theory of problem solving behavior

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The Oxford Handbook of Cognitive Psychology

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48 Problem Solving

Department of Psychological and Brain Sciences, University of California, Santa Barbara

Published: 03 June 2013
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Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. Classic theoretical approaches to the study of problem solving are associationism, Gestalt, and information processing. Current issues and suggested future issues include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common themes concern the domain specificity of problem solving and a focus on problem solving in authentic contexts.

The study of problem solving begins with defining problem solving, problem, and problem types. This introduction to problem solving is rounded out with an examination of cognitive processes in problem solving, the role of knowledge in problem solving, and historical approaches to the study of problem solving.

Definition of Problem Solving

Problem solving refers to cognitive processing directed at achieving a goal for which the problem solver does not initially know a solution method. This definition consists of four major elements (Mayer, 1992 ; Mayer & Wittrock, 2006 ):

Cognitive —Problem solving occurs within the problem solver’s cognitive system and can only be inferred indirectly from the problem solver’s behavior (including biological changes, introspections, and actions during problem solving). Process —Problem solving involves mental computations in which some operation is applied to a mental representation, sometimes resulting in the creation of a new mental representation. Directed —Problem solving is aimed at achieving a goal. Personal —Problem solving depends on the existing knowledge of the problem solver so that what is a problem for one problem solver may not be a problem for someone who already knows a solution method.

The definition is broad enough to include a wide array of cognitive activities such as deciding which apartment to rent, figuring out how to use a cell phone interface, playing a game of chess, making a medical diagnosis, finding the answer to an arithmetic word problem, or writing a chapter for a handbook. Problem solving is pervasive in human life and is crucial for human survival. Although this chapter focuses on problem solving in humans, problem solving also occurs in nonhuman animals and in intelligent machines.

How is problem solving related to other forms of high-level cognition processing, such as thinking and reasoning? Thinking refers to cognitive processing in individuals but includes both directed thinking (which corresponds to the definition of problem solving) and undirected thinking such as daydreaming (which does not correspond to the definition of problem solving). Thus, problem solving is a type of thinking (i.e., directed thinking).

Reasoning refers to problem solving within specific classes of problems, such as deductive reasoning or inductive reasoning. In deductive reasoning, the reasoner is given premises and must derive a conclusion by applying the rules of logic. For example, given that “A is greater than B” and “B is greater than C,” a reasoner can conclude that “A is greater than C.” In inductive reasoning, the reasoner is given (or has experienced) a collection of examples or instances and must infer a rule. For example, given that X, C, and V are in the “yes” group and x, c, and v are in the “no” group, the reasoning may conclude that B is in “yes” group because it is in uppercase format. Thus, reasoning is a type of problem solving.

Definition of Problem

A problem occurs when someone has a goal but does not know to achieve it. This definition is consistent with how the Gestalt psychologist Karl Duncker ( 1945 , p. 1) defined a problem in his classic monograph, On Problem Solving : “A problem arises when a living creature has a goal but does not know how this goal is to be reached.” However, today researchers recognize that the definition should be extended to include problem solving by intelligent machines. This definition can be clarified using an information processing approach by noting that a problem occurs when a situation is in the given state, the problem solver wants the situation to be in the goal state, and there is no obvious way to move from the given state to the goal state (Newell & Simon, 1972 ). Accordingly, the three main elements in describing a problem are the given state (i.e., the current state of the situation), the goal state (i.e., the desired state of the situation), and the set of allowable operators (i.e., the actions the problem solver is allowed to take). The definition of “problem” is broad enough to include the situation confronting a physician who wishes to make a diagnosis on the basis of preliminary tests and a patient examination, as well as a beginning physics student trying to solve a complex physics problem.

Types of Problems

It is customary in the problem-solving literature to make a distinction between routine and nonroutine problems. Routine problems are problems that are so familiar to the problem solver that the problem solver knows a solution method. For example, for most adults, “What is 365 divided by 12?” is a routine problem because they already know the procedure for long division. Nonroutine problems are so unfamiliar to the problem solver that the problem solver does not know a solution method. For example, figuring out the best way to set up a funding campaign for a nonprofit charity is a nonroutine problem for most volunteers. Technically, routine problems do not meet the definition of problem because the problem solver has a goal but knows how to achieve it. Much research on problem solving has focused on routine problems, although most interesting problems in life are nonroutine.

Another customary distinction is between well-defined and ill-defined problems. Well-defined problems have a clearly specified given state, goal state, and legal operators. Examples include arithmetic computation problems or games such as checkers or tic-tac-toe. Ill-defined problems have a poorly specified given state, goal state, or legal operators, or a combination of poorly defined features. Examples include solving the problem of global warming or finding a life partner. Although, ill-defined problems are more challenging, much research in problem solving has focused on well-defined problems.

Cognitive Processes in Problem Solving

The process of problem solving can be broken down into two main phases: problem representation , in which the problem solver builds a mental representation of the problem situation, and problem solution , in which the problem solver works to produce a solution. The major subprocess in problem representation is representing , which involves building a situation model —that is, a mental representation of the situation described in the problem. The major subprocesses in problem solution are planning , which involves devising a plan for how to solve the problem; executing , which involves carrying out the plan; and monitoring , which involves evaluating and adjusting one’s problem solving.

For example, given an arithmetic word problem such as “Alice has three marbles. Sarah has two more marbles than Alice. How many marbles does Sarah have?” the process of representing involves building a situation model in which Alice has a set of marbles, there is set of marbles for the difference between the two girls, and Sarah has a set of marbles that consists of Alice’s marbles and the difference set. In the planning process, the problem solver sets a goal of adding 3 and 2. In the executing process, the problem solver carries out the computation, yielding an answer of 5. In the monitoring process, the problem solver looks over what was done and concludes that 5 is a reasonable answer. In most complex problem-solving episodes, the four cognitive processes may not occur in linear order, but rather may interact with one another. Although some research focuses mainly on the execution process, problem solvers may tend to have more difficulty with the processes of representing, planning, and monitoring.

Knowledge for Problem Solving

An important theme in problem-solving research is that problem-solving proficiency on any task depends on the learner’s knowledge (Anderson et al., 2001 ; Mayer, 1992 ). Five kinds of knowledge are as follows:

Facts —factual knowledge about the characteristics of elements in the world, such as “Sacramento is the capital of California” Concepts —conceptual knowledge, including categories, schemas, or models, such as knowing the difference between plants and animals or knowing how a battery works Procedures —procedural knowledge of step-by-step processes, such as how to carry out long-division computations Strategies —strategic knowledge of general methods such as breaking a problem into parts or thinking of a related problem Beliefs —attitudinal knowledge about how one’s cognitive processing works such as thinking, “I’m good at this”

Although some research focuses mainly on the role of facts and procedures in problem solving, complex problem solving also depends on the problem solver’s concepts, strategies, and beliefs (Mayer, 1992 ).

Historical Approaches to Problem Solving

Psychological research on problem solving began in the early 1900s, as an outgrowth of mental philosophy (Humphrey, 1963 ; Mandler & Mandler, 1964 ). Throughout the 20th century four theoretical approaches developed: early conceptions, associationism, Gestalt psychology, and information processing.

Early Conceptions

The start of psychology as a science can be set at 1879—the year Wilhelm Wundt opened the first world’s psychology laboratory in Leipzig, Germany, and sought to train the world’s first cohort of experimental psychologists. Instead of relying solely on philosophical speculations about how the human mind works, Wundt sought to apply the methods of experimental science to issues addressed in mental philosophy. His theoretical approach became structuralism —the analysis of consciousness into its basic elements.

