cognitive model of problem solving

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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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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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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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A problem-solving conceptual framework and its implications in designing problem-posing tasks

Published: 05 August 2012
Volume 83 , pages 9–26, ( 2013 )

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Florence Mihaela Singer 1 , 2 &
Cristian Voica 3

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The links between the mathematical and cognitive models that interact during problem solving are explored with the purpose of developing a reference framework for designing problem-posing tasks. When the process of solving is a successful one, a solver successively changes his/her cognitive stances related to the problem via transformations that allow different levels of description of the initial wording. Within these transformations, the passage between successive phases of the problem-solving process determines four operational categories: decoding (transposing the text into more explicit relations among the data and the operating schemes, induced by the constraints of the problem), representing (transposing the problem via a generated mental model), processing (identifying an associated mathematical model based on the mental configurations suggested by the problem and own mathematical competence), and implementing (applying identified mathematical techniques to the particular situation of the problem, with the purpose of drafting a conventional solution). The study of this framework in action offers insights for more effective teaching and can be used in problem posing and problem analysis in order to devise questions more relevant for deep learning.

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The paper was partially supported by the project POSDRU/17/1.1/G/37412.

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Singer, F.M., Voica, C. A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educ Stud Math 83 , 9–26 (2013). https://doi.org/10.1007/s10649-012-9422-x

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Problem-Solving Strategies and Obstacles

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

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

Discovery of the problem
Deciding to tackle the issue
Seeking to understand the problem more fully
Researching available options or solutions
Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

Perceptually recognizing the problem
Representing the problem in memory
Considering relevant information that applies to the problem
Identifying different aspects of the problem
Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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

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Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

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

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A Cognitive Trick for Solving Problems Creatively

Theodore Scaltsas

Mental biases can actually help.

Many experts argue that creative thinking requires people to challenge their preconceptions and assumptions about the way the world works. One common claim, for example, is that the mental shortcuts we all rely on to solve problems get in the way of creative thinking. How can you innovate if your thinking is anchored in past experience?

TS Theodore Scaltsas is a Chaired Professor in Classical Philosophy at the University of Edinburgh in Scotland.

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Piaget’s Theory and Stages of Cognitive Development

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Editor-in-Chief for Simply Psychology

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

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Key Takeaways

Jean Piaget is famous for his theories regarding changes in cognitive development that occur as we move from infancy to adulthood.
Cognitive development results from the interplay between innate capabilities (nature) and environmental influences (nurture).
Children progress through four distinct stages , each representing varying cognitive abilities and world comprehension: the sensorimotor stage (birth to 2 years), the preoperational stage (2 to 7 years), the concrete operational stage (7 to 11 years), and the formal operational stage (11 years and beyond).
A child’s cognitive development is not just about acquiring knowledge, the child has to develop or construct a mental model of the world, which is referred to as a schema .
Piaget emphasized the role of active exploration and interaction with the environment in shaping cognitive development, highlighting the importance of assimilation and accommodation in constructing mental schemas.

Stages of Development

Jean Piaget’s theory of cognitive development suggests that children move through four different stages of intellectual development which reflect the increasing sophistication of children’s thought

Each child goes through the stages in the same order (but not all at the same rate), and child development is determined by biological maturation and interaction with the environment.

At each stage of development, the child’s thinking is qualitatively different from the other stages, that is, each stage involves a different type of intelligence.

Although no stage can be missed out, there are individual differences in the rate at which children progress through stages, and some individuals may never attain the later stages.

Piaget did not claim that a particular stage was reached at a certain age – although descriptions of the stages often include an indication of the age at which the average child would reach each stage.

The Sensorimotor Stage

Ages: Birth to 2 Years

The first stage is the sensorimotor stage , during which the infant focuses on physical sensations and learning to coordinate its body.

Major Characteristics and Developmental Changes:

The infant learns about the world through their senses and through their actions (moving around and exploring their environment).
During the sensorimotor stage, a range of cognitive abilities develop. These include: object permanence; self-recognition (the child realizes that other people are separate from them); deferred imitation; and representational play.
They relate to the emergence of the general symbolic function, which is the capacity to represent the world mentally
At about 8 months, the infant will understand the permanence of objects and that they will still exist even if they can’t see them and the infant will search for them when they disappear.

During the beginning of this stage, the infant lives in the present. It does not yet have a mental picture of the world stored in its memory therefore it does not have a sense of object permanence.

If it cannot see something, then it does not exist. This is why you can hide a toy from an infant, while it watches, but it will not search for the object once it has gone out of sight.

The main achievement during this stage is object permanence – knowing that an object still exists, even if it is hidden. It requires the ability to form a mental representation (i.e., a schema) of the object.

Towards the end of this stage the general symbolic function begins to appear where children show in their play that they can use one object to stand for another. Language starts to appear because they realise that words can be used to represent objects and feelings.

The child begins to be able to store information that it knows about the world, recall it, and label it.

Individual Differences

Cultural Practices : In some cultures, babies are carried on their mothers’ backs throughout the day. This constant physical contact and varied stimuli can influence how a child perceives their environment and their sense of object permanence.
Gender Norms : Toys assigned to babies can differ based on gender expectations. A boy might be given more cars or action figures, while a girl might receive dolls or kitchen sets. This can influence early interactions and sensory explorations.

Learn More: The Sensorimotor Stage of Cognitive Development

The Preoperational Stage

Ages: 2 – 7 Years

Piaget’s second stage of intellectual development is the preoperational stage . It takes place between 2 and 7 years. At the beginning of this stage, the child does not use operations, so the thinking is influenced by the way things appear rather than logical reasoning.

A child cannot conserve which means that the child does not understand that quantity remains the same even if the appearance changes.

Furthermore, the child is egocentric; he assumes that other people see the world as he does. This has been shown in the three mountains study.

As the preoperational stage develops, egocentrism declines, and children begin to enjoy the participation of another child in their games, and let’s pretend play becomes more important.

Toddlers often pretend to be people they are not (e.g. superheroes, policemen), and may play these roles with props that symbolize real-life objects. Children may also invent an imaginary playmate.

Toddlers and young children acquire the ability to internally represent the world through language and mental imagery.
During this stage, young children can think about things symbolically. This is the ability to make one thing, such as a word or an object, stand for something other than itself.
A child’s thinking is dominated by how the world looks, not how the world is. It is not yet capable of logical (problem-solving) type of thought.
Moreover, the child has difficulties with class inclusion; he can classify objects but cannot include objects in sub-sets, which involves classifying objects as belonging to two or more categories simultaneously.
Infants at this stage also demonstrate animism. This is the tendency for the child to think that non-living objects (such as toys) have life and feelings like a person’s.

By 2 years, children have made some progress toward detaching their thoughts from the physical world. However, have not yet developed logical (or “operational”) thought characteristics of later stages.

Thinking is still intuitive (based on subjective judgments about situations) and egocentric (centered on the child’s own view of the world).

Cultural Storytelling : Different cultures have unique stories, myths, and folklore. Children from diverse backgrounds might understand and interpret symbolic elements differently based on their cultural narratives.
Race & Representation : A child’s racial identity can influence how they engage in pretend play. For instance, a lack of diverse representation in media and toys might lead children of color to recreate scenarios that don’t reflect their experiences or background.

