thinking problem solving cognition mayer pdf

Internet Archive Audio

This Just In
Grateful Dead
Old Time Radio
78 RPMs and Cylinder Recordings
Audio Books & Poetry
Computers, Technology and Science
Music, Arts & Culture
News & Public Affairs
Spirituality & Religion
Radio News Archive

Flickr Commons
Occupy Wall Street Flickr
NASA Images
Solar System Collection
Ames Research Center

All Software
Old School Emulation
MS-DOS Games
Historical Software
Classic PC Games
Software Library
Kodi Archive and Support File
Vintage Software
CD-ROM Software
CD-ROM Software Library
Software Sites
Tucows Software Library
Shareware CD-ROMs
Software Capsules Compilation
CD-ROM Images
ZX Spectrum
DOOM Level CD

Smithsonian Libraries
FEDLINK (US)
Lincoln Collection
American Libraries
Canadian Libraries
Universal Library
Project Gutenberg
Children's Library
Biodiversity Heritage Library
Books by Language
Additional Collections

Prelinger Archives
Democracy Now!
Occupy Wall Street
TV NSA Clip Library
Animation & Cartoons
Arts & Music
Computers & Technology
Cultural & Academic Films
Ephemeral Films
Sports Videos
Videogame Videos
Youth Media

Search the history of over 866 billion web pages on the Internet.

Mobile Apps

Wayback Machine (iOS)
Wayback Machine (Android)

Browser Extensions

Archive-it subscription.

Explore the Collections
Build Collections

Save Page Now

Capture a web page as it appears now for use as a trusted citation in the future.

Please enter a valid web address

Donate Donate icon An illustration of a heart shape

Thinking, problem solving, cognition

Bookreader item preview, share or embed this item, flag this item for.

Graphic Violence
Explicit Sexual Content
Hate Speech
Misinformation/Disinformation
Marketing/Phishing/Advertising
Misleading/Inaccurate/Missing Metadata

plus-circle Add Review comment Reviews

140 Previews

7 Favorites

DOWNLOAD OPTIONS

No suitable files to display here.

PDF access not available for this item.

IN COLLECTIONS

Uploaded by station16.cebu on April 24, 2021

48 Problem Solving

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

Published: 03 June 2013
Cite Icon Cite
Permissions Icon Permissions

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.

Anderson L. W. , Krathwohl D. R. , Airasian P. W. , Cruikshank K. A. , Mayer R. E. , Pintrich P. R. , Raths, J., & Wittrock M. C. ( 2001 ). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. New York : Longman.

Baron J. ( 2000 ). Thinking and deciding (3rd ed.). New York : Cambridge University Press.

Google Scholar

Google Preview

Bloom B. S. , & Broder B. J. ( 1950 ). Problem-solving processes of college students: An exploratory investigation. Chicago : University of Chicago Press.

Chase W. G. , & Simon H. A. ( 1973 ). Perception in chess. Cognitive Psychology, 4, 55–81.

Chen Z. , & Klahr D. ( 1999 ). All other things being equal: Acquisition and transfer of the control of variable strategy . Child Development, 70, 1098–1120.

Chi M. T. H. , Feltovich P. J. , & Glaser R. ( 1981 ). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5, 121–152.

Covington M. V. , Crutchfield R. S. , Davies L. B. , & Olton R. M. ( 1974 ). The productive thinking program. Columbus, OH : Merrill.

de Groot A. D. ( 1965 ). Thought and choice in chess. The Hague, The Netherlands : Mouton.

Duncker K. ( 1945 ). On problem solving. Psychological Monographs, 58 (3) (Whole No. 270).

Ericsson K. A. , Feltovich P. J. , & Hoffman R. R. (Eds.). ( 2006 ). The Cambridge handbook of expertise and expert performance. New York : Cambridge University Press.

Fridja N. H. , & de Groot A. D. ( 1982 ). Otto Selz: His contribution to psychology. The Hague, The Netherlands : Mouton.

Gentner D. , & Stevens A. L. (Eds.). ( 1983 ). Mental models. Hillsdale, NJ : Erlbaum.

Gigerenzer G. , Todd P. M. , & ABC Research Group (Eds.). ( 1999 ). Simple heuristics that make us smart. Oxford, England : Oxford University Press.

