CHAPTER 9: THINKING: PROBLEM SOLVING AND DECISION MAKING• Finding the solution• Decisions, decisions
Finding the Solution• According to Mayer (1990, p. 284), problem solving is “cognitive processing directed at transforming a given situation into a goal situation when no obvious method of solution is available to the problem solver.”• This definition suggests there are three aspects to problem solving: • It is purposeful in the sense of being goal directed. • It requires the use of cognitive processes rather than automatic ones. • A problem only exists when someone lacks the relevant knowledge to produce an immediate solution.
Finding the Solution• Sternberg (2003) argued that there are seven steps in the problem-solving cycle: • (i) Problem identification: realizing there is a problem. • (ii) Problem definition and representation: clarifying the nature of the problem. • (iii) Strategy formulation: deciding how to tackle the problem. • (iv) Organization of information: assembling information needed to solve the problem. • (v) Resource allocation: deciding which parts of the problem require the greatest allocation of resources. • (vi) Monitoring: checking progress towards problem solution. • (vii) Evaluation: assessing whether the proposed solution to the problem is adequate.
ALTERNATIVE STEPS IN PROBLEM SOLVING• Develop evidence to support views• Analyze situations carefully• Discuss subjects in an organized way• Predict the consequences of actions• Weigh alternatives• Generate and organize ideas• Form and apply concepts• Design systematic plans of action
Types of Problems• Some problems are well-defined whereas others are ill- defined.• Well-defined problems are ones in which all aspects of the problem are clearly specified, including the range of possible moves or strategies and the goal or solution. • Mazes are well-defined problems in which reaching the center is the goal.• In contrast, ill-defined problems are under-specified. • You locked your keys inside your car and want to get into it without causing any damage. • However, you have very urgent business to attend to elsewhere, and there is noone around to help you. • In such circumstances it may be difficult to identify the best solution to the problem. • Most everyday problems are ill-defined.
How Useful is Past Experience?• Past experience is not always useful.• Functional fixedness is a phenomenon in which we fail to solve a problem because we assume from past experience that any given object only has a limited number of uses. • Duncker’s candle problem (1945: see next slide) • Defeyter and German’s (2003) stick problem• Past experience can also lead us to persevere with problem-solving strategies that are no longer appropriate. • Luchins’s (1942) and Luchins and Luchins’s (1959) water-jar problems.
Functional Fixedness• Duncker (1945) • Gave participants a candle, a box of nails, and several other objects. • The task was to attach the candle to a wall by a table so it did not drip onto the table below. • Participants fixated on the box’s function as a container rather than as a platform.
Positive and Negative Transfer• Negative transfer means interfering effects of previous experience on a current problem.• In the real world, the effects of past experience on problem solving are predominantly positive (positive transfer).• This often involves making use of analogies or similarities between the current problem and one or more problems solved in the past. • Gick and Holyoak (1980) used Duncker’s (1945) radiation problem.
Positive and Negative Transfer• Most laboratory research on positive transfer has focused on the immediate application of knowledge and skills from one situation to a rather similar one (near transfer).• In education what matters is positive transfer over long periods of time to situations differing considerably from that of the original learning (far transfer). • Chen and Klahr (1999)• De Corte (2003) wondered whether far transfer depends on metacognition (the beliefs and knowledge we have about our own cognitive processes and strategies). • Business economics students
Does Insight Exist?• There are many problems in which the solution depends on insight or an “aha” experience involving a sudden transformation of the problem.• Take the mutilated checkerboard problem (see next slide).
Does Insight Exist?• The board is initially completely covered by 32 dominoes occupying two squares each.• Then two squares from diagonally opposite corners are removed.• Can the remaining 62 squares be filled by 31 dominoes?• What nearly everyone does is to start by mentally covering squares with dominoes (Kaplan & Simon, 1990).• Alas, this is not a great strategy—there are 758,148 possible permutations of the dominoes!
Does Insight Exist?The mutilated checkerboard problem
Does Insight Exist?• The take-home message from this problem is that how we think about a problem (the problem representation) is of great importance in problem solving.• Eventually we will form the correct problem representation, which involves a sudden restructuring of the problem (known as insight).
