Problem Solving (Chapter 12 HC)
What are the three steps in the process of analogical problem solving? Which of the steps appears to be the most difficult to achieve?
1. Noticing that there is an analogous relationship between the source story and the target problem. This step is the most difficult to achieve. 2. Mapping the correspondence between the source story and the target problem - e.g. connection elements in one story (dictator's fortress) to elements in the target problem (tumor) 3. Applying the mapping to generate a parallel solution to the target problem - e.g. generalizing from the many small groups of soldiers approaching the fortress from different directions to the idea of using many weaker rays that would approach the tumor from different directions
What is the psychological definition of a problem? Distinguish between well-defined and ill-defined problems
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 Well-defined problems: have a correct answer usually, certain procedures when applied correctly will lead to a solution (e.g. math) Ill-defined problems: occur frequently in everyday life, do not necessarily have one correct answer, and the path to their solution is unclear (e.g. picking a career or dealing with relationships)
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?
Acrobat problem: the original was easy to solve for participants, however, the reverse acrobat problem posed a problem because of removing a rule stating that the bigger acrobat can't stand on the shoulders of the small acrobat. harder to visualize larger acrobats on top of smaller ones, which would make the problem more difficult. Mutilated checkerboard: impossible problem to solve because you can't cover 31 pieces with dominos. participants were able to solve it faster after learning about the russian marriage problem, which had 32 pairs but two bachelors died and so they couldn't make exactly 31 heterosexual marriages people consider all possible states
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?
An expert is someone who devoted a large amount of time to learn about a field and practice and apply that learning, have become acknowledged as being extremely knowledgable or skilled in the particular field 1. Experts possess more knowledge about their fields: the chessboard pieces, experts were much better at remembering. knowledge is organized so it can be accessed when needed. 2. Experts' knowledge is organized differently from novices': in a physics problem experiment, the novices solved the problem using surface characteristics (how similar the objects in the problem were) whereas experts used deep structural features (actual principles of physics). 3. Experts spend more time analyzing problems: experts often have a slow start because they spend time trying to understand the problem which allows for a more effective approach to the problem In general, experts are only experts within their own field and perform like anyone else outside their field - one disadvantage of knowing well established facts is that experts can be less open to new ways of looking at a problem
What is analogical encoding? Define the experiment of negotiating strategies.
Analogical encoding: participants compare two cases that illustrate a principle - when learners compare cases, they become more likely to see the underlying structure Experiment: participants learned of trade-off (sisters and orange) or contingency (sales negotiation). Study found that participants tended to use the negotiating strategy they read previously when presented with a new target problem. participants who had compared trad-off examples were more apt to find trade off solutions and the same occurred with contingency examples caused contingency solutions. Having people compare source stories is an effective way to get them to pay attention to structural features that enhance their ability to solve other problems
What is the analogical paradox? How has analogical problem solving been studied in the real world?
Analogical paradox is that participants in lab experiments tend to focus on surface features in analogy problems whereas people in the real world focus on structural features In vivo problem-solving research: observed real world problems at play Researchers listened to molecular biologists and immunologists and found that they used analogies 3 to 15 times per hour. Engineers proposed an analogy every 5 minutes
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, (c) Finke's creative cognition procedure.
Convergent thinking: thinking that words toward finding a solution to a specific problem that usually has a correct answer - well-defined problems Divergent thinking: thinking that is open-ended, involving a large number of potential "solutions" and no "correct" answer - associated with creativity - ill-defined problems a. design fixation: study had participants see a sample design and others didn't but both had the same directions (no straw or mouthpieces). Fixation group (saw the sample) drew more designs of cups with straws or mouthpieces. their fixation inhibited them from solving the problem. b. Velcro: de Mestral used the analogy of the burrs clinging onto his pants that had tiny hooklike structures to invent a fabric fastener with may small hooks on one side and soft loops of the other side (velcro) c. creative cognition: Finke developed a technique to train people to think creatively. Finke presented random objects to participants that had to create an object to match a category. participants picked objects and described what they would use it for and how it functions. their inventions were preinventive forms because they are ideas that precede the creation of a finished creative project. in the end, participants created 65 "creative inventions" even though Finke never told them to be creative. - participants more likely to be creative for preinventive objects they create themselves - lessens chances of fixations
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 Pariticipants worked on an insight problem (triangle problem) and a noninsight problem (algebra) and were asked to rate if they got close to solving (hot) or not (cold). Results found that for insight problems, the warmth ratings remained low until just before the problem is solved. For noninsight problems, participants gradually increased in warmth until the problem was solved. The results showed that insight problem solutions do occur suddenly.
