problem solving task theory

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21 Problem Solving

Miriam Bassok, Department of Psychology, University of Washington, Seattle, WA

Laura R. Novick, Department of Psychology and Human Development, Vanderbilt University, Nashville, TN

• Published: 21 November 2012
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This chapter follows the historical development of research on problem solving. It begins with a description of two research traditions that addressed different aspects of the problem-solving process: ( 1 ) research on problem representation (the Gestalt legacy) that examined how people understand the problem at hand, and ( 2 ) research on search in a problem space (the legacy of Newell and Simon) that examined how people generate the problem's solution. It then describes some developments in the field that fueled the integration of these two lines of research: work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. Next, it presents examples of recent work on problem solving in science and mathematics that highlight the impact of visual perception and background knowledge on how people represent problems and search for problem solutions. The final section considers possible directions for future research.

People are confronted with problems on a daily basis, be it trying to extract a broken light bulb from a socket, finding a detour when the regular route is blocked, fixing dinner for unexpected guests, dealing with a medical emergency, or deciding what house to buy. Obviously, the problems people encounter differ in many ways, and their solutions require different types of knowledge and skills. Yet we have a sense that all the situations we classify as problems share a common core. Karl Duncker defined this core as follows: “A problem arises when a living creature has a goal but does not know how this goal is to be reached. Whenever one cannot go from the given situation to the desired situation simply by action [i.e., by the performance of obvious operations], then there has to be recourse to thinking” (Duncker, 1945 , p. 1). Consider the broken light bulb. The obvious operation—holding the glass part of the bulb with one's fingers while unscrewing the base from the socket—is prevented by the fact that the glass is broken. Thus, there must be “recourse to thinking” about possible ways to solve the problem. For example, one might try mounting half a potato on the broken bulb (we do not know the source of this creative solution, which is described on many “how to” Web sites).

The above definition and examples make it clear that what constitutes a problem for one person may not be a problem for another person, or for that same person at another point in time. For example, the second time one has to remove a broken light bulb from a socket, the solution likely can be retrieved from memory; there is no problem. Similarly, tying shoes may be considered a problem for 5-year-olds but not for readers of this chapter. And, of course, people may change their goal and either no longer have a problem (e.g., take the guests to a restaurant instead of fixing dinner) or attempt to solve a different problem (e.g., decide what restaurant to go to). Given the highly subjective nature of what constitutes a problem, researchers who study problem solving have often presented people with novel problems that they should be capable of solving and attempted to find regularities in the resulting problem-solving behavior. Despite the variety of possible problem situations, researchers have identified important regularities in the thinking processes by which people (a) represent , or understand, problem situations and (b) search for possible ways to get to their goal.

A problem representation is a model constructed by the solver that summarizes his or her understanding of the problem components—the initial state (e.g., a broken light bulb in a socket), the goal state (the light bulb extracted), and the set of possible operators one may apply to get from the initial state to the goal state (e.g., use pliers). According to Reitman ( 1965 ), problem components differ in the extent to which they are well defined . Some components leave little room for interpretation (e.g., the initial state in the broken light bulb example is relatively well defined), whereas other components may be ill defined and have to be defined by the solver (e.g., the possible actions one may take to extract the broken bulb). The solver's representation of the problem guides the search for a possible solution (e.g., possible attempts at extracting the light bulb). This search may, in turn, change the representation of the problem (e.g., finding that the goal cannot be achieved using pliers) and lead to a new search. Such a recursive process of representation and search continues until the problem is solved or until the solver decides to abort the goal.

Duncker ( 1945 , pp. 28–37) documented the interplay between representation and search based on his careful analysis of one person's solution to the “Radiation Problem” (later to be used extensively in research analogy, see Holyoak, Chapter 13 ). This problem requires using some rays to destroy a patient's stomach tumor without harming the patient. At sufficiently high intensity, the rays will destroy the tumor. However, at that intensity, they will also destroy the healthy tissue surrounding the tumor. At lower intensity, the rays will not harm the healthy tissue, but they also will not destroy the tumor. Duncker's analysis revealed that the solver's solution attempts were guided by three distinct problem representations. He depicted these solution attempts as an inverted search tree in which the three main branches correspond to the three general problem representations (Duncker, 1945 , p. 32). We reproduce this diagram in Figure 21.1 . The desired solution appears on the rightmost branch of the tree, within the general problem representation in which the solver aims to “lower the intensity of the rays on their way through healthy tissue.” The actual solution is to project multiple low-intensity rays at the tumor from several points around the patient “by use of lens.” The low-intensity rays will converge on the tumor, where their individual intensities will sum to a level sufficient to destroy the tumor.

A search-tree representation of one subject's solution to the radiation problem, reproduced from Duncker ( 1945 , p. 32).

Although there are inherent interactions between representation and search, some researchers focus their efforts on understanding the factors that affect how solvers represent problems, whereas others look for regularities in how they search for a solution within a particular representation. Based on their main focus of interest, researchers devise or select problems with solutions that mainly require either constructing a particular representation or finding the appropriate sequence of steps leading from the initial state to the goal state. In most cases, researchers who are interested in problem representation select problems in which one or more of the components are ill defined, whereas those who are interested in search select problems in which the components are well defined. The following examples illustrate, respectively, these two problem types.

The Bird-and-Trains problem (Posner, 1973 , pp. 150–151) is a mathematical word problem that tends to elicit two distinct problem representations (see Fig. 21.2a and b ):

Two train stations are 50 miles apart. At 2 p.m. one Saturday afternoon two trains start toward each other, one from each station. Just as the trains pull out of the stations, a bird springs into the air in front of the first train and flies ahead to the front of the second train. When the bird reaches the second train, it turns back and flies toward the first train. The bird continues to do this until the trains meet. If both trains travel at the rate of 25 miles per hour and the bird flies at 100 miles per hour, how many miles will the bird have flown before the trains meet? Fig. 21.2 Open in new tab Download slide Alternative representations of Posner's ( 1973 ) trains-and-bird problem. Adapted from Novick and Hmelo ( 1994 ).

Some solvers focus on the back-and-forth path of the bird (Fig. 21.2a ). This representation yields a problem that would be difficult for most people to solve (e.g., a series of differential equations). Other solvers focus on the paths of the trains (Fig. 21.2b ), a representation that yields a relatively easy distance-rate-time problem.

The Tower of Hanoi problem falls on the other end of the representation-search continuum. It leaves little room for differences in problem representations, and the primary work is to discover a solution path (or the best solution path) from the initial state to the goal state .

There are three pegs mounted on a base. On the leftmost peg, there are three disks of differing sizes. The disks are arranged in order of size with the largest disk on the bottom and the smallest disk on the top. The disks may be moved one at a time, but only the top disk on a peg may be moved, and at no time may a larger disk be placed on a smaller disk. The goal is to move the three-disk tower from the leftmost peg to the rightmost peg.

Figure 21.3 shows all the possible legal arrangements of disks on pegs. The arrows indicate transitions between states that result from moving a single disk, with the thicker gray arrows indicating the shortest path that connects the initial state to the goal state.

The division of labor between research on representation versus search has distinct historical antecedents and research traditions. In the next two sections, we review the main findings from these two historical traditions. Then, we describe some developments in the field that fueled the integration of these lines of research—work on problem isomorphs, on expertise in specific knowledge domains (e.g., chess, mathematics), and on insight solutions. In the fifth section, we present some examples of recent work on problem solving in science and mathematics. This work highlights the role of visual perception and background knowledge in the way people represent problems and search for problem solutions. In the final section, we consider possible directions for future research.

Our review is by no means an exhaustive one. It follows the historical development of the field and highlights findings that pertain to a wide variety of problems. Research pertaining to specific types of problems (e.g., medical problems), specific processes that are involved in problem solving (e.g., analogical inferences), and developmental changes in problem solving due to learning and maturation may be found elsewhere in this volume (e.g., Holyoak, Chapter 13 ; Smith & Ward, Chapter 23 ; van Steenburgh et al., Chapter 24 ; Simonton, Chapter 25 ; Opfer & Siegler, Chapter 30 ; Hegarty & Stull, Chapter 31 ; Dunbar & Klahr, Chapter 35 ; Patel et al., Chapter 37 ; Lowenstein, Chapter 38 ; Koedinger & Roll, Chapter 40 ).

All possible problem states for the three-disk Tower of Hanoi problem. The thicker gray arrows show the optimum solution path connecting the initial state (State #1) to the goal state (State #27).

Problem Representation: The Gestalt Legacy

Research on problem representation has its origins in Gestalt psychology, an influential approach in European psychology during the first half of the 20th century. (Behaviorism was the dominant perspective in American psychology at this time.) Karl Duncker published a book on the topic in his native German in 1935, which was translated into English and published 10 years later as the monograph On Problem-Solving (Duncker, 1945 ). Max Wertheimer also published a book on the topic in 1945, titled Productive Thinking . An enlarged edition published posthumously includes previously unpublished material (Wertheimer, 1959 ). Interestingly, 1945 seems to have been a watershed year for problem solving, as mathematician George Polya's book, How to Solve It , also appeared then (a second edition was published 12 years later; Polya, 1957 ).

The Gestalt psychologists extended the organizational principles of visual perception to the domain of problem solving. They showed that various visual aspects of the problem, as well the solver's prior knowledge, affect how people understand problems and, therefore, generate problem solutions. The principles of visual perception (e.g., proximity, closure, grouping, good continuation) are directly relevant to problem solving when the physical layout of the problem, or a diagram that accompanies the problem description, elicits inferences that solvers include in their problem representations. Such effects are nicely illustrated by Maier's ( 1930 ) nine-dot problem: Nine dots are arrayed in a 3x3 grid, and the task is to connect all the dots by drawing four straight lines without lifting one's pencil from the paper. People have difficulty solving this problem because their initial representations generally include a constraint, inferred from the configuration of the dots, that the lines should not go outside the boundary of the imaginary square formed by the outer dots. With this constraint, the problem cannot be solved (but see Adams, 1979 ). Without this constraint, the problem may be solved as shown in Figure 21.4 (though the problem is still difficult for many people; see Weisberg & Alba, 1981 ).

The nine-dot problem is a classic insight problem (see van Steenburgh et al., Chapter 24 ). According to the Gestalt view (e.g., Duncker, 1945 ; Kohler, 1925 ; Maier, 1931 ; see Ohlsson, 1984 , for a review), the solution to an insight problem appears suddenly, accompanied by an “aha!” sensation, immediately following the sudden “restructuring” of one's understanding of the problem (i.e., a change in the problem representation): “The decisive points in thought-processes, the moments of sudden comprehension, of the ‘Aha!,’ of the new, are always at the same time moments in which such a sudden restructuring of the thought-material takes place” (Duncker, 1945 , p. 29). For the nine-dot problem, one view of the required restructuring is that the solver relaxes the constraint implied by the perceptual form of the problem and realizes that the lines may, in fact, extend past the boundary of the imaginary square. Later in the chapter, we present more recent accounts of insight.

The entities that appear in a problem also tend to evoke various inferences that people incorporate into their problem representations. A classic demonstration of this is the phenomenon of functional fixedness , introduced by Duncker ( 1945 ): If an object is habitually used for a certain purpose (e.g., a box serves as a container), it is difficult to see

A solution to the nine-dot problem.

that object as having properties that would enable it to be used for a dissimilar purpose. Duncker's basic experimental paradigm involved two conditions that varied in terms of whether the object that was crucial for solution was initially used for a function other than that required for solution.

Consider the candles problem—the best known of the five “practical problems” Duncker ( 1945 ) investigated. Three candles are to be mounted at eye height on a door. On the table, for use in completing this task, are some tacks and three boxes. The solution is to tack the three boxes to the door to serve as platforms for the candles. In the control condition, the three boxes were presented to subjects empty. In the functional-fixedness condition, they were filled with candles, tacks, and matches. Thus, in the latter condition, the boxes initially served the function of container, whereas the solution requires that they serve the function of platform. The results showed that 100% of the subjects who received empty boxes solved the candles problem, compared with only 43% of subjects who received filled boxes. Every one of the five problems in this study showed a difference favoring the control condition over the functional-fixedness condition, with average solution rates across the five problems of 97% and 58%, respectively.

The function of the objects in a problem can be also “fixed” by their most recent use. For example, Birch and Rabinowitz ( 1951 ) had subjects perform two consecutive tasks. In the first task, people had to use either a switch or a relay to form an electric circuit. After completing this task, both groups of subjects were asked to solve Maier's ( 1931 ) two-ropes problem. The solution to this problem requires tying an object to one of the ropes and making the rope swing as a pendulum. Subjects could create the pendulum using either the object from the electric-circuit task or the other object. Birch and Rabinowitz found that subjects avoided using the same object for two unrelated functions. That is, those who used the switch in the first task made the pendulum using the relay, and vice versa. The explanations subjects subsequently gave for their object choices revealed that they were unaware of the functional-fixedness constraint they imposed on themselves.

In addition to investigating people's solutions to such practical problems as irradiating a tumor, mounting candles on the wall, or tying ropes, the Gestalt psychologists examined how people understand and solve mathematical problems that require domain-specific knowledge. For example, Wertheimer ( 1959 ) observed individual differences in students' learning and subsequent application of the formula for finding the area of a parallelogram (see Fig. 21.5a ). Some students understood the logic underlying the learned formula (i.e., the fact that a parallelogram can be transformed into a rectangle by cutting off a triangle from one side and pasting it onto the other side) and exhibited “productive thinking”—using the same logic to find the area of the quadrilateral in Figure 21.5b and the irregularly shaped geometric figure in Figure 21.5c . Other students memorized the formula and exhibited “reproductive thinking”—reproducing the learned solution only to novel parallelograms that were highly similar to the original one.

The psychological study of human problem solving faded into the background after the demise of the Gestalt tradition (during World War II), and problem solving was investigated only sporadically until Allen Newell and Herbert Simon's ( 1972 ) landmark book Human Problem Solving sparked a flurry of research on this topic. Newell and Simon adopted and refined Duncker's ( 1945 ) methodology of collecting and analyzing the think-aloud protocols that accompany problem solutions and extended Duncker's conceptualization of a problem solution as a search tree. However, their initial work did not aim to extend the Gestalt findings

Finding the area of ( a ) a parallelogram, ( b ) a quadrilateral, and ( c ) an irregularly shaped geometric figure. The solid lines indicate the geometric figures whose areas are desired. The dashed lines show how to convert the given figures into rectangles (i.e., they show solutions with understanding).

pertaining to problem representation. Instead, as we explain in the next section, their objective was to identify the general-purpose strategies people use in searching for a problem solution.

Search in a Problem Space: The Legacy of Newell and Simon

Newell and Simon ( 1972 ) wrote a magnum opus detailing their theory of problem solving and the supporting research they conducted with various collaborators. This theory was grounded in the information-processing approach to cognitive psychology and guided by an analogy between human and artificial intelligence (i.e., both people and computers being “Physical Symbol Systems,” Newell & Simon, 1976 ; see Doumas & Hummel, Chapter 5 ). They conceptualized problem solving as a process of search through a problem space for a path that connects the initial state to the goal state—a metaphor that alludes to the visual or spatial nature of problem solving (Simon, 1990 ). The term problem space refers to the solver's representation of the task as presented (Simon, 1978 ). It consists of ( 1 ) a set of knowledge states (the initial state, the goal state, and all possible intermediate states), ( 2 ) a set of operators that allow movement from one knowledge state to another, ( 3 ) a set of constraints, and ( 4 ) local information about the path one is taking through the space (e.g., the current knowledge state and how one got there).

We illustrate the components of a problem space for the three-disk Tower of Hanoi problem, as depicted in Figure 21.3 . The initial state appears at the top (State #1) and the goal state at the bottom right (State #27). The remaining knowledge states in the figure are possible intermediate states. The current knowledge state is the one at which the solver is located at any given point in the solution process. For example, the current state for a solver who has made three moves along the optimum solution path would be State #9. The solver presumably would know that he or she arrived at this state from State #5. This knowledge allows the solver to recognize a move that involves backtracking. The three operators in this problem are moving each of the three disks from one peg to another. These operators are subject to the constraint that a larger disk may not be placed on a smaller disk.

Newell and Simon ( 1972 ), as well as other contemporaneous researchers (e.g., Atwood & Polson, 1976 ; Greeno, 1974 ; Thomas, 1974 ), examined how people traverse the spaces of various well-defined problems (e.g., the Tower of Hanoi, Hobbits and Orcs). They discovered that solvers' search is guided by a number of shortcut strategies, or heuristics , which are likely to get the solver to the goal state without an extensive amount of search. Heuristics are often contrasted with algorithms —methods that are guaranteed to yield the correct solution. For example, one could try every possible move in the three-disk Tower of Hanoi problem and, eventually, find the correct solution. Although such an exhaustive search is a valid algorithm for this problem, for many problems its application is very time consuming and impractical (e.g., consider the game of chess).

In their attempts to identify people's search heuristics, Newell and Simon ( 1972 ) relied on two primary methodologies: think-aloud protocols and computer simulations. Their use of think-aloud protocols brought a high degree of scientific rigor to the methodology used by Duncker ( 1945 ; see Ericsson & Simon, 1980 ). Solvers were required to say out loud everything they were thinking as they solved the problem, that is, everything that went through their verbal working memory. Subjects' verbalizations—their think-aloud protocols—were tape-recorded and then transcribed verbatim for analysis. This method is extremely time consuming (e.g., a transcript of one person's solution to the cryptarithmetic problem DONALD + GERALD = ROBERT, with D = 5, generated a 17-page transcript), but it provides a detailed record of the solver's ongoing solution process.

An important caveat to keep in mind while interpreting a subject's verbalizations is that “a protocol is relatively reliable only for what it positively contains, but not for that which it omits” (Duncker, 1945 , p. 11). Ericsson and Simon ( 1980 ) provided an in-depth discussion of the conditions under which this method is valid (but see Russo, Johnson, & Stephens, 1989 , for an alternative perspective). To test their interpretation of a subject's problem solution, inferred from the subject's verbal protocol, Newell and Simon ( 1972 ) created a computer simulation program and examined whether it solved the problem the same way the subject did. To the extent that the computer simulation provided a close approximation of the solver's step-by-step solution process, it lent credence to the researcher's interpretation of the verbal protocol.

