Deck 12: Problem Solving

Question 1

Pick a problem you have had to deal with, and analyze the process of solving it into subgoals, as is done in means-end analysis.

Answer 1

There are four discs arranged from smaller to larger size from top to bottom and there are a total of three pegs. These four discs are placed in one of the three pegs. The goal is to move all four discs to third peg in same order but with the following conditions:
i. Only one disc should be moved at a time from one peg to another.
ii. Only the top disc should be moved.
iii. A disc cannot be kept over a smaller one.
In the means-end analysis, the problem is solved by setting a series of sub-goals to start from the initial state and reaching the goal state and is given as follows:
Sub-goal 1 - First, the smallest disc which at the top in the first peg should be moved to the peg 2.
Sub-goal 2 - The disc currently at the top of first peg can be moved and kept over peg 1.
Sub-goal 3 - As the disc cannot be placed over the smaller disc, the smallest disc at the peg 2 should be moved to peg 3 where one disc is already placed which is bigger than the disc being moved.
Sub-goal 4 - Now the top disc at peg 1 is moved to peg 2 which is empty.
Sub-goal 5 - The smallest disc at peg 3 should be moved to peg 1 where there is a largest disc.
Sub-goal 6 - The disc at peg 3 is moved to peg 2 where there is a disc bigger than the disc being moved.
Sub-goal 7 - The smallest disc is then moved to peg 2 where are two discs kept in order.
Sub-goal 8 - The biggest disc from peg 1 should be moved to peg 3. The goal state is getting achieved.
Sub-goal 9 - The smallest disc should be placed on the biggest disc kept at peg 3.
Sub-goal 10 - The top disc at peg 2 is then moved to peg 1 which is empty now.
Sub-goal 11 - The smallest disc at peg 3 is then moved to peg 1 where there is a disc already which is bigger.
Sub-goal 12 - Now the disc from peg 2 is moved to peg 3 and the disc being moved is second largest.
Sub-goal 13 - The smallest disc is now moved to peg 2 which is empty.
Sub-goal 14 - The disc currently at peg 1 is moved to peg 3 and kept over the two discs already in order.
Sub-goal 15 - The smallest disc is then moved to the peg 3 and all the disc are arranged in order at peg which is the goal state.

Question 2

Have you ever experienced a situation in which you were trying to solve a problem but stopped working on it because you couldn't come up with the answer? Then, after a while, when you returned to the problem, you got the answer right away? What do you think might be behind this process?

Answer 2

Yes, I have experienced a situation where I was trying to solve the problem but felt that I could not reach the solution. But when I returned to the problem after a while, I got the answer right away. This happens usually while solving the insight problems where one does not know when they will be reaching the solution.
Everyone represents the problem in their mind in their own way. Even the solution to a problem also depends on the representation of that problem in one's mind. In many cases, people get the solution to the problem by sudden realization. These types of problems are usually insight problems where there is no standard methodology to get the solution. Non-insight problems are those which have a methodological process and people can feel that they are getting closer to the solution.
In the given case, I am experiencing an insight problem where the solution appears suddenly. Few minutes before I felt that I would not reach the solution. But when I return to the problem after a while, I reached the solution all of a sudden. Two psychologists Janet Metcalfe and David Wiebe conducted many experiments to find the difference between insight and non-insight problems. They also analyzed the feeling of people solving both insight and non-insight problems about progressing towards the solution.
Even before few seconds of finding a solution to the insight problem, participants were not aware of the solution and felt that they will not reach the answer. But in a while, the solution suddenly appears. This is due to the following:
i. The correct use of the objects or concepts to solve the problem must be fixed or else this will act as an obstacle to solve.
ii. Also, when a person returns to the problem after a while, he reconstructs the problem in another way which helps to solve the problem suddenly.
iii. When a person solves an insight problem, the situation of not nearing the answer causes the person to create some other mental set which will make the answer appear suddenly.
iv. Following several sub-goals to reach the final goal also makes a person reach the answer but sometimes the person follows these sub-goals without knowledge and it seems for him that the solution appears suddenly.

Question 3

On August 14, 2003, a power failure caused millions of people in the northeastern and midwestern United States and eastern Canada to lose their electricity. A few days later, after most people had their electricity restored, experts still did not know why the power failure had occurred and said it would take weeks to determine the cause. Imagine that you are a member of a special commission that has the task of solving this problem, or some other major problem. How could the processes described in this chapter be applied to finding a solution? What would the shortcomings of these processes be for solving this kind of problem?

Answer 3

Problems we face in our everyday life can be small or large, easy or difficult and simple or complex. To find the reason for power failure, it would take more than a week. This problem can be said as large, complex and very difficult to solve. Depending on the nature of a problem, it can be solved. The given mentioned problem can only be solved by the experts who have a creative mind or those with greater experience.
Some of the processes for solving the problems are given as follows:
Representing a problem and Restructuring it - According to Gestalt approach, the success in solving a problem is depended on how problem is represented in a person's mind and restructuring it by realization. According to him, the problems, which are insight, require a second to solve, when a person restructures the problem in a different way.
Shortcoming - One of the shortcomings in this process is that there are many chances of functional fixedness, which is defined as the cognitive bias, which limits an individual to use the object in a way it should be used traditionally and not in any other new way. It prevents us to think of creative solutions to a problem. Information-Processing Approach - According to Alan Newell and Herbert Simon, a problem can be solved by understanding the initial and goal states of it. Between the initial and goal state, they divided the problem into many sub-goals. Dividing the problem into sub-goals allows a person to solve the problem in easier way.
Shortcoming - The complex problem, such as finding reason for power failure cannot be divided into sub-goals and is unnecessary in this case. This is because the problem can be divided into sub-goals only when the goal state is known. The above mentioned complex problem does not know the goal and hence, this approach cannot be used. Analogical Problem Solving - According to this approach, the problem is solved by transferring the experience of the similar problem solved in past. The target problem is compared with the past problems, which has similar properties and then solved in the same way.
Shortcoming: The complex problem, which is mentioned above was a very unique problem and the United States and Canada do not had any such problem in the past. Thus, the transferring of experience is impossible and this approach cannot be used for complex and difficult problems occurring for the first time.

Question 4

Think of some examples of situations in which you overcame functional fixedness and found a new use for an object.

Question 5

What is the psychological definition of a problem? Distinguish between welldefi ned and ill-defi ned problems.

Question 6

What is the basic principle behind the Gestalt approach to problem solving? Describe how the following problems illustrate this principle, and also what else these problems demonstrate about problem solving: the circle (radius) problem; the candle problem; the two-string problem; the water-jug problem.

Question 7

What is insight, and what is the evidence that insight does, in fact, occur as people are solving a problem?

Question 8

Describe Newell and Simon's approach to problem solving, in which "search" plays a central role. How does means-end analysis as applied to the Tower of Hanoi problem illustrate this approach? What is the think-aloud protocol?

Question 9

How do the acrobat problem and Kaplan and Simon's mutilated checkerboard experiment illustrate that the way a problem is stated can affect a person's ability to solve the problem? What are the implications of this research for Newell and Simon's "problem space" approach?

Question 10

What is the basic idea behind analogical problem solving? How effective is it to present a source problem and then the target problem, without indicating that the source problem is related to the target problem?

Question 11

What are the three steps in the process of analogical problem solving? Which of the steps appears to be the most difficult to achieve?

Question 12

How do the surface features and structural features of problems influence a person's ability to make effective use of analogies in problem solving? Describe experiments relevant to this question, and also techniques that have been used to improve analogical problem solving.

Question 13

What is the analogical paradox? How has analogical problem solving been studied in the real world?

Question 14

What is an expert? What are some differences between the way experts and nonexperts go about solving problems? How good are experts at solving problems outside of their field?

Question 15

What is convergent thinking? What is divergent thinking? How are these two types of thinking related to creativity? Describe experiments that have shown (a) how fixation can affect creativity; (b) de Mestral's use of analogy to invent Velcro; and (c) Finke's creative cognition procedure.

Question 16

Under what conditions are people with high working memory capacity better at solving math problems than are people with low working memory capacity? Under what conditions do they lose this advantage? Why does this probably occur?