Flashcards in Problem solving Deck (36):
Problem solving.. hmm.. Define 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. (Lovett, 2002).
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. (Lovett, 2002). Is it possible to further divide between different types of problems?
One typical differentiation is between well-defined problems and ill-defined problems.
What are well-defined problems?
Well-defined problems usually have a correct answer; certain procedures, when applied correctly, will lead to a solution.
What are ill-defined problems?
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 ( Pretz et al, 2003)
How was the study of problem solving introduced into psychology?
The Gestalt Approach introduced the study of problem solving to psychology in the 1920s.
Briefly grasp the essence of the gestalt approach to problem solving.
Problem solving, for the Gestalt psychologists, was (1) how people represent a problem in their mind and (2) how solving a problem involves a reorganisation or restructuring of this representation.
The gestalt psychologists also introduced the idea that restructuring is associated with insight - the sudden realisation of a problem's solution. Is there any scientific evidence for this?
Modern researchers have debated whether insight actually exists. Most reports of the specialness of insight experience are anecdotal (Weinberg, 1995; Weinberg & Alba, 19811, 1982). However, Janet Metcalfe and David Wiehe (1987) id an experiment designed to test this. They had participants work on problems anecdotally considered to be insight problems, and another group work on problems considered to be non-insight problems. They would also ask the participants every 15 seconds how close they thought they were to the solution. The results indicated that the "insight problems" indeed had insight participants much less confident of their closeness to the solution right up until they solved it, compared to a more linear curve in the non-insight group.
The gestalt psychologists identified what they meant was the major obstacle to problem solving. What is it?
Fixation - people's tendency to focus on a specific characteristic of the problem that keeps them from arriving at a solution.
Mention a typical problem in which fixation is an obstacle?
Maier's two-string problem, in which the participant's task is to tie together two strings that are hanging from the ceiling. This is difficult because the strings are separated, so ti is impossible to reach one of them while holding the other. Other objects available for solving this problem are a char and a pair of pliers. Fixedness in the normal function of pliers causes people to not consider how it can be used as a pendulum. Maier would set the string into motion by "accidentally" brushing up against it if the participants had not solved the problem within 10 minutes. Then 23/27 participants would solve it within 60 seconds.
In 1956 there were two important AI conferences, one at MIT and one at Dartmouth. Alan Newell and Herbert Simon were at both, and they described their computer program that was designed to simulate human problem solving. Alan Newell and Herbert Simon introduced a new way to look at human problem solving. In what way?
This marked the beginning of a research program that described problem solving as a process that involves search.
What is meant by describing problem solving as a process that involves search?
Instead of just considering the initial structure of a problem and then the new structure achieved when the problem is solved, Newell and Simon described problem solving as a search that occurs between the posing of the problem and its solution.
One key term for Newell-Simon Approach to Problem solving is initial state. Describe what that means, and illustrate with an example from the Tower of Hanoi problem.
The initial state are the conditions at the beginning of a problem. In the tower of hanoi, the initial state has all three discs on the left peg.
One key term for Newell-Simon Approach to Problem solving is goal state. Describe what that means, and illustrate with an example from the Tower of Hanoi problem.
The goal state is the solution to the problem. In the tower of hanoi problem the goal state has all three discs on the right peg.
One key term for Newell-Simon Approach to Problem solving is intermediate state. Describe what that means, and illustrate with an example from the Tower of Hanoi problem.
The intermediate state are the different states that occur when changing the state from the initial state and moving it toward the goal state. In the tower on hanoi this can be moving the first disc.
One key term for Newell-Simon Approach to Problem solving is operators. Describe what that means, and illustrate with an example from the Tower of Hanoi problem.
Operators are actions that take the problem from one state to another. Operators are usually governed by rules. In the tower of hanoi problem, an operator is moving a disc. Moving a disc is governed by the ruke: a larger disc can't be placed on a smaller one.
One key term for Newell-Simon Approach to Problem solving is problem space. Describe what that means, and illustrate with an example from the Tower of Hanoi problem.
The problem space are all possible states that could occur when solving a problem. In the tower of Hanoi this can be represented by a tree-model.
One key term for Newell-Simon Approach to Problem solving is means-end analysis. Describe what that means, and illustrate with an example from the Tower of Hanoi problem.
A means-end analysis is a way of solving a problem in which the goal is to reduce the difference between the initial and goal states. In the Tower of Hanoi puzzle this consists of establishing subgoals, each of which moves the solution closer to the goal state.
One key term for Newell-Simon Approach to Problem solving is subgoals. Describe what that means.
Subgoals are small goals that help create intermediate states that are closer to the goal. Occasionally, a subgoal may appear to increase the distance to the goal state bu tin the long run can result in the shortest path to the goal.
What is the biggest contribution of Newell and Simon to problem solving?
One of the main contributions of Newell and Simon's approach to problem solving is that it provided a way to specify the possible pathways from the initial to goal states. But research has shown that there is more to problem solving than specifying the problem space.
How a problem is stated can affect its difficulty. How?
K. Kotovsky and coworkers (1985) found that participants took an average of 9.51 minutes to solve the reverse acrobat problem, as opposed to 5.63 minutes on average to solve the acrobat problem. The problem space is reverse, but should in theory be equal in both problems. For some reason this was not the case.