Newell and Simon's ( 1972 ) most famous simulation was the General Problem Solver or GPS (Ernst & Newell, 1969 ). GPS successfully modeled human solutions to problems as different as the Tower of Hanoi and the construction of logic proofs using a single general-purpose heuristic: means-ends analysis . This heuristic captures people's tendency to devise a solution plan by setting subgoals that could help them achieve their final goal. It consists of the following steps: ( 1 ) Identify a difference between the current state and the goal (or subgoal ) state; ( 2 ) Find an operator that will remove (or reduce) the difference; (3a) If the operator can be directly applied, do so, or (3b) If the operator cannot be directly applied, set a subgoal to remove the obstacle that is preventing execution of the desired operator; ( 4 ) Repeat steps 1–3 until the problem is solved. Next, we illustrate the implementation of this heuristic for the Tower of Hanoi problem, using the problem space in Figure 21.3 .

As can be seen in Figure 21.3 , a key difference between the initial state and the goal state is that the large disk is on the wrong peg (step 1). To remove this difference (step 2), one needs to apply the operator “move-large-disk.” However, this operator cannot be applied because of the presence of the medium and small disks on top of the large disk. Therefore, the solver may set a subgoal to move that two-disk tower to the middle peg (step 3b), leaving the rightmost peg free for the large disk. A key difference between the initial state and this new subgoal state is that the medium disk is on the wrong peg. Because application of the move-medium-disk operator is blocked, the solver sets another subgoal to move the small disk to the right peg. This subgoal can be satisfied immediately by applying the move-small-disk operator (step 3a), generating State #3. The solver then returns to the previous subgoal—moving the tower consisting of the small and medium disks to the middle peg. The differences between the current state (#3) and the subgoal state (#9) can be removed by first applying the move-medium-disk operator (yielding State #5) and then the move-small-disk operator (yielding State #9). Finally, the move-large-disk operator is no longer blocked. Hence, the solver moves the large disk to the right peg, yielding State #11.

Notice that the subgoals are stacked up in the order in which they are generated, so that they pop up in the order of last in first out. Given the first subgoal in our example, repeated application of the means-ends analysis heuristic will yield the shortest-path solution, indicated by the large gray arrows. In general, subgoals provide direction to the search and allow solvers to plan several moves ahead. By assessing progress toward a required subgoal rather than the final goal, solvers may be able to make moves that otherwise seem unwise. To take a concrete example, consider the transition from State #1 to State #3 in Figure 21.3 . Comparing the initial state to the goal state, this move seems unwise because it places the small disk on the bottom of the right peg, whereas it ultimately needs to be at the top of the tower on that peg. But comparing the initial state to the solver-generated subgoal state of having the medium disk on the middle peg, this is exactly where the small disk needs to go.

Means-ends analysis and various other heuristics (e.g., the hill-climbing heuristic that exploits the similarity, or distance, between the state generated by the next operator and the goal state; working backward from the goal state to the initial state) are flexible strategies that people often use to successfully solve a large variety of problems. However, the generality of these heuristics comes at a cost: They are relatively weak and fallible (e.g., in the means-ends solution to the problem of fixing a hole in a bucket, “Dear Liza” leads “Dear Henry” in a loop that ends back at the initial state; the lyrics of this famous song can be readily found on the Web). Hence, although people use general-purpose heuristics when they encounter novel problems, they replace them as soon as they acquire experience with and sufficient knowledge about the particular problem space (e.g., Anzai & Simon, 1979 ).

Despite the fruitfulness of this research agenda, it soon became evident that a fundamental weakness was that it minimized the importance of people's background knowledge. Of course, Newell and Simon ( 1972 ) were aware that problem solutions require relevant knowledge (e.g., the rules of logical proofs, or rules for stacking disks). Hence, in programming GPS, they supplemented every problem they modeled with the necessary background knowledge. This practice highlighted the generality and flexibility of means-ends analysis but failed to capture how people's background knowledge affects their solutions. As we discussed in the previous section, domain knowledge is likely to affect how people represent problems and, therefore, how they generate problem solutions. Moreover, as people gain experience solving problems in a particular knowledge domain (e.g., math, physics), they change their representations of these problems (e.g., Chi, Feltovich, & Glaser, 1981 ; Haverty, Koedinger, Klahr, & Alibali, 2000 ; Schoenfeld & Herrmann, 1982 ) and learn domain-specific heuristics (e.g., Polya, 1957 ; Schoenfeld, 1979 ) that trump the general-purpose strategies.

It is perhaps inevitable that the two traditions in problem-solving research—one emphasizing representation and the other emphasizing search strategies—would eventually come together. In the next section we review developments that led to this integration.

The Two Legacies Converge

Because Newell and Simon ( 1972 ) aimed to discover the strategies people use in searching for a solution, they investigated problems that minimized the impact of factors that tend to evoke differences in problem representations, of the sort documented by the Gestalt psychologists. In subsequent work, however, Simon and his collaborators showed that such factors are highly relevant to people's solutions of well-defined problems, and Simon ( 1986 ) incorporated these findings into the theoretical framework that views problem solving as search in a problem space.

In this section, we first describe illustrative examples of this work. We then describe research on insight solutions that incorporates ideas from the two legacies described in the previous sections.

Relevance of the Gestalt Ideas to the Solution of Search Problems

In this subsection we describe two lines of research by Simon and his colleagues, and by other researchers, that document the importance of perception and of background knowledge to the way people search for a problem solution. The first line of research used variants of relatively well-defined riddle problems that had the same structure (i.e., “problem isomorphs”) and, therefore, supposedly the same problem space. It documented that people's search depended on various perceptual and conceptual inferences they tended to draw from a specific instantiation of the problem's structure. The second line of research documented that people's search strategies crucially depend on their domain knowledge and on their prior experience with related problems.

Problem Isomorphs

Hayes and Simon ( 1977 ) used two variants of the Tower of Hanoi problem that, instead of disks and pegs, involved monsters and globes that differed in size (small, medium, and large). In both variants, the initial state had the small monster holding the large globe, the medium-sized monster holding the small globe, and the large monster holding the medium-sized globe. Moreover, in both variants the goal was for each monster to hold a globe proportionate to its own size. The only difference between the problems concerned the description of the operators. In one variant (“transfer”), subjects were told that the monsters could transfer the globes from one to another as long as they followed a set of rules, adapted from the rules in the original Tower of Hanoi problem (e.g., only one globe may be transferred at a time). In the other variant (“change”), subjects were told that the monsters could shrink and expand themselves according to a set of rules, which corresponded to the rules in the transfer version of the problem (e.g., only one monster may change its size at a time). Despite the isomorphism of the two variants, subjects conducted their search in two qualitatively different problem spaces, which led to solution times for the change variant being almost twice as long as those for the transfer variant. This difference arose because subjects could more readily envision and track an object that was changing its location with every move than one that was changing its size.

Recent work by Patsenko and Altmann ( 2010 ) found that, even in the standard Tower of Hanoi problem, people's solutions involve object-bound routines that depend on perception and selective attention. The subjects in their study solved various Tower of Hanoi problems on a computer. During the solution of a particular “critical” problem, the computer screen changed at various points without subjects' awareness (e.g., a disk was added, such that a subject who started with a five-disc tower ended with a six-disc tower). Patsenko and Altmann found that subjects' moves were guided by the configurations of the objects on the screen rather than by solution plans they had stored in memory (e.g., the next subgoal).

The Gestalt psychologists highlighted the role of perceptual factors in the formation of problem representations (e.g., Maier's, 1930 , nine-dot problem) but were generally silent about the corresponding implications for how the problem was solved (although they did note effects on solution accuracy). An important contribution of the work on people's solutions of the Tower of Hanoi problem and its variants was to show the relevance of perceptual factors to the application of various operators during search for a problem solution—that is, to the how of problem solving. In the next section, we describe recent work that documents the involvement of perceptual factors in how people understand and use equations and diagrams in the context of solving math and science problems.

Kotovsky, Hayes, and Simon ( 1985 ) further investigated factors that affect people's representation and search in isomorphs of the Tower of Hanoi problem. In one of their isomorphs, three disks were stacked on top of each other to form an inverted pyramid, with the smallest disc on the bottom and the largest on top. Subjects' solutions of the inverted pyramid version were similar to their solutions of the standard version that has the largest disc on the bottom and the smallest on top. However, the two versions were solved very differently when subjects were told that the discs represent acrobats. Subjects readily solved the version in which they had to place a small acrobat on the shoulders of a large one, but they refrained from letting a large acrobat stand on the shoulders of a small one. In other words, object-based inferences that draw on people's semantic knowledge affected the solution of search problems, much as they affect the solution of the ill-defined problems investigated by the Gestalt psychologists (e.g., Duncker's, 1945 , candles problem). In the next section, we describe more recent work that shows similar effects in people's solutions to mathematical word problems.

The work on differences in the representation and solution of problem isomorphs is highly relevant to research on analogical problem solving (or analogical transfer), which examines when and how people realize that two problems that differ in their cover stories have a similar structure (or a similar problem space) and, therefore, can be solved in a similar way. This research shows that minor differences between example problems, such as the use of X-rays versus ultrasound waves to fuse a broken filament of a light bulb, can elicit different problem representations that significantly affect the likelihood of subsequent transfer to novel problem analogs (Holyoak & Koh, 1987 ). Analogical transfer has played a central role in research on human problem solving, in part because it can shed light on people's understanding of a given problem and its solution and in part because it is believed to provide a window onto understanding and investigating creativity (see Smith & Ward, Chapter 23 ). We briefly mention some findings from the analogy literature in the next subsection on expertise, but we do not discuss analogical transfer in detail because this topic is covered elsewhere in this volume (Holyoak, Chapter 13 ).

Expertise and Its Development

In another line of research, Simon and his colleagues examined how people solve ecologically valid problems from various rule-governed and knowledge-rich domains. They found that people's level of expertise in such domains, be it in chess (Chase & Simon, 1973 ; Gobet & Simon, 1996 ), mathematics (Hinsley, Hayes, & Simon, 1977 ; Paige & Simon, 1966 ), or physics (Larkin, McDermott, Simon, & Simon, 1980 ; Simon & Simon, 1978 ), plays a crucial role in how they represent problems and search for solutions. This work, and the work of numerous other researchers, led to the discovery (and rediscovery, see Duncker, 1945 ) of important differences between experts and novices, and between “good” and “poor” students.

One difference between experts and novices pertains to pattern recognition. Experts' attention is quickly captured by familiar configurations within a problem situation (e.g., a familiar configuration of pieces in a chess game). In contrast, novices' attention is focused on isolated components of the problem (e.g., individual chess pieces). This difference, which has been found in numerous domains, indicates that experts have stored in memory many meaningful groups (chunks) of information: for example, chess (Chase & Simon, 1973 ), circuit diagrams (Egan & Schwartz, 1979 ), computer programs (McKeithen, Reitman, Rueter, & Hirtle, 1981 ), medicine (Coughlin & Patel, 1987 ; Myles-Worsley, Johnston, & Simons, 1988 ), basketball and field hockey (Allard & Starkes, 1991 ), and figure skating (Deakin & Allard, 1991 ).

The perceptual configurations that domain experts readily recognize are associated with stored solution plans and/or compiled procedures (Anderson, 1982 ). As a result, experts' solutions are much faster than, and often qualitatively different from, the piecemeal solutions that novice solvers tend to construct (e.g., Larkin et al., 1980 ). In effect, experts often see the solutions that novices have yet to compute (e.g., Chase & Simon, 1973 ; Novick & Sherman, 2003 , 2008 ). These findings have led to the design of various successful instructional interventions (e.g., Catrambone, 1998 ; Kellman et al., 2008 ). For example, Catrambone ( 1998 ) perceptually isolated the subgoals of a statistics problem. This perceptual chunking of meaningful components of the problem prompted novice students to self-explain the meaning of the chunks, leading to a conceptual understanding of the learned solution. In the next section, we describe some recent work that shows the beneficial effects of perceptual pattern recognition on the solution of familiar mathematics problems, as well as the potentially detrimental effects of familiar perceptual chunks to understanding and reasoning with diagrams depicting evolutionary relationships among taxa.

Another difference between experts and novices pertains to their understanding of the solution-relevant problem structure. Experts' knowledge is highly organized around domain principles, and their problem representations tend to reflect this principled understanding. In particular, they can extract the solution-relevant structure of the problems they encounter (e.g., meaningful causal relations among the objects in the problem; see Cheng & Buehner, Chapter 12 ). In contrast, novices' representations tend to be bound to surface features of the problems that may be irrelevant to solution (e.g., the particular objects in a problem). For example, Chi, Feltovich, and Glaser ( 1981 ) examined how students with different levels of physics expertise group mechanics word problems. They found that advanced graduate students grouped the problems based on the physics principles relevant to the problems' solutions (e.g., conservation of energy, Newton's second law). In contrast, undergraduates who had successfully completed an introductory course in mechanics grouped the problems based on the specific objects involved (e.g., pulley problems, inclined plane problems). Other researchers have found similar results in the domains of biology, chemistry, computer programming, and math (Adelson, 1981 ; Kindfield, 1993 / 1994 ; Kozma & Russell, 1997 ; McKeithen et al., 1981 ; Silver, 1979 , 1981 ; Weiser & Shertz, 1983 ).

The level of domain expertise and the corresponding representational differences are, of course, a matter of degree. With increasing expertise, there is a gradual change in people's focus of attention from aspects that are not relevant to solution to those that are (e.g., Deakin & Allard, 1991 ; Hardiman, Dufresne, & Mestre, 1989 ; McKeithen et al., 1981 ; Myles-Worsley et al., 1988 ; Schoenfeld & Herrmann, 1982 ; Silver, 1981 ). Interestingly, Chi, Bassok, Lewis, Reimann, and Glaser ( 1989 ) found similar differences in focus on structural versus surface features among a group of novices who studied worked-out examples of mechanics problems. These differences, which echo Wertheimer's ( 1959 ) observations of individual differences in students' learning about the area of parallelograms, suggest that individual differences in people's interests and natural abilities may affect whether, or how quickly, they acquire domain expertise.

An important benefit of experts' ability to focus their attention on solution-relevant aspects of problems is that they are more likely than novices to recognize analogous problems that involve different objects and cover stories (e.g., Chi et al., 1989 ; Novick, 1988 ; Novick & Holyoak, 1991 ; Wertheimer, 1959 ) or that come from other knowledge domains (e.g., Bassok & Holyoak, 1989 ; Dunbar, 2001 ; Goldstone & Sakamoto, 2003 ). For example, Bassok and Holyoak ( 1989 ) found that, after learning to solve arithmetic-progression problems in algebra, subjects spontaneously applied these algebraic solutions to analogous physics problems that dealt with constantly accelerated motion. Note, however, that experts and good students do not simply ignore the surface features of problems. Rather, as was the case in the problem isomorphs we described earlier (Kotovsky et al., 1985 ), they tend to use such features to infer what the problem's structure could be (e.g., Alibali, Bassok, Solomon, Syc, & Goldin-Meadow, 1999 ; Blessing & Ross, 1996 ). For example, Hinsley et al. ( 1977 ) found that, after reading no more than the first few words of an algebra word problem, expert solvers classified the problem into a likely problem category (e.g., a work problem, a distance problem) and could predict what questions they might be asked and the equations they likely would need to use.

Surface-based problem categorization has a heuristic value (Medin & Ross, 1989 ): It does not ensure a correct categorization (Blessing & Ross, 1996 ), but it does allow solvers to retrieve potentially appropriate solutions from memory and to use them, possibly with some adaptation, to solve a variety of novel problems. Indeed, although experts exploit surface-structure correlations to save cognitive effort, they have the capability to realize that a particular surface cue is misleading (Hegarty, Mayer, & Green, 1992 ; Lewis & Mayer, 1987 ; Martin & Bassok, 2005 ; Novick 1988 , 1995 ; Novick & Holyoak, 1991 ). It is not surprising, therefore, that experts may revert to novice-like heuristic methods when solving problems under pressure (e.g., Beilock, 2008 ) or in subdomains in which they have general but not specific expertise (e.g., Patel, Groen, & Arocha, 1990 ).

Relevance of Search to Insight Solutions

We introduced the notion of insight in our discussion of the nine-dot problem in the section on the Gestalt tradition. The Gestalt view (e.g., Duncker, 1945 ; Maier, 1931 ; see Ohlsson, 1984 , for a review) was that insight problem solving is characterized by an initial work period during which no progress toward solution is made (i.e., an impasse), a sudden restructuring of one's problem representation to a more suitable form, followed immediately by the sudden appearance of the solution. Thus, solving problems by insight was believed to be all about representation, with essentially no role for a step-by-step solution process (i.e., search). Subsequent and contemporary researchers have generally concurred with the Gestalt view that getting the right representation is crucial. However, research has shown that insight solutions do not necessarily arise suddenly or full blown after restructuring (e.g., Weisberg & Alba, 1981 ); and even when they do, the underlying solution process (in this case outside of awareness) may reflect incremental progress toward the goal (Bowden & Jung-Beeman, 2003 ; Durso, Rea, & Dayton, 1994 ; Novick & Sherman, 2003 ).

“Demystifying insight,” to borrow a phrase from Bowden, Jung-Beeman, Fleck, and Kounios ( 2005 ), requires explaining ( 1 ) why solvers initially reach an impasse in solving a problem for which they have the necessary knowledge to generate the solution, ( 2 ) how the restructuring occurred, and ( 3 ) how it led to the solution. A detailed discussion of these topics appears elsewhere in this volume (van Steenburgh et al., Chapter 24 ). Here, we describe briefly three recent theories that have attempted to account for various aspects of these phenomena: Knoblich, Ohlsson, Haider, and Rhenius's ( 1999 ) representational change theory, MacGregor, Ormerod, and Chronicle's ( 2001 ) progress monitoring theory, and Bowden et al.'s ( 2005 ) neurological model. We then propose the need for an integrated approach to demystifying insight that considers both representation and search.

