Chapter 12: Test Yourself RQ
Describe how the following problems illustrate Gestalt principle to problem solving, 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.
1) "Circle (radius) Problem": This problem asks us to determine the length of the segment marked x if the radius of the circle has a length r. One way to describe how this problem is represented on the page is "a circle with vertical and horizontal lines that divide the circle into quarters, with a small triangle in the upper left quadrant". The key to solving this problem is to change the last part of the representation to "a small rectangle in the upper let quadrant, with x being the diagonal between the corners". Once x is recognized as the diagonal of the rectangle, the representation can be reorganized by creating the rectangle's other diagonal. Once we realize that this diagonal is the radius of the circle, and that both diagonals of a rectangle are the same length, we can conclude that the length of x equals the length of the radius, r. What is important about this solution is that it doesn't require mathematical equations. Instead, the solution is obtained by first perceiving the object and then representing it in a different way (Restructuring) 2) "Candle Problem": The candle problem illustrates how functional fixedness can hinder problem solving. In this experiment, participants are asked 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 (candles, matches in a matchbox, some tacks) with cardboard on the wall in a room. The solution to the problem occurs when the person realizes that the matchbox can be used as a support rather than a as a container. When Duncker did this experiment, he presented one group of participants with small cardboard boxes containing the materials and presented another group with the same materials, but outside the boxes, so the boxes were empty. When the two groups were compared, it was found that the group that had been presented with the boxes as containers found the problem more difficult than did the group that was presented with empty boxes 3) "The Two-String Problem": Another demonstration of functional fixedness is provided by Maier's two-string problem, in which the participants' 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. In Gestalt terms, the solution to 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) 4) "The Water-Jug Problem": The Gestalt psychologists showed how 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) 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. All of the participants who began the Luchins' water-jug problem with problem 7 used the shorter solution, but less than a quarter of those who had established a mental set by beginning with problem 1 used the shorter solution to solve problem 7
What is the psychological definition of a problem?
A 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. Thus, a problem, as defined by psychologists, is difficult, and the solution is not immediately obvious
How good are experts at solving problems outside of their field?
Although there are many differences between experts and novices, it appears that these differences hold only when problems are within an expert's field. When James Voss and coworkers posed a real-world problem involving Russian agriculture to expert political scientists, expert chemists, and novice political scientists, they found that the expert political scientists performed best and that the expert chemists performed as poorly as the novice political scientists. In general, experts are experts only within their own field and perform like anyone else outside of their field. This makes sense when we remember that the superior performance of experts occurs largely because they possess a larger and better organized store of knowledge about their specific field.
What is convergent thinking? What is divergent thinking? How are these two types of thinking related to creativity?
Divergent thinking is thinking that is open-ended, involving a large number of potential "solutions" and no "correct" answer; Convergent thinking is thinking that works toward finding a solution to a specific problem that usually has a correct answer; Creativity involves having unique insights and also being able to follow through to transform that insight into a product - be it a work of art, an idea for a scientific experiment, or a commercially viable invention
What is an expert?
Experts are 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
What are some differences between the way experts and non-experts go about solving problems?
Experts in a particular field usually solve problems faster with a higher success rate than do novices (people who are beginners or who have not had the extensive training of experts); 1) Experts possess more knowledge about their fields 2) Experts' knowledge is organized differently from novices' 3) Experts spend more time analyzing problems
What is insight, and what is the evidence that insight does, in fact, occur as people are solving a problem?
Insight is the sudden realization of a problem's solution. For Gestalt psychologists, the solution to most of the problems posed by Gestalt psychologists involves suddenly discovering a crucial element that leads to the solution. Janet Metcalfe and David Wiebe did an experiment designed to distinguish between insight problems and noninsight problems. Their starting point was the idea that there should be a basic difference in how participants feel they are progressing toward a solution as they are working on an insight problem versus a noninsight problem. They predicted that participants working on an insight problem, in which the answer appears suddenly, should not be very good at predicting how near they are to a solution. Participants working on a noninsight problem, which involves a more methodical process, would be more likely to know when they are getting closer to the solution. To test the hypothesis, Metcalfe and Wiebe gave participants insight problems and noninsight problems and asked them to make "warmth" judgments every 15 seconds as they were working on the problems. Ratings closer to "hot" (7 on a 7-point scale) indicated that they believed they were getting close to a solution; ratings closer to "cold" (1 on a scale) indicated that they felt that they were far from a solution. For the insight problems, warmth ratings remain low at 2 or 3 until just before the problem is solved. In contrast, for the algebra problems (noninsight problems), the ratings gradually increased until the problem was solved.
What is the analogical paradox? How has analogical problem solving been studied in the real world?
Many real-world examples of analogical problem solving illustrate what Kevin Dunbar has called the 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. Dunbar reached this conclusion by using a technique called in vivo research
Describe Newell and Simon's approach to problem solving, in which "search" plays a central role.
Newell and Simon saw problems in terms of an initial state - conditions at the beginning of the problem - and a goal state - the solution of the problem. Newell and Simon conceived of problem solving as involving a sequence of choices of steps, with each step creating an intermediate state. Thus, a problem starts with an initial state, continues through a number of intermediate states, and finally reaches the goal state. The initial state, goal state, and all the possible intermediate states for a particular problem is called the "problem space". According to Newell and Simon, the person has to search the problem space to find a solution, and they proposed that one way to direct the search is to use a strategy called means-end analysis.
What is the basic principle behind the Gestalt approach to problem solving?
Problem solving, for the Gestalt psychologists, was about (1) how people represent a problem in their mind and (2) how solving a problem involves a reorganization or restructuring of this representation
How does means-end analysis as applied to the Tower of Hanoi problem illustrate Newell and Simon's approach to problem solving?
The problem apace for the Tower of Hanoi starts with the initial state, marked 1 and the goal state marked 8. All of the other possible configurations of discs on pegs are intermediate states. From the diagram, you can see that there are a number of possible paths from getting from the initial state to the goal state, but that one of these paths is shorter than others. By choosing the path along the right side of the problem space (states 2, 3, 4, 5, 6, and 7), it is possible to reach the goal state by making just seen moves. Our overall goal in applying means-end analysis to the Tower of Hanoi problem is to reduce the size of the difference between initial and goal states. An initial goal would be to move the large disc that is on the left over to the peg on the right. However, if we are to obey the rules, we can't accomplish this in just one step, because we can move only one disc at a time and can't move a disc if another is on top of it. To solve the problem we therefore set a series of subgoals, some of which may involve a few moves.
Distinguish between well-defined and ill-defined problems.
Well-defined problems usually have a correct answer; certain procedures, when applied correctly, will lead to a solution. Ill-defined problems, which occur frequently in everyday life, do not necessarily have one "correct" answer, and the path to their solution is often unclear