Problem Solving

l. Mechanical Solutions. They may be achieved by trial and error or by rote.

Trial and error: If I forget the combination to my bike lock, I may be able to discover it by trial and error. In an era of high-speed computers, many trial-and-error solutions are best left to machines. A computer could generate all possible combinations of the five numbers on my lock in a split second.

Rote: When a problem is solved by rote, thinking is guided by a learned set of rules.

2. Solutions by Understanding. Many problems cannot be solved mechanically or by habitual modes of thought. In this case, a higher level of thinking based on understanding is necessary. Karl Duncker, German psychologists, found that there were two phases to successful problem solving.

General Properties. A solution that correctly states the requirements for success but not in sufficient detail for further action. One discovers the general properties of a correct solution (one who understands the general properties of the puzzle can solve it consistently)

Functional (workable) Solutions. A detailed, practical, and workable solution.

3. Heuristics. Problem-solving strategy. Solving problems often requires a strategy. If the number of alternatives is small, a random search strategy may work. This is another example of trial-and-error problem solving in which all possibilities are tried. Typically, heuristics reduce the number of alternatives that a thinker must consider. In more complex problem solving, heuristics do not guarantee success, but they certainly help. Here are some strategies that often work:

- Try to identify how the current state of affairs differs from the desired goal. Then find steps that will reduce the difference.

- Try working backward from the desired goal to the starting point or current state.

- If you can't reach the goal directly, try to identify an intermediate goal or subproblem that at least gets you closer.

- Represent the problem in other ways, with graphs, diagrams, or analogies, for instnce.

- Generate a possible solution and test it. Doing so may eliminate many alternatives, or it may clarify what is needed for a solution.

4. Ideal Problem Solving. Most valuable heuristic of all is having a general thinking strategy. Psychologist John Bransford and his colleagues list five steps that they believe lead to effective problem solving:

l. Identify the problem.

2. Define it clearly.

3. Explore possible solutions and relevant knowledge.

4. Act by trying a possible solution or hypothesis.

5. Look at the results and learn from them. Of course, each atempted solution may identify further subproblems. These can again be tackled with the "ideal" steps until a final satisfactory solution is found.

5. Insightful Solutions. With humans we say that insight has occurred when an answer suddenly appears after a period of unsuccessful thought. An insight is usually so rapid and clear that we often wonder how such an "obvious" solution could have been missed. If the insight is not rapid, may be heading for a mistake. Psychologists Robert Sternberg and Janet Davidson (1982) have studied people as they solve problems that require insight or "leaps of logic." According to them, insight involves three abilities.

l. Selective encoding. Refers to selecting information that is relevant to a problem, while ignoring distractions.

2. Selective combination. Bringing together seemingly unrelated bits of useful information.

3. Selective comparison. The ability to compare new problems with old information or with problems already solved.