According to Knoblich et al.'s ( 1999 ) representational change theory, problems that are solved with insight are highly likely to evoke initial representations in which solvers place inappropriate constraints on their solution attempts, leading to an impasse. An impasse can be resolved by revising one's representation of the problem. Knoblich and his colleagues tested this theory using Roman numeral matchstick arithmetic problems in which solvers must move one stick to a new location to change a false numerical statement (e.g., I = II + II ) into a statement that is true. According to representational change theory, re-representation may occur through either constraint relaxation or chunk decomposition. (The solution to the example problem is to change II + to III – , which requires both methods of re-representation, yielding I = III – II ). Good support for this theory has been found based on measures of solution rate, solution time, and eye fixation (Knoblich et al., 1999 ; Knoblich, Ohlsson, & Raney, 2001 ; Öllinger, Jones, & Knoblich, 2008 ).

Progress monitoring theory (MacGregor et al., 2001 ) was proposed to account for subjects' difficulty in solving the nine-dot problem, which has traditionally been classified as an insight problem. According to this theory, solvers use the hill-climbing search heuristic to solve this problem, just as they do for traditional search problems (e.g., Hobbits and Orcs). In particular, solvers are hypothesized to monitor their progress toward solution using a criterion generated from the problem's current state. If solvers reach criterion failure, they seek alternative solutions by trying to relax one or more problem constraints. MacGregor et al. found support for this theory using several variants of the nine-dot problem (also see Ormerod, MacGregor, & Chronicle, 2002 ). Jones ( 2003 ) suggested that progress monitoring theory provides an account of the solution process up to the point an impasse is reached and representational change is sought, at which point representational change theory picks up and explains how insight may be achieved. Hence, it appears that a complete account of insight may require an integration of concepts from the Gestalt (representation) and Newell and Simon's (search) legacies.

Bowden et al.'s ( 2005 ) neurological model emphasizes the overlap between problem solving and language comprehension, and it hinges on differential processing in the right and left hemispheres. They proposed that an impasse is reached because initial processing of the problem produces strong activation of information irrelevant to solution in the left hemisphere. At the same time, weak semantic activation of alternative semantic interpretations, critical for solution, occurs in the right hemisphere. Insight arises when the weakly activated concepts reinforce each other, eventually rising above the threshold required for conscious awareness. Several studies of problem solving using compound remote associates problems, involving both behavioral and neuroimaging data, have found support for this model (Bowden & Jung-Beeman, 1998 , 2003 ; Jung-Beeman & Bowden, 2000 ; Jung-Beeman et al., 2004 ; also see Moss, Kotovsky, & Cagan, 2011 ).

Note that these three views of insight have received support using three quite distinct types of problems (Roman numeral matchstick arithmetic problems, the nine-dot problem, and compound remote associates problems, respectively). It remains to be established, therefore, whether these accounts can be generalized across problems. Kershaw and Ohlsson ( 2004 ) argued that insight problems are difficult because the key behavior required for solution may be hindered by perceptual factors (the Gestalt view), background knowledge (so expertise may be important; e.g., see Novick & Sherman, 2003 , 2008 ), and/or process factors (e.g., those affecting search). From this perspective, solving visual problems (e.g., the nine-dot problem) with insight may call upon more general visual processes, whereas solving verbal problems (e.g., anagrams, compound remote associates) with insight may call upon general verbal/semantic processes.

The work we reviewed in this section shows the relevance of problem representation (the Gestalt legacy) to the way people search the problem space (the legacy of Newell and Simon), and the relevance of search to the solution of insight problems that require a representational change. In addition to this inevitable integration of the two legacies, the work we described here underscores the fact that problem solving crucially depends on perceptual factors and on the solvers' background knowledge. In the next section, we describe some recent work that shows the involvement of these factors in the solution of problems in math and science.

Effects of Perception and Knowledge in Problem Solving in Academic Disciplines

Although the use of puzzle problems continues in research on problem solving, especially in investigations of insight, many contemporary researchers tackle problem solving in knowledge-rich domains, often in academic disciplines (e.g., mathematics, biology, physics, chemistry, meteorology). In this section, we provide a sampling of this research that highlights the importance of visual perception and background knowledge for successful problem solving.

The Role of Visual Perception

We stated at the outset that a problem representation (e.g., the problem space) is a model of the problem constructed by solvers to summarize their understanding of the problem's essential nature. This informal definition refers to the internal representations people construct and hold in working memory. Of course, people may also construct various external representations (Markman, 1999 ) and even manipulate those representations to aid in solution (see Hegarty & Stull, Chapter 31 ). For example, solvers often use paper and pencil to write notes or draw diagrams, especially when solving problems from formal domains (e.g., Cox, 1999 ; Kindfield, 1993 / 1994 ; S. Schwartz, 1971 ). In problems that provide solvers with external representation, such as the Tower of Hanoi problem, people's planning and memory of the current state is guided by the actual configurations of disks on pegs (Garber & Goldin-Meadow, 2002 ) or by the displays they see on a computer screen (Chen & Holyoak, 2010 ; Patsenko & Altmann, 2010 ).

In STEM (science, technology, engineering, and mathematics) disciplines, it is common for problems to be accompanied by diagrams or other external representations (e.g., equations) to be used in determining the solution. Larkin and Simon ( 1987 ) examined whether isomorphic sentential and diagrammatic representations are interchangeable in terms of facilitating solution. They argued that although the two formats may be equivalent in the sense that all of the information in each format can be inferred from the other format (informational equivalence), the ease or speed of making inferences from the two formats might differ (lack of computational equivalence). Based on their analysis of several problems in physics and math, Larkin and Simon further argued for the general superiority of diagrammatic representations (but see Mayer & Gallini, 1990 , for constraints on this general conclusion).

Novick and Hurley ( 2001 , p. 221) succinctly summarized the reasons for the general superiority of diagrams (especially abstract or schematic diagrams) over verbal representations: They “(a) simplify complex situations by discarding unnecessary details (e.g., Lynch, 1990 ; Winn, 1989 ), (b) make abstract concepts more concrete by mapping them onto spatial layouts with familiar interpretational conventions (e.g., Winn, 1989 ), and (c) substitute easier perceptual inferences for more computationally intensive search processes and sentential deductive inferences (Barwise & Etchemendy, 1991 ; Larkin & Simon, 1987 ).” Despite these benefits of diagrammatic representations, there is an important caveat, noted by Larkin and Simon ( 1987 , p. 99) at the very end of their paper: “Although every diagram supports some easy perceptual inferences, nothing ensures that these inferences must be useful in the problem-solving process.” We will see evidence of this in several of the studies reviewed in this section.

Next we describe recent work on perceptual factors that are involved in people's use of two types of external representations that are provided as part of the problem in two STEM disciplines: equations in algebra and diagrams in evolutionary biology. Although we focus here on effects of perceptual factors per se, it is important to note that such factors only influence performance when subjects have background knowledge that supports differential interpretation of the alternative diagrammatic depictions presented (Hegarty, Canham, & Fabricant, 2010 ).

In the previous section, we described the work of Patsenko and Altmann ( 2010 ) that shows direct involvement of visual attention and perception in the sequential application of move operators during the solution of the Tower of Hanoi problem. A related body of work documents similar effects in tasks that require the interpretation and use of mathematical equations (Goldstone, Landy, & Son, 2010 ; Landy & Goldstone, 2007a , b). For example, Landy and Goldstone ( 2007b ) varied the spatial proximity of arguments to the addition (+) and multiplication (*) operators in algebraic equations, such that the spatial layout of the equation was either consistent or inconsistent with the order-of-operations rule that multiplication precedes addition. In consistent equations , the space was narrower around multiplication than around addition (e.g., g*m + r*w = m*g + w*r ), whereas in inconsistent equations this relative spacing was reversed (e.g., s * n+e * c = n * s+c * e ). Subjects' judgments of the validity of such equations (i.e., whether the expressions on the two sides of the equal sign are equivalent) were significantly faster and more accurate for consistent than inconsistent equations.

In discussing these findings and related work with other external representations, Goldstone et al. ( 2010 ) proposed that experience with solving domain-specific problems leads people to “rig up” their perceptual system such that it allows them to look at the problem in a way that is consistent with the correct rules. Similar logic guides the Perceptual Learning Modules developed by Kellman and his collaborators to help students interpret and use algebraic equations and graphs (Kellman et al., 2008 ; Kellman, Massey, & Son, 2009 ). These authors argued and showed that, consistent with the previously reviewed work on expertise, perceptual training with particular external representations supports the development of perceptual fluency. This fluency, in turn, supports students' subsequent use of these external representations for problem solving.

This research suggests that extensive experience with particular equations or graphs may lead to perceptual fluency that could replace the more mindful application of domain-specific rules. Fisher, Borchert, and Bassok ( 2011 ) reported results from algebraic-modeling tasks that are consistent with this hypothesis. For example, college students were asked to represent verbal statements with algebraic equations, a task that typically elicits systematic errors (e.g., Clement, Lochhead, & Monk, 1981 ). Fisher et al. found that such errors were very common when subjects were asked to construct “standard form” equations ( y = ax ), which support fluent left-to-right translation of words to equations, but were relatively rare when subjects were asked to construct nonstandard division-format equations (x = y/a) that do not afford such translation fluency.

In part because of the left-to-right order in which people process equations, which mirrors the linear order in which they process text, equations have traditionally been viewed as sentential representations. However, Landy and Goldstone ( 2007a ) have proposed that equations also share some properties with diagrammatic displays and that, in fact, in some ways they are processed like diagrams. That is, spatial information is used to represent and to support inferences about syntactic structure. This hypothesis received support from Landy and Goldstone's ( 2007b ) results, described earlier, in which subjects' judgments of the validity of equations were affected by the Gestalt principle of grouping: Subjects did better when the grouping was consistent rather than inconsistent with the underlying structure of the problem (order of operations). Moreover, Landy and Goldstone ( 2007a ) found that when subjects wrote their own equations they grouped numbers and operators (+, *, =) in a way that reflected the hierarchical structure imposed by the order-of-operations rule.

In a recent line of research, Novick and Catley ( 2007 ; Novick, Catley, & Funk, 2010 ; Novick, Shade, & Catley, 2011 ) have examined effects of the spatial layout of diagrams depicting the evolutionary history of a set of taxa on people's ability to reason about patterns of relationship among those taxa. We consider here their work that investigates the role of another Gestalt perceptual principle—good continuation—in guiding students' reasoning. According to this principle, a continuous line is perceived as a single entity (Kellman, 2000 ). Consider the diagrams shown in Figure 21.6 . Each is a cladogram, a diagram that depicts nested sets of taxa that are related in terms of levels of most recent common ancestry. For example, chimpanzees and starfish are more closely related to each other than either is to spiders. The supporting evidence for their close relationship is their most recent common ancestor, which evolved the novel character of having radial cleavage. Spiders do not share this ancestor and thus do not have this character.

Cladograms are typically drawn in two isomorphic formats, which Novick and Catley ( 2007 ) referred to as trees and ladders. Although these formats are informationally equivalent (Larkin & Simon, 1987 ), Novick and Catley's ( 2007 ) research shows that they are not computationally equivalent (Larkin & Simon, 1987 ). Imagine that you are given evolutionary relationships in the ladder format, such as in Figure 21.6a (but without the four characters—hydrostatic skeleton, bilateral symmetry, radial cleavage, and trocophore larvae—and associated short lines indicating their locations on the cladogram), and your task is to translate that diagram to the tree format. A correct translation is shown in Figure 21.6b . Novick and Catley ( 2007 ) found that college students were much more likely to get such problems correct when the presented cladogram was in the nested circles (e.g., Figure 21.6d ) rather than the ladder format. Because the Gestalt principle of good continuation makes the long slanted line at the base of the ladder appear to represent a single hierarchical level, a common translation error for the ladder to tree problems was to draw a diagram such as that shown in Figure 21.6c .

The difficulty that good continuation presents for interpreting relationships depicted in the ladder format extends to answering reasoning questions as well. Novick and Catley (unpublished data) asked comparable questions about relationships depicted in the ladder and tree formats. For example, using the cladograms depicted in Figures 21.6a and 21.6b , consider the following questions: (a) Which taxon—jellyfish or earthworm—is the closest evolutionary relation to starfish, and what evidence supports your answer? (b) Do the bracketed taxa comprise a clade (a set of taxa consisting of the most recent common ancestor and all of its descendants), and what evidence supports your answer? For both such questions, students had higher accuracy and evidence quality composite scores when the relationships were depicted in the tree than the ladder format.

Four cladograms depicting evolutionary relationships among six animal taxa. Cladogram ( a ) is in the ladder format, cladograms ( b ) and ( c ) are in the tree format, and cladogram ( d ) is in the nested circles format. Cladograms ( a ), ( b ), and ( d ) are isomorphic.

If the difficulty in extracting the hierarchical structure of the ladder format is due to good continuation (which leads problem solvers to interpret continuous lines that depict multiple hierarchical levels as depicting only a single level), then a manipulation that breaks good continuation at the points where a new hierarchical level occurs should improve understanding. Novick et al. ( 2010 ) tested this hypothesis using a translation task by manipulating whether characters that are the markers for the most recent common ancestor of each nested set of taxa were included on the ladders. Figure 21.6a shows a ladder with such characters. As predicted, translation accuracy increased dramatically simply by adding these characters to the ladders, despite the additional information subjects had to account for in their translations.

The Role of Background Knowledge

As we mentioned earlier, the specific entities in the problems people encounter evoke inferences that affect how people represent these problems (e.g., the candle problem; Duncker, 1945 ) and how they apply the operators in searching for the solution (e.g., the disks vs. acrobats versions of the Tower of Hanoi problem; Kotovsky et al., 1985 ). Such object-based inferences draw on people's knowledge about the properties of the objects (e.g., a box is a container, an acrobat is a person who can be hurt). Here, we describe the work of Bassok and her colleagues, who found that similar inferences affect how people select mathematical procedures to solve problems in various formal domains. This work shows that the objects in the texts of mathematical word problems affect how people represent the problem situation (i.e., the situation model they construct; Kintsch & Greeno, 1985 ) and, in turn, lead them to select mathematical models that have a corresponding structure. To illustrate, a word problem that describes constant change in the rate at which ice is melting off a glacier evokes a model of continuous change, whereas a word problem that describes constant change in the rate at which ice is delivered to a restaurant evokes a model of discrete change. These distinct situation models lead subjects to select corresponding visual representations (e.g., Bassok & Olseth, 1995 ) and solutions methods, such as calculating the average change over time versus adding the consecutive changes (e.g., Alibali et al., 1999 ).

In a similar manner, people draw on their general knowledge to infer how the objects in a given problem are related to each other and construct mathematical solutions that correspond to these inferred object relations. For example, a word problem that involves doctors from two hospitals elicits a situation model in which the two sets of doctors play symmetric roles (e.g., work with each other), whereas a mathematically isomorphic problem that involves mechanics and cars elicits a situation model in which the sets play asymmetric roles (e.g., mechanics fix cars). The mathematical solutions people construct to such problems reflect this difference in symmetry (Bassok, Wu, & Olseth, 1995 ). In general, people tend to add objects that belong to the same taxonomic category (e.g., doctors + doctors) but divide functionally related objects (e.g., cars ÷ mechanics). People establish this correspondence by a process of analogical alignment between semantic and arithmetic relations, which Bassok and her colleagues refer to as “semantic alignment” (Bassok, Chase, & Martin, 1998 ; Doumas, Bassok, Guthormsen, & Hummel, 2006 ; Fisher, Bassok, & Osterhout, 2010 ).

Semantic alignment occurs very early in the solution process and can prime arithmetic facts that are potentially relevant to the problem solution (Bassok, Pedigo, & Oskarsson, 2008 ). Although such alignments can lead to erroneous solutions, they have a high heuristic value because, in most textbook problems, object relations indeed correspond to analogous mathematical relations (Bassok et al., 1998 ). Interestingly, unlike in the case of reliance on specific surface-structure correlations (e.g., the keyword “more” typically appears in word problems that require addition; Lewis & Mayer, 1987 ), people are more likely to exploit semantic alignment when they have more, rather than less modeling experience. For example, Martin and Bassok ( 2005 ) found very strong semantic-alignment effects when subjects solved simple division word problems, but not when they constructed algebraic equations to represent the relational statements that appeared in the problems. Of course, these subjects had significantly more experience with solving numerical word problems than with constructing algebraic models of relational statements. In a subsequent study, Fisher and Bassok ( 2009 ) found semantic-alignment effects for subjects who constructed correct algebraic models, but not for those who committed modeling errors.

Conclusions and Future Directions

In this chapter, we examined two broad components of the problem-solving process: representation (the Gestalt legacy) and search (the legacy of Newell and Simon). Although many researchers choose to focus their investigation on one or the other of these components, both Duncker ( 1945 ) and Simon ( 1986 ) underscored the necessity to investigate their interaction, as the representation one constructs for a problem determines (or at least constrains) how one goes about trying to generate a solution, and searching the problem space may lead to a change in problem representation. Indeed, Duncker's ( 1945 ) initial account of one subject's solution to the radiation problem was followed up by extensive and experimentally sophisticated work by Simon and his colleagues and by other researchers, documenting the involvement of visual perception and background knowledge in how people represent problems and search for problem solutions.

The relevance of perception and background knowledge to problem solving illustrates the fact that, when people attempt to find or devise ways to reach their goals, they draw on a variety of cognitive resources and engage in a host of cognitive activities. According to Duncker ( 1945 ), such goal-directed activities may include (a) placing objects into categories and making inferences based on category membership, (b) making inductive inferences from multiple instances, (c) reasoning by analogy, (d) identifying the causes of events, (e) deducing logical implications of given information, (f) making legal judgments, and (g) diagnosing medical conditions from historical and laboratory data. As this list suggests, many of the chapters in the present volume describe research that is highly relevant to the understanding of problem-solving behavior. We believe that important advancements in problem-solving research would emerge by integrating it with research in other areas of thinking and reasoning, and that research in these other areas could be similarly advanced by incorporating the insights gained from research on what has more traditionally been identified as problem solving.