Does Insight Exist?• Bowden, Jung-Beeman, Fleck, and Kounios (2005) identified a part of the brain involved in insight. Participants performed the Remote Associates Test. • They found that brain activity was centered on the right anterior temporal gyrus. This brain area seems to be especially important to insight because it is involved in processing general semantic (meaning) relationships.• Novick and Sherman’s (2003) anagram task: • Found that some relevant processing occurs BEFORE “insight” anagram solutions even though people have no conscious awareness of such processing.
What Produces Insight?• Ohlsson (1992): We often encounter a block in problem solving because we are using an inappropriate representation of the problem.• Insight typically occurs only when we change such a problem representation into the correct one. This can occur in three ways: (1) Constraint relaxation: Inhibitions on what is regarded as permissible are removed. (2) Re-encoding: Some aspect of the problem representation is re-interpreted. (3) Elaboration: New problem information is added to the representation.
What Produces Insight?• Knoblich, Ohlsson, Haider, and Rhenius (1999) found that insight can involve relaxing constraints.• They used mathematical problems involving sticks representing Roman numerals. • Each problem presented was initially false, and the task was to move ONE stick to turn it into a true statement. • For example, VI = VII + I (6 = 7 + I) becomes true by turning it into VII = VI + I (7 = 6 + I). • Knoblich et al. (1999) found that problems like these were typically solved easily. • However, most participants struggled to solve problems such as: IV = III – I (4 = 3 – I)? • The correct answer is IV – III = I (4 – 3 = 1).
What Produces Insight?• Many people believe that putting a problem to one side for a while or simply “sleeping on it” can be effective in getting around a block in problem solving.• Psychologists use the term incubation to refer to this phenomenon.• Dodds, Ward, and Smith (2004) reviewed 39 studies on incubation, of which 29 produced incubation effects.• Wagner et al. (2004) found that sleep can be a useful form of incubation.• Simon (1966) argued that incubation involves a special kind of forgetting. • Support for that viewpoint was reported by Smith and Blankenship (1991) using the Remote Associates Test.
Information-Processing Approach• One of the greatest landmarks in problem-solving research was the publication in 1972 of Allen Newell and Herb Simon’s book entitled Human problem solving.• They assumed we have strictly limited short-term memory capacity and that complex information processing is typically serial.• Newell and Simon argued that we use heuristics and algorithms to select mental operators as we move through a problem—the most important being means–end analysis, which can be illustrated with the “Tower of Hanoi” problem (see next slide).• Hill climbing involves changing the present state within the problem into one that is closer to the goal or problem solution.
Means–Ends Analysis• Note the difference between the current state of the problem and the goal state.• Form a sub-goal that will reduce the difference between the current and goal states.• Select a mental operator that will permit attainment of the sub-goal.• Example: the Tower of Hanoi Problem (see next slide).
The initial state of the five-disk version of the Tower of Hanoi problem.
Information-Processing Approach• Newell and Simon (1972) argued that it is possible to produce systematic computer simulations of human problem solving—the “General Problem Solver”, which was designed to solve a fairly wide range of well-defined problems.• They made several assumptions: • Information processing is serial. • People possess limited short-term memory capacity. • People can retrieve relevant information from long-term memory.
Information-Processing Approach• According to Newell and Simon, the process of problem solving involves a sequence of different knowledge states, which intervene between the initial state and the goal state, with mental operators producing the shift from one knowledge state to the next.
Information-Processing Approach• In the General Problem Solver, problems are represented as a problem space. The problem space consists of the following: • The initial state of the problem. • The goal state. • All the possible mental operators (i.e., moves) that can be applied to any state to change it into a different state. • All the intermediate states of the problem.
Findings• Simon and Reed (1976) studied a more complex version of the “missionaries and cannibals” problem and found evidence firstly of a balancing strategy, then the means–end strategy, and an anti-looping heuristic.• Sweller and Levine (1982) used a problem in which use of means–ends analysis would lead problem solvers to make consistently wrong moves.