Wundt’s main contribution to the study of problem solving, however, was to call for its banishment. According to Wundt, complex cognitive processing was too complicated to be studied by experimental methods, so “nothing can be discovered in such experiments” (Wundt, 1911/1973 ). Despite his admonishments, however, a group of his former students began studying thinking mainly in Wurzburg, Germany. Using the method of introspection, subjects were asked to describe their thought process as they solved word association problems, such as finding the superordinate of “newspaper” (e.g., an answer is “publication”). Although the Wurzburg group—as they came to be called—did not produce a new theoretical approach, they found empirical evidence that challenged some of the key assumptions of mental philosophy. For example, Aristotle had proclaimed that all thinking involves mental imagery, but the Wurzburg group was able to find empirical evidence for imageless thought .

Associationism

The first major theoretical approach to take hold in the scientific study of problem solving was associationism —the idea that the cognitive representations in the mind consist of ideas and links between them and that cognitive processing in the mind involves following a chain of associations from one idea to the next (Mandler & Mandler, 1964 ; Mayer, 1992 ). For example, in a classic study, E. L. Thorndike ( 1911 ) placed a hungry cat in what he called a puzzle box—a wooden crate in which pulling a loop of string that hung from overhead would open a trap door to allow the cat to escape to a bowl of food outside the crate. Thorndike placed the cat in the puzzle box once a day for several weeks. On the first day, the cat engaged in many extraneous behaviors such as pouncing against the wall, pushing its paws through the slats, and meowing, but on successive days the number of extraneous behaviors tended to decrease. Overall, the time required to get out of the puzzle box decreased over the course of the experiment, indicating the cat was learning how to escape.

Thorndike’s explanation for how the cat learned to solve the puzzle box problem is based on an associationist view: The cat begins with a habit family hierarchy —a set of potential responses (e.g., pouncing, thrusting, meowing, etc.) all associated with the same stimulus (i.e., being hungry and confined) and ordered in terms of strength of association. When placed in the puzzle box, the cat executes its strongest response (e.g., perhaps pouncing against the wall), but when it fails, the strength of the association is weakened, and so on for each unsuccessful action. Eventually, the cat gets down to what was initially a weak response—waving its paw in the air—but when that response leads to accidentally pulling the string and getting out, it is strengthened. Over the course of many trials, the ineffective responses become weak and the successful response becomes strong. Thorndike refers to this process as the law of effect : Responses that lead to dissatisfaction become less associated with the situation and responses that lead to satisfaction become more associated with the situation. According to Thorndike’s associationist view, solving a problem is simply a matter of trial and error and accidental success. A major challenge to assocationist theory concerns the nature of transfer—that is, where does a problem solver find a creative solution that has never been performed before? Associationist conceptions of cognition can be seen in current research, including neural networks, connectionist models, and parallel distributed processing models (Rogers & McClelland, 2004 ).

Gestalt Psychology

The Gestalt approach to problem solving developed in the 1930s and 1940s as a counterbalance to the associationist approach. According to the Gestalt approach, cognitive representations consist of coherent structures (rather than individual associations) and the cognitive process of problem solving involves building a coherent structure (rather than strengthening and weakening of associations). For example, in a classic study, Kohler ( 1925 ) placed a hungry ape in a play yard that contained several empty shipping crates and a banana attached overhead but out of reach. Based on observing the ape in this situation, Kohler noted that the ape did not randomly try responses until one worked—as suggested by Thorndike’s associationist view. Instead, the ape stood under the banana, looked up at it, looked at the crates, and then in a flash of insight stacked the crates under the bananas as a ladder, and walked up the steps in order to reach the banana.

According to Kohler, the ape experienced a sudden visual reorganization in which the elements in the situation fit together in a way to solve the problem; that is, the crates could become a ladder that reduces the distance to the banana. Kohler referred to the underlying mechanism as insight —literally seeing into the structure of the situation. A major challenge of Gestalt theory is its lack of precision; for example, naming a process (i.e., insight) is not the same as explaining how it works. Gestalt conceptions can be seen in modern research on mental models and schemas (Gentner & Stevens, 1983 ).

Information Processing

The information processing approach to problem solving developed in the 1960s and 1970s and was based on the influence of the computer metaphor—the idea that humans are processors of information (Mayer, 2009 ). According to the information processing approach, problem solving involves a series of mental computations—each of which consists of applying a process to a mental representation (such as comparing two elements to determine whether they differ).

In their classic book, Human Problem Solving , Newell and Simon ( 1972 ) proposed that problem solving involved a problem space and search heuristics . A problem space is a mental representation of the initial state of the problem, the goal state of the problem, and all possible intervening states (based on applying allowable operators). Search heuristics are strategies for moving through the problem space from the given to the goal state. Newell and Simon focused on means-ends analysis , in which the problem solver continually sets goals and finds moves to accomplish goals.

Newell and Simon used computer simulation as a research method to test their conception of human problem solving. First, they asked human problem solvers to think aloud as they solved various problems such as logic problems, chess, and cryptarithmetic problems. Then, based on an information processing analysis, Newell and Simon created computer programs that solved these problems. In comparing the solution behavior of humans and computers, they found high similarity, suggesting that the computer programs were solving problems using the same thought processes as humans.

An important advantage of the information processing approach is that problem solving can be described with great clarity—as a computer program. An important limitation of the information processing approach is that it is most useful for describing problem solving for well-defined problems rather than ill-defined problems. The information processing conception of cognition lives on as a keystone of today’s cognitive science (Mayer, 2009 ).

Classic Issues in Problem Solving

Three classic issues in research on problem solving concern the nature of transfer (suggested by the associationist approach), the nature of insight (suggested by the Gestalt approach), and the role of problem-solving heuristics (suggested by the information processing approach).

Transfer refers to the effects of prior learning on new learning (or new problem solving). Positive transfer occurs when learning A helps someone learn B. Negative transfer occurs when learning A hinders someone from learning B. Neutral transfer occurs when learning A has no effect on learning B. Positive transfer is a central goal of education, but research shows that people often do not transfer what they learned to solving problems in new contexts (Mayer, 1992 ; Singley & Anderson, 1989 ).

Three conceptions of the mechanisms underlying transfer are specific transfer , general transfer , and specific transfer of general principles . Specific transfer refers to the idea that learning A will help someone learn B only if A and B have specific elements in common. For example, learning Spanish may help someone learn Latin because some of the vocabulary words are similar and the verb conjugation rules are similar. General transfer refers to the idea that learning A can help someone learn B even they have nothing specifically in common but A helps improve the learner’s mind in general. For example, learning Latin may help people learn “proper habits of mind” so they are better able to learn completely unrelated subjects as well. Specific transfer of general principles is the idea that learning A will help someone learn B if the same general principle or solution method is required for both even if the specific elements are different.

In a classic study, Thorndike and Woodworth ( 1901 ) found that students who learned Latin did not subsequently learn bookkeeping any better than students who had not learned Latin. They interpreted this finding as evidence for specific transfer—learning A did not transfer to learning B because A and B did not have specific elements in common. Modern research on problem-solving transfer continues to show that people often do not demonstrate general transfer (Mayer, 1992 ). However, it is possible to teach people a general strategy for solving a problem, so that when they see a new problem in a different context they are able to apply the strategy to the new problem (Judd, 1908 ; Mayer, 2008 )—so there is also research support for the idea of specific transfer of general principles.

Insight refers to a change in a problem solver’s mind from not knowing how to solve a problem to knowing how to solve it (Mayer, 1995 ; Metcalfe & Wiebe, 1987 ). In short, where does the idea for a creative solution come from? A central goal of problem-solving research is to determine the mechanisms underlying insight.

