Chapter 10 (Thinking and Problem solving )

Using incomplete or incorrect representations

- Dominoes/checker board: Because a domino must cover two differently colored squares, there is no way to arrange 31 dominoes to cover the mutilated checkerboard. The difficulty most people have with this problem is that they fail to include these two pieces of crucial information in their initial representation of the problem. Thus the representation is incomplete. Similarly, in the baseball game (man at home) problem given earlier, representing the problem in terms of a person sitting in a house would lead you down the wrong path. It would be a case of using an incorrect representation—one that included information not presented in the problem and not correct.

Understand the importance of critical thinking

According to Perkins, good thinking requires a large knowledge base and some means of using it efficiently. Good thinking also requires the kind of objection-raising just illustrated, showing the thinker actively trying to ques- tion him- or herself and to construct examples and counterexamples to his or her conclusions. What often hampers critical thinking is a kind of mental laziness—stopping thinking whenever you get any answer at all. Perkins et al. (1983) urged people to overcome this tendency to think about an issue only until things make superficial sense and, instead, to search harder and look longer for other possibilities and interpretations. Also - Applying Why a formula works, Not simply blindly applying a formula, Generalizing, applying.

Generate and Test technique,

As the name suggests, it consists of generat- ing possible solutions (for example, "Let's call people at American Express and see if they can help") and then testing them (for example, "Hello, American Ex- press? Can you help me with the following problem . . . ?"). Loses effectiveness when there are tons of possibilities. I.e. Generating and testing all the locker combinations. Good example, Lost keys, generate all the possible locations they could be, and check those places.

Identify the key components involved in critical thinking as outlined by Dewey (1933)

Dewey (1933), who called it "reflective think- ing," defined it as "active, persistent, and careful consideration of any belief or supposed form of knowledge in the light of the grounds that support it and the further conclusions to which it tends" (p. 9). Dewey distinguished between re- flective thought and other kinds: random ideas, rote recall, beliefs for which a person has no evidence.

Lack of problem-specific knowledge or expertise

Effects of expertise are not limited to perceptual abilities, how- ever. Familiarity with a domain of knowledge seems to change the way one solves problems within that frame of reference. A good example is to compare the ability of undergraduate psychology majors and their professors to design experiments. Glaser and Chi (1988), reviewing this and other studies of expert-novice differences, described several qualitative distinctions between the two groups. First, experts excel in their own domains; that is, their knowledge is domain specific. A grand master chess player, for example, would not be expected to solve chemistry problems as well as a chemist would. We have already noted in Chapter 3 that experts perceive larger meaningful patterns in their domain of expertise than novices do. Experts are faster than novices at performing skills in their domain of expertise, and they show greater memorial abilities for information within that domain. In problem solving, experts see and represent a problem in their domain at a deeper and more principled level than do novices, who tend to represent in- formation superficially

Be familiar with the study by Gobet & Simon (1996) examining Gary Kasparov

Gobet and Simon (1996) examined the sophistication of play of Gary Kasparov, a Professional Chess Association world champion, as he played si- multaneous games against four to eight opponents who were all chess masters. His opponents were each allowed 3 minutes per move (on average); Kasparov, one fourth to one eighth that amount of time for each game (because he was playing multiple games simultaneously). Despite the tremendous time con- straints, Kasparov played almost as well as he did under tournament condi- tions, when facing only one opponent and having four to eight times as much time to think through and plan his moves. Gobet and Simon concluded that Kasparov's superiority came from his ability to recognize patterns more than from his ability to plan future moves. They based this conclusion on the fact that the time pressure of simultaneous games would severely hamper Kasparov's ability to think ahead, yet the overall quality of his play did not suffer.

Backtracking

In solving a problem, you often need to make certain provisional assump- tions. Sometimes they turn out to be wrong and need to be "unmade." In those instances, it is useful to have some means of keeping track of when and which assumptions were made so you can back up to certain points of choice and start over, a process known as backtracking. The key to backtracking, then, is that the problem solver keep close track of choice points—places where she made a provisional assumption—so that, if subsequent work leads to a dead end, she can "back up" to that choice point and make a different assumption. eg. women Dogs, children, occupation problem.

