A Numeric Calculation
Source: Bodycombe, D. J. (1997). The mammoth puzzle carnival. New York: Carroll & Graf: 23.
This emphasis on using alternative thinking lan- guages, especially visual thinking, is now becoming the new frontier in scientific research (McKim, 1997). With the advent of the digital revolution, scientists are increasingly working with pictures and simulated images rather than with numerical data. “Scientists who are using the new computer graphics say that by viewing images instead of numbers, a fundamental change in the way researchers think and work is occurring. People have a lot easier time getting an intuition from pictures than they do from numbers and tables or formulas. In most physics experiments, the answer used to be a number or a string of numbers. In the last few years the answer has increasingly become a picture” (Markoff, 1988: D3).
To illustrate the differences among thinking lan- guages, consider the following two simple problems:
Assume that the numbers in Figure 1 are on a scoreboard. Shade in six segments of the num- bers and place a mathematical sign in the circle to create a correct calculation.
Figure 2 shows seven matchsticks. By moving only one matchstick, make the figure into a true equality (i.e., the value on one side equals the value on the other side). Before looking up the answers in the Appendix, try defining the problems differently by using dif- ferent thinking languages. How many answers can you find?
Commitment can also serve as a conceptual block to creative problem solving. Once individuals become committed to a particular point of view, definition, or solution, it is likely that they will follow through on that commitment. Cialdini (2001) reported a study in which investigators asked Californians to put a large, poorly lettered sign on their front lawns saying DRIVE CAREFULLY. Only 17 percent agreed to do so. However, after signing a petition favoring “keeping California beautiful,” the people were again asked to put the DRIVE CAREFULLY sign on their lawns, and 76 percent agree to do so. Once they had committed to being active and involved citizens (i.e., to keeping California beautiful), it was consistent for these people to agree to the large unsightly sign as visible evidence of their commitment. Most people have the same inclination toward being consistent and maintaining commitments.
A host of other studies have demonstrated the same phenomenon, even though commitment can sometimes lead to dysfunctional or foolish decisions, rigidly defended. Two forms of commitment that pro- duce conceptual blocks are stereotyping based on past experiences and ignoring commonalities.
The Matchstick Configuration
SOLVING PROBLEMS ANALYTICALLY AND CREATIVELY