The search for insight has led to five major (but not mutually exclusive) explanatory mechanisms—insight as completing a schema, insight as suddenly reorganizing visual information, insight as reformulation of a problem, insight as removing mental blocks, and insight as finding a problem analog (Mayer, 1995 ). Completing a schema is exemplified in a study by Selz (Fridja & de Groot, 1982 ), in which people were asked to think aloud as they solved word association problems such as “What is the superordinate for newspaper?” To solve the problem, people sometimes thought of a coordinate, such as “magazine,” and then searched for a superordinate category that subsumed both terms, such as “publication.” According to Selz, finding a solution involved building a schema that consisted of a superordinate and two subordinate categories.

Reorganizing visual information is reflected in Kohler’s ( 1925 ) study described in a previous section in which a hungry ape figured out how to stack boxes as a ladder to reach a banana hanging above. According to Kohler, the ape looked around the yard and found the solution in a flash of insight by mentally seeing how the parts could be rearranged to accomplish the goal.

Reformulating a problem is reflected in a classic study by Duncker ( 1945 ) in which people are asked to think aloud as they solve the tumor problem—how can you destroy a tumor in a patient without destroying surrounding healthy tissue by using rays that at sufficient intensity will destroy any tissue in their path? In analyzing the thinking-aloud protocols—that is, transcripts of what the problem solvers said—Duncker concluded that people reformulated the goal in various ways (e.g., avoid contact with healthy tissue, immunize healthy tissue, have ray be weak in healthy tissue) until they hit upon a productive formulation that led to the solution (i.e., concentrating many weak rays on the tumor).

Removing mental blocks is reflected in classic studies by Duncker ( 1945 ) in which solving a problem involved thinking of a novel use for an object, and by Luchins ( 1942 ) in which solving a problem involved not using a procedure that had worked well on previous problems. Finding a problem analog is reflected in classic research by Wertheimer ( 1959 ) in which learning to find the area of a parallelogram is supported by the insight that one could cut off the triangle on one side and place it on the other side to form a rectangle—so a parallelogram is really a rectangle in disguise. The search for insight along each of these five lines continues in current problem-solving research.

Heuristics are problem-solving strategies, that is, general approaches to how to solve problems. Newell and Simon ( 1972 ) suggested three general problem-solving heuristics for moving from a given state to a goal state: random trial and error , hill climbing , and means-ends analysis . Random trial and error involves randomly selecting a legal move and applying it to create a new problem state, and repeating that process until the goal state is reached. Random trial and error may work for simple problems but is not efficient for complex ones. Hill climbing involves selecting the legal move that moves the problem solver closer to the goal state. Hill climbing will not work for problems in which the problem solver must take a move that temporarily moves away from the goal as is required in many problems.

Means-ends analysis involves creating goals and seeking moves that can accomplish the goal. If a goal cannot be directly accomplished, a subgoal is created to remove one or more obstacles. Newell and Simon ( 1972 ) successfully used means-ends analysis as the search heuristic in a computer program aimed at general problem solving, that is, solving a diverse collection of problems. However, people may also use specific heuristics that are designed to work for specific problem-solving situations (Gigerenzer, Todd, & ABC Research Group, 1999 ; Kahneman & Tversky, 1984 ).

Current and Future Issues in Problem Solving

Eight current issues in problem solving involve decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific problem solving, everyday thinking, and the cognitive neuroscience of problem solving.

Decision Making

Decision making refers to the cognitive processing involved in choosing between two or more alternatives (Baron, 2000 ; Markman & Medin, 2002 ). For example, a decision-making task may involve choosing between getting $240 for sure or having a 25% change of getting $1000. According to economic theories such as expected value theory, people should chose the second option, which is worth $250 (i.e., .25 x $1000) rather than the first option, which is worth $240 (1.00 x $240), but psychological research shows that most people prefer the first option (Kahneman & Tversky, 1984 ).

Research on decision making has generated three classes of theories (Markman & Medin, 2002 ): descriptive theories, such as prospect theory (Kahneman & Tversky), which are based on the ideas that people prefer to overweight the cost of a loss and tend to overestimate small probabilities; heuristic theories, which are based on the idea that people use a collection of short-cut strategies such as the availability heuristic (Gigerenzer et al., 1999 ; Kahneman & Tversky, 2000 ); and constructive theories, such as mental accounting (Kahneman & Tversky, 2000 ), in which people build a narrative to justify their choices to themselves. Future research is needed to examine decision making in more realistic settings.

Intelligence and Creativity

Although researchers do not have complete consensus on the definition of intelligence (Sternberg, 1990 ), it is reasonable to view intelligence as the ability to learn or adapt to new situations. Fluid intelligence refers to the potential to solve problems without any relevant knowledge, whereas crystallized intelligence refers to the potential to solve problems based on relevant prior knowledge (Sternberg & Gregorenko, 2003 ). As people gain more experience in a field, their problem-solving performance depends more on crystallized intelligence (i.e., domain knowledge) than on fluid intelligence (i.e., general ability) (Sternberg & Gregorenko, 2003 ). The ability to monitor and manage one’s cognitive processing during problem solving—which can be called metacognition —is an important aspect of intelligence (Sternberg, 1990 ). Research is needed to pinpoint the knowledge that is needed to support intelligent performance on problem-solving tasks.

Creativity refers to the ability to generate ideas that are original (i.e., other people do not think of the same idea) and functional (i.e., the idea works; Sternberg, 1999 ). Creativity is often measured using tests of divergent thinking —that is, generating as many solutions as possible for a problem (Guilford, 1967 ). For example, the uses test asks people to list as many uses as they can think of for a brick. Creativity is different from intelligence, and it is at the heart of creative problem solving—generating a novel solution to a problem that the problem solver has never seen before. An important research question concerns whether creative problem solving depends on specific knowledge or creativity ability in general.

Teaching of Thinking Skills

How can people learn to be better problem solvers? Mayer ( 2008 ) proposes four questions concerning teaching of thinking skills:

What to teach —Successful programs attempt to teach small component skills (such as how to generate and evaluate hypotheses) rather than improve the mind as a single monolithic skill (Covington, Crutchfield, Davies, & Olton, 1974 ). How to teach —Successful programs focus on modeling the process of problem solving rather than solely reinforcing the product of problem solving (Bloom & Broder, 1950 ). Where to teach —Successful programs teach problem-solving skills within the specific context they will be used rather than within a general course on how to solve problems (Nickerson, 1999 ). When to teach —Successful programs teaching higher order skills early rather than waiting until lower order skills are completely mastered (Tharp & Gallimore, 1988 ).

Overall, research on teaching of thinking skills points to the domain specificity of problem solving; that is, successful problem solving depends on the problem solver having domain knowledge that is relevant to the problem-solving task.

Expert Problem Solving

Research on expertise is concerned with differences between how experts and novices solve problems (Ericsson, Feltovich, & Hoffman, 2006 ). Expertise can be defined in terms of time (e.g., 10 years of concentrated experience in a field), performance (e.g., earning a perfect score on an assessment), or recognition (e.g., receiving a Nobel Prize or becoming Grand Master in chess). For example, in classic research conducted in the 1940s, de Groot ( 1965 ) found that chess experts did not have better general memory than chess novices, but they did have better domain-specific memory for the arrangement of chess pieces on the board. Chase and Simon ( 1973 ) replicated this result in a better controlled experiment. An explanation is that experts have developed schemas that allow them to chunk collections of pieces into a single configuration.