Goel V. ( 2005 ). Cognitive neuroscience of deductive reasoning. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 475–492). New York : Cambridge University Press.

Guilford J. P. ( 1967 ). The nature of human intelligence. New York : McGraw-Hill.

Holyoak K. J. ( 2005 ). Analogy. In K. J. Holyoak & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 117–142). New York : Cambridge University Press.

Humphrey G. ( 1963 ). Thinking: An introduction to experimental psychology. New York : Wiley.

Judd C. H. ( 1908 ). The relation of special training and general intelligence. Educational Review, 36, 28–42.

Kahneman D. , & Tversky A. ( 1984 ). Choices, values, and frames. American Psychologist, 39, 341–350.

Kahneman D. , & Tversky A. (Eds.). ( 2000 ). Choices, values, and frames. New York : Cambridge University Press.

Kohler W. ( 1925 ). The mentality of apes. New York : Liveright.

Larkin J. H. , McDermott J. , Simon D. P. , & Simon H. A. ( 1980 ). Expert and novice performance in solving physics problems. Science, 208, 1335–1342.

Luchins A. ( 1942 ). Mechanization in problem solving. Psychological Monographs, 54 (6) (Whole No. 248).

Mandler J. M. , & Mandler G. ( 1964 ). Thinking from associationism to Gestalt. New York : Wiley.

Markman A. B. , & Medin D. L. ( 2002 ). Decision making. In D. Medin (Ed.), Stevens’ handbook of experimental psychology, Vol. 2. Memory and cognitive processes (2nd ed., pp. 413–466). New York : Wiley.

Mayer R. E. ( 1992 ). Thinking, problem solving, cognition (2nd ed). New York : Freeman.

Mayer R. E. ( 1995 ). The search for insight: Grappling with Gestalt psychology’s unanswered questions. In R. J. Sternberg & J. E. Davidson (Eds.), The nature of insight (pp. 3–32). Cambridge, MA : MIT Press.

Mayer R. E. ( 2008 ). Learning and instruction. Upper Saddle River, NJ : Merrill Prentice Hall.

Mayer R. E. ( 2009 ). Information processing. In T. L. Good (Ed.), 21st century education: A reference handbook (pp. 168–174). Thousand Oaks, CA : Sage.

Mayer R. E. , & Wittrock M. C. ( 2006 ). Problem solving. In P. A. Alexander & P. H. Winne (Eds.), Handbook of educational psychology (2nd ed., pp. 287–304). Mahwah, NJ : Erlbaum.

McCloskey M. ( 1983 ). Intuitive physics. Scientific American, 248 (4), 122–130.

Metcalfe J. , & Wiebe D. ( 1987 ). Intuition in insight and non-insight problem solving. Memory and Cognition, 15, 238–246.

Newell A. , & Simon H. A. ( 1972 ). Human problem solving. Englewood Cliffs, NJ : Prentice-Hall.

Nickerson R. S. ( 1999 ). Enhancing creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 392–430). New York : Cambridge University Press.

Nunes T. , Schliemann A. D. , & Carraher D. W , ( 1993 ). Street mathematics and school mathematics. Cambridge, England : Cambridge University Press.

Robbins P. , & Aydede M. (Eds.). ( 2009 ). The Cambridge handbook of situated cognition. New York : Cambridge University Press.

Rogers T. T. , & McClelland J. L. ( 2004 ). Semantic cognition: A parallel distributed processing approach. Cambridge, MA : MIT Press.

Singley M. K. , & Anderson J. R. ( 1989 ). The transfer of cognitive skill. Cambridge, MA : Harvard University Press.

Sternberg R. J. ( 1990 ). Metaphors of mind: Conceptions of the nature of intelligence. New York : Cambridge University Press.

Sternberg R. J. ( 1999 ). Handbook of creativity. New York : Cambridge University Press.

Sternberg R. J. , & Gregorenko E. L. (Eds.). ( 2003 ). The psychology of abilities, competencies, and expertise. New York : Cambridge University Press.

Tharp R. G. , & Gallimore R. ( 1988 ). Rousing minds to life: Teaching, learning, and schooling in social context. New York : Cambridge University Press.

Thorndike E. L. ( 1911 ). Animal intelligence. New York: Hafner.

Thorndike E. L. , & Woodworth R. S. ( 1901 ). The influence of improvement in one mental function upon the efficiency of other functions. Psychological Review, 8, 247–261.