What is the basic principle behind the Gestalt approach to problem solving? Describe how the following problems illustrate this principle: (1) the circle problem, (2) the candle problem, (3) the two-string problem, and (4) the water-jug problem
Problem solving for Gestalt psychologists was about how people represent a problem in their mind and how solving a problem involves a reorganization or restructuring of its representations 1. solution of the circle problem (x = r) is obtained by first perceiving the object and then representing it in a different way which is known as restructuring (viewing the rectangles) 2. The candle problem is solved once a person realizes that the matchbox can be used as a support for the candle rather than as a container for the matches. Participants who were given the items with empty boxes were quicker at solving the problem than participants who had the box filled with matches. Example of functional fixedness. 3. The two-string problem is solved once a person uses the pliers to swing the string to them in the center. 60% didn't solve the problem because they focused on the usual function of the pliers. When given hints (e.g. showing the string swinging), insight was triggered and participants solved the problem. the solution to the problem occurred once the participants restructured their representation of how to achieve the solution and their representation of the function of the pliers. 4. for the water-jug problem, the last two problems were much simplier to figure out compared to the previous six. one group of participants were told to just solve the last two problems (no mental set). the other participants were told to go through all problems in order (mental set). results showed that participants in the mental set had a hard time solving the last two problems because they kept using previous experience from past problems.
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
Surface features: specific elements that make up the problem (e.g. the rays and the tumor versus lightbulb and lasers) - the more different the surface features, the harder it is for analogical transfer - similar can allow for effective analogical problem solving Structural features: underlying principle that governs the solutions (e.g. weak laser beams are used to avoid breaking glass versus weak rays are used to avoid damaging healthy tissue) Effect of making surface features more similar: the lightbulb problem, where laser beams couldn't break a glass bulb (target problem). when students learned about the radiology problem (source problem), they had successful analogical transfer that allowed them to solve the problem. Effect of varying the structural features: fragile-glass version (similar structural features) was solved much easier than the insufficient-intensity version (different structural features) which was a lot more difficult to solve. Analogical transfer is better when the structural and surface features of the source and target problems are more similar
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?
They described problem solving as a search that occurs between the posing of the problem and its solution Tower of Hanoi problem: initial state - conditions at the beginning of the problem (three discs on the left peg) goal state - the solution of the problem (three discs on the right peg) operators - actions that take the problem from one state to another - well-defined and intermediate processing. 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 example, establishing subgoals, each of which moves the solution closer to the goal state - subgoals are the movements of the discs - intermediate states are conditions after each step is made toward solving a problem Approach can be applied to real world settings
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?
Using the solution to a similar problem to guide solution of a new problem. the transfer is called: - analogical transfer, participants who are trying to solve a target problem are presented with a problem or a story called the source problem that shares some similarities with the target problem and that illustrates ways to solve the target problem - can be effective - e.g. radiation problem is given to participants. the problem is where a doctor needs to find out how to get radiation to a tumor without destroying healthy tissue in one blast. most participants couldn't solve it. but once they learned the fortress story, where an army was divided into small groups and dispatched onto each roads, then participants were able to solve the radiation problem.
What is fixation? What is functional fixedness?
fixation is people's tendency to focus on a specific characteristic of the problem that keeps them from arriving at a solution functional fixedness is restricting the use of an object to its familiar functions - the candle problem is an example
Why was the candle problem and the two-string problem difficult to solve?
mental set, preconceived notion about how to approach a problem which is determined by a person's experience or what has worked in the past. - the person's mental set was the knowledge about the usual use of the objects
What is the method of analogy?
process of noticing connections between similar problems and applying the solution for one problem to other problems - e.g. russian marriage problem and mutilated checkerboard