REPRESENTATION OF THE PROBLEM
Usually the problem solving process follows a typical sequence of identifying the problem, representation of the problem, planning the solution, execute the plan, evaluate the plan and evaluate the solution. Although all stages are important, the representation of a problem appears to be very important. Representation of the problem refers to the way a problem is depicted in the mind i.e. an internal representation of the problem.
A problem can have more than one representation, because the person often redefines the problem in his or her own way. For example the representation can be visual, imagery, algebraic, verbal analogy etc. The question is, what is the best way to think of a problem in order to solve it more easily? Here we find some individual differences for example, some people claim they usually think visually. However, some problems can be solved much more easily with one form of representation than another.
ROLE OF REPRESENTATION
The following illustration helps us understanding how the problem of representation influences the problem.
"Of course, I could go out and buy one, but that would take time and money. I could make one from an old newspaper, or wrapping paper, but the paper must be sturdy. Then there is the matter of use. Streets are not so good, the beach is perfect, and an open field is also ok. Finally, the weather needs to be good; kind of windy, and definitely no rainstorms.
As you read the above paragraph, you can undoubtedly understand every word and sentence, and yet you have a gnawing feeling that you really do not understand what is going on. However. if you were informed of the theme of the paragraph is how to make and fly a kite, everything falls into place and you comprehend the entire passage and problem. Thus representation of information is very important in problem solving.
ALTERNATIVE REPRESENTATIONS
In solving the problems of deduction, people may use either analytical or nonanalytical representations to which they apply logical tests. People also use a variety of imaginal and linguistic representations in solving problems of linear ordering. Under some conditions, we may construct an integrated representation containing all the forms of representation. Whether subjects form a holistic or a piecemeal representation, however, depends upon the materials, the procedure used to present the items, and the test that is administered.
The representation of the problem may vary in reasoning problems
The kind of change in representation necessary to allow a solution to a problem is very subtle. One well-known example is the 'nine-dot" problem. The problem is to draw four straight lines through all of the nine dots depicted in Figure 28.a without lifting the pencil from the paper.
One way to solve this problem is to look at the dots and imagine drawing the four lines so as to connect all of the dots. This imaginal strategy involves constructing visual representations of the dots and the lines.
Adams (1974) calls this difficulty as "Conceptual block"-problem solvers impose an unnecessary constraint on the problem that actually blocks its solution. If problem solvers can modify their internal representation of the problem by eliminating this constraint, they may experience a feeling of insight.
Wickelgren (1974) suggests that insight usually involves making some crucial inference from the information given (either explicitly or implicitly) in the problem. For example, in the nine-dot problem, the range of legal operations-lines one can draw is not explicitly stated. However, people typically first assume that the lines must be inside the square. To solve this problem it is necessary to infer that one can extend the lines outside the boundary of the dots.
People use representations other than imaginal ones in order to solve problems. For example, solve this simple verbal analogy.
Daughter : Mother :: Cousin : ?
People tend to encode a particular object in different ways in different contexts. By changing the context, then one may devise new ways of representing the problem. The ability to adjust the representation to fit the task at hand arises through experience. This experience comes through reducing functional fixedness, proper organization of the problem. and by syllogistic reasoning.
In this section we have seen that the way a problem is represented is most important in finding its solution. In the following section we will discuss the phenomenon of fixating on an inappropriate representation of the problem.
FUNCTIONAL FIXEDNESS
Functional fixedness is one of the obstacle in problem solving. Karl Duncker, Gestalt psychologist discovered the phenomenon of functional fixedness.
Functional fixedness refers to the tendency to see objects as having only a single, typical use. For example a hammer is for pounding nails and other things. We categorize objects based on their functional features as well as their features and the prototypical function dominates the way we think. The tendency to perceive things in terms of their 1 familiar uses often make it difficult to use them in an unfamiliar way. In effect, objects or ideas become set in their functions and, when they are part of a problem-solving task that requires that they serve a different function, the subject must overcome that "set" .
In a classic experiment of functional fixedness, Duncker ( 1945) gave subjects three cardboard boxes, matches, thumb tacks, and candles and asked them to devise a plan whereby the candle could be mounted on a screen to serve as a lamp. One group of the subjects were given the screen; the candles, the tacks, and the matches were each presented in their own box. Another group of subjects were given these objects along with the three boxes-that is, the objects were not in the boxes. The solution to this puzzle was to use the matches to light the candles, drip some wax on a box, stick the candle on it, and thumbtack the box to the screen. When the boxes were modeled ahead of time as containers, subjects had much more difficulty in solving this problem than when the boxes were not. Later experimenters demonstrated that simply labeling an object with a name fjxed in the subjects mind a certain set that could either facilitate or impede the solving of a problem.
REDUCING FUNCTIONAL FIXEDNESS
i) When the labels of the object suggest novel functions or help the subjects to reorganize the materials in novel ways, functional fixedness may be reduced or ' even presented.
For example in the candle problem which is mentioned earlier labeling the box clearly facilitated the solution of the problem.
ii) Functional fixedness can also be reduced through nonverbal pre training, as shown by the studies of two-string problem, which is mentioned in Activity 2. Thus training in novel uses can reduce functional fixedness.
iii) Generating and exploring several different representations of a problem in the early stages of problem solving helps to prevent fixation and increases the chances for occurring insight.
If a problem solver is able to successfully overcome functional fixedness and use an object in a new way to solve a problem, this may lead to a feeling of insight. In fact, Kohler) s ( 1918) demonstration of "insight learning" by chimpanzees involved overcoming functional fixedness. In one classic sequence, the chimp sultan was in a cage and noticed a banana lying outside out of reach. In the cage was a bushy tree. Sultan suddenly went to the tree, broke off a branch, ran back to the bars and used the branch to bring the banana into reach. What was not even a separate object was suddenly recognized as a potential tool.
SUMMARY
Finding solutions to one or the other kind of problem is a part of our daily routine. Various stages are involved in problem solving. Among them representation of the problem is a critical step for the type of representation limit~ the kinds of strategies that can be used and determines the types of moves the solver will try. The internal representation of the problem can be visual, imagery, algebraic or verbal. Representation of information and representing the problem in novel ways are important in problem solving.
Functional fixedness is one of the impediment in problem solving. Functional fixedness refers to the tendency to perceive things in terms of their familiar uses. By labeling the objects in novel ways and by giving training in novel uses can reduce functional fixedness.