In another landmark study, Larkin et al. ( 1980 ) compared how experts (e.g., physics professors) and novices (e.g., first-year physics students) solved textbook physics problems about motion. Experts tended to work forward from the given information to the goal, whereas novices tended to work backward from the goal to the givens using a means-ends analysis strategy. Experts tended to store their knowledge in an integrated way, whereas novices tended to store their knowledge in isolated fragments. In another study, Chi, Feltovich, and Glaser ( 1981 ) found that experts tended to focus on the underlying physics concepts (such as conservation of energy), whereas novices tended to focus on the surface features of the problem (such as inclined planes or springs). Overall, research on expertise is useful in pinpointing what experts know that is different from what novices know. An important theme is that experts rely on domain-specific knowledge rather than solely general cognitive ability.

Analogical Reasoning

Analogical reasoning occurs when people solve one problem by using their knowledge about another problem (Holyoak, 2005 ). For example, suppose a problem solver learns how to solve a problem in one context using one solution method and then is given a problem in another context that requires the same solution method. In this case, the problem solver must recognize that the new problem has structural similarity to the old problem (i.e., it may be solved by the same method), even though they do not have surface similarity (i.e., the cover stories are different). Three steps in analogical reasoning are recognizing —seeing that a new problem is similar to a previously solved problem; abstracting —finding the general method used to solve the old problem; and mapping —using that general method to solve the new problem.

Research on analogical reasoning shows that people often do not recognize that a new problem can be solved by the same method as a previously solved problem (Holyoak, 2005 ). However, research also shows that successful analogical transfer to a new problem is more likely when the problem solver has experience with two old problems that have the same underlying structural features (i.e., they are solved by the same principle) but different surface features (i.e., they have different cover stories) (Holyoak, 2005 ). This finding is consistent with the idea of specific transfer of general principles as described in the section on “Transfer.”

Mathematical and Scientific Problem Solving

Research on mathematical problem solving suggests that five kinds of knowledge are needed to solve arithmetic word problems (Mayer, 2008 ):

Factual knowledge —knowledge about the characteristics of problem elements, such as knowing that there are 100 cents in a dollar Schematic knowledge —knowledge of problem types, such as being able to recognize time-rate-distance problems Strategic knowledge —knowledge of general methods, such as how to break a problem into parts Procedural knowledge —knowledge of processes, such as how to carry our arithmetic operations Attitudinal knowledge —beliefs about one’s mathematical problem-solving ability, such as thinking, “I am good at this”

People generally possess adequate procedural knowledge but may have difficulty in solving mathematics problems because they lack factual, schematic, strategic, or attitudinal knowledge (Mayer, 2008 ). Research is needed to pinpoint the role of domain knowledge in mathematical problem solving.

Research on scientific problem solving shows that people harbor misconceptions, such as believing that a force is needed to keep an object in motion (McCloskey, 1983 ). Learning to solve science problems involves conceptual change, in which the problem solver comes to recognize that previous conceptions are wrong (Mayer, 2008 ). Students can be taught to engage in scientific reasoning such as hypothesis testing through direct instruction in how to control for variables (Chen & Klahr, 1999 ). A central theme of research on scientific problem solving concerns the role of domain knowledge.

Everyday Thinking

Everyday thinking refers to problem solving in the context of one’s life outside of school. For example, children who are street vendors tend to use different procedures for solving arithmetic problems when they are working on the streets than when they are in school (Nunes, Schlieman, & Carraher, 1993 ). This line of research highlights the role of situated cognition —the idea that thinking always is shaped by the physical and social context in which it occurs (Robbins & Aydede, 2009 ). Research is needed to determine how people solve problems in authentic contexts.

Cognitive Neuroscience of Problem Solving

The cognitive neuroscience of problem solving is concerned with the brain activity that occurs during problem solving. For example, using fMRI brain imaging methodology, Goel ( 2005 ) found that people used the language areas of the brain to solve logical reasoning problems presented in sentences (e.g., “All dogs are pets…”) and used the spatial areas of the brain to solve logical reasoning problems presented in abstract letters (e.g., “All D are P…”). Cognitive neuroscience holds the potential to make unique contributions to the study of problem solving.

Problem solving has always been a topic at the fringe of cognitive psychology—too complicated to study intensively but too important to completely ignore. Problem solving—especially in realistic environments—is messy in comparison to studying elementary processes in cognition. The field remains fragmented in the sense that topics such as decision making, reasoning, intelligence, expertise, mathematical problem solving, everyday thinking, and the like are considered to be separate topics, each with its own separate literature. Yet some recurring themes are the role of domain-specific knowledge in problem solving and the advantages of studying problem solving in authentic contexts.

Future Directions

Some important issues for future research include the three classic issues examined in this chapter—the nature of problem-solving transfer (i.e., How are people able to use what they know about previous problem solving to help them in new problem solving?), the nature of insight (e.g., What is the mechanism by which a creative solution is constructed?), and heuristics (e.g., What are some teachable strategies for problem solving?). In addition, future research in problem solving should continue to pinpoint the role of domain-specific knowledge in problem solving, the nature of cognitive ability in problem solving, how to help people develop proficiency in solving problems, and how to provide aids for problem solving.

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In This Article Expand or collapse the "in this article" section Problem Solving and Decision Making

Introduction.

General Approaches to Problem Solving
Representational Accounts
Problem Space and Search
Working Memory and Problem Solving
Domain-Specific Problem Solving
The Rational Approach
Prospect Theory
Dual-Process Theory
Cognitive Heuristics and Biases

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Problem Solving and Decision Making by Emily G. Nielsen , John Paul Minda LAST REVIEWED: 26 June 2019 LAST MODIFIED: 26 June 2019 DOI: 10.1093/obo/9780199828340-0246

Problem solving and decision making are both examples of complex, higher-order thinking. Both involve the assessment of the environment, the involvement of working memory or short-term memory, reliance on long term memory, effects of knowledge, and the application of heuristics to complete a behavior. A problem can be defined as an impasse or gap between a current state and a desired goal state. Problem solving is the set of cognitive operations that a person engages in to change the current state, to go beyond the impasse, and achieve a desired outcome. Problem solving involves the mental representation of the problem state and the manipulation of this representation in order to move closer to the goal. Problems can vary in complexity, abstraction, and how well defined (or not) the initial state and the goal state are. Research has generally approached problem solving by examining the behaviors and cognitive processes involved, and some work has examined problem solving using computational processes as well. Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions that deviate from rationality. The current bibliography first outlines some general resources on the psychology of problem solving and decision making before examining each of these topics in detail. Specifically, this review covers cognitive, neuroscientific, and computational approaches to problem solving, as well as decision making models and cognitive heuristics and biases.

General Overviews

Current research in the area of problem solving and decision making is published in both general and specialized scientific journals. Theoretical and scholarly work is often summarized and developed in full-length books and chapter. These may focus on the subfields of problem solving and decision making or the larger field of thinking and higher-order cognition.

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Problem-Solving Theory: The Task-Centred Model

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First Online: 12 April 2022
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Blanca M. Ramos 5 &
Randall L. Stetson 6

Part of the book series: Social Work ((SOWO))

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This chapter examines the task-centred model to illustrate the application of problem-solving theory for social work intervention. First, it provides a brief description of the problem-solving model. Its historical development and key principles and concepts are presented. Next, the chapter offers a general overview of the crisis intervention model. The task-centred model and crisis intervention share principles and methods drawn from problem-solving theory. The remainder of the chapter focuses on the task-centred model. It reviews its historical background, viability as a framework for social work generalist practice, as well as its applicability with diverse client populations and across cultural settings. The structured steps that guide task-centred implementation throughout the helping process are described. A brief critical review of the model’s strengths and limitations is provided. The chapter concludes with a brief summary and some closing thoughts.

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Ramos, B.M., Stetson, R.L. (2022). Problem-Solving Theory: The Task-Centred Model. In: Hölscher, D., Hugman, R., McAuliffe, D. (eds) Social Work Theory and Ethics. Social Work. Springer, Singapore. https://doi.org/10.1007/978-981-16-3059-0_9-1

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DOI : https://doi.org/10.1007/978-981-16-3059-0_9-1

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Cognitive Behavioral Therapy

Solving problems the cognitive-behavioral way, problem solving is another part of behavioral therapy..

Posted February 2, 2022 | Reviewed by Ekua Hagan

What Is Cognitive Behavioral Therapy?
Find a therapist who practices CBT
Problem-solving is one technique used on the behavioral side of cognitive-behavioral therapy.
The problem-solving technique is an iterative, five-step process that requires one to identify the problem and test different solutions.
The technique differs from ad-hoc problem-solving in its suspension of judgment and evaluation of each solution.

As I have mentioned in previous posts, cognitive behavioral therapy is more than challenging negative, automatic thoughts. There is a whole behavioral piece of this therapy that focuses on what people do and how to change their actions to support their mental health. In this post, I’ll talk about the problem-solving technique from cognitive behavioral therapy and what makes it unique.

The problem-solving technique

While there are many different variations of this technique, I am going to describe the version I typically use, and which includes the main components of the technique:

The first step is to clearly define the problem. Sometimes, this includes answering a series of questions to make sure the problem is described in detail. Sometimes, the client is able to define the problem pretty clearly on their own. Sometimes, a discussion is needed to clearly outline the problem.

The next step is generating solutions without judgment. The "without judgment" part is crucial: Often when people are solving problems on their own, they will reject each potential solution as soon as they or someone else suggests it. This can lead to feeling helpless and also discarding solutions that would work.

The third step is evaluating the advantages and disadvantages of each solution. This is the step where judgment comes back.

Fourth, the client picks the most feasible solution that is most likely to work and they try it out.

The fifth step is evaluating whether the chosen solution worked, and if not, going back to step two or three to find another option. For step five, enough time has to pass for the solution to have made a difference.

This process is iterative, meaning the client and therapist always go back to the beginning to make sure the problem is resolved and if not, identify what needs to change.

Advantages of the problem-solving technique

The problem-solving technique might differ from ad hoc problem-solving in several ways. The most obvious is the suspension of judgment when coming up with solutions. We sometimes need to withhold judgment and see the solution (or problem) from a different perspective. Deliberately deciding not to judge solutions until later can help trigger that mindset change.

Another difference is the explicit evaluation of whether the solution worked. When people usually try to solve problems, they don’t go back and check whether the solution worked. It’s only if something goes very wrong that they try again. The problem-solving technique specifically includes evaluating the solution.

Lastly, the problem-solving technique starts with a specific definition of the problem instead of just jumping to solutions. To figure out where you are going, you have to know where you are.

One benefit of the cognitive behavioral therapy approach is the behavioral side. The behavioral part of therapy is a wide umbrella that includes problem-solving techniques among other techniques. Accessing multiple techniques means one is more likely to address the client’s main concern.

Salene M. W. Jones, Ph.D., is a clinical psychologist in Washington State.

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Front Psychol

The Role of Motivation in Complex Problem Solving

C. dominik güss.

1 Department of Psychology, University of North Florida, Jacksonville, FL, United States

Madison Lee Burger

Dietrich dörner.

2 Trimberg Research Academy, University of Bamberg, Bamberg, Germany

The role of motivation in complex problem solving

Previous research on Complex Problem Solving (CPS) has primarily focused on cognitive factors as outlined below. The current paper discusses the role of motivation during CPS and argues that motivation, emotion, and cognition interact and cannot be studied in an isolated manner. Motivation is the process that determines the energization and direction of behavior (Heckhausen, 1991 ).

Three motivation theories and their relation to CPS are examined: McClelland's achievement motivation, Maslow's hierarchy of needs, and Dörner's needs as outlined in PSI-theory. We chose these three theories for several reasons. First, space forces us to be selective. Second, the three theories are among the most prominent motivational theories. Finally, they are need theories postulating several motivations and not just one. A thinking-aloud protocol is provided to illustrate the role of motivational and cognitive dynamics in CPS.

Problems are part of all the domains of human life. The field of CPS investigates problems that are complex, dynamic, and non-transparent (Dörner, 1996 ). Complex problems consist of many interactively interrelated variables. Dynamic ones change and develop further over time, regardless of whether the involved people take action. And non-transparent problems have many aspects of the problem situation that are unclear or unknown to the involved people.

CPS researchers focus exactly on such kinds of problems. Under a narrow perspective, CPS can be defined as thinking that aims to overcome barriers and to reach goals in situations that are complex, dynamic, and non-transparent (Frensch and Funke, 1995 ). Indeed, past research has shown the influential role of task properties (Berry and Broadbent, 1984 ; Funke, 1985 ) and of cognitive factors on CPS strategies and performance, such as intelligence (e.g., Süß, 2001 ; Stadler et al., 2015 ), domain-specific knowledge (e.g., Wenke et al., 2005 ), cognitive biases and errors (e.g., Dörner, 1996 ; Güss et al., 2015 ), or self-reflection (e.g., Donovan et al., 2015 ).

Under a broader perspective, CPS can be defined as the study of cognitive, emotional, motivational, and social processes when people are confronted with such complex, dynamic and non-transparent problem situations (Schoppek and Putz-Osterloh, 2003 ; Dörner and Güss, 2011 , 2013 ; Funke, 2012 ). The assumption here is that focusing solely on cognitive processes reveals an incomplete picture or an inaccurate one.

To study CPS, researchers have often used computer-simulated problem scenarios also called microworlds or virtual environments or strategy games. In these situations, participants are confronted with a complex problem simulated on the computer from which they gather information, and identify solutions. These decisions are then implemented into the system and result in changes to the problem situation.

Previous research on motivation and CPS

The idea to study the interaction of motivation, emotion, and cognition is not new (Simon, 1967 ). However, in practice this has been rarely examined in the field of CPS. One study assessed the need for cognition (i.e., the tendency to engage in thinking and reflecting) and showed how high need of cognition was related to broader information collection and better performance in a management simulation (Nair and Ramnarayan, 2000 ).

Vollmeyer and Rheinberg ( 1999 , 2000 ) explored in two studies the role of motivational factors in CPS. They assessed mastery confidence (similar to self-efficacy), incompetence fear, interest, and challenge as motivational factors. Their results demonstrated that mastery confidence and incompetence fear were good predictors for learning and for knowledge acquisition.

CPS assessment

Before we describe three theories of motivation and how they might be related and applicable to CPS, we will briefly describe the WINFIRE computer simulation (Gerdes et al., 1993 ; Schaub, 2009 ) and provide a part of a thinking-aloud protocol of one participant while working on WINFIRE. WINFIRE is the simulation of small cities surrounded by forests. Participants take the role of fire-fighting commanders who try to protect cities and forests from approaching fires. Participants can give a series of commands to several fire trucks and helicopters. In WINFIRE quick decisions and multitasking are required in order to avoid fires spreading. In one study, participants were also instructed to think aloud, i.e., to say aloud everything that went through their minds while working on WINFIRE. These thinking-aloud protocols, also called verbal protocols, were audiotaped and transcribed in five countries and compared (see Güss et al., 2010 ).