As we have described in this chapter, many of the important findings in the field have been established by a careful investigation of various riddle problems. Although there are good methodological reasons for using such problems, many researchers choose to investigate problem solving using ecologically valid educational materials. This choice, which is increasingly common in contemporary research, provides researchers with the opportunity to apply their basic understanding of problem solving to benefit the design of instruction and, at the same time, allows them to gain a better understanding of the processes by which domain knowledge and educational conventions affect the solution process. We believe that the trend of conducting educationally relevant research is likely to continue, and we expect a significant expansion of research on people's understanding and use of dynamic and technologically rich external representations (e.g., Kellman et al., 2008 ; Mayer, Griffith, Jurkowitz, & Rothman, 2008 ; Richland & McDonough, 2010 ; Son & Goldstone, 2009 ). Such investigations are likely to yield both practical and theoretical payoffs.

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In This Article Expand or collapse the "in this article" section Brief Therapies in Social Work: Task-Centered Model and Solution-Focused Therapy

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Brief Therapies in Social Work: Task-Centered Model and Solution-Focused Therapy by Cynthia Franklin , Krystallynne Mikle LAST REVIEWED: 30 September 2013 LAST MODIFIED: 30 September 2013 DOI: 10.1093/obo/9780195389678-0188

Brief therapies serve as evidenced-based practices that place a strong emphasis on effective, time-limited treatments that aid in resolving clients’ presenting problems. The resources presented in this article summarize for professionals and educators the abundant literature evaluating brief therapies within social work practice. Brief therapies have appeared in many different schools of psychotherapy, and several approaches have also evolved within social work practice, but two approaches—the task-centered model and solution-focused brief therapy (SFBT)—stand out as being grounded in research and have also gained international acclaim as important interventions for implementation and further study. These two approaches are the focus of this bibliography. The task-centered model and SFBT were developed by social work practitioners and researchers for the purposes of making clinical practice more effective, and they share a common bond in hoping to improve the services delivered to clients. Since the development of the task-centered and solution-focused approaches, brief therapies have become essential to the work of all types of psychotherapists and clinicians, and many of the principles and practices of brief therapy that are a part of the task-centered and solution-focused approaches are now essential to psychotherapy training. Clinical social workers practicing from the perspective of the task-centered model and SFBT approaches work from several brief therapy assumptions. The first regards the client/therapist relationship. The best way to help clients is to work within a collaborative relationship to discover options for coping and new behavior that may also lead to specific tasks and solutions for change that are identified by the client. Second is the assumption that change can happen quickly and can be lasting. Third, focus on the past may not be as helpful to most clients as a focus on the present and the future. The fourth regards a pragmatic perspective about where the change occurs. The best approach to practice is pragmatic, and effective practitioners recognize that what happens in a client’s life is more important than what happens in a social worker’s office. The fifth assumption is that change can happen more quickly and be maintained when practitioners utilize the strengths and resources that exist within the client and his or her environment. The next assumption is that a small change made by clients may cause significant and major life changes. The seventh assumption is associated with creating goals. It is important to focus on small, concrete goal construction and helping the client move toward small steps to achieve those goals. The next regards change. Change is viewed as hard work and involves focused effort and commitment from the client and social worker. There will be homework assignments and following through on tasks. Also, it is assumed that it is important to establish and maintain a clear treatment focus (often considered the most important element in brief treatment). Parsimony is also considered to be a guiding principle (i.e., given two equally effective treatments, the one requiring less investment of time and energy is preferable). Last, it is assumed that without evidence to the contrary, the client’s stated problem is taken as the valid focus of treatment. The task-centered model and SFBT have developed a strong empirical base, and both approaches operate from a goal-oriented and strengths perspective. Both approaches have numerous applications and have successfully been used with many different types of clients and practice settings. Both approaches have also been expanded to applications in macro social work that focus on work within management- and community-based practices. For related Oxford Bibliographies entries, see Task-Centered Practice and Solution-Focused Therapy .

Task-Centered Model Literature

The task-centered model is an empirically grounded approach to social work practice that appeared in the mid-1960s at Columbia University and was developed in response to research reports that indicated social work was not effective with clients. William J. Reid was the chief researcher who helped develop this model, and he integrated many therapeutic perspectives to create the task-centered approach, including ideas from behavioral therapies. The task-centered model evolved out of the psychodynamic practice and uses a brief, problem-solving approach to help clients resolve presenting problems. The task-centered model is currently used in clinical social work and group work and may also be applied to other types of social work practice.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

7.3 Problem-Solving

Learning objectives.

By the end of this section, you will be able to:

• Describe problem solving strategies
• Define algorithm and heuristic
• Explain some common roadblocks to effective problem solving

   People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.

The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.

PROBLEM-SOLVING STRATEGIES

   When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.

Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.

A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.

   Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?

A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):

• When one is faced with too much information
• When the time to make a decision is limited
• When the decision to be made is unimportant
• When there is access to very little information to use in making the decision
• When an appropriate heuristic happens to come to mind in the same moment

Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.

Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.

Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.

Additional Problem Solving Strategies :

• Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
• Analogy – is using a solution that solves a similar problem.
• Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
• Divide and conquer – breaking down large complex problems into smaller more manageable problems.
• Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
• Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
• Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
• Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
• Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
• Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
• Reduction – adapting the problem to be as similar problems where a solution exists.
• Research – using existing knowledge or solutions to similar problems to solve the problem.
• Root cause analysis – trying to identify the cause of the problem.

The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.

One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :

Missionary-Cannibal Problem

Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.

Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.

The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:

• 1. Only one disk can be moved at a time.
• 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
• 3. No disc may be placed on top of a smaller disk.

  Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.

Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.

The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.

GESTALT PSYCHOLOGY AND PROBLEM SOLVING

As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.

As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage  (1990) suggesting that while collecting data for what would later be his book  The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.

While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as  insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).

While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.

Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground.  Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).

Solving puzzles.

   Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.

How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)

   Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:

Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.

   Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).

What steps did you take to solve this puzzle? You can read the solution at the end of this section.

Pitfalls to problem solving.

   Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.

Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.

   Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).

In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.

The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.

Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.

Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.

   Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.

References:

Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology

Review Questions:

1. A specific formula for solving a problem is called ________.

a. an algorithm

b. a heuristic

c. a mental set

d. trial and error

2. Solving the Tower of Hanoi problem tends to utilize a  ________ strategy of problem solving.

a. divide and conquer

b. means-end analysis

d. experiment

3. A mental shortcut in the form of a general problem-solving framework is called ________.

4. Which type of bias involves becoming fixated on a single trait of a problem?

a. anchoring bias

b. confirmation bias

c. representative bias

d. availability bias

5. Which type of bias involves relying on a false stereotype to make a decision?

6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.

a. social adjustment

b. student load payment options

c. emotional learning

d. insight learning

7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.

a. functional fixedness

c. working memory

Critical Thinking Questions:

1. What is functional fixedness and how can overcoming it help you solve problems?

2. How does an algorithm save you time and energy when solving a problem?

Personal Application Question:

1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?

anchoring bias

availability heuristic

confirmation bias

functional fixedness

hindsight bias

problem-solving strategy

representative bias

trial and error

working backwards

Answers to Exercises

algorithm:  problem-solving strategy characterized by a specific set of instructions

anchoring bias:  faulty heuristic in which you fixate on a single aspect of a problem to find a solution

availability heuristic:  faulty heuristic in which you make a decision based on information readily available to you

confirmation bias:  faulty heuristic in which you focus on information that confirms your beliefs

functional fixedness:  inability to see an object as useful for any other use other than the one for which it was intended

heuristic:  mental shortcut that saves time when solving a problem

hindsight bias:  belief that the event just experienced was predictable, even though it really wasn’t

mental set:  continually using an old solution to a problem without results

problem-solving strategy:  method for solving problems

representative bias:  faulty heuristic in which you stereotype someone or something without a valid basis for your judgment

trial and error:  problem-solving strategy in which multiple solutions are attempted until the correct one is found

working backwards:  heuristic in which you begin to solve a problem by focusing on the end result

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14.3 Problem Solving and Decision Making in Groups

Learning objectives.

• Discuss the common components and characteristics of problems.
• Explain the five steps of the group problem-solving process.
• Describe the brainstorming and discussion that should take place before the group makes a decision.
• Compare and contrast the different decision-making techniques.
• Discuss the various influences on decision making.

Although the steps of problem solving and decision making that we will discuss next may seem obvious, we often don’t think to or choose not to use them. Instead, we start working on a problem and later realize we are lost and have to backtrack. I’m sure we’ve all reached a point in a project or task and had the “OK, now what?” moment. I’ve recently taken up some carpentry projects as a functional hobby, and I have developed a great respect for the importance of advanced planning. It’s frustrating to get to a crucial point in building or fixing something only to realize that you have to unscrew a support board that you already screwed in, have to drive back to the hardware store to get something that you didn’t think to get earlier, or have to completely start over. In this section, we will discuss the group problem-solving process, methods of decision making, and influences on these processes.

Group Problem Solving

The problem-solving process involves thoughts, discussions, actions, and decisions that occur from the first consideration of a problematic situation to the goal. The problems that groups face are varied, but some common problems include budgeting funds, raising funds, planning events, addressing customer or citizen complaints, creating or adapting products or services to fit needs, supporting members, and raising awareness about issues or causes.

Problems of all sorts have three common components (Adams & Galanes, 2009):

• An undesirable situation. When conditions are desirable, there isn’t a problem.
• A desired situation. Even though it may only be a vague idea, there is a drive to better the undesirable situation. The vague idea may develop into a more precise goal that can be achieved, although solutions are not yet generated.
• Obstacles between undesirable and desirable situation. These are things that stand in the way between the current situation and the group’s goal of addressing it. This component of a problem requires the most work, and it is the part where decision making occurs. Some examples of obstacles include limited funding, resources, personnel, time, or information. Obstacles can also take the form of people who are working against the group, including people resistant to change or people who disagree.

Discussion of these three elements of a problem helps the group tailor its problem-solving process, as each problem will vary. While these three general elements are present in each problem, the group should also address specific characteristics of the problem. Five common and important characteristics to consider are task difficulty, number of possible solutions, group member interest in problem, group member familiarity with problem, and the need for solution acceptance (Adams & Galanes, 2009).

• Task difficulty. Difficult tasks are also typically more complex. Groups should be prepared to spend time researching and discussing a difficult and complex task in order to develop a shared foundational knowledge. This typically requires individual work outside of the group and frequent group meetings to share information.
• Number of possible solutions. There are usually multiple ways to solve a problem or complete a task, but some problems have more potential solutions than others. Figuring out how to prepare a beach house for an approaching hurricane is fairly complex and difficult, but there are still a limited number of things to do—for example, taping and boarding up windows; turning off water, electricity, and gas; trimming trees; and securing loose outside objects. Other problems may be more creatively based. For example, designing a new restaurant may entail using some standard solutions but could also entail many different types of innovation with layout and design.
• Group member interest in problem. When group members are interested in the problem, they will be more engaged with the problem-solving process and invested in finding a quality solution. Groups with high interest in and knowledge about the problem may want more freedom to develop and implement solutions, while groups with low interest may prefer a leader who provides structure and direction.
• Group familiarity with problem. Some groups encounter a problem regularly, while other problems are more unique or unexpected. A family who has lived in hurricane alley for decades probably has a better idea of how to prepare its house for a hurricane than does a family that just recently moved from the Midwest. Many groups that rely on funding have to revisit a budget every year, and in recent years, groups have had to get more creative with budgets as funding has been cut in nearly every sector. When group members aren’t familiar with a problem, they will need to do background research on what similar groups have done and may also need to bring in outside experts.
• Need for solution acceptance. In this step, groups must consider how many people the decision will affect and how much “buy-in” from others the group needs in order for their solution to be successfully implemented. Some small groups have many stakeholders on whom the success of a solution depends. Other groups are answerable only to themselves. When a small group is planning on building a new park in a crowded neighborhood or implementing a new policy in a large business, it can be very difficult to develop solutions that will be accepted by all. In such cases, groups will want to poll those who will be affected by the solution and may want to do a pilot implementation to see how people react. Imposing an excellent solution that doesn’t have buy-in from stakeholders can still lead to failure.

Group problem solving can be a confusing puzzle unless it is approached systematically.

Muness Castle – Problem Solving – CC BY-SA 2.0.

Group Problem-Solving Process

There are several variations of similar problem-solving models based on US American scholar John Dewey’s reflective thinking process (Bormann & Bormann, 1988). As you read through the steps in the process, think about how you can apply what we learned regarding the general and specific elements of problems. Some of the following steps are straightforward, and they are things we would logically do when faced with a problem. However, taking a deliberate and systematic approach to problem solving has been shown to benefit group functioning and performance. A deliberate approach is especially beneficial for groups that do not have an established history of working together and will only be able to meet occasionally. Although a group should attend to each step of the process, group leaders or other group members who facilitate problem solving should be cautious not to dogmatically follow each element of the process or force a group along. Such a lack of flexibility could limit group member input and negatively affect the group’s cohesion and climate.

Step 1: Define the Problem

Define the problem by considering the three elements shared by every problem: the current undesirable situation, the goal or more desirable situation, and obstacles in the way (Adams & Galanes, 2009). At this stage, group members share what they know about the current situation, without proposing solutions or evaluating the information. Here are some good questions to ask during this stage: What is the current difficulty? How did we come to know that the difficulty exists? Who/what is involved? Why is it meaningful/urgent/important? What have the effects been so far? What, if any, elements of the difficulty require clarification? At the end of this stage, the group should be able to compose a single sentence that summarizes the problem called a problem statement . Avoid wording in the problem statement or question that hints at potential solutions. A small group formed to investigate ethical violations of city officials could use the following problem statement: “Our state does not currently have a mechanism for citizens to report suspected ethical violations by city officials.”

Step 2: Analyze the Problem

During this step a group should analyze the problem and the group’s relationship to the problem. Whereas the first step involved exploring the “what” related to the problem, this step focuses on the “why.” At this stage, group members can discuss the potential causes of the difficulty. Group members may also want to begin setting out an agenda or timeline for the group’s problem-solving process, looking forward to the other steps. To fully analyze the problem, the group can discuss the five common problem variables discussed before. Here are two examples of questions that the group formed to address ethics violations might ask: Why doesn’t our city have an ethics reporting mechanism? Do cities of similar size have such a mechanism? Once the problem has been analyzed, the group can pose a problem question that will guide the group as it generates possible solutions. “How can citizens report suspected ethical violations of city officials and how will such reports be processed and addressed?” As you can see, the problem question is more complex than the problem statement, since the group has moved on to more in-depth discussion of the problem during step 2.

Step 3: Generate Possible Solutions

During this step, group members generate possible solutions to the problem. Again, solutions should not be evaluated at this point, only proposed and clarified. The question should be what could we do to address this problem, not what should we do to address it. It is perfectly OK for a group member to question another person’s idea by asking something like “What do you mean?” or “Could you explain your reasoning more?” Discussions at this stage may reveal a need to return to previous steps to better define or more fully analyze a problem. Since many problems are multifaceted, it is necessary for group members to generate solutions for each part of the problem separately, making sure to have multiple solutions for each part. Stopping the solution-generating process prematurely can lead to groupthink. For the problem question previously posed, the group would need to generate solutions for all three parts of the problem included in the question. Possible solutions for the first part of the problem (How can citizens report ethical violations?) may include “online reporting system, e-mail, in-person, anonymously, on-the-record,” and so on. Possible solutions for the second part of the problem (How will reports be processed?) may include “daily by a newly appointed ethics officer, weekly by a nonpartisan nongovernment employee,” and so on. Possible solutions for the third part of the problem (How will reports be addressed?) may include “by a newly appointed ethics commission, by the accused’s supervisor, by the city manager,” and so on.

Step 4: Evaluate Solutions

During this step, solutions can be critically evaluated based on their credibility, completeness, and worth. Once the potential solutions have been narrowed based on more obvious differences in relevance and/or merit, the group should analyze each solution based on its potential effects—especially negative effects. Groups that are required to report the rationale for their decision or whose decisions may be subject to public scrutiny would be wise to make a set list of criteria for evaluating each solution. Additionally, solutions can be evaluated based on how well they fit with the group’s charge and the abilities of the group. To do this, group members may ask, “Does this solution live up to the original purpose or mission of the group?” and “Can the solution actually be implemented with our current resources and connections?” and “How will this solution be supported, funded, enforced, and assessed?” Secondary tensions and substantive conflict, two concepts discussed earlier, emerge during this step of problem solving, and group members will need to employ effective critical thinking and listening skills.

Decision making is part of the larger process of problem solving and it plays a prominent role in this step. While there are several fairly similar models for problem solving, there are many varied decision-making techniques that groups can use. For example, to narrow the list of proposed solutions, group members may decide by majority vote, by weighing the pros and cons, or by discussing them until a consensus is reached. There are also more complex decision-making models like the “six hats method,” which we will discuss later. Once the final decision is reached, the group leader or facilitator should confirm that the group is in agreement. It may be beneficial to let the group break for a while or even to delay the final decision until a later meeting to allow people time to evaluate it outside of the group context.

Step 5: Implement and Assess the Solution

Implementing the solution requires some advanced planning, and it should not be rushed unless the group is operating under strict time restraints or delay may lead to some kind of harm. Although some solutions can be implemented immediately, others may take days, months, or years. As was noted earlier, it may be beneficial for groups to poll those who will be affected by the solution as to their opinion of it or even to do a pilot test to observe the effectiveness of the solution and how people react to it. Before implementation, groups should also determine how and when they would assess the effectiveness of the solution by asking, “How will we know if the solution is working or not?” Since solution assessment will vary based on whether or not the group is disbanded, groups should also consider the following questions: If the group disbands after implementation, who will be responsible for assessing the solution? If the solution fails, will the same group reconvene or will a new group be formed?

Once a solution has been reached and the group has the “green light” to implement it, it should proceed deliberately and cautiously, making sure to consider possible consequences and address them as needed.

Jocko Benoit – Prodigal Light – CC BY-NC-ND 2.0.

Certain elements of the solution may need to be delegated out to various people inside and outside the group. Group members may also be assigned to implement a particular part of the solution based on their role in the decision making or because it connects to their area of expertise. Likewise, group members may be tasked with publicizing the solution or “selling” it to a particular group of stakeholders. Last, the group should consider its future. In some cases, the group will get to decide if it will stay together and continue working on other tasks or if it will disband. In other cases, outside forces determine the group’s fate.