Wertheimer M. ( 1959 ). Productive thinking. New York : Harper and Collins.

Wundt W. ( 1973 ). An introduction to experimental psychology. New York : Arno Press. (Original work published in 1911).

Thinking, problem solving, cognition

By richard e. mayer.

5 Want to read
1 Currently reading
0 Have read

Preview Book

My Reading Lists:

Use this Work

Create a new list

My book notes.

My private notes about this edition:

Check nearby libraries

Library.link

Buy this book

This edition doesn't have a description yet. Can you add one ?

Previews available in: English

Showing 3 featured editions. View all 3 editions?

Add another edition?

Book Details

Published in, edition notes.

Includes bibliographical references (p. 509-543) and indexes.

Classifications

The physical object, community reviews (0).

Created April 1, 2008
12 revisions

Wikipedia citation

Copy and paste this code into your Wikipedia page. Need help?

Business & Money
Management & Leadership

Fulfillment by Amazon (FBA) is a service we offer sellers that lets them store their products in Amazon's fulfillment centers, and we directly pack, ship, and provide customer service for these products. Something we hope you'll especially enjoy: FBA items qualify for FREE Shipping and Amazon Prime.

If you're a seller, Fulfillment by Amazon can help you grow your business. Learn more about the program.

Download the free Kindle app and start reading Kindle books instantly on your smartphone, tablet, or computer - no Kindle device required .

Read instantly on your browser with Kindle for Web.

Using your mobile phone camera - scan the code below and download the Kindle app.

Image Unavailable

To view this video download Flash Player

Follow the author

Thinking, Problem Solving, Cognition Second Edition

ISBN-10 0716722151
ISBN-13 978-0716722151
Edition Second Edition
Publisher Worth Publishers
Publication date October 15, 1991
Language English
Dimensions 6.64 x 1.15 x 9.24 inches
Print length 560 pages
See all details

Popular titles by this author

E-Learning and the Science of Instruction: Proven Guidelines for Consumers and Designers of Multimedia Learning

Product details

Publisher ‏ : ‎ Worth Publishers; Second Edition (October 15, 1991)
Language ‏ : ‎ English
Paperback ‏ : ‎ 560 pages
ISBN-10 ‏ : ‎ 0716722151
ISBN-13 ‏ : ‎ 978-0716722151
Item Weight ‏ : ‎ 1.9 pounds
Dimensions ‏ : ‎ 6.64 x 1.15 x 9.24 inches
#1,932 in Cognitive Psychology (Books)
#7,050 in Medical Cognitive Psychology
#9,344 in Decision-Making & Problem Solving

About the author

Richard e. mayer.

Richard E. Mayer is Professor of Psychology at the University of California, Santa Barbara (UCSB) where he has served since 1975. In 2000, he received the E. L. Thorndike Award for career achievement in educational psychology. In 2008, he received the American Psychological Association's Distinguished Contribution of Applications of Psychology to Education award. He was ranked #1 as the most productive educational psychologist in the world for 1991-2001 (Contemporary Educational Psychology, vol. 28, pp. 422-430). He is the author of more than 390 publications including 23 books, such as Multimedia Learning: Second Edition (2009), Learning and Instruction: Second Edition (2008), E-Learning and the Science of Instruction: Second Edition (with R. Clark, 2008), and the Cambridge Handbook of Multimedia Learning (editor, 2005).

Customer reviews

Customer Reviews, including Product Star Ratings help customers to learn more about the product and decide whether it is the right product for them.

To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzed reviews to verify trustworthiness.

Sort reviews by Top reviews Most recent Top reviews

Top review from the United States

There was a problem filtering reviews right now. please try again later..

