answers to the problems on the spot. The fact that their
answers often correspond to traditional theories simply reflects the fact (as it would
on any account) that these theories explain the most obvious phenomena and are
based on the most obvious analogies. After all, balls thrown with spin on them keep
spinning; why should not balls shot out of a curved tube keep curving as well?
The home heat-control theories seem to provide yet another example of restructuring
(assuming that some people change from the valve theory to the feedback
theory). Like the Copernican theory of astronomy, the fully correct theory requires
new concepts, such as the concept of heat flow over a temperature difference and that
of radiant heat. The theory establishes new relationships among concepts, such as
thermostat settings and heat flow. It also explains different phenomena, such as the
fact that the house temperature stays roughly at the setting on the thermostat.
Understanding
Students and their teachers often make a distinction between understanding something
and “just memorizing it” (or perhaps just not learning it at all). Everyone wants
to learn with understanding and teach for understanding, but there is a lot of misunderstanding
about what understanding is. The issue has a history worth reviewing.
Wertheimer and Katona
Max Wertheimer (1945/1959), one of the founders of Gestalt psychology in the early
part of the last century, is the psychologist who called our attention most forcefully
to the problem of understanding. Wertheimer’s main example was the formula for
finding the area of the parallelogram, A = b · h, where A is the area, b is the base,
and h is the height. Wertheimer examined a group of students who had learned this
formula to their teacher’s satisfaction. On close examination, though, they turned
out not to understand it. They could apply it in familiar cases such as the following
parallelogram: