Problem Solving-Cognitive Psychology

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When does a problem occur?

when there is an obstacle between a present state and a goal and it is not immediately obvious how to get around the obstacle.

The Gestalt psychologists

focused on how people represent a problem in their mind. They devised a number of problems to illustrate how solving a problem involves a restructuring of this representation and to demonstrate factors that pose obstacles to problem solving.

The Gestalt psychologists introduced?

the idea that reorganization is associated with insight

Insight

a sudden realization of a problem's solution. This has been demonstrated experimentally by tracking how close people feel they are to solving insight and noninsight problems.

Functional fixedness.

an obstacle to problem solving that is illustrated by Duncker's candle problem and Maier's two-string problem.

Lunchins' water-jug problem

illustrates the mental set created while solving a problem.

Alan Newell and Herbert Simon

were early proponents of the information-processing approach to problem-solving. They saw problem solving as the searching for a problem space to find the path between the statement of the problem (the initial state) and the solution to the problem (the goal state). This search is governed by operators and is usually accomplished by setting subgoals. The Tower of Hanoi problem has been used to illustrate this process.

The acrobat problem and the reverse acrobat problem

illustrate that how the problem is presented can influence problem difficulty. Research on the mutilated checker-board problem also illustrates the importance of how a problem is presented.

the technique of think-aloud protocols

developed by Newell and Simon to study participants' thought process as they are solving a problem.

Analogical problem solving

occurs when experience with a previously solved source problem or a source story is used to help solve a new target problem. Research involving Duncker's radiation problem has shown that even when people are exposed to analogous source problems or stories, most people do not make the connection between the source problem or story and the target problem.

Analogical problem solving is facilitated when?

hints are given regarding the relevance of the source problem, when the source and target problems have similar surface features, and when structural features are made more obvious.

Analogical encoding

a process that helps people discover similar structural features.

The analogical paradox is?

that participants in psychological experiments tend to focus on surface features in analogy problems, whereas people in the real world frequently focus on deeper, more structural features. In vivo problem-solving research has shown that analogical problem solving is often used in real-world settings.

Experts

They are better than novices at solving problems in their field of expertise. They have more knowledge of the field, organize this knowledge based more on deep structure than on surface features, and spend more time analyzing a problem when it is first presented.

Creative problem solving

is associated with divergent thinking rather than with convergent thinking. We have only a limited understanding of the processes involved in creative problem solving and creativity in general. There is evidence that fixation can inhibit creative problem solving, and that using analogical thinking can enhance it. A technique called creative cognition has been used to train people to think creatively.

Mathematical problem-solving performance is affected by?

working memory capacity.

Higher-working memory capacity is associated with?

better performance than low working memory capacity under low-stress conditions, but this advantage disappears under high-stress conditions.

Acrobat problem

Three circus acrobats developed an amazing routine in which they jumped to and from each other's shoulders to form human towers. The routine was quite spectacular because it was performed atop three very tall flagpoles. It was made even more impressive because the acrobats were very different in size: The large acrobat weighed 400 pounds; the medium acrobat, 200 pounds; and the small acrobat, a mere 40 pounds. These differences forced them to follow these safety rules: 1. Only one acrobat may jump at a time 2. Whenever two acrobats are on the same flagpole, one must be standing on the shoulders of each other 3. An acrobat may not jumped when someone is standing on his or her shoulders 4. A bigger acrobat may not stand on the shoulders of a smaller acrobat. At the beginning of their act, the medium acrobat was on the left, the large acrobat in the middle, and the small acrobat on the right. At the end of the act, they were arranged small, medium, and large from left to right.

Analogical paradox

Participants in psychological experiments tend to focus on surface features in analogy problems, whereas people in the real world frequently use deeper, more structural features.

Analogical problem solving

One tactic that is sometimes helpful is to consider whether another problem that the person has solved before is similar to the new problem, and ask "Can I apply the same methods to solving this problem?" This is the technique of using the solution to a similar problem to guide solutions of a new problem.

Analogical transfer

The starting point for much of the research on analogical problem solving has been to first determine how well people can transfer their experience from solving one problem to solving another, similar problem. This is the transfer from one problem to another. To study this term, participants who are trying to solve a target problem are presented with a problem or a story, called the source problem or source story, that shares some similarities with the target problem and that illustrates a way to solve the target problem.

Method of analogy

The process of noticing connections between similar problems and applying the solution for one problem to other problems.

Candle problem

First described by Karl Duncker, illustrates how functional fixedness can hinder problem solving. In this experiment, he asked participants to use various objects to complete a task. The following demonstration asks you to try to solve Duncker's problem by imagining that you have the specified objects. You are in a room with a corkboard on the wall. You are given the materials; some candles, matches in a matchbox, and some tacks. Your task is to mount a candle on the corkboard so it will burn without dripping wax on the floor. The solution to the problem occurs when the person realizes that the matchbox can be used as support rather than as a container. Participants who were presented with empty boxes were twice as likely to solve the problem as participants who were presented with boxes that were used as containers.

Convergent thinking

is most closely associated with well-defined problems. This thinking works toward finding a solution to a specific problem that usually has a correct answer. Thinking converges on the correct answer.

Creative cognition

Cognitive psychologist Ronald Finke developed this technique to train people to think creatively. This figure shows 15 object parts and their names. Close your eyes and touch the page three times, in order to randomly pick three of these object parts. After reading these instructions, take 1 minute to construct a new object using these three parts. The object should be interesting looking and possibly useful, but try to avoid making your object correspond to a familiar object, and don't worry what it might be used for. You can vary the size, position, orientation, and material of the parts, as long as you don't alter the basic shape (except for the wire and the tube, which can be bent). Once you come up with something in your mind, draw a picture of it.

Design fixation

The average number of designs per person was approximately the same for the two groups, but the fixation group's designs included many more instances of cups with straws and mouthpieces. Apparently, they were influenced by the sample design, even though they were told not to include straws or mouthpieces. This effect is analous to the Gestalt psychologists' demonstrations of how fixation can inhibit problem solving.

Divergent thinking

is most closely associated with ill-defined problems. Thinking that is open-minded, involving a large number of potential "solutions" and no "correct" answer

Experts

people who, by devoting a large amount of time to learning about a field and practicing and applying that learning, have become acknowledged as being extremely knowledgeable or skilled in the particular field.

Fixation

People's tendency to focus on a specific characteristic of the problem that keeps them from arriving at a solution.

Functional fixedness

Restricting the use of an object to its familiar functions

Goal state

the solution of a problem.

Ill-defined problem

Examples would be dealing with relationships or picking a career. These occur frequently in everyday life, do not necessarily have one "correct" answer, and the path to their solutions is often unclear.

Initial state

conditions at the beginning of the problem

Insight

The sudden realization of a problem's solution. Was first introduced by the Gestalt psychologists.

Intermediate state

Conditions after each step is made toward solving a problem.

In vivo problem-solving research

involves observing people to determine how they solve problems in real-world situations. This method has been used to study the use of analogy in a number of different settings, including laboratory meetings of a university research group and brainstorming sessions in which the goal was to develop a new product.

Means-end analysis

A way of solving a problem in which the goal is to reduce the difference between the initial and goal states.

Mental set

a preconceived notion about how to approach a problem, which is determined by a person's experience or what has worked in the past.

Mutilated checkerboard problem

A checkerboard consists of 64 squares. These 64 squares can be completely covered by placing 32 dominos on the board so that each domino covers two squares. If we eliminate two corners of the checkerboard, can we now cover the remaining squares with 31 dominos? Craig Kaplan and Herbert Simon (1990) used this problem and variations of it to study how the way a problem is stated affects its difficulty. There were four conditions in their experiment. Each group received a different version of the problem. The four conditions were (1)blank-a board with all blank squares; (2)color-alternating black and pink squares as might appear on a regular checkerboard; (3) black and pink-the words black and pink on the board; and (4) bread and butter- the words bread and butter on the board. The key to solving this problem is to realize that when a domino is placed on the board so it covers just two squares, it is always covering two squares that are different (pink and black, for example). There is no way to place a domino so it covers two pink squares or two black squares. Therefore, for 31 dominos to cover the board there must be 31 pink squares and 31 black squares. However, this isn't the case, because two pink squares were removed. Thus, the board can't be covered by 31 dominos.

Operators

actions that take the problem from one state to another. Introduced by Newell and Simon.

Problem

Occurs when there is an obstacle between a present state and a goal and it is not immediately obvious how to get around the obstacle. It is defined by psychologists as being difficult, and the solution is not immediately obvious.

Problem space

The initial state, goal state, and all possible intermediate states for a particular problem.