Amazon Newsletter
About Amazon
Accessibility
Sustainability
Press Center
Investor Relations
Amazon Devices
Amazon Science
Sell on Amazon
Sell apps on Amazon
Supply to Amazon
Protect & Build Your Brand
Become an Affiliate
Become a Delivery Driver
Start a Package Delivery Business
Advertise Your Products
Self-Publish with Us
Become an Amazon Hub Partner
› See More Ways to Make Money
Amazon Visa
Amazon Store Card
Amazon Secured Card
Amazon Business Card
Shop with Points
Credit Card Marketplace
Reload Your Balance
Amazon Currency Converter
Your Account
Your Orders
Shipping Rates & Policies
Amazon Prime
Returns & Replacements
Manage Your Content and Devices
Recalls and Product Safety Alerts
Conditions of Use
Privacy Notice
Consumer Health Data Privacy Disclosure
Your Ads Privacy Choices

IMAGES

Unit 7 Cognition Thinking Problem Solving AP Psy
Cognition: Problem Solving (Biases, Algorithms and Heuristics)
Amazon
Thinking Skills_ Critical Thinking and Problem Solving ( PDFDrive.com ) (1)
Thinking, problem solving, cognition : Mayer, Richard E., 1947- : Free
UNIT 3.docx

VIDEO

Math Encounters
Computational Models of Cognition: Part 1
The Hard Problem of Consciousness: Can Science Explain the Mind?
Lec 9
Problem Solving
Lecture 2.3: Josh Tenenbaum

COMMENTS

Thinking, problem solving, cognition : Mayer, Richard E., 1947- : Free
Thinking, problem solving, cognition by Mayer, Richard E., 1947-Publication date 1983 Topics Thought and thinking, Problem solving, Cognition, Cognition, Pensée, Résolution de problème, Pensée, ... EPUB and PDF access not available for this item. IN COLLECTIONS
Thinking, problem solving, cognition by Richard E. Mayer
Thinking, problem solving, cognition by Richard E. Mayer, 1983, W.H. Freeman edition,
Thinking and problem solving : an introduction to human cognition and
Thinking and problem solving : an introduction to human cognition and learning ... Mayer, Richard E., 1947-Publication date 1977 Topics Thought and thinking, Problem solving Publisher Glenview, Ill. : Scott, Foresman ... Pdf_module_version 0.0.20 Ppi 500 ...
PDF Thinking, Problem Solving, Cognition
COGNITION SECOND EDITION Richard E. Mayer University of California, Santa Barbara E W. H. Freeman and Company ... Chapter 10 Cognitive Development: Thinking as 283 Influenced by Growth Chapter 11 Intelligence: Thinking as a Measurable 324 ... Chapter 12 Creativity Training: Thinking as a * 360 Learnable Skill Chapter 1 3 Expert Problem Solving ...
Thinking, Problem Solving, Cognition
Thinking, Problem Solving, Cognition By Richard E. Mayer. New York: W. H. Freeman, 1983. 464 pp. Cloth, $25.00. Paper, $15.00 After an introductory chapter, chapters 2, 3, and 4 deal with "Association-ism, "Gestalt," and "Meaning." "Rule Induction," and "Deductive Reason-ing" are covered in chapters 5 and 6. A section dealing with the information
Thinking, Problem Solving, Cognition
Reflecting important new research developments of the past eight years as well as classic theories of problem solving, this book provides a balanced survey of the higher cognitive processes, human thinking, problem solving, and learning. Divided into four parts, the book discusses associationism and Gestalt theory before introducing current research and theories of induction and deduction in ...
Thinking, problem solving, cognition, 2nd ed.
This second edition of "Thinking, Problem Solving, Cognition" retains the same goal as the first: to introduce the reader to our current understanding of the cognition side of cognitive psychology. . . . The book's intended audience is also the same: students in such courses as cognitive psychology, learning and memory, problem solving, critical thinking, and educational psychology, as well as ...
Thinking, Problem Solving, Cognition
Richard E. Mayer. W.H. Freeman, 1983 - Cognition - 426 pages. A balanced survey of the higher cognitive processes--human thinking, problem solving, and learning which reflects important research developments and classic theories of problem solving. Intended for courses in cognitive psychology, learning and memory, problem solving, critical ...
Thinking, Problem Solving, Cognition
Thinking, Problem Solving, Cognition. R. Mayer. Published 1983. Psychology, Education. Reflecting important new research developments of the past eight years as well as classic theories of problem solving, this book provides a balanced survey of the higher cognitive processes, human thinking, problem solving, and learning.
Thinking, problem solving, cognition : Mayer, Richard E., 1947- : Free
Thinking, problem solving, cognition by Mayer, Richard E., 1947-Publication date 1992 Topics Thought and thinking, Problem solving, Cognition Publisher New York : W.H. Freeman ... Pdf_degraded invalid-page-size Pdf_module_version 0.0.12 Ppi 360 Rcs_key 24143 Republisher_date 20210503104718 ...