What is the acrobat problem and reverse acrobat problem?
Three circus acrobats developed an amazing routine in which the jumped to and from each other's shoulders to form human towers. The routine was performed on three very tall flagpoles. The acrobats varied in size, from small to medium, to large. To get from the initial state ( medium - large - small) they to the goal state (small - medium - large) they need to adhere to the following 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 the other.
3. An acrobat may not jump when someone is standing on his or her shoulders.
4. A bigger acrobat may not stand on the shoulders of a smaller acrobat.
The reverse problem is the same except for the fact that rule 4 is changed to state that a smaller acrobat cannot stand on a larger one.
What can explain the puzzling fact that people use more time to solve the reverse acrobat problem?
1. The idea of a 400-pound acrobat standing on the shoulders of a 40-pound acrobat is not consistent with out knowledge of the real world, which might make it more difficult to imagine and therefore think of. This might increase the load on the problem-solver's memory.
Using the solution to a similar problem to guide solution of a new problem is called ...
analogical problem solving
How has analogical problem solving been looked at by researchers?
They've tried to test whether being presented with a source problem that shares some similarities with the target problem and that illustrates a way to solve the target problem, helps them solve the target problem.
Mention a problem that has been widely used in research on analogical problem solving.
A problem that has been widely used in research on analogical problem solving is Karl Duncker's radiation problem. In Gick and Holyoak's 1983 study they had one group of people read a story of a fortress siege, that highly suggested the method in which to solve the radiation problem. 10% would solve the radiation problem without hearing the story first, 30% of those who heard the story first were able to solve the problem. When told to think about the story when they were solving the problem, 75% solved the problem.
The results from Gick and Holyoak's study led them to propose that the process of analogical problem solving involves three steps. Which?
1. Noticing that there is an analogous relationship between the source story and the target problem.
2. Mapping the correspondence between the source story and the target problem.
3. Applying the mapping to generate a parallell solution to the target problem.
Once they determined that analogies can help with problem solving, but that hints are required to help participants notice the presence of the source problem, Gick and Holyoak (1983) proceeded to look for factors that help facilitate the noticing and mapping steps. Which did they find?
1. Effect of making surface features more similar.
2. Effect of varying the structural features.
Once they determined that analogies can help with problem solving, but that hints are required to help participants notice the presence of the source problem, Gick and Holyoak (1983) proceeded to look for factors that help facilitate the noticing and mapping steps. One of the factors they looked at was the effect of making surface features more similar. How did they do this and what were the implications of their results?
Holyoak and Koh (1987) used the radiation problem as the source problem and the lightbulb problem as the target problem. They hypothesised that these problems would have a high surface similarity because rays (radiation problem ) and lasers (lightbulb problem) are very similar. 81% of participants who knew about the radiation problem solved the lightbulb problem, but only 10% of the controls did.
Once they determined that analogies can help with problem solving, but that hints are required to help participants notice the presence of the source problem, Gick and Holyoak (1983) proceeded to look for factors that help facilitate the noticing and mapping steps. One of the factors they looked at was the effect of varying the structural features. How did they do this and what were the implications of their results?
The presented two different versions of the source problem. One in which the source and target problems had similar structural features, and one where they did not. Solution was still the same, but the results indicated that it was much easier to solve the target problem if the source problem and target problem had similar structural features.
How ecological are the analogy experiments?
Not very, they're all controlled trials. Bo Christensen and Chrsitian Schunn (2007) recorded meetings of design engineers who were creating new plastic products, they found that the engineers proposed an analogy about every 5 minutes. Thus, analogies play an important role both in solving scientific problems and in designing new products.
How do experts in a field approach problems differently than non experts?
1. Experts possess more knowledge about their fields.
2. Expert's knowledge is organised differently from novices.
3. Experts spend more time analysing problems.
Experts possess more knowledge about their fields. True? How does it affect problem solving?
Chase and Simon (1973a, 1973b) researched how well chess masters and novices can reproduce positions on a chessboard that they hav seen briefly. The results showed that experts excelled at this task when the chess pieces were arranged in actual game positions, but were no better than novices when the pieces were arranged randomly. An expert in a field probably has a lot of knowledge that can aid in the solving of problems in that field.
Expert's knowledge is organised differently from novices. True? How does it affect problem solving?
Michelin Chi and coworkers (1982) presented 24 physics problems to a group of experts and a group of novices and asked them to sort the problems into groups based on their similarities. The novices organised the problems based on surface characteristics (such as how similar the objects in the problem were), but the experts would organise them based on structural features such as general principles of physics. An expert in a field is much more efficient at organising the problem field, recognising what is relevant and not.
Experts spend more time analysing problems. True? How does it affect problem solving?
Lesgold (1988) showed that experts often get off to what appears to be a slow start on a problem, because they spend time trying to understand the problem rather than immediately trying to solve it. This can help them solve the problem in a more effective manner.
Is being an expert always an advantage?
Not always. One disadvantage is that knowing about the established facts and theories in a field may make experts less open to new ways of looking at problems.