Radiation problem

Suppose you are a doctor faced with a patient who has a malignant tumor in his stomach. It is impossible to operate on the patient but unless the tumor is destroyed the patient will die. There is a kind of ray that can be used to destroy the tumor. If the ray reaches the tumor at a sufficiently high intensity, the tumor will be destroyed. Unfortunately, at this intensity the healthy tissue that the ray passes through on the way to the tumor will also be destroyed. At lower intensities the ray is harmless to healthy tissue, but it will not affect the tumor either. What type of procedure might be used to destroy the tumor and at the same time avoid destroying the healthy tissue. When Duncker (1945) originally posed this problem, most of his participants could not solve it, and Mary Gick and Keith Holyoak (1980,1983) found that only 10 percent of their participants arrived at the correct solution. The solution is to bombard the tumor with a number of low-intensity rays from different directions, which destroys the tumor without damaging the tissue the rays are passing through. The solution to this problem is actually the procedure used in modern radiosurgery, in which a tumor is bombarded with 201 gamma ray beams that intersect at the tumor.

Restructuring

It doesn't require mathematical equations. The solution is obtained by first perceiving the object and then representing it in a different way. The Gestalt psychologists called this the process of changing the problem's representation.

Reverse acrobat problem

Is the same as the acrobat problem, except that rule 4 above was changed to state that a smaller acrobat cannot stand on a larger one. Kotovsky's participants took an average of 9.51 minutes to solve this problem. There are a number of possible reasons that this problem is more difficult. One possibility is that the idea of a 400-pound acrobat standing on the shoulders of a 40-pound acrobat is not consistent with our knowledge of the real world, in which it would be highly unlikely that the small acrobat could support the large one. In addition, it may be harder to visualize larger acrobats on top of smaller ones, which would make the problem more difficult by increasing the load on the problem-solver's memory. Whatever the reason, these results show that to understand problem solving, we need to go beyond analyzing the structure of the problem space.

Source problem (or source story)

The Russian Marriage problem.

Structural features

the underlying principles involved.

Subgoals

Small goals that help create intermediate states that are closer to the goal. These may appear to increase the distance to the goal state but in the long run can result in the shortest path to the goal.

Surface features

what the objects looked like

Target problem

The checkerboard problem.

Think-aloud protocol

The idea is that talking should focus the person's attention on the problem and away from the stress.

Tower of Hanoi problem

The following rules specify which actions are allowed and which are not. 1. Discs are moved one at a time from one peg to another 2. A disc can be moved only when there are no discs on top of it 3. A larger disc can never be placed on top of a smaller disc. This problem got it's name from a legend that there are monks in a monastery near Hanoi who are working on this problem. According to the legend, the world will end when the problem is solved. Luckily, this will take close to a trillion years to accomplish even if the monks make one move every second and every move is correct.

Two-string problem

This is another demonstration of functional fixedness which was provided by Maier (1931). The participant's task was to tie together two strings that were hanging from the ceiling. This is difficult because the strings are separated, so it is impossible to reach one of them while holding the other. Other objects available for solving this problem were a chair and a pair of pliers. To solve this problem, participants needed to tie the pliers to one of the strings to create a pendulum, which could then be swung to within the person's reach. Two things are particularly significant about this problem. First, 60 percent of the participants did not solve the problem because they were focused on the usual function of pliers and did not think of using them as a weight. Second, when Maier set the string into motion by "accidentally" brushing against it, 23 of 37 participants who hadn't solved the problem after 10 minutes proceeded to solve it within 60 seconds. Seeing the string swinging from side to side apparently triggered the insight the pliers could be used as a weight to create a pendulum. In Gestalt terms, the solution of the problem occurred once the participants restructured their representation of how to achieve the solution (get the strings to swing from side to side) and their representation of the function of the pliers (they can be used as a weight to create a pendulum).

Water-jug problem

Provided by Lunchins, in which participants are given three jugs of different capacities and are required to use these jugs to measure out a specific quantity of water.

Well-defined problem

An example would be solving a math or physics problem. They usually have a correct answer; certain procedures, when applied correctly, will lead to a solution.

Analogical encoding

Proposed by Dedre Gentner and Susan Goldin-Meadow (2003) to get people to discover similar structural features. Participants compare two cases that illustrate a principle. The idea behind this is that when learners compare cases, they become more likely to see the underlying structure.

How can the Acrobat problem be solved?

by making 5 moves, as indicated by the solution. K. Kotovsky and coworkers (1985) found that it took their participants an average of 5.63 minutes to solve this problem. However, when they made one small change in the problem, it became much more difficult.

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