The following is a verbatim WINFIRE thinking-aloud protocol of a US participant (Güss et al., 2010 ):

Ok, I don't see any fires yet. I'm trying to figure out how the helicopters pick up the water from the ponds. I put helicopters on patrol mode. Not really sure what that does. It doesn't seem to be moving. Oh, there it goes, it's moving…I guess you have to wait till there's a fire showing…Ok, fire just started in the middle, so I have to get some people to extinguish it. Ok, now I have another fire going here. I'm in trouble here. Ok. Ok, when I click extinguish, it don't seem to respond. Guess I'm not clear how to get trucks right to the fire. Ok, one fire has been extinguished, but a new one started in the same area. I'm getting more trucks out there trying to figure out, how to get helicopters to the pond. I still haven't figured that out, because they have to pick up the water. Ok, got a pretty good fire going here, so I'm going to put all the trucks on action, ok, water thing is making me mad. Ok. I'm not sure how it goes? Ok, the forest is burning up now—extinguish! Ok, ok, I'm in big trouble here…

Psychological theories of motivation and their application to CPS

Mcclelland's human motivation theory.

In his Human Motivation theory, McClelland distinguishes three needs (power, affiliation, and achievement) and argues that human motivation is a response to changes in affective states. A specific situation will cause a change in the affective state through the non-specific response of the autonomic nervous system. This response will motivate a person toward a goal to reach a different affective state (McClelland et al., 1953 ). An affective state may either be positive or negative, determining the direction of motivated behavior as either approach oriented, i.e., to maintain the state, or avoidance oriented, i.e., to avoid or discontinue the state (McClelland et al., 1953 ).

Motivation intensity varies among individuals based on perception of the stimulus and the adaptive abilities of the individual. Hence, when a discrepancy exists between expectation and perception, then a person will be motivated to eliminate this discrepancy (McClelland et al., 1953 ). In the statement from the thinking-aloud protocol we can infer the participant's achievement motivation, “ Guess I'm not clear how to get trucks right to the fire. Ok, one fire has been extinguished, but a new one started in the same area.” The participant at first begins to give up and reduce effort, but then achieves a step toward the goal. This achievement causes the reevaluation of the discrepancy between ability and the goal as not too large to overcome. This realization motivates the participant to continue working through the scenario. Whereas, the need for achievement seems to guide CPS, the needs for power and affiliation cannot be observed in the current thinking-aloud protocol.

Based on the previous discussion we can derive the following predictions:

Prediction 1 : Approach-orientation will lead to greater engagement in CPS compared to avoidance-orientation.
Prediction 2 : Based on an individual's experience either power, affiliation, or achievement will become dominant and guide the strategic approach in CPS.

Maslow's hierarchy of needs

Maslow's Hierarchy of Needs (Maslow, 1943 , 1954 ) suggests that everyone has five basic needs that act as motivating forces in a person's life. Maslow's hierarchy takes the form of a pyramid in which needs lower in the pyramid are primary motivators. They have to be met before higher needs can become motivating forces. At the bottom of the pyramid are the most basic needs beginning with physiological needs, such as hunger, and followed by safety needs. Then follow the psychological needs of belongingness and love, and then esteem. Once these four groups of needs have been met, a person may reach the self-fulfillment stage of self-actualization at which time a person can be motivated to achieve ones full potential (Maslow, 1943 ).

The first four groups of needs are external motivators because they motivate through both deficiency and fulfillment. In essence, a person fulfills a need which then releases the next unsatisfied need to be the dominant motivator (Maslow, 1943 , 1954 ). The safety need is often understood as seeking shelter, but Maslow also understands safety also as wanting “a predictable, orderly world” (Maslow, 1943 , p. 377), “an organized world rather than an unorganized or unstructured one” (Maslow, 1943 , p. 377). Safety refers to the “common preference for familiar rather than unfamiliar things” (Maslow, 1943 , p. 379).

In this sense the safety need becomes active when the person does not understand what is happening in the microworld, as the following passage of the thinking-aloud protocol illustrates. “ I put helicopters on patrol mode. Not really sure what that does. It doesn't seem to be moving.” The safety need is demonstrated in the person's desire for organization, since unknown and unexpected events are seen as threats to safety.

The esteem need as a motivator becomes evident through the statement, “ Guess I'm not clear how to get trucks right to the fire.” The participant becomes aware of his inability to control the situation which affects his self-esteem. The esteem need is never fulfilled in the described situation and remains the primary motivator. The following statements show how affected the participant's esteem need is by the inability to control the burning fires. “ Ok. I'm not sure how it goes? Ok, the forest is burning up now—extinguish! Ok, ok, I'm in big trouble .”

Prediction 3 : A strong safety need will be related to elaborate and detailed information collection in CPS compared to low safety need.
Prediction 4 : People with high esteem needs will be affected more by difficulties in CPS and engage more often in behaviors to protect their esteem compared to people with low esteem needs.

Dörner's theory of motivation as part of PSI-theory

PSI-theory described the interaction of cognitive, emotional, and motivational processes (Dörner, 2003 ; Dörner and Güss, 2011 ). Only a small part of the theory is examined here. Briefly, the theory encompasses five basic human needs: the existential needs (thirst, hunger, and pain avoidance), the sexuality need, and the social need for affiliation (group binding), the need for certainty (predictability), and the need for competence (mastery). If the environment is unpredictable, the certainty need becomes active. If we are not able to cope with problems, the competence need becomes active. The need for competence also becomes active when any other need becomes activated. With an increase in needs, the arousal increases.

The first three needs cannot be observed or inferred from the thinking-aloud protocol provided. Statements like, “I'm trying to figure out how the helicopters pick up the water from the ponds.” and “Guess I'm not clear how to get trucks right to the fire,” demonstrate the needs for certainty and competence, i.e., to make the environment predictable and controllable.

The following statements reflect the participant's need for competence, i.e., the inefficacy or incapability of coping with problems. “ I'm in trouble here…ok, water thing is making me mad .” Not being able to extinguish the fires that are approaching cities and are destroying forests is experienced as anger. The arousal rises as the resolution level of thinking decreases. So, the participant does not think about different options in an elaborate manner. Yet, the participant becomes aware of his failure. The competence need then causes the participant to search for possible solutions, “ I still haven't figured that out because they have to pick up the water…” The need for competence is satisfied when the problem solver is able to change either the environment or ones views of the environment.

Prediction 5 : A strong certainty need is positively related to a strong competence need.
Prediction 6 : High need for certainty paired with high need for competence can lead to safeguarding behavior, i.e., background monitoring.
Prediction 7 : An increase in the competence and uncertainty needs leads to increased arousal and a lower resolution level of thinking. CPS becomes one-dimensional and possible long-term and side-effects are not considered adequately.

Summary and evaluation

We have briefly discussed three motivation theories and their relation to CPS referring to one thinking-aloud protocol: McClelland's achievement motivation, Maslow's hierarchy of needs, and Dörner's needs as outlined in PSI-theory.

A Comparison of Three Need Theories in the Context of CPS.

Comparing the scope of the three theories and referring to the scope and different needs covered in the three theories, McClelland's theory describes three needs (power, affiliation, and achievement), Maslow's theory describes five groups of needs (physiological, safety, love and belonging, esteem, self-actualization), and Dörner's theory describes five different needs (existential, sexuality, affiliation, certainty, and competence).

All three theories can be applied to CPS. McClelland's need for achievement, Maslow's needs for esteem and safety, and Dörner's needs for certainty and competence could be inferred from the thinking–aloud passage. The need for affiliation which is a part of each of the three theories could play an important role when groups solve complex problems.

The existential needs and the need for affiliation outlined in PSI-theory can also be found in Maslow's hierarchy of needs. These two theories differ in the adaptability of the needs. However, Maslow's esteem needs are only activated as the primary motivator as the physiological needs, belongingness, and love needs are met. The needs are more fluidly described as motivators in PSI-theory. One need becomes the dominant motive according to the expectancy–value principle. Expectancy stands for the estimated likelihood of success. The value of a motive stands for the strength of the need. According to McClelland's theory, the role of three motivations develops through life experience in a specific culture; and often times, one of the three becomes the main driving force for a person, almost like a personality trait. In that sense, there is not much flexibility.

Motivation and emotion are closely related as became partially clear in the discussion of McClelland's theory. Emotions are discussed in detail in PSI-theory, but space does not allow us to discuss those in detail here (see Dörner, 2003 ). Emotions are not described in detail in Maslow's Hierarchy of Needs.

Individual differences in motivation and needs are discussed in two of the three theories. According to McClelland, a person develops an individual achievement motive by learning one's own abilities from past achievements and failures. Based on different learning histories, different persons will have a different dominant motivation guiding behavior in a given situation. Learning history also influences the competence need in PSI-theory. Additionally PSI-theory assumes individual differences that are simulated through different individual motivational parameters in the theory. The certainty need, for example, becomes active when there is a deviation from a given set point. Individual differences are related to different set points and how sensitive the deviations are (e.g., deviation starts quickly vs. deviation starts slowly).

The thinking-aloud example from the WINFIRE microworld described earlier demonstrates that a person's CPS process is influenced by the person's needs. We have focused in our discussion on motivational processes that are considered in the framework of need theories. Beyond that, other motivational theories exist that focus on the importance of motivation for learning and achievement (e.g., expectancy, reasons for engagement, see Eccles and Wigfield, 2002 ). Thus, the applicability of these theories to CPS could be explored in future studies as well.

We discussed the three motivational theories of McClelland's Achievement Motivation, Maslow's Hierarchy of Need, and Dörner's Theory of Motivation as part of PSI-Theory. Although, the theories differ our discussion has shown that the three theories can be applied to CPS. Problem solving is a motivated process and determined by human motivations and needs.

Author contributions

The first author CG conceptualized the manuscript, selected the thinking-aloud passage, the second author MB primarily summarized McClellands and Maslow's theories. All authors contributed to writing up the manuscript.

Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Guest Essay

I Thought the Bragg Case Against Trump Was a Legal Embarrassment. Now I Think It’s a Historic Mistake.

A black-and-white photo with a camera in the foreground and mid-ground and a building in the background.

By Jed Handelsman Shugerman

Mr. Shugerman is a law professor at Boston University.

About a year ago, when Alvin Bragg, the Manhattan district attorney, indicted former President Donald Trump, I was critical of the case and called it an embarrassment. I thought an array of legal problems would and should lead to long delays in federal courts.

After listening to Monday’s opening statement by prosecutors, I still think the district attorney has made a historic mistake. Their vague allegation about “a criminal scheme to corrupt the 2016 presidential election” has me more concerned than ever about their unprecedented use of state law and their persistent avoidance of specifying an election crime or a valid theory of fraud.

To recap: Mr. Trump is accused in the case of falsifying business records. Those are misdemeanor charges. To elevate it to a criminal case, Mr. Bragg and his team have pointed to potential violations of federal election law and state tax fraud. They also cite state election law, but state statutory definitions of “public office” seem to limit those statutes to state and local races.

Both the misdemeanor and felony charges require that the defendant made the false record with “intent to defraud.” A year ago, I wondered how entirely internal business records (the daily ledger, pay stubs and invoices) could be the basis of any fraud if they are not shared with anyone outside the business. I suggested that the real fraud was Mr. Trump’s filing an (allegedly) false report to the Federal Election Commission, and that only federal prosecutors had jurisdiction over that filing.

A recent conversation with Jeffrey Cohen, a friend, Boston College law professor and former prosecutor, made me think that the case could turn out to be more legitimate than I had originally thought. The reason has to do with those allegedly falsified business records: Most of them were entered in early 2017, generally before Mr. Trump filed his Federal Election Commission report that summer. Mr. Trump may have foreseen an investigation into his campaign, leading to its financial records. He may have falsely recorded these internal records before the F.E.C. filing as consciously part of the same fraud: to create a consistent paper trail and to hide intent to violate federal election laws, or defraud the F.E.C.

In short: It’s not the crime; it’s the cover-up.

Looking at the case in this way might address concerns about state jurisdiction. In this scenario, Mr. Trump arguably intended to deceive state investigators, too. State investigators could find these inconsistencies and alert federal agencies. Prosecutors could argue that New York State agencies have an interest in detecting conspiracies to defraud federal entities; they might also have a plausible answer to significant questions about whether New York State has jurisdiction or whether this stretch of a state business filing law is pre-empted by federal law.

However, this explanation is a novel interpretation with many significant legal problems. And none of the Manhattan district attorney’s filings or today’s opening statement even hint at this approach.

Instead of a theory of defrauding state regulators, Mr. Bragg has adopted a weak theory of “election interference,” and Justice Juan Merchan described the case , in his summary of it during jury selection, as an allegation of falsifying business records “to conceal an agreement with others to unlawfully influence the 2016 election.”

As a reality check: It is legal for a candidate to pay for a nondisclosure agreement. Hush money is unseemly, but it is legal. The election law scholar Richard Hasen rightly observed , “Calling it election interference actually cheapens the term and undermines the deadly serious charges in the real election interference cases.”

In Monday’s opening argument, the prosecutor Matthew Colangelo still evaded specifics about what was illegal about influencing an election, but then he claimed , “It was election fraud, pure and simple.” None of the relevant state or federal statutes refer to filing violations as fraud. Calling it “election fraud” is a legal and strategic mistake, exaggerating the case and setting up the jury with high expectations that the prosecutors cannot meet.

The most accurate description of this criminal case is a federal campaign finance filing violation. Without a federal violation (which the state election statute is tethered to), Mr. Bragg cannot upgrade the misdemeanor counts into felonies. Moreover, it is unclear how this case would even fulfill the misdemeanor requirement of “intent to defraud” without the federal crime.

In stretching jurisdiction and trying a federal crime in state court, the Manhattan district attorney is now pushing untested legal interpretations and applications. I see three red flags raising concerns about selective prosecution upon appeal.

First, I could find no previous case of any state prosecutor relying on the Federal Election Campaign Act either as a direct crime or a predicate crime. Whether state prosecutors have avoided doing so as a matter of law, norms or lack of expertise, this novel attempt is a sign of overreach.

Second, Mr. Trump’s lawyers argued that the New York statute requires that the predicate (underlying) crime must also be a New York crime, not a crime in another jurisdiction. The district attorney responded with judicial precedents only about other criminal statutes, not the statute in this case. In the end, the prosecutors could not cite a single judicial interpretation of this particular statute supporting their use of the statute (a plea deal and a single jury instruction do not count).

Third, no New York precedent has allowed an interpretation of defrauding the general public. Legal experts have noted that such a broad “election interference” theory is unprecedented, and a conviction based on it may not survive a state appeal.

Mr. Trump’s legal team also undercut itself for its decisions in the past year: His lawyers essentially put all of their eggs in the meritless basket of seeking to move the trial to federal court, instead of seeking a federal injunction to stop the trial entirely. If they had raised the issues of selective or vindictive prosecution and a mix of jurisdictional, pre-emption and constitutional claims, they could have delayed the trial past Election Day, even if they lost at each federal stage.

Another reason a federal crime has wound up in state court is that President Biden’s Justice Department bent over backward not to reopen this valid case or appoint a special counsel. Mr. Trump has tried to blame Mr. Biden for this prosecution as the real “election interference.” The Biden administration’s extra restraint belies this allegation and deserves more credit.

