simultaneously on the several aspects of the problem. The more detailed the factorization of the problem, the more simultaneous activ- ity is possible, hence, the greater the speed of problem solving.
A Slice of Cake
To see how subdivision helps develop more alter- natives and speeds the process of problem solving, con- sider the problem, common in the creativity literature, of listing alternative uses for a familiar object. For example, in one minute, how many uses can you list for a Ping Pong ball?
Source: Dispezio, M. J. (1998). Challenging critical thinking puzzles. New York: Sterling Press: 49.
The more uses you identify, the greater is your flu- ency in thinking. The more variety in your list, the greater is your flexibility in thinking. You may have included the following in your list: bob for a fishing line, Christmas ornament, toy for a cat, gearshift knob, model for a molecular structure, wind gauge when hung from a string, head for a finger puppet, miniature basketball. Your list will be much longer.
Now that you have produced your list, apply the technique of subdivision by identifying the specific characteristics of a Ping Pong ball, that is, dividing it into its component attributes. For example, weight, color, texture, shape, porosity, strength, hardness, chemical properties, and conduction potential are all attributes of Ping Pong balls that help expand the uses you might think of. By dividing an object mentally into more specific attributes, you can arrive at many more alternative uses (e.g., reflector, holder when cut in half, bug bed, ball for lottery drawing, etc.).
One exercise we have used with students and executives to illustrate this technique is to have them write down as many of their managerial strengths as they can think of. Most people list 10 or 12 attributes relatively easily. Then we analyze the various dimen- sions of the manager’s role, the activities in which managers engage, the challenges that most managers face from inside and outside the organization, and so on. We then ask these same people to write down another list of their strengths as managers. The list is almost always twice as long or more. By identifying the subcomponents of any problem, far more alterna- tives can be generated than by considering the prob- lem as a whole.
One final illustration: Assume that someone stole one-fourth of the cake shown in Figure 10. Four hun- gry athletes want equal pieces of what’s left. Divide the cake into exactly four pieces equal in size, shape, and area. Try to do it in a minute or less. The problem is easy if you use subdivision. It is more difficult if you don’t. One of the answers to the problem is in Appendix 1.
Combine Unrelated Attributes
A third technique focuses on helping problem solvers expand alternatives by forcing the integration of seem- ingly unrelated elements. Research into creative prob- lem solving has shown that an ability to see common relationships among disparate factors is a major factor differentiating creative from noncreative individuals (Feldman, 1999). Two ways to do this are through morphological synthesis (Koberg & Bagnall, 2003) and the relational algorithm (Crovitz, 1970). (For literature reviews, see Fine, Ward, & Smith, 1992; and Starko, 2001.)
With morphological synthesis, a four-step pro- cedure is involved. First, the problem is written down. Second, attributes of the problem are listed. Third, alternatives to each attribute are listed. Fourth, differ- ent alternatives from the attributes list are combined.
To illustrate this procedure, suppose you are faced with the problem of an operator who takes an extended lunch break almost every day despite your reminders to be on time. Think of alternative ways to solve this problem. The first solution that comes to mind for most people is to sit down and have a talk with (or threaten) the operator. If that doesn’t work, most of us would just fire or transfer the person. However, look at what other alternatives can be gener- ated by using morphological synthesis (see Table 7).
You can see how many more alternatives come to mind when you force together attributes that aren’t obviously connected. The matrix of attributes can cre- ate a very long list of possible solutions. In more com- plicated problems—for example, how to improve qual- ity, how to better serve customers, how to improve the reward system—the potential number of alternatives is even greater, and, hence, more creativity is required to analyze them.
The second technique for combining unrelated attributes in problem solving, the relational algo- rithm, involves applying connecting words that force a relationship between two elements in a problem. For
SOLVING PROBLEMS ANALYTICALLY AND CREATIVELY