Learn More: The Preoperational Stage of Cognitive Development

The Concrete Operational Stage

Ages: 7 – 11 Years

By the beginning of the concrete operational stage , the child can use operations (a set of logical rules) so they can conserve quantities, realize that people see the world in a different way (decentring), and demonstrate improvement in inclusion tasks. Children still have difficulties with abstract thinking.

During this stage, children begin to think logically about concrete events.
Children begin to understand the concept of conservation; understanding that, although things may change in appearance, certain properties remain the same.
During this stage, children can mentally reverse things (e.g., picture a ball of plasticine returning to its original shape).
During this stage, children also become less egocentric and begin to think about how other people might think and feel.

The stage is called concrete because children can think logically much more successfully if they can manipulate real (concrete) materials or pictures of them.

Piaget considered the concrete stage a major turning point in the child’s cognitive development because it marks the beginning of logical or operational thought. This means the child can work things out internally in their head (rather than physically try things out in the real world).

Children can conserve number (age 6), mass (age 7), and weight (age 9). Conservation is the understanding that something stays the same in quantity even though its appearance changes.

But operational thought is only effective here if the child is asked to reason about materials that are physically present. Children at this stage will tend to make mistakes or be overwhelmed when asked to reason about abstract or hypothetical problems.

Cultural Context in Conservation Tasks : In a society where resources are scarce, children might demonstrate conservation skills earlier due to the cultural emphasis on preserving and reusing materials.
Gender & Learning : Stereotypes about gender abilities, like “boys are better at math,” can influence how children approach logical problems or classify objects based on perceived gender norms.

Learn More: The Concrete Operational Stage of Development

The Formal Operational Stage

Ages: 12 and Over

The formal operational period begins at about age 11. As adolescents enter this stage, they gain the ability to think in an abstract manner, the ability to combine and classify items in a more sophisticated way, and the capacity for higher-order reasoning.

Adolescents can think systematically and reason about what might be as well as what is (not everyone achieves this stage). This allows them to understand politics, ethics, and science fiction, as well as to engage in scientific reasoning.

Adolescents can deal with abstract ideas: e.g. they can understand division and fractions without having to actually divide things up, and solve hypothetical (imaginary) problems.

Concrete operations are carried out on things whereas formal operations are carried out on ideas. Formal operational thought is entirely freed from physical and perceptual constraints.
During this stage, adolescents can deal with abstract ideas (e.g. no longer needing to think about slicing up cakes or sharing sweets to understand division and fractions).
They can follow the form of an argument without having to think in terms of specific examples.
Adolescents can deal with hypothetical problems with many possible solutions. E.g. if asked ‘What would happen if money were abolished in one hour’s time? they could speculate about many possible consequences.

From about 12 years children can follow the form of a logical argument without reference to its content. During this time, people develop the ability to think about abstract concepts, and logically test hypotheses.

This stage sees the emergence of scientific thinking, formulating abstract theories and hypotheses when faced with a problem.

Culture & Abstract Thinking : Cultures emphasize different kinds of logical or abstract thinking. For example, in societies with a strong oral tradition, the ability to hold complex narratives might develop prominently.
Gender & Ethics : Discussions about morality and ethics can be influenced by gender norms. For instance, in some cultures, girls might be encouraged to prioritize community harmony, while boys might be encouraged to prioritize individual rights.

Learn More: The Formal Operational Stage of Development

Piaget’s Theory

Piaget’s theory places a strong emphasis on the active role that children play in their own cognitive development.
According to Piaget, children are not passive recipients of information; instead, they actively explore and interact with their surroundings.
This active engagement with the environment is crucial because it allows them to gradually build their understanding of the world.

1. How Piaget Developed the Theory

Piaget was employed at the Binet Institute in the 1920s, where his job was to develop French versions of questions on English intelligence tests. He became intrigued with the reasons children gave for their wrong answers to the questions that required logical thinking.

He believed that these incorrect answers revealed important differences between the thinking of adults and children.

Piaget branched out on his own with a new set of assumptions about children’s intelligence:

Children’s intelligence differs from an adult’s in quality rather than in quantity. This means that children reason (think) differently from adults and see the world in different ways.
Children actively build up their knowledge about the world . They are not passive creatures waiting for someone to fill their heads with knowledge.
The best way to understand children’s reasoning is to see things from their point of view.

Piaget did not want to measure how well children could count, spell or solve problems as a way of grading their I.Q. What he was more interested in was the way in which fundamental concepts like the very idea of number , time, quantity, causality , justice , and so on emerged.

Piaget studied children from infancy to adolescence using naturalistic observation of his own three babies and sometimes controlled observation too. From these, he wrote diary descriptions charting their development.

He also used clinical interviews and observations of older children who were able to understand questions and hold conversations.

2. Piaget’s Theory Differs From Others In Several Ways:

Piaget’s (1936, 1950) theory of cognitive development explains how a child constructs a mental model of the world. He disagreed with the idea that intelligence was a fixed trait, and regarded cognitive development as a process that occurs due to biological maturation and interaction with the environment.

Children’s ability to understand, think about, and solve problems in the world develops in a stop-start, discontinuous manner (rather than gradual changes over time).

It is concerned with children, rather than all learners.
It focuses on development, rather than learning per se, so it does not address learning of information or specific behaviors.
It proposes discrete stages of development, marked by qualitative differences, rather than a gradual increase in number and complexity of behaviors, concepts, ideas, etc.

The goal of the theory is to explain the mechanisms and processes by which the infant, and then the child, develops into an individual who can reason and think using hypotheses.

To Piaget, cognitive development was a progressive reorganization of mental processes as a result of biological maturation and environmental experience.

Children construct an understanding of the world around them, then experience discrepancies between what they already know and what they discover in their environment.

Piaget claimed that knowledge cannot simply emerge from sensory experience; some initial structure is necessary to make sense of the world.

According to Piaget, children are born with a very basic mental structure (genetically inherited and evolved) on which all subsequent learning and knowledge are based.

Schemas are the basic building blocks of such cognitive models, and enable us to form a mental representation of the world.

Piaget (1952, p. 7) defined a schema as: “a cohesive, repeatable action sequence possessing component actions that are tightly interconnected and governed by a core meaning.”

In more simple terms, Piaget called the schema the basic building block of intelligent behavior – a way of organizing knowledge. Indeed, it is useful to think of schemas as “units” of knowledge, each relating to one aspect of the world, including objects, actions, and abstract (i.e., theoretical) concepts.

Wadsworth (2004) suggests that schemata (the plural of schema) be thought of as “index cards” filed in the brain, each one telling an individual how to react to incoming stimuli or information.

When Piaget talked about the development of a person’s mental processes, he was referring to increases in the number and complexity of the schemata that a person had learned.

When a child’s existing schemas are capable of explaining what it can perceive around it, it is said to be in a state of equilibrium, i.e., a state of cognitive (i.e., mental) balance.

Operations are more sophisticated mental structures which allow us to combine schemas in a logical (reasonable) way.

As children grow they can carry out more complex operations and begin to imagine hypothetical (imaginary) situations.

Apart from the schemas we are born with schemas and operations are learned through interaction with other people and the environment.

Piaget emphasized the importance of schemas in cognitive development and described how they were developed or acquired.

A schema can be defined as a set of linked mental representations of the world, which we use both to understand and to respond to situations. The assumption is that we store these mental representations and apply them when needed.

Examples of Schemas

A person might have a schema about buying a meal in a restaurant. The schema is a stored form of the pattern of behavior which includes looking at a menu, ordering food, eating it and paying the bill.

