Analogies describe similar structures and interconnect them to clarify and explain certain relations. In a recent study, for example, a song that got stuck in your head is compared to an itching of the brain that can only be scratched by repeating the song over and over again.
One special kind of restructuring, the way already mentioned during the discussion of the Gestalt approach, is analogical problem solving. Here, to find a solution to one problem - the so called target problem, an analogous solution to another problem - the source problem, is presented. An example for this kind of strategy is the radiation problem posed by K. Duncker in 1945:
“As a doctor you have to treat a patient with a malignant, inoperable tumour, buried deep inside the body. There exists a special kind of ray, which is perfectly harmless at a low intensity, but at the sufficient high intensity is able to destroy the tumour - as well as the healthy tissue on his way to it. What can be done to avoid the latter?”
When this question was asked to participants in an experiment, most of them couldn't come up with the appropriate answer to the problem. Then they were told a story that went something like this:
A General wanted to capture his enemy's fortress. He gathered a large army to launch a full-scale direct attack, but then learned, that all the roads leading directly towards the fortress were blocked by mines. These roadblocks were designed in such a way, that it was possible for small groups of the fortress-owner's men to pass them safely, but every large group of men would initially set them off. Now the General figured out the following plan: He divided his troops into several smaller groups and made each of them march down a different road, timed in such a way, that the entire army would reunite exactly when reaching the fortress and could hit with full strength.
Here, the story about the General is the source problem, and the radiation problem is the target problem. The fortress is analogous to the tumour and the big army corresponds to the highly intensive ray. Consequently a small group of soldiers represents a ray at low intensity. The solution to the problem is to split the ray up, as the general did with his army, and send the now harmless rays towards the tumour from different angles in such a way that they all meet when reaching it. No healthy tissue is damaged but the tumour itself gets destroyed by the ray at its full intensity. M. Gick and K. Holyoak presented Duncker's radiation problem to a group of participants in 1980 and 1983. Only 10 percent of them were able to solve the problem right away, 30 percent could solve it when they read the story of the general before. After given an additional hint - to use the story as help - 75 percent of them solved the problem.
With this results, Gick and Holyoak concluded, that analogical problem solving depends on three steps:
1. Noticing that an analogical connection exists between the source and the target problem.
2. Mapping corresponding parts of the two problems onto each other (fortress → tumour, army → ray, etc.)
3. Applying the mapping to generate a parallel solution to the target problem (using little groups of soldiers approaching from different directions →sending several weaker rays from different directions)
Next, Gick and Holyoak started looking for factors that could be helpful for the noticing and the mapping parts, for example: Discovering the basic linking concept behind the source and the target problem.
The concept that links the target problem with the analogy (the “source problem“) is called problem schema. Gick and Holyoak obtained the activation of a schema on their participants by giving them two stories and asking them to compare and summarise them. This activation of problem schemata is called “schema induction“.
The two presented texts were picked out of six stories which describe analogical problems and their solution. One of these stories was "The General" (remember example in Chapter 4.1).
After solving the task the participants were asked to solve the radiation problem (see chapter 4.2). The experiment showed that in order to solve the target problem reading of two stories with analogical problems is more helpful than reading only one story: After reading two stories 52% of the participants were able to solve the radiation problem (As told in chapter 4.2 only 30% were able to solve it after reading only one story, namely: “The General“). Gick and Holyoak found out that the quality of the schema a participant developed differs. They classified them into three groups:
1. Good schemata: In good schemata it was recognised that the same concept was used in order to solve the problem (21% of the participants created a good schema and 91% of them were able to solve the radiation problem).
2. Intermediate schemata: The creator of an intermediate schema has figured out thatthe root of the matter equals (here: many small forces solved the problem). (20% created one, 40% of them had the right solution).
3. Poor schemata: The poor schemata were hardly related to the target problem. Inmany poor schemata the participant only detected that the hero of the story was rewarded for his efforts (59% created one, 30% of them had the right solution).
The process of using a schema or analogy, i.e. applying it to a novel situation is called transduction. One can use a common strategy to solve problems of a new kind. To create a good schema and finally get to a solution is a problem-solving skill that requires practice and some background knowledge.