“Getting Competent”

Problem Solving and Group Presentations

Giving a group presentation requires that individual group members and the group as a whole solve many problems and make many decisions. Although having more people involved in a presentation increases logistical difficulties and has the potential to create more conflict, a well-prepared and well-delivered group presentation can be more engaging and effective than a typical presentation. The main problems facing a group giving a presentation are (1) dividing responsibilities, (2) coordinating schedules and time management, and (3) working out the logistics of the presentation delivery.

In terms of dividing responsibilities, assigning individual work at the first meeting and then trying to fit it all together before the presentation (which is what many college students do when faced with a group project) is not the recommended method. Integrating content and visual aids created by several different people into a seamless final product takes time and effort, and the person “stuck” with this job at the end usually ends up developing some resentment toward his or her group members. While it’s OK for group members to do work independently outside of group meetings, spend time working together to help set up some standards for content and formatting expectations that will help make later integration of work easier. Taking the time to complete one part of the presentation together can help set those standards for later individual work. Discuss the roles that various group members will play openly so there isn’t role confusion. There could be one point person for keeping track of the group’s progress and schedule, one point person for communication, one point person for content integration, one point person for visual aids, and so on. Each person shouldn’t do all that work on his or her own but help focus the group’s attention on his or her specific area during group meetings (Stanton, 2009).

Scheduling group meetings is one of the most challenging problems groups face, given people’s busy lives. From the beginning, it should be clearly communicated that the group needs to spend considerable time in face-to-face meetings, and group members should know that they may have to make an occasional sacrifice to attend. Especially important is the commitment to scheduling time to rehearse the presentation. Consider creating a contract of group guidelines that includes expectations for meeting attendance to increase group members’ commitment.

Group presentations require members to navigate many logistics of their presentation. While it may be easier for a group to assign each member to create a five-minute segment and then transition from one person to the next, this is definitely not the most engaging method. Creating a master presentation and then assigning individual speakers creates a more fluid and dynamic presentation and allows everyone to become familiar with the content, which can help if a person doesn’t show up to present and during the question-and-answer section. Once the content of the presentation is complete, figure out introductions, transitions, visual aids, and the use of time and space (Stanton, 2012). In terms of introductions, figure out if one person will introduce all the speakers at the beginning, if speakers will introduce themselves at the beginning, or if introductions will occur as the presentation progresses. In terms of transitions, make sure each person has included in his or her speaking notes when presentation duties switch from one person to the next. Visual aids have the potential to cause hiccups in a group presentation if they aren’t fluidly integrated. Practicing with visual aids and having one person control them may help prevent this. Know how long your presentation is and know how you’re going to use the space. Presenters should know how long the whole presentation should be and how long each of their segments should be so that everyone can share the responsibility of keeping time. Also consider the size and layout of the presentation space. You don’t want presenters huddled in a corner until it’s their turn to speak or trapped behind furniture when their turn comes around.

• Of the three main problems facing group presenters, which do you think is the most challenging and why?
• Why do you think people tasked with a group presentation (especially students) prefer to divide the parts up and have members work on them independently before coming back together and integrating each part? What problems emerge from this method? In what ways might developing a master presentation and then assigning parts to different speakers be better than the more divided method? What are the drawbacks to the master presentation method?

Decision Making in Groups

We all engage in personal decision making daily, and we all know that some decisions are more difficult than others. When we make decisions in groups, we face some challenges that we do not face in our personal decision making, but we also stand to benefit from some advantages of group decision making (Napier & Gershenfeld, 2004). Group decision making can appear fair and democratic but really only be a gesture that covers up the fact that certain group members or the group leader have already decided. Group decision making also takes more time than individual decisions and can be burdensome if some group members do not do their assigned work, divert the group with self-centered or unproductive role behaviors, or miss meetings. Conversely, though, group decisions are often more informed, since all group members develop a shared understanding of a problem through discussion and debate. The shared understanding may also be more complex and deep than what an individual would develop, because the group members are exposed to a variety of viewpoints that can broaden their own perspectives. Group decisions also benefit from synergy, one of the key advantages of group communication that we discussed earlier. Most groups do not use a specific method of decision making, perhaps thinking that they’ll work things out as they go. This can lead to unequal participation, social loafing, premature decisions, prolonged discussion, and a host of other negative consequences. So in this section we will learn some practices that will prepare us for good decision making and some specific techniques we can use to help us reach a final decision.

Brainstorming before Decision Making

Before groups can make a decision, they need to generate possible solutions to their problem. The most commonly used method is brainstorming, although most people don’t follow the recommended steps of brainstorming. As you’ll recall, brainstorming refers to the quick generation of ideas free of evaluation. The originator of the term brainstorming said the following four rules must be followed for the technique to be effective (Osborn, 1959):

• Evaluation of ideas is forbidden.
• Wild and crazy ideas are encouraged.
• Quantity of ideas, not quality, is the goal.
• New combinations of ideas presented are encouraged.

To make brainstorming more of a decision-making method rather than an idea-generating method, group communication scholars have suggested additional steps that precede and follow brainstorming (Cragan & Wright, 1991).

• Do a warm-up brainstorming session. Some people are more apprehensive about publicly communicating their ideas than others are, and a warm-up session can help ease apprehension and prime group members for task-related idea generation. The warm-up can be initiated by anyone in the group and should only go on for a few minutes. To get things started, a person could ask, “If our group formed a band, what would we be called?” or “What other purposes could a mailbox serve?” In the previous examples, the first warm up gets the group’s more abstract creative juices flowing, while the second focuses more on practical and concrete ideas.
• Do the actual brainstorming session. This session shouldn’t last more than thirty minutes and should follow the four rules of brainstorming mentioned previously. To ensure that the fourth rule is realized, the facilitator could encourage people to piggyback off each other’s ideas.
• Eliminate duplicate ideas. After the brainstorming session is over, group members can eliminate (without evaluating) ideas that are the same or very similar.
• Clarify, organize, and evaluate ideas. Before evaluation, see if any ideas need clarification. Then try to theme or group ideas together in some orderly fashion. Since “wild and crazy” ideas are encouraged, some suggestions may need clarification. If it becomes clear that there isn’t really a foundation to an idea and that it is too vague or abstract and can’t be clarified, it may be eliminated. As a caution though, it may be wise to not throw out off-the-wall ideas that are hard to categorize and to instead put them in a miscellaneous or “wild and crazy” category.

Discussion before Decision Making

The nominal group technique guides decision making through a four-step process that includes idea generation and evaluation and seeks to elicit equal contributions from all group members (Delbecq & Ven de Ven, 1971). This method is useful because the procedure involves all group members systematically, which fixes the problem of uneven participation during discussions. Since everyone contributes to the discussion, this method can also help reduce instances of social loafing. To use the nominal group technique, do the following:

• Silently and individually list ideas.
• Create a master list of ideas.
• Clarify ideas as needed.
• Take a secret vote to rank group members’ acceptance of ideas.

During the first step, have group members work quietly, in the same space, to write down every idea they have to address the task or problem they face. This shouldn’t take more than twenty minutes. Whoever is facilitating the discussion should remind group members to use brainstorming techniques, which means they shouldn’t evaluate ideas as they are generated. Ask group members to remain silent once they’ve finished their list so they do not distract others.

During the second step, the facilitator goes around the group in a consistent order asking each person to share one idea at a time. As the idea is shared, the facilitator records it on a master list that everyone can see. Keep track of how many times each idea comes up, as that could be an idea that warrants more discussion. Continue this process until all the ideas have been shared. As a note to facilitators, some group members may begin to edit their list or self-censor when asked to provide one of their ideas. To limit a person’s apprehension with sharing his or her ideas and to ensure that each idea is shared, I have asked group members to exchange lists with someone else so they can share ideas from the list they receive without fear of being personally judged.

During step three, the facilitator should note that group members can now ask for clarification on ideas on the master list. Do not let this discussion stray into evaluation of ideas. To help avoid an unnecessarily long discussion, it may be useful to go from one person to the next to ask which ideas need clarifying and then go to the originator(s) of the idea in question for clarification.

During the fourth step, members use a voting ballot to rank the acceptability of the ideas on the master list. If the list is long, you may ask group members to rank only their top five or so choices. The facilitator then takes up the secret ballots and reviews them in a random order, noting the rankings of each idea. Ideally, the highest ranked idea can then be discussed and decided on. The nominal group technique does not carry a group all the way through to the point of decision; rather, it sets the group up for a roundtable discussion or use of some other method to evaluate the merits of the top ideas.

Specific Decision-Making Techniques

Some decision-making techniques involve determining a course of action based on the level of agreement among the group members. These methods include majority, expert, authority, and consensus rule. Table 14.1 “Pros and Cons of Agreement-Based Decision-Making Techniques” reviews the pros and cons of each of these methods.

Majority rule is a simple method of decision making based on voting. In most cases a majority is considered half plus one.

Becky McCray – Voting – CC BY-NC-ND 2.0.

Majority rule is a commonly used decision-making technique in which a majority (one-half plus one) must agree before a decision is made. A show-of-hands vote, a paper ballot, or an electronic voting system can determine the majority choice. Many decision-making bodies, including the US House of Representatives, Senate, and Supreme Court, use majority rule to make decisions, which shows that it is often associated with democratic decision making, since each person gets one vote and each vote counts equally. Of course, other individuals and mediated messages can influence a person’s vote, but since the voting power is spread out over all group members, it is not easy for one person or party to take control of the decision-making process. In some cases—for example, to override a presidential veto or to amend the constitution—a super majority of two-thirds may be required to make a decision.

Minority rule is a decision-making technique in which a designated authority or expert has final say over a decision and may or may not consider the input of other group members. When a designated expert makes a decision by minority rule, there may be buy-in from others in the group, especially if the members of the group didn’t have relevant knowledge or expertise. When a designated authority makes decisions, buy-in will vary based on group members’ level of respect for the authority. For example, decisions made by an elected authority may be more accepted by those who elected him or her than by those who didn’t. As with majority rule, this technique can be time saving. Unlike majority rule, one person or party can have control over the decision-making process. This type of decision making is more similar to that used by monarchs and dictators. An obvious negative consequence of this method is that the needs or wants of one person can override the needs and wants of the majority. A minority deciding for the majority has led to negative consequences throughout history. The white Afrikaner minority that ruled South Africa for decades instituted apartheid, which was a system of racial segregation that disenfranchised and oppressed the majority population. The quality of the decision and its fairness really depends on the designated expert or authority.

Consensus rule is a decision-making technique in which all members of the group must agree on the same decision. On rare occasions, a decision may be ideal for all group members, which can lead to unanimous agreement without further debate and discussion. Although this can be positive, be cautious that this isn’t a sign of groupthink. More typically, consensus is reached only after lengthy discussion. On the plus side, consensus often leads to high-quality decisions due to the time and effort it takes to get everyone in agreement. Group members are also more likely to be committed to the decision because of their investment in reaching it. On the negative side, the ultimate decision is often one that all group members can live with but not one that’s ideal for all members. Additionally, the process of arriving at consensus also includes conflict, as people debate ideas and negotiate the interpersonal tensions that may result.

Table 14.1 Pros and Cons of Agreement-Based Decision-Making Techniques

“Getting Critical”

Six Hats Method of Decision Making

Edward de Bono developed the Six Hats method of thinking in the late 1980s, and it has since become a regular feature in decision-making training in business and professional contexts (de Bono, 1985). The method’s popularity lies in its ability to help people get out of habitual ways of thinking and to allow group members to play different roles and see a problem or decision from multiple points of view. The basic idea is that each of the six hats represents a different way of thinking, and when we figuratively switch hats, we switch the way we think. The hats and their style of thinking are as follows:

• White hat. Objective—focuses on seeking information such as data and facts and then processes that information in a neutral way.
• Red hat. Emotional—uses intuition, gut reactions, and feelings to judge information and suggestions.
• Black hat. Negative—focuses on potential risks, points out possibilities for failure, and evaluates information cautiously and defensively.
• Yellow hat. Positive—is optimistic about suggestions and future outcomes, gives constructive and positive feedback, points out benefits and advantages.
• Green hat. Creative—tries to generate new ideas and solutions, thinks “outside the box.”
• Blue hat. Philosophical—uses metacommunication to organize and reflect on the thinking and communication taking place in the group, facilitates who wears what hat and when group members change hats.

Specific sequences or combinations of hats can be used to encourage strategic thinking. For example, the group leader may start off wearing the Blue Hat and suggest that the group start their decision-making process with some “White Hat thinking” in order to process through facts and other available information. During this stage, the group could also process through what other groups have done when faced with a similar problem. Then the leader could begin an evaluation sequence starting with two minutes of “Yellow Hat thinking” to identify potential positive outcomes, then “Black Hat thinking” to allow group members to express reservations about ideas and point out potential problems, then “Red Hat thinking” to get people’s gut reactions to the previous discussion, then “Green Hat thinking” to identify other possible solutions that are more tailored to the group’s situation or completely new approaches. At the end of a sequence, the Blue Hat would want to summarize what was said and begin a new sequence. To successfully use this method, the person wearing the Blue Hat should be familiar with different sequences and plan some of the thinking patterns ahead of time based on the problem and the group members. Each round of thinking should be limited to a certain time frame (two to five minutes) to keep the discussion moving.

• This decision-making method has been praised because it allows group members to “switch gears” in their thinking and allows for role playing, which lets people express ideas more freely. How can this help enhance critical thinking? Which combination of hats do you think would be best for a critical thinking sequence?
• What combinations of hats might be useful if the leader wanted to break the larger group up into pairs and why? For example, what kind of thinking would result from putting Yellow and Red together, Black and White together, or Red and White together, and so on?
• Based on your preferred ways of thinking and your personality, which hat would be the best fit for you? Which would be the most challenging? Why?

Influences on Decision Making

Many factors influence the decision-making process. For example, how might a group’s independence or access to resources affect the decisions they make? What potential advantages and disadvantages come with decisions made by groups that are more or less similar in terms of personality and cultural identities? In this section, we will explore how situational, personality, and cultural influences affect decision making in groups.

Situational Influences on Decision Making

A group’s situational context affects decision making. One key situational element is the degree of freedom that the group has to make its own decisions, secure its own resources, and initiate its own actions. Some groups have to go through multiple approval processes before they can do anything, while others are self-directed, self-governing, and self-sustaining. Another situational influence is uncertainty. In general, groups deal with more uncertainty in decision making than do individuals because of the increased number of variables that comes with adding more people to a situation. Individual group members can’t know what other group members are thinking, whether or not they are doing their work, and how committed they are to the group. So the size of a group is a powerful situational influence, as it adds to uncertainty and complicates communication.

Access to information also influences a group. First, the nature of the group’s task or problem affects its ability to get information. Group members can more easily make decisions about a problem when other groups have similarly experienced it. Even if the problem is complex and serious, the group can learn from other situations and apply what it learns. Second, the group must have access to flows of information. Access to archives, electronic databases, and individuals with relevant experience is necessary to obtain any relevant information about similar problems or to do research on a new or unique problem. In this regard, group members’ formal and information network connections also become important situational influences.

The urgency of a decision can have a major influence on the decision-making process. As a situation becomes more urgent, it requires more specific decision-making methods and types of communication.

Judith E. Bell – Urgent – CC BY-SA 2.0.

The origin and urgency of a problem are also situational factors that influence decision making. In terms of origin, problems usually occur in one of four ways:

• Something goes wrong. Group members must decide how to fix or stop something. Example—a firehouse crew finds out that half of the building is contaminated with mold and must be closed down.
• Expectations change or increase. Group members must innovate more efficient or effective ways of doing something. Example—a firehouse crew finds out that the district they are responsible for is being expanded.
• Something goes wrong and expectations change or increase. Group members must fix/stop and become more efficient/effective. Example—the firehouse crew has to close half the building and must start responding to more calls due to the expanding district.
• The problem existed from the beginning. Group members must go back to the origins of the situation and walk through and analyze the steps again to decide what can be done differently. Example—a firehouse crew has consistently had to work with minimal resources in terms of building space and firefighting tools.

In each of the cases, the need for a decision may be more or less urgent depending on how badly something is going wrong, how high the expectations have been raised, or the degree to which people are fed up with a broken system. Decisions must be made in situations ranging from crisis level to mundane.

Personality Influences on Decision Making

A long-studied typology of value orientations that affect decision making consists of the following types of decision maker: the economic, the aesthetic, the theoretical, the social, the political, and the religious (Spranger, 1928).

• The economic decision maker makes decisions based on what is practical and useful.
• The aesthetic decision maker makes decisions based on form and harmony, desiring a solution that is elegant and in sync with the surroundings.
• The theoretical decision maker wants to discover the truth through rationality.
• The social decision maker emphasizes the personal impact of a decision and sympathizes with those who may be affected by it.
• The political decision maker is interested in power and influence and views people and/or property as divided into groups that have different value.
• The religious decision maker seeks to identify with a larger purpose, works to unify others under that goal, and commits to a viewpoint, often denying one side and being dedicated to the other.

In the United States, economic, political, and theoretical decision making tend to be more prevalent decision-making orientations, which likely corresponds to the individualistic cultural orientation with its emphasis on competition and efficiency. But situational context, as we discussed before, can also influence our decision making.

Personality affects decision making. For example, “economic” decision makers decide based on what is practical and useful.

One Way Stock – Tough Decisions Ahead – CC BY-ND 2.0.

The personalities of group members, especially leaders and other active members, affect the climate of the group. Group member personalities can be categorized based on where they fall on a continuum anchored by the following descriptors: dominant/submissive, friendly/unfriendly, and instrumental/emotional (Cragan & Wright, 1999). The more group members there are in any extreme of these categories, the more likely that the group climate will also shift to resemble those characteristics.

• Dominant versus submissive. Group members that are more dominant act more independently and directly, initiate conversations, take up more space, make more direct eye contact, seek leadership positions, and take control over decision-making processes. More submissive members are reserved, contribute to the group only when asked to, avoid eye contact, and leave their personal needs and thoughts unvoiced or give into the suggestions of others.
• Friendly versus unfriendly. Group members on the friendly side of the continuum find a balance between talking and listening, don’t try to win at the expense of other group members, are flexible but not weak, and value democratic decision making. Unfriendly group members are disagreeable, indifferent, withdrawn, and selfish, which leads them to either not invest in decision making or direct it in their own interest rather than in the interest of the group.
• Instrumental versus emotional. Instrumental group members are emotionally neutral, objective, analytical, task-oriented, and committed followers, which leads them to work hard and contribute to the group’s decision making as long as it is orderly and follows agreed-on rules. Emotional group members are creative, playful, independent, unpredictable, and expressive, which leads them to make rash decisions, resist group norms or decision-making structures, and switch often from relational to task focus.