Thinking and problem solving: An introduction to human cognition and
Citation. Mayer, R. E. (1977). Thinking and problem solving: An introduction to human cognition and learning. Scott, Foresman. Abstract. Text: book; for ...
Problem Solving
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 ...
Thinking, problem solving, cognition, 2nd ed.
Toward a design theory of problem solving. D. Jonassen. Education, Psychology. 2000. TLDR. The purpose of this paper is to propose a metatheory of problem solving in order to initiate dialogue and research rather than offering a definitive answer regarding its processes. Expand. 1,768. Highly Influenced.
Thinking, problem solving, cognition by Richard E. Mayer
Thinking, problem solving, cognition by Richard E. Mayer, 1992, W.H. Freeman edition, in English - 2nd ed.
Cognitive, metacognitive, and motivational aspects of problem solving
This article examines the role of cognitive, metacognitive, and motivational skills in problem solving. Cognitive skills include instructional objectives, components in a learning hierarchy, and components in information processing. Metacognitive skills include strategies for reading comprehension, writing, and mathematics. Motivational skills include motivation based on interest, self ...
Thinking, Problem Solving, Cognition
Part three considers recent cognitive theories and discusses information-processing analysis, outlining techniques for analyzing cognition into processes, strategies, and knowledge structures. Finally, the implications and applications of findings in cognitive psychology are examined, with emphasis on applications such as teaching creative ...
PDF The Cambridge Handbook of Thinking and Reasoning
TheCambridge Handbook of Thinking and Rea- soningis the ﬁrst comprehensive and authorita- tive handbook covering all the core topics of the ﬁeld of thinking and reasoning. Written by the foremost experts from cognitive psychology, cog- nitive science, and cognitive neuroscience, indi- vidual chapters summarize basic concepts and ﬁndings ...
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. The major cognitive processes in problem solving are representing, planning, executing ...
Cognition and Instruction: Their Historic Meeting within Educational
The purpose of this article is to examine the emergence of cognitive approaches to instruction, with hope that an understanding of the origins of this field will yield perspective on where it is going. First, an historical analysis of the relation between psychology and education, especially cognitive psychology and instruction, is undertaken. Then, an historical overview is provided of the ...
Critical Thinking
Case (1994) described critical thinking as a process and cognitive skill that functions in identifying and defining problems and opportunities for improve ment; generating, examining, and evaluating options; reaching appropriate conclusions, and creating criteria to evaluate decisions. To employ the critical thinking process, the nurse.
(PDF) Metacognitive Skills and Problem-Solving
reasoning and problem-solving (Ader, 2019). Metacognitive skills play a critical role in monitoring and. regulating cognitive processes (Chan & Mansoor, 2007) and help stude nts to understand when ...
Problem solving.
A major challenge of education is improving students' minds--a goal that is reflected in people being able to solve novel problems they encounter. This is the premise underlying much of the interest in problem solving, including how to teach in ways that enable students to apply what they have learned to new situations and how to teach thinking skills. In this chapter, after defining key terms ...

Internet Archive Audio

Mobile Apps

Browser Extensions

Save Page Now

Thinking, problem solving, cognition

plus-circle Add Review comment Reviews

DOWNLOAD OPTIONS

IN COLLECTIONS

SIMILAR ITEMS (based on metadata)

48 Problem Solving

Definition of Problem Solving

Definition of Problem

Types of Problems

Cognitive Processes in Problem Solving

Knowledge for Problem Solving

Historical Approaches to Problem Solving

Early Conceptions

Associationism

Gestalt Psychology

Information Processing

Classic Issues in Problem Solving

Current and Future Issues in Problem Solving

Decision Making

Intelligence and Creativity

Teaching of Thinking Skills

Expert Problem Solving

Analogical Reasoning

Mathematical and Scientific Problem Solving

Everyday Thinking

Cognitive Neuroscience of Problem Solving

Future Directions

Further Reading

Thinking, problem solving, cognition

Preview Book

Create a new list

Book Details

Classifications

Wikipedia citation

Image Unavailable

Follow the author

Thinking, Problem Solving, Cognition Second Edition

Popular titles by this author

Product details

About the author

Customer reviews

Top review from the United States

IMAGES

VIDEO

COMMENTS