Findings• Delaney, Ericsson, and Knowles (2004) used water-jar problems and found that the control participants showed little evidence of planning ahead.• MacGregor, Ormerod, and Chronicle (2001) argued that problem solvers use a heuristic known as progress monitoring. With this heuristic, the rate of progress towards the goal is assessed. • They obtained evidence for the importance of progress monitoring in a study on the nine-dot problem (see next slide).
Most people find it hard to solvethe nine-dot problem because theyassume that the lines joining allthe dots together have to staywithin the square.
Evaluation• The Newell and Simon approach works well with several well-defined problems.• The approach is generally consistent with our knowledge of human information processing (e.g., limited short-term memory capacity).• The General Problem Solver is of limited applicability to the ill-defined problems of everyday life.• The General Problem Solver is better than humans at remembering what has happened on a problem but inferior at planning future moves. It focuses on only a single move whereas people often plan small sequences of moves (e.g., Greeno, 1974).• Newell and Simon (1972) didn’t focus enough on the motivational factors causing us to shift strategies. This gap was filled by MacGregor et al. (2001) with their progress monitoring heuristic.
Decisions, Decisions• Evidence that we sometimes simply give up when confronted by too many choices was reported by Iyengar and Lepper (2000).• Carlson and Russo (2001) showed potential jurors a video explaining the importance of not making decisions before seeing all the evidence. • Most participants showed “pre-decisional distortion”— they often regarded the new evidence as supporting whichever party (plaintiff or defendant) they favored before it was presented.• Worrying evidence that important real-life decisions may be inadequate was reported by Elstein et al. (1999).• Many experts argue that most decisions are like gambling in that they are made under uncertainty.
Losses and Gains• Kahneman and Tversky’s (1984) prospect theory is based on two key theoretical assumptions: (1) People identify a reference point generally representing their current state. (2) People are much more sensitive to potential losses than to potential gains; this is known as loss aversion.• Support for prospect theory has come from studies of loss aversion (e.g., Tversky & Shafir, 1992).
Losses and Gains• When people make decisions, they attach more weight to low-probability events than they merit according to their actual probability of occurrence.• In contrast, high-probability events receive less weight than they deserve.• Prospect theory can be contrasted with previous theoretical views based on the notion of “rational man” (or “rational person”). • According to this approach, we work systematically through the available evidence and make the decision most likely to produce a desirable outcome. • This notion is found in normative theories, which focus on how people should make decisions rather than on how they actually make them.
Losses and Gains• Some framing effects can be accounted for in terms of loss aversion (e.g., Tversky & Kahneman, 1981—the “Asian disease problem”).• Why don’t we learn from experience that losses often have less negative emotional impact than we had anticipated? • One reason is that people often rationalize or explain away losses in ways that are difficult to predict ahead of time.
Losses and Gains• Wang (1996) showed that considerations of fairness could also influence decision making in the “Asian disease problem”.• Rottenstreich and Shu (2004) argued that decision making can be based on “two separate systems—an affective [emotional] system and a perhaps more cognitive system compatible with prospect theory.”• Another limitation of prospect theory is that it ignores individual differences, in spite of the fact that we all know some people are more willing to take risks than others (Josephs et al., 1992).• A final limitation with prospect theory is that it ignores cross- cultural differences (Weber & Hsee, 2000).
Evaluation• Prospect theory provides a more accurate account of human decision making than previous theories.• The notion that we attach more weight to losses than to gains provides an explanation for many phenomena (e.g., loss aversion; framing effect).• The theory doesn’t consider the impact of social and emotional factors on decision making (e.g., Wang, 1996; Rottenstreich & Hsee, 2001).• The theory neglects individual differences in the willingness to take risks (e.g., Josephs et al., 1992).• The theory ignores cultural differences in risk taking (e.g., Weber & Hsee, 2000).• As Hardman and Harries (2002, p. 76) pointed out, “There is no apparent rationale for ... the value function ...The value function is descriptive of behavior but does not go beyond this.”