Cultural Context and Decision Making

Just like neighborhoods, schools, and countries, small groups vary in terms of their degree of similarity and difference. Demographic changes in the United States and increases in technology that can bring different people together make it more likely that we will be interacting in more and more heterogeneous groups (Allen, 2011). Some small groups are more homogenous, meaning the members are more similar, and some are more heterogeneous, meaning the members are more different. Diversity and difference within groups has advantages and disadvantages. In terms of advantages, research finds that, in general, groups that are culturally heterogeneous have better overall performance than more homogenous groups (Haslett & Ruebush, 1999). Additionally, when group members have time to get to know each other and competently communicate across their differences, the advantages of diversity include better decision making due to different perspectives (Thomas, 1999). Unfortunately, groups often operate under time constraints and other pressures that make the possibility for intercultural dialogue and understanding difficult. The main disadvantage of heterogeneous groups is the possibility for conflict, but given that all groups experience conflict, this isn’t solely due to the presence of diversity. We will now look more specifically at how some of the cultural value orientations we’ve learned about already in this book can play out in groups with international diversity and how domestic diversity in terms of demographics can also influence group decision making.

International Diversity in Group Interactions

Cultural value orientations such as individualism/collectivism, power distance, and high-/low-context communication styles all manifest on a continuum of communication behaviors and can influence group decision making. Group members from individualistic cultures are more likely to value task-oriented, efficient, and direct communication. This could manifest in behaviors such as dividing up tasks into individual projects before collaboration begins and then openly debating ideas during discussion and decision making. Additionally, people from cultures that value individualism are more likely to openly express dissent from a decision, essentially expressing their disagreement with the group. Group members from collectivistic cultures are more likely to value relationships over the task at hand. Because of this, they also tend to value conformity and face-saving (often indirect) communication. This could manifest in behaviors such as establishing norms that include periods of socializing to build relationships before task-oriented communication like negotiations begin or norms that limit public disagreement in favor of more indirect communication that doesn’t challenge the face of other group members or the group’s leader. In a group composed of people from a collectivistic culture, each member would likely play harmonizing roles, looking for signs of conflict and resolving them before they become public.

Power distance can also affect group interactions. Some cultures rank higher on power-distance scales, meaning they value hierarchy, make decisions based on status, and believe that people have a set place in society that is fairly unchangeable. Group members from high-power-distance cultures would likely appreciate a strong designated leader who exhibits a more directive leadership style and prefer groups in which members have clear and assigned roles. In a group that is homogenous in terms of having a high-power-distance orientation, members with higher status would be able to openly provide information, and those with lower status may not provide information unless a higher status member explicitly seeks it from them. Low-power-distance cultures do not place as much value and meaning on status and believe that all group members can participate in decision making. Group members from low-power-distance cultures would likely freely speak their mind during a group meeting and prefer a participative leadership style.

How much meaning is conveyed through the context surrounding verbal communication can also affect group communication. Some cultures have a high-context communication style in which much of the meaning in an interaction is conveyed through context such as nonverbal cues and silence. Group members from high-context cultures may avoid saying something directly, assuming that other group members will understand the intended meaning even if the message is indirect. So if someone disagrees with a proposed course of action, he or she may say, “Let’s discuss this tomorrow,” and mean, “I don’t think we should do this.” Such indirect communication is also a face-saving strategy that is common in collectivistic cultures. Other cultures have a low-context communication style that places more importance on the meaning conveyed through words than through context or nonverbal cues. Group members from low-context cultures often say what they mean and mean what they say. For example, if someone doesn’t like an idea, they might say, “I think we should consider more options. This one doesn’t seem like the best we can do.”

In any of these cases, an individual from one culture operating in a group with people of a different cultural orientation could adapt to the expectations of the host culture, especially if that person possesses a high degree of intercultural communication competence (ICC). Additionally, people with high ICC can also adapt to a group member with a different cultural orientation than the host culture. Even though these cultural orientations connect to values that affect our communication in fairly consistent ways, individuals may exhibit different communication behaviors depending on their own individual communication style and the situation.

Domestic Diversity and Group Communication

While it is becoming more likely that we will interact in small groups with international diversity, we are guaranteed to interact in groups that are diverse in terms of the cultural identities found within a single country or the subcultures found within a larger cultural group.

Gender stereotypes sometimes influence the roles that people play within a group. For example, the stereotype that women are more nurturing than men may lead group members (both male and female) to expect that women will play the role of supporters or harmonizers within the group. Since women have primarily performed secretarial work since the 1900s, it may also be expected that women will play the role of recorder. In both of these cases, stereotypical notions of gender place women in roles that are typically not as valued in group communication. The opposite is true for men. In terms of leadership, despite notable exceptions, research shows that men fill an overwhelmingly disproportionate amount of leadership positions. We are socialized to see certain behaviors by men as indicative of leadership abilities, even though they may not be. For example, men are often perceived to contribute more to a group because they tend to speak first when asked a question or to fill a silence and are perceived to talk more about task-related matters than relationally oriented matters. Both of these tendencies create a perception that men are more engaged with the task. Men are also socialized to be more competitive and self-congratulatory, meaning that their communication may be seen as dedicated and their behaviors seen as powerful, and that when their work isn’t noticed they will be more likely to make it known to the group rather than take silent credit. Even though we know that the relational elements of a group are crucial for success, even in high-performance teams, that work is not as valued in our society as the task-related work.

Despite the fact that some communication patterns and behaviors related to our typical (and stereotypical) gender socialization affect how we interact in and form perceptions of others in groups, the differences in group communication that used to be attributed to gender in early group communication research seem to be diminishing. This is likely due to the changing organizational cultures from which much group work emerges, which have now had more than sixty years to adjust to women in the workplace. It is also due to a more nuanced understanding of gender-based research, which doesn’t take a stereotypical view from the beginning as many of the early male researchers did. Now, instead of biological sex being assumed as a factor that creates inherent communication differences, group communication scholars see that men and women both exhibit a range of behaviors that are more or less feminine or masculine. It is these gendered behaviors, and not a person’s gender, that seem to have more of an influence on perceptions of group communication. Interestingly, group interactions are still masculinist in that male and female group members prefer a more masculine communication style for task leaders and that both males and females in this role are more likely to adapt to a more masculine communication style. Conversely, men who take on social-emotional leadership behaviors adopt a more feminine communication style. In short, it seems that although masculine communication traits are more often associated with high status positions in groups, both men and women adapt to this expectation and are evaluated similarly (Haslett & Ruebush, 1999).

Other demographic categories are also influential in group communication and decision making. In general, group members have an easier time communicating when they are more similar than different in terms of race and age. This ease of communication can make group work more efficient, but the homogeneity may sacrifice some creativity. As we learned earlier, groups that are diverse (e.g., they have members of different races and generations) benefit from the diversity of perspectives in terms of the quality of decision making and creativity of output.

In terms of age, for the first time since industrialization began, it is common to have three generations of people (and sometimes four) working side by side in an organizational setting. Although four generations often worked together in early factories, they were segregated based on their age group, and a hierarchy existed with older workers at the top and younger workers at the bottom. Today, however, generations interact regularly, and it is not uncommon for an older person to have a leader or supervisor who is younger than him or her (Allen, 2011). The current generations in the US workplace and consequently in work-based groups include the following:

• The Silent Generation. Born between 1925 and 1942, currently in their midsixties to mideighties, this is the smallest generation in the workforce right now, as many have retired or left for other reasons. This generation includes people who were born during the Great Depression or the early part of World War II, many of whom later fought in the Korean War (Clarke, 1970).
• The Baby Boomers. Born between 1946 and 1964, currently in their late forties to midsixties, this is the largest generation in the workforce right now. Baby boomers are the most populous generation born in US history, and they are working longer than previous generations, which means they will remain the predominant force in organizations for ten to twenty more years.
• Generation X. Born between 1965 and 1981, currently in their early thirties to midforties, this generation was the first to see technology like cell phones and the Internet make its way into classrooms and our daily lives. Compared to previous generations, “Gen-Xers” are more diverse in terms of race, religious beliefs, and sexual orientation and also have a greater appreciation for and understanding of diversity.
• Generation Y. Born between 1982 and 2000, “Millennials” as they are also called are currently in their late teens up to about thirty years old. This generation is not as likely to remember a time without technology such as computers and cell phones. They are just starting to enter into the workforce and have been greatly affected by the economic crisis of the late 2000s, experiencing significantly high unemployment rates.

The benefits and challenges that come with diversity of group members are important to consider. Since we will all work in diverse groups, we should be prepared to address potential challenges in order to reap the benefits. Diverse groups may be wise to coordinate social interactions outside of group time in order to find common ground that can help facilitate interaction and increase group cohesion. We should be sensitive but not let sensitivity create fear of “doing something wrong” that then prevents us from having meaningful interactions. Reviewing Chapter 8 “Culture and Communication” will give you useful knowledge to help you navigate both international and domestic diversity and increase your communication competence in small groups and elsewhere.

Key Takeaways

• Every problem has common components: an undesirable situation, a desired situation, and obstacles between the undesirable and desirable situations. Every problem also has a set of characteristics that vary among problems, including task difficulty, number of possible solutions, group member interest in the problem, group familiarity with the problem, and the need for solution acceptance.

The group problem-solving process has five steps:

• Define the problem by creating a problem statement that summarizes it.
• Analyze the problem and create a problem question that can guide solution generation.
• Generate possible solutions. Possible solutions should be offered and listed without stopping to evaluate each one.
• Evaluate the solutions based on their credibility, completeness, and worth. Groups should also assess the potential effects of the narrowed list of solutions.
• Implement and assess the solution. Aside from enacting the solution, groups should determine how they will know the solution is working or not.
• Before a group makes a decision, it should brainstorm possible solutions. Group communication scholars suggest that groups (1) do a warm-up brainstorming session; (2) do an actual brainstorming session in which ideas are not evaluated, wild ideas are encouraged, quantity not quality of ideas is the goal, and new combinations of ideas are encouraged; (3) eliminate duplicate ideas; and (4) clarify, organize, and evaluate ideas. In order to guide the idea-generation process and invite equal participation from group members, the group may also elect to use the nominal group technique.
• Common decision-making techniques include majority rule, minority rule, and consensus rule. With majority rule, only a majority, usually one-half plus one, must agree before a decision is made. With minority rule, a designated authority or expert has final say over a decision, and the input of group members may or may not be invited or considered. With consensus rule, all members of the group must agree on the same decision.

Several factors influence the decision-making process:

• Situational factors include the degree of freedom a group has to make its own decisions, the level of uncertainty facing the group and its task, the size of the group, the group’s access to information, and the origin and urgency of the problem.
• Personality influences on decision making include a person’s value orientation (economic, aesthetic, theoretical, political, or religious), and personality traits (dominant/submissive, friendly/unfriendly, and instrumental/emotional).
• Cultural influences on decision making include the heterogeneity or homogeneity of the group makeup; cultural values and characteristics such as individualism/collectivism, power distance, and high-/low-context communication styles; and gender and age differences.
• Scenario 1. Task difficulty is high, number of possible solutions is high, group interest in problem is high, group familiarity with problem is low, and need for solution acceptance is high.
• Scenario 2. Task difficulty is low, number of possible solutions is low, group interest in problem is low, group familiarity with problem is high, and need for solution acceptance is low.
• Scenario 1: Academic. A professor asks his or her class to decide whether the final exam should be an in-class or take-home exam.
• Scenario 2: Professional. A group of coworkers must decide which person from their department to nominate for a company-wide award.
• Scenario 3: Personal. A family needs to decide how to divide the belongings and estate of a deceased family member who did not leave a will.
• Scenario 4: Civic. A local branch of a political party needs to decide what five key issues it wants to include in the national party’s platform.
• Group communication researchers have found that heterogeneous groups (composed of diverse members) have advantages over homogenous (more similar) groups. Discuss a group situation you have been in where diversity enhanced your and/or the group’s experience.

Adams, K., and Gloria G. Galanes, Communicating in Groups: Applications and Skills , 7th ed. (Boston, MA: McGraw-Hill, 2009), 220–21.

Allen, B. J., Difference Matters: Communicating Social Identity , 2nd ed. (Long Grove, IL: Waveland, 2011), 5.

Bormann, E. G., and Nancy C. Bormann, Effective Small Group Communication , 4th ed. (Santa Rosa, CA: Burgess CA, 1988), 112–13.

Clarke, G., “The Silent Generation Revisited,” Time, June 29, 1970, 46.

Cragan, J. F., and David W. Wright, Communication in Small Group Discussions: An Integrated Approach , 3rd ed. (St. Paul, MN: West Publishing, 1991), 77–78.

de Bono, E., Six Thinking Hats (Boston, MA: Little, Brown, 1985).

Delbecq, A. L., and Andrew H. Ven de Ven, “A Group Process Model for Problem Identification and Program Planning,” The Journal of Applied Behavioral Science 7, no. 4 (1971): 466–92.

Haslett, B. B., and Jenn Ruebush, “What Differences Do Individual Differences in Groups Make?: The Effects of Individuals, Culture, and Group Composition,” in The Handbook of Group Communication Theory and Research , ed. Lawrence R. Frey (Thousand Oaks, CA: Sage, 1999), 133.

Napier, R. W., and Matti K. Gershenfeld, Groups: Theory and Experience , 7th ed. (Boston, MA: Houghton Mifflin, 2004), 292.

Osborn, A. F., Applied Imagination (New York: Charles Scribner’s Sons, 1959).

Spranger, E., Types of Men (New York: Steckert, 1928).

Stanton, C., “How to Deliver Group Presentations: The Unified Team Approach,” Six Minutes Speaking and Presentation Skills , November 3, 2009, accessed August 28, 2012, http://sixminutes.dlugan.com/group-presentations-unified-team-approach .

Thomas, D. C., “Cultural Diversity and Work Group Effectiveness: An Experimental Study,” Journal of Cross-Cultural Psychology 30, no. 2 (1999): 242–63.

Communication in the Real World Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Vygotsky’s Zone of Proximal Development and Scaffolding Theory

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

The zone of proximal development (ZPD) refers to the difference between what a learner can do without help and what he or she can achieve with guidance and encouragement from a skilled partner.

It represents tasks beyond the learner’s current abilities but are attainable with the help and guidance of the more knowledgeable other (MKO). The ZPD is the range of tasks a person can’t complete independently but can accomplish with support.

Thus, the term “proximal” refers to skills the learner is “close” to mastering. The ZPD ensures challenge is not too hard or too easy.

ZPD is the zone where instruction is the most beneficial, as it is when the task is just beyond the individual’s capabilities.

To learn, we must be presented with tasks just out of our ability range. Challenging tasks promote maximum cognitive growth.

The zone of proximal development was developed by Soviet psychologist and social constructivist Lev Vygotsky (1896 – 1934).

Vygotsky introduced the ZPD concept to criticize psychometric testing which only measured current abilities, not potential for development. He argued assessment should be collaborative to reveal emerging skills.

The zone of proximal development (ZPD) has been defined as:

“the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem-solving under adult guidance, or in collaboration with more capable peers” (Vygotsky, 1978, p. 86).

For teachers, the ZPD is the space between current teaching knowledge and potential new level with assistance. Willingness to learn enables ZPD progression.

Vygotsky believed that when a student is in the zone of proximal development for a particular task, providing the appropriate assistance will give the student enough of a “boost” to achieve the task.

To assist a person to move through the zone of proximal development, educators are encouraged to focus on three important components which aid the learning process:

• The presence of someone with knowledge and skills beyond that of the learner (a more knowledgeable other).
• Social interactions with a skillful tutor that allow the learner to observe and practice their skills.
• Scaffolding, or supportive activities provided by the educator, or more competent peer, to support the student as he or she is led through the ZPD.

Scaffolding Theory

The ZPD has become synonymous in the literature with the term scaffolding. However, it is important to note that Vygotsky never used this term in his writing, and it was introduced by Wood, Bruner, and Ross (1976).

Scaffolding consists of the activities provided by the educator, or more competent peer, to support the student as he or she is led through the zone of proximal development.

Support is tapered off (i.e., withdrawn) as it becomes unnecessary, much as a scaffold is removed from a building during construction. The student will then be able to complete the task again independently.

Wood et al. (1976, p. 90) define scaffolding as a process “that enables a child or novice to solve a task or achieve a goal that would be beyond his unassisted efforts.”

As they note, scaffolds require the adult to “controlling those elements of the task that are initially beyond the learner’s capability, thus permitting him to concentrate upon and complete only those elements that are within his range of competence” (p. 90).

It is important to note that the terms cooperative learning, scaffolding and guided learning all have the same meaning within the literature.

The following study provides empirical support both the concept of scaffolding and the ZPD.

Wood and Middleton (1975)

Procedure : 4-year-old children had to use a set of blocks and pegs to build a 3D model shown in a picture. Building the model was too difficult a task for a 4-year-old child to complete alone.

Wood and Middleton (1975) observed how mothers interacted with their children to build the 3D model. The type of support included:

• General encouragement e.g., ‘now you have a go.’ • Specific instructions e.g., ‘get four big blocks.’ • Direct demonstration, e.g., showing the child how to place one block on another.

The results of the study showed that no single strategy was best for helping the child to progress. Mothers whose assistance was most effective were those who varied their strategy according to how the child was doing.

When the child was doing well, they became less specific with their help. When the child started to struggle, they gave increasingly specific instructions until the child started to make progress again.

The study illustrates scaffolding and Vygotsky’s concept of the ZPD. Scaffolding (i.e., assistance) is most effective when the support is matched to the needs of the learner. This puts them in a position to achieve success in an activity that they would previously not have been able to do alone.

Wood et al. (1976) named certain processes that aid effective scaffolding:

• Gaining and maintaining the learner’s interest in the task.
• Making the task simple.
• Emphasizing certain aspects that will help with the solution.
• Control the child’s level of frustration.
• Demonstrate the task.

Intersubjectivity

Intersubjectivity is when two people (i.e., the child and helper) start a task together with different levels of skill and understanding, and both end up with a shared understanding.