This is an example of a schema called a “script.” Whenever they are in a restaurant, they retrieve this schema from memory and apply it to the situation.

The schemas Piaget described tend to be simpler than this – especially those used by infants. He described how – as a child gets older – his or her schemas become more numerous and elaborate.

Piaget believed that newborn babies have a small number of innate schemas – even before they have had many opportunities to experience the world. These neonatal schemas are the cognitive structures underlying innate reflexes. These reflexes are genetically programmed into us.

For example, babies have a sucking reflex, which is triggered by something touching the baby’s lips. A baby will suck a nipple, a comforter (dummy), or a person’s finger. Piaget, therefore, assumed that the baby has a “sucking schema.”

Similarly, the grasping reflex which is elicited when something touches the palm of a baby’s hand, or the rooting reflex, in which a baby will turn its head towards something which touches its cheek, are innate schemas. Shaking a rattle would be the combination of two schemas, grasping and shaking.

4. The Process of Adaptation

Piaget also believed that a child developed as a result of two different influences: maturation, and interaction with the environment. The child develops mental structures (schemata) which enables him to solve problems in the environment.

Adaptation is the process by which the child changes its mental models of the world to match more closely how the world actually is.

Adaptation is brought about by the processes of assimilation (solving new experiences using existing schemata) and accommodation (changing existing schemata in order to solve new experiences).

The importance of this viewpoint is that the child is seen as an active participant in its own development rather than a passive recipient of either biological influences (maturation) or environmental stimulation.

When our existing schemas can explain what we perceive around us, we are in a state of equilibration . However, when we meet a new situation that we cannot explain it creates disequilibrium, this is an unpleasant sensation which we try to escape, and this gives us the motivation to learn.

According to Piaget, reorganization to higher levels of thinking is not accomplished easily. The child must “rethink” his or her view of the world. An important step in the process is the experience of cognitive conflict.

In other words, the child becomes aware that he or she holds two contradictory views about a situation and they both cannot be true. This step is referred to as disequilibrium .

Jean Piaget (1952; see also Wadsworth, 2004) viewed intellectual growth as a process of adaptation (adjustment) to the world. This happens through assimilation, accommodation, and equilibration.

To get back to a state of equilibration, we need to modify our existing schemas to learn and adapt to the new situation.

This is done through the processes of accommodation and assimilation . This is how our schemas evolve and become more sophisticated. The processes of assimilation and accommodation are continuous and interactive.

5. Assimilation

Piaget defined assimilation as the cognitive process of fitting new information into existing cognitive schemas, perceptions, and understanding. Overall beliefs and understanding of the world do not change as a result of the new information.

Assimilation occurs when the new experience is not very different from previous experiences of a particular object or situation we assimilate the new situation by adding information to a previous schema.

This means that when you are faced with new information, you make sense of this information by referring to information you already have (information processed and learned previously) and trying to fit the new information into the information you already have.

Imagine a young child who has only ever seen small, domesticated dogs. When the child sees a cat for the first time, they might refer to it as a “dog” because it has four legs, fur, and a tail – features that fit their existing schema of a dog.
A person who has always believed that all birds can fly might label penguins as birds that can fly. This is because their existing schema or understanding of birds includes the ability to fly.
A 2-year-old child sees a man who is bald on top of his head and has long frizzy hair on the sides. To his father’s horror, the toddler shouts “Clown, clown” (Siegler et al., 2003).
If a baby learns to pick up a rattle he or she will then use the same schema (grasping) to pick up other objects.

6. Accommodation

Accommodation: when the new experience is very different from what we have encountered before we need to change our schemas in a very radical way or create a whole new schema.

Psychologist Jean Piaget defined accommodation as the cognitive process of revising existing cognitive schemas, perceptions, and understanding so that new information can be incorporated.

This happens when the existing schema (knowledge) does not work, and needs to be changed to deal with a new object or situation.

In order to make sense of some new information, you actually adjust information you already have (schemas you already have, etc.) to make room for this new information.

A baby tries to use the same schema for grasping to pick up a very small object. It doesn’t work. The baby then changes the schema by now using the forefinger and thumb to pick up the object.
A child may have a schema for birds (feathers, flying, etc.) and then they see a plane, which also flies, but would not fit into their bird schema.
In the “clown” incident, the boy’s father explained to his son that the man was not a clown and that even though his hair was like a clown’s, he wasn’t wearing a funny costume and wasn’t doing silly things to make people laugh. With this new knowledge, the boy was able to change his schema of “clown” and make this idea fit better to a standard concept of “clown”.
A person who grew up thinking all snakes are dangerous might move to an area where garden snakes are common and harmless. Over time, after observing and learning, they might accommodate their previous belief to understand that not all snakes are harmful.

7. Equilibration

Piaget believed that all human thought seeks order and is uncomfortable with contradictions and inconsistencies in knowledge structures. In other words, we seek “equilibrium” in our cognitive structures.

Equilibrium occurs when a child’s schemas can deal with most new information through assimilation. However, an unpleasant state of disequilibrium occurs when new information cannot be fitted into existing schemas (assimilation).

Piaget believed that cognitive development did not progress at a steady rate, but rather in leaps and bounds. Equilibration is the force which drives the learning process as we do not like to be frustrated and will seek to restore balance by mastering the new challenge (accommodation).

Once the new information is acquired the process of assimilation with the new schema will continue until the next time we need to make an adjustment to it.

Equilibration is a regulatory process that maintains a balance between assimilation and accommodation to facilitate cognitive growth. Think of it this way: We can’t merely assimilate all the time; if we did, we would never learn any new concepts or principles.

Everything new we encountered would just get put in the same few “slots” we already had. Neither can we accommodate all the time; if we did, everything we encountered would seem new; there would be no recurring regularities in our world. We’d be exhausted by the mental effort!

Applications to Education

Think of old black and white films that you’ve seen in which children sat in rows at desks, with ink wells, would learn by rote, all chanting in unison in response to questions set by an authoritarian old biddy like Matilda!

Children who were unable to keep up were seen as slacking and would be punished by variations on the theme of corporal punishment. Yes, it really did happen and in some parts of the world still does today.

Piaget is partly responsible for the change that occurred in the 1960s and for your relatively pleasurable and pain-free school days!

“Children should be able to do their own experimenting and their own research. Teachers, of course, can guide them by providing appropriate materials, but the essential thing is that in order for a child to understand something, he must construct it himself, he must re-invent it. Every time we teach a child something, we keep him from inventing it himself. On the other hand that which we allow him to discover by himself will remain with him visibly”. Piaget (1972, p. 27)

Plowden Report

Piaget (1952) did not explicitly relate his theory to education, although later researchers have explained how features of Piaget’s theory can be applied to teaching and learning.

Piaget has been extremely influential in developing educational policy and teaching practice. For example, a review of primary education by the UK government in 1966 was based strongly on Piaget’s theory. The result of this review led to the publication of the Plowden Report (1967).

In the 1960s the Plowden Committee investigated the deficiencies in education and decided to incorporate many of Piaget’s ideas into its final report published in 1967, even though Piaget’s work was not really designed for education.

The report makes three Piaget-associated recommendations:

Children should be given individual attention and it should be realized that they need to be treated differently.
Children should only be taught things that they are capable of learning
Children mature at different rates and the teacher needs to be aware of the stage of development of each child so teaching can be tailored to their individual needs.