What Will People Think?• Tetlock (2002) argued, we often behave like intuitive politicians concerned to justify our decisions to other people.• He put forward the social functionalist approach, in which the social context of decision making is taken into account and people anticipate objections.
Findings• Camerer et al. (1997) found New York cab drivers work unnecessarily long hours when business is poor and miss out on easy money when business is good. • Why? Behavior is “an adaptive response to no-excuses accountability pressures from the home front to bring home the bacon” (Tetlock & Mellers, 2002, p. 98).• Simonson and Staw’s (1992) study focused on the sunk-cost effect, which involves a tendency to throw good money after bad in an attempt to recoup one’s losses.• Schwartz et al. (2004) found that even the decisions of medical experts can be swayed by considerations of accountability.
Evaluation• The assumption within the social functionalist approach that our decisions in everyday life are generally influenced by social and cultural factors is absolutely right.• We often experience pressure to justify our decisions to others, and this is the case even with experts (e.g., Schwartz et al., 2004).• Important factors within prospect theory (e.g., our greater sensitivity to losses than gains) are ignored by the social functionalist approach.• Tetlock and others favoring the social functionalist approach have often criticized other researchers for conducting experiments not making any real demands on social responsibility. Ironically, much the same can be said of their own research!
Complex Decision Making• Multi-attribute utility theory (Wright, 1984): the decision maker should go through the following stages: • Identify dimensions relevant to the decision. • Decide how to weight those dimensions. • Obtain a total utility (i.e., subjective desirability) for each option by summing its weighted dimensional values. • Select the option with the highest weighted total.
Bounded Rationality• Herb Simon (1957) drew an important distinction between unbounded rationality and bounded rationality.• Within models of unbounded rationality (multi- attribute utility theory is an example), it is assumed that all relevant information is used by the decision maker. • As a consequence, people are in a position to make the best possible decision or choice.
Bounded Rationality• Simon (1957) argued that we possess bounded rationality rather than unbounded rationality; we produce reasonable solutions to problems in spite of our limited processing capacity by using short-cut strategies including heuristics or rules of thumb.• More specifically, decision making can be “bounded” by constraints in the environment (e.g., information costs; time costs) or by constraints in the mind (e.g., limited attention; limited memory).• The essence of satisficing (formed by combining satisfactory and sufficing) is that individuals consider various options one at a time and select the first one meeting their minimum requirements.
Bounded Rationality• Tversky (1972) put forward his elimination-by- aspects theory, in which decision makers eliminate options by considering one relevant attribute after another.• Dijksterhuis and Nordgren (2006) proposed unconscious thought theory in which there is an important distinction between conscious thought (involving attention) and unconscious thought (thinking occurring without attention).
Bounded Rationality• Payne (1976) addressed the issue of the extent to which decision makers behave as predicted by Simon and by Tversky.• Payne, Bettman, and Johnson (1988) found that moderate time pressure led decision makers to become slightly more selective in their processing. When the time pressure was severe decision makers speeded up their processing, focused their attention on only a fraction of the available information, and changed their processing strategies.• Simons, Krawczyk, and Holyoak (2004) found preferences for desirable attributes of the chosen job increased and preferences for undesirable attributes of that job decreased.• Dijksterhuis’s (2004) apartments in Amsterdam study.• Dijksterhuis, Bos, Nordgren, and van Baaren’s (2006) hypothetical cars study.
Evaluation• There is much support for the assumptions that humans possess bounded rationality and frequently use the satisficing heuristic.• Several factors influencing decision making (e.g., number of choices remaining to be considered; extent of time pressure) have been identified.• Some of the strengths and limitations of conscious thought and of unconscious thought have been identified.
Evaluation• Most theories implicitly assume that attribute preferences don’t change over time, but there is evidence (e.g., Simons et al., 2004) that this assumption is incorrect.• Insufficient attention has been paid to individual differences.• Superiority of unconscious thought over conscious thought with complex decision making would probably not be found if people had full access to problem information throughout the decision-making process.