Means-End Analysis

It involves comparing the goal (Summit, New Jersey) with the start- ing point (Pomona, California), thinking of possible ways of overcoming the difference (walking, bicycling, taking a taxi, and so on), and choosing the best one. The selected option (taking a plane) may have certain prerequisite condi- tions (for example, being at the airport, with a ticket). If the preconditions aren't met, then a subgoal is created (for example, "How can you get to the airport?"). Through the creation of subgoals, the task is broken down into manageable steps that allow a full solution to be constructed. Not always the best approach to reaching a solution, because sometimes the optimal way involves taking a temporary step back- ward or further from the goal. Means-ends analysis can make it more difficult to see that the most efficient path toward a goal isn't always the most direct one. -

Mental set

Mental set is the tendency to adopt a certain framework, strategy, or pro- cedure or, more generally, to see things in a certain way instead of in other, equally plausible ways. Mental set is analogous to perceptual set, the tendency to perceive an object or pattern in a certain way on the basis of your immediate perceptual experience. Like perceptual set, mental set seems to be induced by even short amounts of practice. Working on several water jug problems in a row that follow a common pattern makes it easy to apply the formula but harder to see new relationships among the three terms. Mental set often causes people to make certain unwarranted assumptions without being aware of making them. Most people, when asked to solve the famous nine-dot problem, make the assump- tion that the four lines must stay within the "borders" of the dots. functional fixedness. It appears to be an instance of mental set, in that a person subject to functional fixedness has apparently adopted a rigid mental set toward an object. - Screw Driver.

Be Familiar with the Muckraker System.

One example of an expert system is MUckraker, an expert system designed to give advice to investigative reporters regarding the best way to approach peo- ple for interviews, to prepare for interviews, and to examine public documents while investigating an issue. The format of the rules used includes several antecedents, or conditions. Rule 2, for example, has three antecedents: (a) The probable source will not talk by telephone with the reporter; (b) the interview is crucial; and (c) there are more than six days in which to get the interview. Each of these antecedents specifies a condition that must be met for the rule to be activated. Rules also have a consequent part, indicated by the word THEN. These consequents are actions to be taken if the rule is applied. For example, the ac- tion of Rule 2 is to set a variable (send_by_mail2) to a certain value (namely, 80). Some rules also include an explanation or justification, preceded by the word BECAUSE. Notice the references to "send_by_mail1," "send_by_mail2," and so forth. These are names of variables used by the program. Rules 1 through 4 assign values to send_by_mail1 through send_by_mail4, respectively. Rule 5 checks to see whether any of these four variables have been assigned a value greater than 79. If so, Rule 5 directs the reporter to send the potential inter- viewee a request by mail.

What is the Problem space hypothesis?

The main idea behind this problem space hy- pothesis is that every possible state of affairs within a problem corresponds to a node in a mental graph. The entire set of nodes occupies some mental area, and this area, together with the graph, is the problem space. Each circle, or node, corresponds to a certain state of affairs at some point during the problem-solving process. If the problem is to win a chess game, for example, each node corresponds to a possible chessboard configuration at each point in the game. The node labeled "initial state" corresponds to the conditions at the beginning of a problem—for example, a chessboard before the first move. The goal states correspond to conditions when the problem is solved—for example, configurations in which a game is won. In- termediate states (unlabeled in this diagram) are depicted by the other nodes. Good problem solving is thought to be the creation of efficient paths: ones that are as short as possible and take as few detours as possible between the initial state and the goal state. It is assumed the best paths are found through searching, with thorough searches being more likely to turn up solutions.

What do Expert systems teach us about thinking and problem solving?