“The report’s recurring themes are individual learning, flexibility in the curriculum, the centrality of play in children’s learning, the use of the environment, learning by discovery and the importance of the evaluation of children’s progress – teachers should “not assume that only what is measurable is valuable.”

Discovery learning – the idea that children learn best through doing and actively exploring – was seen as central to the transformation of the primary school curriculum.

How to teach

Within the classroom learning should be student-centered and accomplished through active discovery learning. The role of the teacher is to facilitate learning, rather than direct tuition.

Because Piaget’s theory is based upon biological maturation and stages, the notion of “readiness” is important. Readiness concerns when certain information or concepts should be taught.

According to Piaget’s theory, children should not be taught certain concepts until they have reached the appropriate stage of cognitive development.

According to Piaget (1958), assimilation and accommodation require an active learner, not a passive one, because problem-solving skills cannot be taught, they must be discovered.

Therefore, teachers should encourage the following within the classroom:

Educational programs should be designed to correspond to Piaget’s stages of development. Children in the concrete operational stage should be given concrete means to learn new concepts e.g. tokens for counting.
Devising situations that present useful problems, and create disequilibrium in the child.
Focus on the process of learning, rather than the end product of it. Instead of checking if children have the right answer, the teacher should focus on the student’s understanding and the processes they used to get to the answer.
Child-centered approach. Learning must be active (discovery learning). Children should be encouraged to discover for themselves and to interact with the material instead of being given ready-made knowledge.
Accepting that children develop at different rates so arrange activities for individual children or small groups rather than assume that all the children can cope with a particular activity.
Using active methods that require rediscovering or reconstructing “truths.”
Using collaborative, as well as individual activities (so children can learn from each other).
Evaluate the level of the child’s development so suitable tasks can be set.
Adapt lessons to suit the needs of the individual child (i.e. differentiated teaching).
Be aware of the child’s stage of development (testing).
Teach only when the child is ready. i.e. has the child reached the appropriate stage.
Providing support for the “spontaneous research” of the child.
Using collaborative, as well as individual activities.
Educators may use Piaget’s stages to design age-appropriate assessment tools and strategies.

Classroom Activities

Sensorimotor stage (0-2 years):.

Although most kids in this age range are not in a traditional classroom setting, they can still benefit from games that stimulate their senses and motor skills.

Object Permanence Games : Play peek-a-boo or hide toys under a blanket to help babies understand that objects still exist even when they can’t see them.
Sensory Play : Activities like water play, sand play, or playdough encourage exploration through touch.
Imitation : Children at this age love to imitate adults. Use imitation as a way to teach new skills.

Preoperational Stage (2-7 years):

Role Playing : Set up pretend play areas where children can act out different scenarios, such as a kitchen, hospital, or market.
Use of Symbols : Encourage drawing, building, and using props to represent other things.
Hands-on Activities : Children should interact physically with their environment, so provide plenty of opportunities for hands-on learning.
Egocentrism Activities : Use exercises that highlight different perspectives. For instance, having two children sit across from each other with an object in between and asking them what the other sees.

Concrete Operational Stage (7-11 years):

Classification Tasks : Provide objects or pictures to group, based on various characteristics.
Hands-on Experiments : Introduce basic science experiments where they can observe cause and effect, like a simple volcano with baking soda and vinegar.
Logical Games : Board games, puzzles, and logic problems help develop their thinking skills.
Conservation Tasks : Use experiments to showcase that quantity doesn’t change with alterations in shape, such as the classic liquid conservation task using different shaped glasses.

Formal Operational Stage (11 years and older):

Hypothesis Testing : Encourage students to make predictions and test them out.
Abstract Thinking : Introduce topics that require abstract reasoning, such as algebra or ethical dilemmas.
Problem Solving : Provide complex problems and have students work on solutions, integrating various subjects and concepts.
Debate and Discussion : Encourage group discussions and debates on abstract topics, highlighting the importance of logic and evidence.
Feedback and Questioning : Use open-ended questions to challenge students and promote higher-order thinking. For instance, rather than asking, “Is this the right answer?”, ask, “How did you arrive at this conclusion?”

While Piaget’s stages offer a foundational framework, they are not universally experienced in the same way by all children.

Social identities play a critical role in shaping cognitive development, necessitating a more nuanced and culturally responsive approach to understanding child development.

Piaget’s stages may manifest differently based on social identities like race, gender, and culture:

Race & Teacher Interactions : A child’s race can influence teacher expectations and interactions. For example, racial biases can lead to children of color being perceived as less capable or more disruptive, influencing their cognitive challenges and supports.
Racial and Cultural Stereotypes : These can affect a child’s self-perception and self-efficacy . For instance, stereotypes about which racial or cultural groups are “better” at certain subjects can influence a child’s self-confidence and, subsequently, their engagement in that subject.
Gender & Peer Interactions : Children learn gender roles from their peers. Boys might be mocked for playing “girl games,” and girls might be excluded from certain activities, influencing their cognitive engagements.
Language : Multilingual children might navigate the stages differently, especially if their home language differs from their school language. The way concepts are framed in different languages can influence cognitive processing. Cultural idioms and metaphors can shape a child’s understanding of concepts and their ability to use symbolic representation, especially in the pre-operational stage.

Curriculum Development

According to Piaget, children’s cognitive development is determined by a process of maturation which cannot be altered by tuition so education should be stage-specific.

For example, a child in the concrete operational stage should not be taught abstract concepts and should be given concrete aid such as tokens to count with.

According to Piaget children learn through the process of accommodation and assimilation so the role of the teacher should be to provide opportunities for these processes to occur such as new material and experiences that challenge the children’s existing schemas.

Furthermore, according to this theory, children should be encouraged to discover for themselves and to interact with the material instead of being given ready-made knowledge.

Curricula need to be developed that take into account the age and stage of thinking of the child. For example there is no point in teaching abstract concepts such as algebra or atomic structure to children in primary school.

Curricula also need to be sufficiently flexible to allow for variations in the ability of different students of the same age. In Britain, the National Curriculum and Key Stages broadly reflect the stages that Piaget laid down.

For example, egocentrism dominates a child’s thinking in the sensorimotor and preoperational stages. Piaget would therefore predict that using group activities would not be appropriate since children are not capable of understanding the views of others.

However, Smith et al. (1998), point out that some children develop earlier than Piaget predicted and that by using group work children can learn to appreciate the views of others in preparation for the concrete operational stage.

The national curriculum emphasizes the need to use concrete examples in the primary classroom.

Shayer (1997), reported that abstract thought was necessary for success in secondary school (and co-developed the CASE system of teaching science). Recently the National curriculum has been updated to encourage the teaching of some abstract concepts towards the end of primary education, in preparation for secondary courses. (DfEE, 1999).

Child-centered teaching is regarded by some as a child of the ‘liberal sixties.’ In the 1980s the Thatcher government introduced the National Curriculum in an attempt to move away from this and bring more central government control into the teaching of children.

So, although the British National Curriculum in some ways supports the work of Piaget, (in that it dictates the order of teaching), it can also be seen as prescriptive to the point where it counters Piaget’s child-oriented approach.

However, it does still allow for flexibility in teaching methods, allowing teachers to tailor lessons to the needs of their students.

Social Media (Digital Learning)

Jean Piaget could not have anticipated the expansive digital age we now live in.

Today, knowledge dissemination and creation are democratized by the Internet, with platforms like blogs, wikis, and social media allowing for vast collaboration and shared knowledge. This development has prompted a reimagining of the future of education.