Eight years after the alleged crime itself, it is reasonable to ask if this is more about Manhattan politics than New York law. This case should serve as a cautionary tale about broader prosecutorial abuses in America — and promote bipartisan reforms of our partisan prosecutorial system.

Nevertheless, prosecutors should have some latitude to develop their case during trial, and maybe they will be more careful and precise about the underlying crime, fraud and the jurisdictional questions. Mr. Trump has received sufficient notice of the charges, and he can raise his arguments on appeal. One important principle of “ our Federalism ,” in the Supreme Court’s terms, is abstention , that federal courts should generally allow state trials to proceed first and wait to hear challenges later.

This case is still an embarrassment, in terms of prosecutorial ethics and apparent selectivity. Nevertheless, each side should have its day in court. If convicted, Mr. Trump can fight many other days — and perhaps win — in appellate courts. But if Monday’s opening is a preview of exaggerated allegations, imprecise legal theories and persistently unaddressed problems, the prosecutors might not win a conviction at all.

Jed Handelsman Shugerman (@jedshug) is a law professor at Boston University.

The Times is committed to publishing a diversity of letters to the editor. We’d like to hear what you think about this or any of our articles. Here are some tips . And here’s our email: [email protected] .

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A Theory of Problem-Solving Behavior
In this paper we develop a formal, testable theory of problem-solving behavior with special relevance to individuals and small groups. The theory is consistent with principles drawn from operant behavior and social exchange theories but also incorporates elements of cognitive psychology. Problem solving is defined as a nonroutine activity ...
Theory of Problem Solving
The problem solving is a personal and aimed process. That means that the activities done by an individual during the problem solving process are led to his/her personal aim (Mayer and Wittrock, 2006). An individual has to identify the problem first and then seek for possible solutions (Mayer and Wittrock, 2006).
A theory of problem-solving behavior.
Develops a formal, testable theory of problem-solving (PS) behavior with special relevance to individuals and small groups. The theory is consistent with principles drawn from operant behavior, social exchange theories, and elements of cognitive psychology. PS is defined as a nonroutine activity oriented toward changing an undesirable state of affairs. The focus on change differentiates PS ...
(PDF) Theory of Problem Solving
inconsistency" of the situation; the problem solving consists of the removal of the conflict and the finding. of the desired object. b) a disorder in the objective situation or in the structure of ...
Problem Solving from a Behavioral Perspective: Implications for
The nature of problem solving has been a difficult one to pin down, with much of the focus placed on hypothetical cognitive structures based on technological metaphors that change as quickly as the currently popular technologies after which they are modeled. While behavior analysts have made use of several effective instructional methodologies to produce reliable and impressive convergent ...
A theory of problem-solving behavior
In this paper we develop a formal, testable theory of problem-solving behavior with special relevance to individuals and small groups. The theory is consistent with principles drawn from operant behavior and social exchange theories but also incorporates elements of cognitive psychology. Problem solving is defined as a nonroutine activity oriented toward changing an undersirable state of affairs.
Problem Solving
Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or nonroutine, and as well defined or ill defined.
What Can We Learn by Treating Perspective Taking as Problem Solving
A wide range of behavioral theory and experimental tools have been developed to account for (and change) the type of behavior that is involved in "mind reading" or "ToM" explanations of perspective taking, including conversing, thinking, and imagining. ... Because problem-solving behavior is selected according to its function, it can ...
Problem Solving and Decision Making
Decision making is the process of selecting and choosing one action or behavior out of several alternatives. Like problem solving, decision making involves the coordination of memories and executive resources. Research on decision making has paid particular attention to the cognitive biases that account for suboptimal decisions and decisions ...
Reasoning and Problem Solving
This chapter provides a revised review of the psychological literature on reasoning and problem solving. Four classes of deductive reasoning are presented, including rule (mental logic) theories, semantic (mental model) theories, evolutionary theories, and heuristic theories. Major developments in the study of reasoning are also presented such ...
What is problem solving? A review of theory, research and applications
Structured training or therapy programmes designed to develop cognitive problem-solving skills are now widely used in criminal justice and mental health settings. Method. This paper describes the conceptual origins and theoretical models on which such programmes are based, and provides a historical overview of their development.
Empirical Evaluations of Skinner's Analysis of Problem Solving
Step 2 could be analyzed as a covert self-echoic problem-solving behavior in which the student covertly repeats what the other person said. Step 3 could be analyzed as discriminating when the person is and is not talking. Step 4 could be analyzed as a covert self-rehearsal prior to overt emission.
PDF Problem Behavior Theory
Problem Behavior Theory: A Half-Century of Research 241 "theory of the middle range," a theory relevant to a cir cumscribed domain of social action~in this case, prob lem behavior~and that can guide empirical inquiry, rather than a "grand" theory of the sort that had, in the past, characterized so much of sociology (e.g., Parsons,
Problem-Solving Theory: The Task-Centred Model
This chapter focuses on the task-centred model (Reid and Epstein 1972) as a prime example of the major influence problem-solving theory has exerted in the practice of social work.First, as background for understanding the development of the task-centred model, the chapter offers a brief account of the historical development of the problem-solving model (Perlman 1957) and describes its key ...
Solving Problems the Cognitive-Behavioral Way
The behavioral part of therapy is a wide umbrella that includes problem-solving techniques among other techniques. Accessing multiple techniques means one is more likely to address the client's ...
Understanding the Health Behavior Decision-Making Process with
The second gap is not taking the public's varying communication behaviors into account. Using the situational theory of problem solving (STOPS), communication behavior involves the collection, selection, and dissemination of information [8,9]. On the other hand, research examining the link between communication behavior and health behavior is ...
The Role of Motivation in Complex Problem Solving
Motivation is the process that determines the energization and direction of behavior (Heckhausen, 1991). Three motivation theories and their relation to CPS are examined: McClelland's achievement motivation, Maslow's hierarchy of needs, and Dörner's needs as outlined in PSI-theory. We chose these three theories for several reasons. First ...
Problem Behavior Theory
Problem behavior theory (PBT) is a social-psychological framework that helps to explain the development and nature of problem behaviors, for example, risky sex or alcohol use (Jessor & Jessor, 1977a; Jessor, 2001). Jessor (1987) described problem behavior as any behavior that deviates from both social and legal norms.
Problem solving and behavior modification.
Selectively reviewed problem-solving theory and research for possible applications in behavior modification. Problem solving was defined as a behavioral process which (a) makes available a variety of response alternatives for dealing with a problematic situation, and (b) increases the probability of selecting the most effective response from among these alternatives. 5 stages of problem ...
Educational Strategies Problem-Solving Concepts and Theories
Educational theories describing problem solving in the context of behavioral, cognitive, and information-processing pedagogy are discussed. The final section of the article describes prior findings regarding expert-novice differences in problem solving of various kinds. Any problem has at least three components: givens, goal, and operations.
Social problem solving: Theory, research, and training
Throughout history, philosophers have argued that the capacity to solve problems successfully in the real world is a crucial component for one's well-being. Psychologists have since been looking to understand the nuances of problem solving specifically as it applies to the self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover ...
(PDF) Situational theory of problem solving (STOPS): A foundational
The situational theory of problem solving (STOPS) was first published in 2011 as a generalized extension of the situational theory of publics (STP) (J.-N. Kim & Grunig, 2011).
Opinion
Instead of a theory of defrauding state regulators, Mr. Bragg has adopted a weak theory of "election interference," and Justice Juan Merchan described the case, in his summary of it during ...