As each member of the dyad adjusts to the perspective of the other, the helper has to translate their own insights in a ways that is within the grasp of the child, and the child develops a more complete understanding of the task.

It is essential that they work towards the same goal, otherwise there won’t be any collaboration. It is important that they negotiate, or compromise by always working for a shared view.

If you try to force someone to change their mind, then you”ll just get conflict. You need to stay within the boundaries of the other person’s zone of proximal development.

Example of Scaffolding

Vygotsky emphasized scaffolding, or providing support to learners to help them reach higher levels of understanding. This can be mapped to progressing through Bloom’s taxonomy , where educators scaffold tasks from basic understanding to more complex analysis and creation.

For example, a teacher might start by providing information (Remembering) and then ask questions that require understanding.

As students become more proficient, tasks can be scaffolded to require application, analysis, evaluation, and creation.

Example : In teaching a concept like photosynthesis:

• Remembering : The teacher provides the basic definition.
• Understanding : Students explain the process in their own words.
• Application : They might conduct an experiment on plants.
• Analysis : Dive deeper into how different variables affect the process.
• Evaluation : Debate the most critical components of photosynthesis.
• Creation : Design an optimal environment for plant growth.

Each step can be scaffolded, starting with substantial teacher support and gradually releasing responsibility to the students as they climb Bloom’s taxonomy, guiding students from foundational knowledge to higher-order thinking skills.

Scaffolding vs. Discovery Learning

Freund (1990) wanted to investigate if children learn more effectively via Piaget’s concept of discovery learning or guided learning via the ZPD.

She asked a group of children between the ages of three and five years to help a puppet decide which furniture should be placed in the various rooms of a doll’s house. First, Freund assessed what each child already understood about the placement of furniture (as a baseline measure).

Next, each child worked on a similar task, either alone (re: discovery-based learning) or with their mother (re: scaffolding / guided learning). To assess what each child had learned, they were each given a more complex, furniture sorting task.

The study’s results showed that children assisted by their mothers performed better at furniture sorting than the children who worked independently.

More Knowledgeable Other

The more knowledgeable other (MKO) refers to anyone who has a better understanding or a higher ability level in a particular task, process, or concept than the learner.

It’s essential to note that the MKO isn’t necessarily an adult or a teacher. It could be a peer, a younger person, or even technology or media, as long as they provide the learner with the knowledge or scaffolding needed to perform a task.

Often, a child’s peers or an adult’s children may be the individuals with more knowledge or experience.

The relationship between the MKO and the ZPD is vital to Vygotsky’s theory. The MKO assists or scaffolds the learning experience to help the learner function within their ZPD.

Through this guidance, the learner can tackle and master tasks they couldn’t accomplish independently.

Over time, as the learner internalizes this support and becomes more capable, the scaffolding can be reduced, and the learner can perform the task without assistance. The ZPD moves as learners acquire new skills and knowledge with the help of the MKO.

In educational settings, the concepts of MKO and ZPD have inspired practices like cooperative learning, differentiated instruction, and scaffolded learning experiences.

Teachers aim to identify each student’s ZPD and then act as the MKO, or facilitate interactions with other MKOs, to provide the right level of support, allowing students to achieve and learn effectively.

Educational Applications

Vygotsky believes the role of education is to provide children with experiences which are in their ZPD, thereby encouraging and advancing their individual learning. (Berk, & Winsler, (1995).

“From a Vygotskian perspective, the teacher’s role is mediating the child’s learning activity as they share knowledge through social interaction” (Dixon-Krauss, 1996, p. 18).

Cooperative Learning

According to Vygotsky (1978), much important learning by the child occurs through social interaction with a skillful tutor. The tutor may model behaviors and/or provide verbal instructions for the child.

Vygotsky refers to this as cooperative or collaborative dialogue.

The child seeks to understand the actions or instructions provided by the tutor (often the parent or teacher) and then internalizes the information, using it to guide or regulate their own performance.

Lev Vygotsky views interaction with peers as an effective way of developing skills and strategies. He suggests that teachers use cooperative learning exercises where less competent children develop with help from more skillful peers – within the zone of proximal development.

Scaffolding is a key feature of effective teaching, where the adult continually adjusts the level of his or her help in response to the learner’s level of performance.

In the classroom, scaffolding can include modeling a skill, providing hints or cues, and adapting material or activity (Copple & Bredekamp, 2009).

Consider these guidelines for scaffolding instruction (Silver, 2011).

• Assess the learner’s current knowledge and experience with the academic content.
• Relate content to what students already understand or can do.
• Break a task into small, more manageable tasks with opportunities for intermittent feedback.
• Use verbal cues and prompts to assist students.

Scaffolding not only produces immediate results, but also instills the skills necessary for independent problem-solving in the future.

A contemporary application of Vygotsky’s theories is “reciprocal teaching,” used to improve students” ability to learn from text.

In this method, teachers and students collaborate in learning and practicing four key skills: summarizing, questioning, clarifying, and predicting. The teacher’s role in the process is reduced over time.

Vygotsky’s theories also feed into current interest in collaborative learning, suggesting that group members should have different levels of ability so more advanced peers can help less advanced members operate within their zone of proximal development.

Examples of ZPD

Maria just entered college this semester and decided to take an introductory tennis course.  Her class spends each week learning and practicing a different shot.  Weeks go by, and they learn how to properly serve and hit a backhand.

During the week of learning the forehand, the instructor noticed that Maria was very frustrated because she kept hitting her forehand shots either into the net or far past the baseline.

He examines her preparation and swing.  He notices that her stance is perfect, she prepares early, she turns her torso appropriately, and she hits the ball at precisely the right height.

However, he notices that she is still gripping her racquet the same way she hits her backhand, so he goes over to her and shows her how to reposition her hand to hit a proper forehand, stressing that she should keep her index finger parallel to the racquet.

He models a good forehand for her, and then assists her in changing her grip. With a little practice, Maria’s forehand turns into a formidable weapon for her!

In this case, Maria was in the zone of proximal development for successfully hitting a forehand shot.  She was doing everything else correctly, but just needed a little coaching and scaffolding from a “More Knowledgeable Other” to help her succeed in this task.

When that assistance was given, she was able to achieve her goal. Provided with appropriate support at the right moments, students in classrooms will be able to achieve tasks that would otherwise be too difficult for them.

Clinical psychology trainees at the Center for Children and Families at Florida International University are trained using approaches aligned with Vygotsky’s zone of proximal development (Hong & del Busto, 2020).

• Trainees are paired with more senior trainees (e.g., a first-year student with a second or third-year student) for co-therapy sessions. The senior trainee scaffolds the junior trainee’s learning by initially taking the lead and modeling skills, then gradually encouraging the junior trainee to become more independent in leading sessions as they demonstrate competence.
• This allows trainees to be involved in clinical care early in their training, with support and coaching from a more experienced peer. It meets them in their zone of proximal development – what they can do with guidance vs what they cannot yet do independently.
• Supervisors assign trainees different roles based on experience level. More senior trainees are given opportunities to develop supervisory skills by training junior peers. Junior trainees are supported in gaining clinical skills.
• The zone of proximal development concept is applied not just for patients in case conceptualization but also for trainees’ own professional development. Supervisors provide individualized support and scaffolding to help each trainee progress.

Social interaction, aided by cultural tools, supports teachers in developing new aspects of their practice and identity. The interpersonal activity facilitates the transformation of their teaching expertise.

This demonstrates the value of mediation through the ZPD (Shabani et al., 2010).

• Collaborative peers and mentors : Observing and discussing teaching practices with experienced colleagues helps teachers learn new instructional approaches and strategies. This social exchange facilitates development within their ZPD.
• Action research : By studying their own teaching through classroom inquiry, teachers can gain insights into improving their methods. The self-reflection shifts their ZPD forward.
• Diaries : Writing reflectively about teaching experiences enables teachers to analyze their development and assumptions. This metacognition expands their ZPD.
• Technology : Using digital tools and platforms introduces teachers to innovative teaching techniques. The technology mediates new pedagogical capabilities.
• TESOL discourse : Engaging with academic research and theory opens teachers to alternative perspectives on teaching and learning. This discourse stretches their ZPD.
• Coursework : Formal professional development courses scaffold teachers’ learning of new knowledge and competencies. The instruction targets their ZPD.
• Student data : Responses and achievement metrics provide feedback to teachers on areas needing growth. This evidence shifts teachers’ self-perception.

Berk, L., & Winsler, A. (1995). Scaffolding children’s learning: Vygotsky and early childhood learning. Washington, DC: National Association for Education of Young Children.

Copple, C., & Bredekamp, S. (2009). Developmentally appropriate practice in early childhood programs . Washington, DC: National Association for the Education of Young Children.

Dixon-Krauss, L. (1996). Vygotsky in the classroom. Mediated literacy instruction and assessment. White Plains, NY: Longman Publishers.

Freund, L. S. (1990). Maternal Regulation of Children’s Problem-solving behavior and Its Impact on Children’s Performance. Child Development , 61, 113-126.

Hong, N., & del Busto, C. T. (2020). Collaboration, scaffolding, and successive approximations: A developmental science approach to training in clinical psychology.  Training and Education in Professional Psychology ,  14 (3), 228.

Shabani, K., Khatib, M., & Ebadi, S. (2010). Vygotsky’s zone of proximal development: Instructional implications and teachers’ professional development.  English Language Teaching ,  3 (4), 237-248.

Silver, D. (2011). Using the ‘Zone’Help Reach Every Learner. Kappa Delta Pi Record, 47(sup1) , 28-31.

Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes . Cambridge, MA: Harvard University Press.

Wass, R., & Golding, C. (2014). Sharpening a tool for teaching: the zone of proximal development.  Teaching in Higher Education ,  19 (6), 671-684.

Wood, D., Bruner, J., & Ross, G. (1976). The role of tutoring in problem solving. Journal of Child Psychology and Child Psychiatry , 17, 89−100.

Wood, D., & Middleton, D. (1975). A study of assisted problem-solving. British Journal of Psychology , 66(2), 181−191.

Further Reading

• Educational implications of Vygotsky’s ZPD
• Vygotsky’s Zone of Proximal Development: Instructional Implications and Teachers” Professional Development
• Scaffolds for Learning: The Key to Guided Instruction

Related Articles

Child Psychology

Vygotsky vs. Piaget: A Paradigm Shift

Interactional Synchrony

Internal Working Models of Attachment

Learning Theory of Attachment

Stages of Attachment Identified by John Bowlby And Schaffer & Emerson (1964)

Child Psychology , Personality

How Anxious Ambivalent Attachment Develops in Children

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The 3-body problem is real, and it’s really unsolvable

Oh god don’t make me explain math

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Everybody seems to be talking about 3 Body Problem , the new Netflix series based on Cixin Liu’s Remembrance of Earth’s Past book trilogy . Fewer people are talking about the two series’ namesake: The unsolvable physics problem of the same name.

This makes sense, because it’s confusing . In physics, the three-body problem attempts to find a way to predict the movements of three objects whose gravity interacts with each of the others — like three stars that are close together in space. Sounds simple enough, right? Yet I myself recently pulled up the Wikipedia article on the three-body problem and closed the tab in the same manner that a person might stagger away from a bright light. Apparently the Earth, sun, and moon are a three-body system? Are you telling me we don’t know how the moon moves ? Scientists have published multiple solutions for the three-body problem? Are you telling me Cixin Liu’s books are out of date?

All I’d wanted to know was why the problem was considered unsolvable, and now memories of my one semester of high school physics were swimming before my eyes like so many glowing doom numbers. However, despite my pains, I have readied several ways that we non-physicists can be confident that the three-body problem is, in fact, unsolvable.

Reason 1: This is a special definition of ‘unsolvable’

The three-body problem is extra confusing, because scientists are seemingly constantly finding new solutions to the three-body problem! They just don’t mean a one-solution-for-all solution. Such a formula does exist for a two-body system, and apparently Isaac Newton figured it out in 1687 . But systems with more than two bodies are, according to physicists, too chaotic (i.e., not in the sense of a child’s messy bedroom, but in the sense of “chaos theory”) to be corralled by a single solution.

When physicists say they have a new solution to the three-body problem, they mean that they’ve found a specific solution for three-body systems that have certain theoretical parameters. Don’t ask me to explain those parameters, because they’re all things like “the three masses are collinear at each instant” or “a zero angular momentum solution with three equal masses moving around a figure-eight shape.” But basically: By narrowing the focus of the problem to certain arrangements of three-body systems, physicists have been able to derive formulas that predict the movements of some of them, like in our solar system. The mass of the Earth and the sun create a “ restricted three-body problem ,” where a less-big body (in this case, the moon) moves under the influence of two massive ones (the Earth and the sun).

What physicists mean when they say the three-body problem has no solution is simply that there isn’t a one-formula-fits-all solution to every way that the gravity of three objects might cause those objects to move — which is exactly what Three-Body Problem bases its whole premise on.

Reason 2: 3 Body Problem picked an unsolved three-body system on purpose

Henri Poincaré’s research into a general solution to the three-body problem formed the basis of what would become known as chaos theory (you might know it from its co-starring role in Jurassic Park ). And 3 Body Problem itself isn’t about any old three-body system. It’s specifically about an extremely chaotic three-body system, the exact kind of arrangement of bodies that Poincaré was focused on when he showed that the problem is “unsolvable.”

[ Ed. note: The rest of this section includes some spoilers for 3 Body Problem .]

In both Liu’s books and Netflix’s 3 Body Problem , humanity faces an invasion by aliens (called Trisolarans in the English translation of the books, and San-Ti in the TV series) whose home solar system features three suns in a chaotic three-body relationship. It is a world where, unlike ours, the heavens are fundamentally unpredictable. Periods of icy cold give way to searing heat that give way to swings in gravity that turn into temporary reprieves that can never be trusted. The unpredictable nature of the San-Ti environment is the source of every detail of their physicality, their philosophy, and their desire to claim Earth for their own.

In other words, 3 Body Problem ’s three-body problem is unsolvable because Liu wanted to write a story with an unsolvable three-body system, so he chose one of the three-body systems for which we have not discovered a solution, and might never.

Reason 3: Scientists are still working on the three-body problem

Perhaps the best reason I can give you to believe that the three-body problem is real, and is really unsolvable, is that some scientists published a whole set of new solutions for specific three-body systems very recently .

If physicists are still working on the three-body problem, we can safely assume that it has not been solved. Scientists, after all, are the real experts. And I am definitely not.

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Facility for Rare Isotope Beams

At michigan state university, international research team uses wavefunction matching to solve quantum many-body problems, new approach makes calculations with realistic interactions possible.

FRIB researchers are part of an international research team solving challenging computational problems in quantum physics using a new method called wavefunction matching. The new approach has applications to fields such as nuclear physics, where it is enabling theoretical calculations of atomic nuclei that were previously not possible. The details are published in Nature (“Wavefunction matching for solving quantum many-body problems”) .

Ab initio methods and their computational challenges

An ab initio method describes a complex system by starting from a description of its elementary components and their interactions. For the case of nuclear physics, the elementary components are protons and neutrons. Some key questions that ab initio calculations can help address are the binding energies and properties of atomic nuclei not yet observed and linking nuclear structure to the underlying interactions among protons and neutrons.

Yet, some ab initio methods struggle to produce reliable calculations for systems with complex interactions. One such method is quantum Monte Carlo simulations. In quantum Monte Carlo simulations, quantities are computed using random or stochastic processes. While quantum Monte Carlo simulations can be efficient and powerful, they have a significant weakness: the sign problem. The sign problem develops when positive and negative weight contributions cancel each other out. This cancellation results in inaccurate final predictions. It is often the case that quantum Monte Carlo simulations can be performed for an approximate or simplified interaction, but the corresponding simulations for realistic interactions produce severe sign problems and are therefore not possible.

Using ‘plastic surgery’ to make calculations possible

The new wavefunction-matching approach is designed to solve such computational problems. The research team—from Gaziantep Islam Science and Technology University in Turkey; University of Bonn, Ruhr University Bochum, and Forschungszentrum Jülich in Germany; Institute for Basic Science in South Korea; South China Normal University, Sun Yat-Sen University, and Graduate School of China Academy of Engineering Physics in China; Tbilisi State University in Georgia; CEA Paris-Saclay and Université Paris-Saclay in France; and Mississippi State University and the Facility for Rare Isotope Beams (FRIB) at Michigan State University (MSU)—includes  Dean Lee , professor of physics at FRIB and in MSU’s Department of Physics and Astronomy and head of the Theoretical Nuclear Science department at FRIB, and  Yuan-Zhuo Ma , postdoctoral research associate at FRIB.

“We are often faced with the situation that we can perform calculations using a simple approximate interaction, but realistic high-fidelity interactions cause severe computational problems,” said Lee. “Wavefunction matching solves this problem by doing plastic surgery. It removes the short-distance part of the high-fidelity interaction, and replaces it with the short-distance part of an easily computable interaction.”

This transformation is done in a way that preserves all of the important properties of the original realistic interaction. Since the new wavefunctions look similar to that of the easily computable interaction, researchers can now perform calculations using the easily computable interaction and apply a standard procedure for handling small corrections called perturbation theory.  A team effort

The research team applied this new method to lattice quantum Monte Carlo simulations for light nuclei, medium-mass nuclei, neutron matter, and nuclear matter. Using precise ab initio calculations, the results closely matched real-world data on nuclear properties such as size, structure, and binding energies. Calculations that were once impossible due to the sign problem can now be performed using wavefunction matching.

“It is a fantastic project and an excellent opportunity to work with the brightest nuclear scientist s in FRIB and around the globe,” said Ma. “As a theorist , I'm also very excited about programming and conducting research on the world's most powerful exascale supercomputers, such as Frontier , which allows us to implement wavefunction matching to explore the mysteries of nuclear physics.”

While the research team focused solely on quantum Monte Carlo simulations, wavefunction matching should be useful for many different ab initio approaches, including both classical and  quantum computing calculations. The researchers at FRIB worked with collaborators at institutions in China, France, Germany, South Korea, Turkey, and United States.