Classrooms, traditionally seen as primary sites of learning, are being overshadowed by the rise of mobile technologies and platforms like MOOCs (Passey, 2013).

The millennial generation, defined as the first to grow up with cable TV, the internet, and cell phones, relies heavily on technology.

They view it as an integral part of their identity, with most using it extensively in their daily lives, from keeping in touch with loved ones to consuming news and entertainment (Nielsen, 2014).

Social media platforms offer a dynamic environment conducive to Piaget’s principles. These platforms allow for interactions that nurture knowledge evolution through cognitive processes like assimilation and accommodation.

They emphasize communal interaction and shared activity, fostering both cognitive and socio-cultural constructivism. This shared activity promotes understanding and exploration beyond individual perspectives, enhancing social-emotional learning (Gehlbach, 2010).

A standout advantage of social media in an educational context is its capacity to extend beyond traditional classroom confines. As the material indicates, these platforms can foster more inclusive learning, bridging diverse learner groups.

This inclusivity can equalize learning opportunities, potentially diminishing biases based on factors like race or socio-economic status, resonating with Kegan’s (1982) concept of “recruitability.”

However, there are challenges. While the potential of social media in learning is vast, its practical application necessitates intention and guidance. Cuban, Kirkpatrick, and Peck (2001) note that certain educators and students are hesitant about integrating social media into educational contexts.

This hesitancy can stem from technological complexities or potential distractions. Yet, when harnessed effectively, social media can provide a rich environment for collaborative learning and interpersonal development, fostering a deeper understanding of content.

In essence, the rise of social media aligns seamlessly with constructivist philosophies. Social media platforms act as tools for everyday cognition, merging daily social interactions with the academic world, and providing avenues for diverse, interactive, and engaging learning experiences.

Applications to Parenting

Parents can use Piaget’s stages to have realistic developmental expectations of their children’s behavior and cognitive capabilities.

For instance, understanding that a toddler is in the pre-operational stage can help parents be patient when the child is egocentric.

Play Activities

Recognizing the importance of play in cognitive development, many parents provide toys and games suited for their child’s developmental stage.

Parents can offer activities that are slightly beyond their child’s current abilities, leveraging Vygotsky’s concept of the “Zone of Proximal Development,” which complements Piaget’s ideas.

Peek-a-boo : Helps with object permanence.
Texture Touch : Provide different textured materials (soft, rough, bumpy, smooth) for babies to touch and feel.
Sound Bottles : Fill small bottles with different items like rice, beans, bells, and have children shake and listen to the different sounds.
Memory Games : Using cards with pictures, place them face down, and ask students to find matching pairs.
Role Playing and Pretend Play : Let children act out roles or stories that enhance symbolic thinking. Encourage symbolic play with dress-up clothes, playsets, or toy cash registers. Provide prompts or scenarios to extend their imagination.
Story Sequencing : Give children cards with parts of a story and have them arranged in the correct order.
Number Line Jumps : Create a number line on the floor with tape. Ask students to jump to the correct answer for math problems.
Classification Games : Provide a mix of objects and ask students to classify them based on different criteria (e.g., color, size, shape).
Logical Puzzle Games : Games that involve problem-solving using logic, such as simple Sudoku puzzles or logic grid puzzles.
Debate and Discussion : Provide a topic and let students debate on pros and cons. This promotes abstract thinking and logical reasoning.
Hypothesis Testing Games : Present a scenario and have students come up with hypotheses and ways to test them.
Strategy Board Games : Games like chess, checkers, or Settlers of Catan can help in developing strategic and forward-thinking skills.

Critical Evaluation

The influence of Piaget’s ideas on developmental psychology has been enormous. He changed how people viewed the child’s world and their methods of studying children.

He was an inspiration to many who came after and took up his ideas. Piaget’s ideas have generated a huge amount of research which has increased our understanding of cognitive development.

Piaget (1936) was one of the first psychologists to make a systematic study of cognitive development. His contributions include a stage theory of child cognitive development, detailed observational studies of cognition in children, and a series of simple but ingenious tests to reveal different cognitive abilities.
His ideas have been of practical use in understanding and communicating with children, particularly in the field of education (re: Discovery Learning). Piaget’s theory has been applied across education.
According to Piaget’s theory, educational programs should be designed to correspond to the stages of development.
Are the stages real? Vygotsky and Bruner would rather not talk about stages at all, preferring to see development as a continuous process. Others have queried the age ranges of the stages. Some studies have shown that progress to the formal operational stage is not guaranteed.

For example, Keating (1979) reported that 40-60% of college students fail at formal operation tasks, and Dasen (1994) states that only one-third of adults ever reach the formal operational stage.

The fact that the formal operational stage is not reached in all cultures and not all individuals within cultures suggests that it might not be biologically based.

According to Piaget, the rate of cognitive development cannot be accelerated as it is based on biological processes however, direct tuition can speed up the development which suggests that it is not entirely based on biological factors.
Because Piaget concentrated on the universal stages of cognitive development and biological maturation, he failed to consider the effect that the social setting and culture may have on cognitive development.

Cross-cultural studies show that the stages of development (except the formal operational stage) occur in the same order in all cultures suggesting that cognitive development is a product of a biological process of maturation.

However, the age at which the stages are reached varies between cultures and individuals which suggests that social and cultural factors and individual differences influence cognitive development.

Dasen (1994) cites studies he conducted in remote parts of the central Australian desert with 8-14-year-old Indigenous Australians. He gave them conservation of liquid tasks and spatial awareness tasks. He found that the ability to conserve came later in the Aboriginal children, between ages of 10 and 13 (as opposed to between 5 and 7, with Piaget’s Swiss sample).

However, he found that spatial awareness abilities developed earlier amongst the Aboriginal children than the Swiss children. Such a study demonstrates cognitive development is not purely dependent on maturation but on cultural factors too – spatial awareness is crucial for nomadic groups of people.

Vygotsky , a contemporary of Piaget, argued that social interaction is crucial for cognitive development. According to Vygotsky the child’s learning always occurs in a social context in cooperation with someone more skillful (MKO). This social interaction provides language opportunities and Vygotsky considered language the foundation of thought.

Piaget’s methods (observation and clinical interviews) are more open to biased interpretation than other methods. Piaget made careful, detailed naturalistic observations of children, and from these, he wrote diary descriptions charting their development. He also used clinical interviews and observations of older children who were able to understand questions and hold conversations.

Because Piaget conducted the observations alone the data collected are based on his own subjective interpretation of events. It would have been more reliable if Piaget conducted the observations with another researcher and compared the results afterward to check if they are similar (i.e., have inter-rater reliability).

Although clinical interviews allow the researcher to explore data in more depth, the interpretation of the interviewer may be biased.

For example, children may not understand the question/s, they have short attention spans, they cannot express themselves very well, and may be trying to please the experimenter. Such methods meant that Piaget may have formed inaccurate conclusions.

As several studies have shown Piaget underestimated the abilities of children because his tests were sometimes confusing or difficult to understand (e.g., Hughes , 1975).

Piaget failed to distinguish between competence (what a child is capable of doing) and performance (what a child can show when given a particular task). When tasks were altered, performance (and therefore competence) was affected. Therefore, Piaget might have underestimated children’s cognitive abilities.

For example, a child might have object permanence (competence) but still not be able to search for objects (performance). When Piaget hid objects from babies he found that it wasn’t till after nine months that they looked for it.