The problem space hypothesis has been used to create expert systems, com- puter programs designed to model the judgments of one or more human ex- perts in a particular field. Expert systems contain a knowledge base, which stores facts relevant within that field. They typically also contain a set of in- ference rules (of the form "If X is true, then Y is true"), a search engine that the program uses to search the knowledge base using the inference rules, and some interface, or means of interacting with a human user who has a question or problem for which he or she is consulting the expert system. Creating expert systems is a complex undertaking. Typically, one or more human experts in the domain are interviewed, often repeatedly. They are often asked to generate a verbal online protocol, thinking aloud as they classify in- stances or solve problems (Stefik, 1995). Part of the difficulty comes from the fact that it is difficult for any expert to state all of his or her knowledge.

Know the difference between well-defined and ill-defined problems

Well-defined problems have a clear goal (you know immediately if you've reached the solution), present a small set of information to start from, and often (but not always) present a set of rules or guidelines to abide by while you are working toward a solution. In Contrast ill-defined problems don't have their goals, starting information, or steps clearly spelled out. e.g., Figuring out sales tax, vs. composing a letter that articulately and sensitively conveys a difficult message, like asking for a raise. Psychologists rarely study ill defined problems.

Reasoning by analogy + Glick and Holyoak

the tumor problem and the problem of the general differ in their surface features but share an underlying structure. The components of one correspond at least roughly with the components of the other: The army is analogous to the rays; the capturing of enemy forces, to the destruction of the tumor; the con- vergence of soldiers at the fortress, to the convergence of rays at the site of the tumor. To use the analogy, participants must engage in the "principle-finding" analysis described by Duncker, moving beyond the details and focusing on the relevant structures of the problem. It is interesting that participants often had to be explicitly told to use the story of the general to solve the tumor problem. Only 30% of participants spon- taneously noticed the analogy, although 75% solved the problem if told that the story of the general would be useful in constructing the solution (for compari- son, only about 10% solved the problem without the story). In later work, Gick and Holyoak (1983) found that they could do away with explicit hints if they gave two analogous stories rather than one. Participants read the story of the general and a story about a fire chief 's putting out a fire by having a circle of firefighters surround it, each one throwing buckets of water at once. Participants were told the experiment was about story comprehension and were asked to write summaries of each story and a comparison of the two before being given the tumor problem to solve. The authors proposed that pro- viding multiple examples helps participants to form an abstract schema (in this case, what the authors called a "convergence" schema), which they later apply to new, analogous problems. Catrambone and Holyoak (1989) further sug- gested that unless participants were explicitly asked to compare stories, they did not form the necessary schema with which to solve the problem.

Be familiar with the perceived benefits to unconscious processing and Incubation, and also with the actual benefits.

unconscious pro- cessing, or incubation. The idea is that while my mind was actively running other cognitive processes, some other sort of processing was happening in the background. (Those of you who like computer metaphors might describe this as "batch processing" as opposed to "interactive processing.") The unconscious processing churned away, even as I slept, until the answer was found; then the answer announced itself all at once, even if it had to wake me from a sound sleep. Those who believe in incubation typically believe in the existence of an unconscious layer of the mind that can process information without giving rise to conscious awareness. -Given Solving Task -16th task with misleading cue. Those who were given a break between 15th and 16th more likely to solve correctly- reset. Most empirical studies, however, fail to find positive effects of incubation: Participants who take physical and mental breaks during problem solving, and who therefore have more opportunity for incubation, rarely show increased ability to solve problems more thoroughly or more quickly than participants who work steadily at the problem e.g. participants prevented from any covert thinking don't show same effects. - its hard to know if people art thinking during incubation interval. Probably whats happening is that when given a break we start fresh, re set, letting go of misleading cues.

Working Backwards

working backward. Its user analyzes the goal to determine the last step needed to achieve it, then the next-to-last step, and so on. necessary to solve the tower of Hanoi. Working backward is most effective when the backward path is unique, which makes the process more efficient than working forward. And, as you may have noticed, working backward shares with means-ends analysis the tech- nique of reducing differences between the current state and the goal state.