“The work is the culmination of effort over many years to handle the computational problems associated with realistic high-fidelity nuclear interactions,” said Lee. “It is very satisfying to see that the computational problems are cleanly resolved with this new approach. We are grateful to all of the collaboration members who contributed to this project, in particular, the lead author, Serdar Elhatisari.”

This material is based upon work supported by the U.S. Department of Energy, the U.S. National Science Foundation, the German Research Foundation, the National Natural Science Foundation of China, the Chinese Academy of Sciences President’s International Fellowship Initiative, Volkswagen Stiftung, the European Research Council, the Scientific and Technological Research Council of Turkey, the National Natural Science Foundation of China, the National Security Academic Fund, the Rare Isotope Science Project of the Institute for Basic Science, the National Research Foundation of Korea, the Institute for Basic Science, and the Espace de Structure et de réactions Nucléaires Théorique.

Michigan State University operates the Facility for Rare Isotope Beams (FRIB) as a user facility for the U.S. Department of Energy Office of Science (DOE-SC), supporting the mission of the DOE-SC Office of Nuclear Physics. Hosting what is designed to be the most powerful heavy-ion accelerator, FRIB enables scientists to make discoveries about the properties of rare isotopes in order to better understand the physics of nuclei, nuclear astrophysics, fundamental interactions, and applications for society, including in medicine, homeland security, and industry.

The U.S. Department of Energy Office of Science is the single largest supporter of basic research in the physical sciences in the United States and is working to address some of today’s most pressing challenges. For more information, visit energy.gov/science.

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The Possible Collapse of the U.S. Home Insurance System

A times investigation found climate change may now be a concern for every homeowner in the country..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

From “The New York Times,” I’m Sabrina Tavernise. And this is “The Daily.”

[MUSIC PLAYING]

Today, my colleague, Christopher Flavelle, on a “Times” investigation into one of the least known and most consequential effects of climate change — insurance — and why it may now be a concern for every homeowner in the country.

It’s Wednesday, May 15.

So, Chris, you and I talked a while ago about how climate change was really wreaking havoc in the insurance market in Florida. You’ve just done an investigation that takes a look into the insurance markets more broadly and more deeply. Tell us about it.

Yeah, so I cover climate change, in particular the way climate shocks affect different parts of American life. And insurance has become a really big part of that coverage. And Florida is a great example. As hurricanes have gotten worse and more frequent, insurers are paying out more and more money to rebuild people’s homes. And that’s driving up insurance costs and ultimately driving up the cost of owning a home in Florida.

So we’re already seeing that climate impact on the housing market in Florida. My colleagues and I started to think, well, could it be that that kind of disruption is also happening in other states, not just in the obvious coastal states but maybe even through the middle of the US? So we set out to find out just how much it is happening, how much that Florida turmoil has, in fact, become really a contagion that is spreading across the country.

So how did you go about reporting this? I mean, where did you start?

All we knew at the start of this was that there was reason to think this might be a problem. If you just look at how the federal government tracks disasters around the country, there’s been a big increase almost every year in the number and severity of all kinds of disasters around the country. So we thought, OK, it’s worth trying to find out, what does that mean for insurers?

The problem is getting data on the insurance industry is actually really hard. There’s no federal regulation. There’s no government agency you can go to that holds this data. If you talk to the insurers directly, they tend to be a little reluctant to share information about what they’re going through. So we weren’t sure where to go until, finally, we realized the best people to ask are the people whose job it is to gauge the financial health of insurance companies.

Those are rating agencies. In particular, there’s one rating company called AM Best, whose whole purpose is to tell investors how healthy an insurance company is.

Whoa. So this is way down in the nuts and bolts of the US insurance industry.

Right. This is a part of the broader economy that most people would never experience. But we asked them to do something special for us. We said, hey, can you help us find the one number that would tell us reporters just how healthy or unhealthy this insurance market is state by state over time? And it turns out, there is just such a number. It’s called a combined ratio.

OK, plain English?

Plain English, it is the ratio of revenue to costs, how much money these guys take in for homeowner’s insurance and how much they pay out in costs and losses. You want your revenue to be higher than your costs. If not, you’re in trouble.

So what did you find out?

Well, we got that number for every state, going back more than a decade. And what it showed us was our suspicions were right. This market turmoil that we were seeing in Florida and California has indeed been spreading across the country. And in fact, it turns out that in 18 states, last year, the homeowner’s insurance market lost money. And that’s a big jump from 5 or 10 years ago and spells real trouble for insurance and for homeowners and for almost every part of the economy.

So the contagion was real.

Right. This is our first window showing us just how far that contagion had spread. And one of the really striking things about this data was it showed the contagion had spread to places that I wouldn’t have thought of as especially prone to climate shocks — for example, a lot of the Midwest, a lot of the Southeast. In fact, if you think of a map of the country, there was no state between Pennsylvania and the Dakotas that didn’t lose money on homeowner’s insurance last year.

So just huge parts of the middle of the US have become unprofitable for homeowner’s insurance. This market is starting to buckle under the cost of climate change.

And this is all happening really fast. When we did the Florida episode two years ago, it was a completely new phenomenon and really only in Florida. And now it’s everywhere.

Yeah. And that’s exactly what’s so striking here. The rate at which this is becoming, again, a contagion and spreading across the country is just demolishing the expectations of anyone I’ve spoken to. No one thought that this problem would affect so much of the US so quickly.

So in these states, these new places that the contagion has spread to, what exactly is happening that’s causing the insurance companies to fold up shop?

Yeah. Something really particular is happening in a lot of these states. And it’s worth noting how it’s surprised everyone. And what that is, is formally unimportant weather events, like hailstorms or windstorms, those didn’t used to be the kind of thing that would scare insurance companies. Obviously, a big problem if it destroys your home or damages your home. But for insurers, it wasn’t going to wipe them out financially.

Right. It wasn’t just a complete and utter wipeout that the company would then have to pony up a lot of money for.

Exactly. And insurers call them secondary perils, sort of a belittling term, something other than a big deal, like a hurricane.

These minor league weather events.

Right. But those are becoming so frequent and so much more intense that they can cause existential threats for insurance companies. And insurers are now fleeing states not because of hurricanes but because those former things that were small are now big. Hailstorms, wildfires in some places, previous annoyances are becoming real threats to insurers.

Chris, what’s the big picture on what insurers are actually facing? What’s happening out there numbers-wise?

This is a huge threat. In terms of the number of states where this industry is losing money, it’s more than doubled from 10 years ago to basically a third of the country. The amount they’re losing is enormous. In some states, insurers are paying out $1.25 or even $1.50 for every dollar they bring in, in revenue, which is totally unsustainable.

And the result is insurers are making changes. They are pulling back from these markets. They’re hiking premiums. And often, they’re just dropping customers. And that’s where this becomes real, not just for people who surf balance sheets and trade in the stock market. This is becoming real for homeowners around the country, who all of a sudden increasingly can’t get insurance.

So, Chris, what’s the actual implication? I mean, what happens when people in a state can’t get insurance for their homes?

Getting insurance for a home is crucial if you want to sell or buy a home. Most people can’t buy a home without a mortgage. And banks won’t issue a mortgage without home insurance. So if you’ve got a home that insurance company doesn’t want to cover, you got a real problem. You need to find insurance, or that home becomes very close to unsellable.

And as you get fewer buyers, the price goes down. So this doesn’t just hurt people who are paying for these insurance premiums. It hurts people who want to sell their homes. It even could hurt, at some point, whole local economies. If home values fall, governments take in less tax revenue. That means less money for schools and police. It also means people who get hit by disasters and have to rebuild their homes all of a sudden can’t, because their insurance isn’t available anymore. It’s hard to overstate just how big a deal this is.

And is that actually happening, Chris? I mean, are housing markets being dragged down because of this problem with the insurance markets right now?

Anecdotally, we’ve got reports that in places like Florida and Louisiana and maybe in parts of California, the difficulty of getting insurance, the crazy high cost of insurance is starting to depress demand because not everyone can afford to pay these really high costs, even if they have insurance. But what we wanted to focus on with this story was also, OK, we know where this goes eventually. But where is it beginning? What are the places that are just starting to feel these shocks from the insurance market?

And so I called around and asked insurance agents, who are the front lines of this. They’re the ones who are struggling to find insurance for homeowners. And I said, hey, is there one place that I should go if I want to understand what it looks like to homeowners when all of a sudden insurance becomes really expensive or you can’t even find it? And those insurance agents told me, if you want to see what this looks like in real life, go to a little town called Marshalltown in the middle of Iowa.

We’ll be right back.

So, Chris, you went to Marshalltown, Iowa. What did you find?

Even before I got to Marshalltown, I had some idea I was in the right spot. When I landed in Des Moines and went to rent a car, the nice woman at the desk who rented me a car, she said, what are you doing here? I said, I’m here to write a story about people in Iowa who can’t get insurance because of storms. She said, oh, yeah, I know all about that. That’s a big problem here.

Even the rental car lady.

Even the rental car lady knew something was going on. And so I got into my rental car and drove about an hour northeast of Des Moines, through some rolling hills, to this lovely little town of Marshalltown. Marshalltown is a really cute, little Midwestern town with old homes and a beautiful courthouse in the town square. And when I drove through, I couldn’t help noticing all the roofs looked new.

What does that tell you?

Turns out Marshalltown, despite being a pastoral image of Midwestern easy living, was hit by two really bad disasters in recent years — first, a devastating tornado in 2018 and then, in 2020, what’s called a derecho, a straight-line wind event that’s also just enormously damaging. And the result was lots of homes in this small town got severely damaged in a short period of time. And so when you drive down, you see all these new roofs that give you the sense that something’s going on.

So climate had come to Marshalltown?

Exactly. A place that had previously seemed maybe safe from climate change, if there is such a thing, all of a sudden was not. So I found an insurance agent in Marshalltown —

We talked to other agents but haven’t talked to many homeowners.

— named Bobby Shomo. And he invited me to his office early one morning and said, come meet some people. And so I parked on a quiet street outside of his office, across the street from the courthouse, which also had a new roof, and went into his conference room and met a procession of clients who all had versions of the same horror story.

It was more — well more of double.

A huge reduction in coverage with a huge price increase.

Some people had faced big premium hikes.

I’m just a little, small business owner. So every little bit I do feel.

They had so much trouble with their insurance company.

I was with IMT Insurance forever. And then when I moved in 2020, Bobby said they won’t insure a pool.

Some people had gotten dropped.

Where we used to see carriers canceling someone for frequency of three or four or five claims, it’s one or two now.

Some people couldn’t get the coverage they needed. But it was versions of the same tale, which is all of a sudden, having homeowner’s insurance in Marshalltown was really difficult. But I wanted to see if it was bigger than just Marshalltown. So the next day, I got back in my car and drove east to Cedar Rapids, where I met another person having a version of the same problem, a guy named Dave Langston.

Tell me about Dave.

Dave lives in a handsome, modest, little townhouse on a quiet cul-de-sac on a hill at the edge of Cedar Rapids. He’s the president of his homeowners association. There’s 17 homes on this little street. And this is just as far as you could get from a danger zone. It looks as safe as could be. But in January, they got a letter from the company that insures him and his neighbors, saying his policy was being canceled, even though it wasn’t as though they’d just been hit by some giant storm.

So then what was the reason they gave?

They didn’t give a reason. And I think people might not realize, insurers don’t have to give a reason. Insurance policies are year to year. And if your insurance company decides that you’re too much of a risk or your neighborhood is too much of a risk or your state is too much of a risk, they can just leave. They can send you a letter saying, forget it. We’re canceling your insurance. There’s almost no protection people have.

And in this case, the reason was that this insurance company was losing too much money in Iowa and didn’t want to keep on writing homeowner’s insurance in the state. That was the situation that Dave shared with tens of thousands of people across the state that were all getting similar letters.

What made Dave’s situation a little more challenging was that he couldn’t get new insurance. He tried for months through agent after agent after agent. And every company told him the same thing. We won’t cover you. Even though these homes are perfectly safe in a safe part of the state, nobody would say yes. And it took them until basically two days before their insurance policy was going to run out until they finally found new coverage that was far more expensive and far more bare-bones than what they’d had.

But at least it was something.

It was something. But the problem was it wasn’t that good. Under this new policy, if Dave’s street got hit by another big windstorm, the damage from that storm and fixing that damage would wipe out all the savings set aside by these homeowners. The deductible would be crushingly high — $120,000 — to replace those roofs if the worst happened because the insurance money just wouldn’t cover anywhere close to the cost of rebuilding.

He said to me, we didn’t do anything wrong. This is just what insurance looks like today. And today, it’s us in Cedar Rapids. Everyone, though, is going to face a situation like this eventually. And Dave is right. I talked to insurance agents around the country. And they confirmed for me that this kind of a shift towards a new type of insurance, insurance that’s more expensive and doesn’t cover as much and makes it harder to rebuild after a big disaster, it’s becoming more and more common around the country.

So, Chris, if Dave and the people you spoke to in Iowa were really evidence that your hunch was right, that the problem is spreading and rapidly, what are the possible fixes here?

The fix that people seem most hopeful about is this idea that, what if you could reduce the risk and cause there to be less damage in the first place? So what some states are doing is they’re trying to encourage homeowners to spend more money on hardening their home or adding a new roof or, if it’s a wildfire zone, cut back the vegetation, things that can reduce your risk of having really serious losses. And to help pay for that, they’re telling insurers, you’ve got to offer a discount to people who do that.

And everyone who works in this field says, in theory, that’s the right approach. The problem is, number one, hardening a home costs a fantastic amount of money. So doing this at scale is hugely expensive. Number two, it takes a long time to actually get enough homes hardened in this way that you can make a real dent for insurance companies. We’re talking about years or probably decades before that has a real effect, if it ever works.

OK. So that sounds not particularly realistic, given the urgency and the timeline we’re on here. So what else are people looking at?

Option number two is the government gets involved. And instead of most Americans buying home insurance from a private company, they start buying it from government programs that are designed to make sure that people, even in risky places, can still buy insurance. That would be just a gargantuan undertaking. The idea of the government providing homeowner’s insurance because private companies can’t or won’t would lead to one of the biggest government programs that exists, if we could even do it.

So huge change, like the federal government actually trying to write these markets by itself by providing homeowner’s insurance. But is that really feasible?

Well, in some areas, we’re actually already doing it. The government already provides flood insurance because for decades, most private insurers have not wanted to cover flood. It’s too risky. It’s too expensive. But that change, with governments taking over that role, creates a new problem of its own because the government providing flood insurance that you otherwise couldn’t get means people have been building and building in flood-prone areas because they know they can get that guaranteed flood insurance.

Interesting. So that’s a huge new downside. The government would be incentivizing people to move to places that they shouldn’t be.

That’s right. But there’s even one more problem with that approach of using the government to try to solve this problem, which is these costs keep growing. The number of billion-dollar disasters the US experiences every year keeps going up. And at some point, even if the government pays the cost through some sort of subsidized insurance, what happens when that cost is so great that we can no longer afford to pay it? That’s the really hard question that no official can answer.

So that’s pretty doomsday, Chris. Are we looking at the end of insurance?

I think it’s fair to say that we’re looking at the end of insurance as we know it, the end of insurance that means most Americans can rest assured that if they get hit by a disaster, their insurance company will provide enough money they can rebuild. That idea might be going away. And what it shows is maybe the threat of climate change isn’t quite what we thought.

Maybe instead of climate change wrecking communities in the form of a big storm or a wildfire or a flood, maybe even before those things happen, climate change can wreck communities by something as seemingly mundane and even boring as insurance. Maybe the harbinger of doom is not a giant storm but an anodyne letter from your insurance company, saying, we’re sorry to inform you we can no longer cover your home.

Maybe the future of climate change is best seen not by poring over weather data from NOAA but by poring over spreadsheets from rating firms, showing the profitability from insurance companies, and how bit by bit, that money that they’re losing around the country tells its own story. And the story is these shocks are actually already here.

Chris, as always, terrifying to talk to you.

Always a pleasure, Sabrina.

Here’s what else you should know today. On Tuesday, the United Nations has reclassified the number of women and children killed in Gaza, saying that it does not have enough identifying information to know exactly how many of the total dead are women and children. The UN now estimates that about 5,000 women and about 8,000 children have been killed, figures that are about half of what it was previously citing. The UN says the numbers dropped because it is using a more conservative estimate while waiting for information on about 10,000 other dead Gazans who have not yet been identified.

And Mike Johnson, the Speaker of the House, gave a press conference outside the court in Lower Manhattan, where Michael Cohen, the former fixer for Donald Trump, was testifying for a second day, answering questions from Trump’s lawyers. Trump is bound by a gag order. So Johnson joined other stand-ins for the former president to discredit the proceedings. Johnson, one of the most important Republicans in the country, attacked Cohen but also the trial itself, calling it a sham and political theater.

Today’s episode was produced by Nina Feldman, Shannon Lin, and Jessica Cheung. It was edited by MJ Davis Lin, with help from Michael Benoist, contains original music by Dan Powell, Marion Lozano, and Rowan Niemisto, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly.

That’s it for “The Daily.” I’m Sabrina Tavernise. See you tomorrow.

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Hosted by Sabrina Tavernise

Featuring Christopher Flavelle

Produced by Nina Feldman ,  Shannon M. Lin and Jessica Cheung

Edited by MJ Davis Lin

With Michael Benoist

Original music by Dan Powell ,  Marion Lozano and Rowan Niemisto

Engineered by Alyssa Moxley

Listen and follow The Daily Apple Podcasts | Spotify | Amazon Music | YouTube

Across the United States, more frequent extreme weather is starting to cause the home insurance market to buckle, even for those who have paid their premiums dutifully year after year.

Christopher Flavelle, a climate reporter, discusses a Times investigation into one of the most consequential effects of the changes.

On today’s episode

Christopher Flavelle , a climate change reporter for The New York Times.

Background reading

As American insurers bleed cash from climate shocks , homeowners lose.

See how the home insurance crunch affects the market in each state .

Here are four takeaways from The Times’s investigation.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

Christopher Flavelle contributed reporting.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Mike Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, John Ketchum, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Dan Farrell, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Summer Thomad, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Renan Borelli, Maddy Masiello, Isabella Anderson and Nina Lassam.

Christopher Flavelle is a Times reporter who writes about how the United States is trying to adapt to the effects of climate change. More about Christopher Flavelle

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