However, Piaget relied on manual search methods – whether the child was looking for the object or not.

Later, researchers such as Baillargeon and Devos (1991) reported that infants as young as four months looked longer at a moving carrot that didn’t do what it expected, suggesting they had some sense of permanence, otherwise they wouldn’t have had any expectation of what it should or shouldn’t do.

The concept of schema is incompatible with the theories of Bruner (1966) and Vygotsky (1978). Behaviorism would also refute Piaget’s schema theory because is cannot be directly observed as it is an internal process. Therefore, they would claim it cannot be objectively measured.
Piaget studied his own children and the children of his colleagues in Geneva to deduce general principles about the intellectual development of all children. His sample was very small and composed solely of European children from families of high socio-economic status. Researchers have, therefore, questioned the generalisability of his data.
For Piaget, language is considered secondary to action, i.e., thought precedes language. The Russian psychologist Lev Vygotsky (1978) argues that the development of language and thought go together and that the origin of reasoning has more to do with our ability to communicate with others than with our interaction with the material world.

Piaget’s Theory vs Vygotsky

Piaget maintains that cognitive development stems largely from independent explorations in which children construct knowledge of their own.

Whereas Vygotsky argues that children learn through social interactions, building knowledge by learning from more knowledgeable others such as peers and adults. In other words, Vygotsky believed that culture affects cognitive development.

These factors lead to differences in the education style they recommend: Piaget would argue for the teacher to provide opportunities that challenge the children’s existing schemas and for children to be encouraged to discover for themselves.

Alternatively, Vygotsky would recommend that teachers assist the child to progress through the zone of proximal development by using scaffolding.

However, both theories view children as actively constructing their own knowledge of the world; they are not seen as just passively absorbing knowledge.

They also agree that cognitive development involves qualitative changes in thinking, not only a matter of learning more things.

What is cognitive development?

Cognitive development is how a person’s ability to think, learn, remember, problem-solve, and make decisions changes over time.

This includes the growth and maturation of the brain, as well as the acquisition and refinement of various mental skills and abilities.

Cognitive development is a major aspect of human development, and both genetic and environmental factors heavily influence it. Key domains of cognitive development include attention, memory, language skills, logical reasoning, and problem-solving.

Various theories, such as those proposed by Jean Piaget and Lev Vygotsky, provide different perspectives on how this complex process unfolds from infancy through adulthood.

What are the 4 stages of Piaget’s theory?

Piaget divided children’s cognitive development into four stages; each of the stages represents a new way of thinking and understanding the world.

He called them (1) sensorimotor intelligence , (2) preoperational thinking , (3) concrete operational thinking , and (4) formal operational thinking . Each stage is correlated with an age period of childhood, but only approximately.

According to Piaget, intellectual development takes place through stages that occur in a fixed order and which are universal (all children pass through these stages regardless of social or cultural background).

Development can only occur when the brain has matured to a point of “readiness”.

What are some of the weaknesses of Piaget’s theory?

However, the age at which the stages are reached varies between cultures and individuals, suggesting that social and cultural factors and individual differences influence cognitive development.

What are Piaget’s concepts of schemas?

Schemas are mental structures that contain all of the information relating to one aspect of the world around us.

According to Piaget, we are born with a few primitive schemas, such as sucking, which give us the means to interact with the world.

These are physical, but as the child develops, they become mental schemas. These schemas become more complex with experience.

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Cognitive control, intentions, and problem solving in skill learning

Wayne christensen.

1 Philosophy, University of Barcelona, Barcelona, Spain

Kath Bicknell

2 School of Social Sciences and School of Psychological Sciences, Macquarie University, Sydney, Australia

We investigate flexibility and problem solving in skilled action. We conducted a field study of mountain bike riding that required a learner rider to cope with major changes in technique and equipment. Our results indicate that relatively inexperienced individuals can be capable of fairly complex 'on-the-fly' problem solving which allows them to cope with new conditions. This problem solving is hard to explain for classical theories of skill because the adjustments are too large to be achieved by automatic mechanisms and too complex and rapid to be achieved by cognitive processes as they are usually understood. A recent theory, Mesh, can explain these results because it posits that skill-specific cognitive abilities develop during skill learning and that control typically involves an interplay between cognitive and automatic mechanisms. Here we develop Mesh further, providing a detailed explanation for these problem solving abilities. We argue that causal representation, metacognitive awareness and other forms of performance awareness combine in the formulation and control of action strategies. We also argue that the structure of control present in this case is inconsistent with Bratman's model of intentions, and that, in the face of high uncertainty and risk, intentions can be much more labile than Bratman recognises. In addition, we found limitations and flaws in problem solving which illuminate the representations involved. Finally, we highlight the crucial role of social and cultural learning in the development of complex skills.

Introduction

What is learned during skill learning? What role does cognitive control—the form of control involved in flexible, goal-directed thought and action—play in the learning process? Classical skill theories, such as those of Fitts and Posner ( 1967 ) and Anderson ( 1982 ), treat cognitive control as responsible for discovering the structure of the actions that the skill requires, and for their initial implementation, but as being supplanted by more efficient automatic processes as learning progresses. Most work on skill focuses on the development of automaticity and the abilities and mechanisms that automatically-produced skills might involve. But humans show an exceptionally high degree of flexibility in skilled action, including forms of flexibility that rely on problem solving to construct solutions, as opposed to the deployment of pre-learned solutions. This kind of flexibility has not received much attention, even though it is arguably the critical ability underlying the richness and diversity of human skill.

The classical view sees skill as automating because it regards cognitive control as fundamentally unsuited to the demands of skilled action control. Cognitive control is thought to be slow, serial, and as having limited capacity, whereas automatic processes are fast, parallel, and have high capacity (Shiffrin & Schneider, 1977 ; Evans & Stanovich, 2013 ). Cognitive control uses highly generalised representations and problem solving methods which are an inefficient means for producing the specialised responses of skill (Anderson, 1982 ). In other words, cognitive control is specialised for reasoning, not action control, and it is a clumsy tool to use for action control. But it's questionable whether cognitive control is really fundamentally unsuited to skilled action control, as assumed by the classical view. Certainly, early cognitively-driven efforts to perform a skill are clumsy, and working memory is often overloaded by task demands. But significant degrees of fluency emerge long before strong automaticity could be in place. Skill research tends to focus on motor skill in particular, but if we consider expertise research more generally it is clear that experts can acquire domain-specific cognitive skills which can allow them to rapidly process large amounts of information (Ericsson & Kintsch, 1995 ) and engage in powerful, domain-specific forms of problem solving (Chi et al., 1982 ). There is no obvious reason why skills that involve a strong motor component might not also incorporate cognitive abilities involved in control and problem solving.

A recent skill theory called Mesh proposes just this (Christensen & Sutton, 2018 ; Christensen et al., 2016 , 2019 ). It claims that almost all skills incorporate an important cognitive component, including those which are paradigmatically motoric like golf putting. Skilled performance is produced by meshed cognitive and automatic processes which are generated by the cooperative operation of many neural systems. Cognitive processes provide flexibility by shaping action to the context and by solving the problems that complex, variable environments and tasks present. This paper extends Mesh by investigating the nature of skilled problem solving more closely. We conducted a field study investigating adjustments to major task changes by a rider with several years mountain bike riding experience (and many years of road riding experience) but beginner-level mountain bike technique. This was one of the authors, Wayne. Kath, who is a highly experienced rider, provided instruction. Guidance from Kath prompted major changes in Wayne's riding technique. A change in bike during the field study also encouraged significant adjustments in Wayne’s riding.

Because Wayne was not a raw novice he possessed mountain-biking-specific problem solving abilities which allowed him to cope with these large changes more fluently than might be expected based on the classical view. His experiences navigating rocky descents and ascents, and challenging log roll-overs, help to illuminate the nature of the control involved in this kind of problem solving. These problems involve high uncertainty and significant risk, and control processes flexibly adjust action to manage this risk and uncertainty. The learner is learning the structure of the problem as they try out solutions, and the strategy is monitored, modified and sometimes abandoned during execution. Evaluation is complex, employing a rich set of criteria and flexible holistic assessment. To understand these features of control we need a more expansive concept of control and a more labile picture of intentions than the standard picture recognises (Bratman, 1987 ).

The problem solving that Wayne engaged in also helps to illuminate the nature of the representations involved. Recently there has been considerable interest in characterising the type of the representations that are required for the ability to perform actions (Pacherie, 2011 ). Most accounts have focused on representations of action form , with an emphasis on schemas (e.g. Mylopoulos & Pacherie, 2018 ; Fridland, 2021 ). In contrast, some accounts have focused on the representation of causal structure (Christensen et al., 2015 ; Goldenberg, 2013 ).

Here we endorse the view that causal representation plays an important role, and show how this kind of representation supports flexibility. We suggest that Wayne employed causal representation to identify the structure of the problems he faced and formulate solutions. Because he could understand the causal significance of some of the features of the altered technique and equipment he could rapidly formulate new strategies to cope with and exploit the changes. But Wayne's problem solving abilities showed strong limitations which are also revealing. Wayne failed to properly implement a key riding technique even though he understood the technique abstractly and thought he was implementing it. The problem was diagnosed by Kath, who corrected his implementation. His difficulty involved a failure to properly map between an abstract representation of the technique and the representations used in the control of execution. The latter have particular a type of content, in particular a systematic representation of the state space of execution control . They also have a characteristic perspective that we call the perspective of execution control . This perspective is related to, though distinct from, the type of perspective described by (Pavese, 2019 ) in her concept of practical modes of presentation.

In Sect. 2 we present the theoretical context for the study and describe its conception. In Sect. 3 we give an overview of the activities we conducted. Section 4 then analyses these experiences in close detail using the theoretical ideas developed in Sect. 2 .

Context and approach

This paper centers on a field study which is analysed for its theoretical implications. In both philosophy and psychology this is an unusual method which requires some explanation and defense. In a separate paper, Christensen (in preparation) develops a general argument that cognitive ecology should be a central discipline in psychology, that ecological methods should be incorporated into philosophy just as experimental methods have been, and that the present lack of attention to cognitive ecology is a serious limitation on the development of deep theory in both psychology and philosophy of mind (see also Bicknell & Sutton, 2022 ). Here we focus on a more restricted argument which highlights some of the ways that the theoretical issues we are concerned with in this paper are sensitive to ecological data.

As noted, we are concerned with skill learning, and with the role of cognitive control, intentions, and action strategies in skill learning. These are evolved adaptive traits whose structure and function are shaped by a complex mixture of evolutionary adaptation and learning. It follows that understanding the nature of the adaptive functions and mechanisms depends critically on understanding the ecological problems they respond to. Consequently, we need to investigate these phenomena in the context of the ecological problems they are adapted to solve. This requires the use of ecological methods to investigate the nature of these problems. We currently lack a detailed understanding of these ecological problems.

Bratman's ( 1987 ) theory of intentions is an especially relevant case where theory is sensitive to the details of these ecological problems. 1 Bratman’s account is widely accepted and is used as a framework by numerous contemporary researchers. Mylopoulos and Pacherie’s ( 2018 ) account of intentional action control is an example which we will compare with our own model. Bratman characterises intentions based on an analysis of human planning behavior. In developing his theory Bratman focuses primarily on "ordinary, humdrum cases in which future-directed intentions and partial plans lead without great difficulty from prior deliberation to later conduct" (p. 12). He sees these kinds of cases as contrasting with more complex cases that involve difficulties of self-control. He writes,

Such examples are quite fascinating. But I think we get a distorted view of future-directed intention if we take them as paradigmatic of intention. It is best, I think, to begin with ordinary, garden-variety cases in which, without major psychological resistance, future-directed intentions and partial plans support coordination in the lives of limited agents like us. It is here that we need to look to get at the major regularities, roles, and norms in terms of which we can understand intention and its associated commitment . (p. 12, emphasis added.)

In this passage Bratman shows an awareness of the importance of the ecological representativeness of types of cases. However, Bratman's ecological picture is itself flawed. Bratman appears to assume that ordinary humdrum cases “without great difficulty” are ecologically typical or predominant while cases with major psychological conflict are exceptional. He also assumes that these are the only significant variations to be considered. Bratman's examples are indeed, for the most part, mundane, such as going to the library to borrow a book, or deciding whether to have a milkshake for lunch. These cases involve low stakes, high information, low complexity, context stability, and low time pressure. Only one of his examples, a presidential TV debate, involves high stakes, high complexity and high time pressure. Bratman uses the complexity and time pressure of the case in his analysis but he doesn't systematically examine these features as such or consider the significance of variation in them for his theory. All these features vary greatly across naturally occurring human ecological contexts. And crucially, these variations have important theoretical implications. The basic structure of Bratman’s model of intention involves a phase of deliberation in which an intention is formed, followed by a phase in which evaluation of the intention has ceased and cognitive processes are devoted to implementation. Intentions serve as fixed anchor points which structure cognition and behavior after they have been adopted. But this model may be best suited to cases that involve low stakes and high information. In cases with significant uncertainty and high stakes we might expect evaluation of the intention to be ongoing during execution as information comes in. In some kinds of cases it is possible to abort an action part way through or change its fundamental nature. Accordingly, in these kinds of contexts intentions may be relatively labile, being evaluated, modified, and sometimes abandoned during execution as information about the action is acquired. Skill learning is an important context in which this kind of pattern is likely.

Lack of ecological data is also a problem for skill theory. Classical skill theories, such as those of Fitts and Posner ( 1967 ) and Dreyfus and Dreyfus ( 1986 ), propose that skill acquisition has a well-defined stage structure culminating in a final stage of full automaticity. Fitts and Posner's model has just three stages, while Dreyfus and Dreyfus's account has five. Yet skills are extremely diverse, ranging from the ability to play tic-tac-toe to being a concert pianist or astrophysicist. It is unlikely that a simple three or five stage model provides a satisfactory fit to all the skill acquisition pathways involved in developing such diverse expert abilities. In athletics, high jumping has a standardised, invariant task structure, and a single action strategy, the Fosbury Flop, has dominated since the late 1960s. In contrast, in competition bouldering route setters set highly diverse novel climbing problems at each competition. Climbers are allowed only four minutes to inspect the wall and formulate strategies. Climbers try out varied strategies, often employing strategies which suit their individual abilities and physical characteristics, such as explosive strength, limb and hand size, or flexibility and balance. 2 Multiple strategies may succeed on a given problem, including strategies not anticipated by the route setters. 3 At odds with classical skill theories, climbers and commentators often describe bouldering at elite levels as highly cognitive. This is less often said about high jump. To get a better understanding of skill we need a fuller picture of this diversity.

In this paper we take a small step towards filling out this picture. Our objective is to bring detailed theoretical analysis into a close engagement with detailed empirical ecological reporting and analysis. While our sample is a tiny slice of the big picture, close analysis reveals that it has features with wide-ranging theoretical significance.

Ecological context

The ecological context we have focused on is that of socially-guided learning of a complex, fast-paced skill in a variable, physically demanding environment. Specifically, we have focused on the problems of coping with major changes in mountain biking technique and equipment in an individual at a relatively early stage of skill development, with some experience but beginner-level technique. The ability to acquire complex, fast-paced sensorimotor skills is highly developed in primates, with arboreal lifestyle being a primary ecological basis for this. Primates show high levels of behavioral flexibility, manifested in foraging strategies, communication, social behavior and tool use. Amongst primates, humans are exceptional in showing an extremely highly developed capacity for flexible skill acquisition. This plays a fundamental role in human lifestyles. Human skills tend to be highly social, often acquired through social learning and exercised in social contexts.

Cognitive control plays a central role in learning complex novel skills. It is accordingly likely that in human evolution there has been selection on the capacity for cognitive control for functions that contribute to complex skill learning. Some contributions of cognitive control are probably not specific adaptations for skill learning, but rather more general abilities that contribute to skill learning amongst other important adaptive human capacities. Conversely, skill learning is likely to shape the mechanisms of cognitive control generally, both via selection and activity-dependent plasticity. During skill learning, new capacities for cognitive control are acquired, so some of the capacities and mechanisms involved in cognitive control may be more apparent (see for example, Bicknell, 2021 ; Bicknell & Brümmer, 2022 ; Downey, 2022 ).

Our rationale for focusing on the ability to cope with major changes in technique and equipment is that this is a demanding context which should illuminate mechanisms for control of performance and skill learning.

Testing the classical procedural-cognitive contrast

We can make an initial framing in terms of the standard distinction between implicit and explicit processes. Broadly, the kind of procedural or implicit learning usually associated with skill acquisition occurs slowly and incrementally, and the abilities which result are relatively inflexible (Reber et al., 2019 ). These mechanisms should hence be unable to respond to large, rapid changes. In addition, the classical view of skill claims that cognitive processes are ill-suited to the control of skilled action. Cognitive control processes should therefore struggle to cope with major novel changes to the way a task is performed. In contrast, Mesh theory claims that cognitive control of action improves with skill learning and incorporates several features which allow relatively efficient control, including representation of the causal structure of action problems and metacognitive and other kinds of performance awareness (Christensen et al., 2015 , 2019 ). It is consequently better placed to explain relatively fluent adjustments to major novel changes if, as we expected, these do occur.

Forms of flexibility

We also need a more fine-grained framing of the rationale for looking at large changes in technique and equipment. This is because numerous motor control mechanisms have been proposed which are capable of flexibility in various forms. In the situations we're concerned with it is plausible that multiple forms of flexibility play important roles.

One of the simplest forms of flexible control is feedback control. Here, feedback corrects deviation from a reference. The goal can be achieved from any point in a state space 'basin' defined by the abilities to detect deviations and produce control inputs which drive the system towards the goal state. Trace theory (Adams, 1971 ) and the control law model (Fajen, 2005 ; Gibson, 1979 ) are theories of skilled action production based on feedback. Another class of control system achieves greater flexibility by means of generalised sensorimotor mappings. Theories of this type include Schmidt's ( 1975 ) schema theory , the internal models approach (Daniel M. Wolpert & Kawato, 1998 ; Wolpert et al., 1995 ), Optimal Feedback Control theory (Todorov, 2004 ), and the coordinative structures of dynamical systems theory (e.g. Kelso & Zanone, 2002), which generate high order patterns in movement. The perception-motor mappings are generalised in the sense that they generalise from practiced to unpracticed contexts based on similarity.

Calibration is a form of flexibility in which the parameters of a control function are adjusted to suit the context. A different kind of flexibility is achieved by restricting regulation only to variables that affect goal-achievement (Todorov, 2004 ; Tseng et al., 2003 ). Restricting control only to variables that affect goal-achievement is resource-efficient and can have the effect of decoupling variables important for the goal from those which aren't, which buffers performance against variations in unimportant variables. Yet another kind of flexibility involves control of the way a strategy is executed. Impedance control , or the control of the stiffness of the motor system, is an example (Franklin et al., 2008 ). Thus, a given action type can be performed while maintaining varying degrees and forms of stiffness. Control of stiffness can have a variety of functional benefits. For instance, increasing stiffness can reduce the degrees of freedom present in a movement and hence simplify the movement problem, while reducing stiffness can reduce the negative consequences of impacts that arise as a result of errors.

A key form of flexibility, sometimes called equivalence , involves the ability to achieve a given goal using multiple qualitatively distinct movement patterns. Ranganathan et al. ( 2020 ) identify two kinds of mechanism capable of this kind of flexibility. The first type involve high order task-specific coordination functions which constrain the dynamics of the system in a way that allows multiple coordination modes, or synergies . The second consist of explicit strategies (Christensen & Bicknell, 2019 ; Christensen et al., 2015 , 2019 ; Shepherd, 2017 ; Taylor & Ivry, 2012 ). Ranganathan et al. ( 2020 ) suggest that flexibility is likely to be based on synergies when the variations in movement pattern are relatively small and the task constraints can be learned over a long period of time. Explicit strategies are likely to be used when the variations in movement patterns are large and the task constraints change over short time scales. The situation we are examining has these features so it should evoke the use of strategies.

Problem solving

The key question that then arises with regard to action strategies is how they are formulated and controlled using cognitive processes. As we saw, according to the classical view (e.g. Anderson, 1982 ) cognitive control includes no specialisations for action control. An alternative view, adopted in Mesh, is that control of action is one of the primary functions performed by cognitive control, and it incorporates mechanisms acquired through evolution and learning that are specialised for this role. These mechanisms engage in problem solving processes which represent the structure of action problems and construct solution strategies. Cognitive control then governs the implementation of these strategies.

Problem solving is a relatively understudied issue in motor control research, which is surprising on ecological grounds given the high degree of diversity and flexibility of human motor abilities, and the importance of flexible motor abilities in human evolution. Bernstein's ( 1996 ) concept of dexterity is an exception to this neglect. Bernstein characterises dexterity as the ability to find solutions to novel motor problems, and he regards it as central to human motor ability. Dexterity in this sense is likely to have fairly deep evolutionary roots, being important for locomotion in arboreal primates, for example. A recent study of squirrels illuminates some of the kinds of motor problem solving that an arboreal lifestyle involves, including adjusting to the flexibility of branches, distances, and the three-dimensional configuration of space and surfaces. 4 Human dexterity shows greatly enhanced range and depth, in the sense that humans are able to solve a much wider variety of motor problems and much more complex problems (Gibson 1979 ).

Causal representation and problem solving

Mesh treats the capacity for flexible problem solving as central to human skill and proposes that it incorporates three key ingredients. Firstly, there is the ability to flexibly represent problems as causally structured wholes by means of causal models . These represent problems as structured wholes incorporating constituents and relations. At least some constituents must be represented as able to vary in state, requiring a distinction between variables and the values that variables can take. We will refer to some variables as parameters , where by this we mean key features of a type, such as an action type. The representation of causal relations requires that parameters are represented as related by production relations, such that, in the simplest case, a change in the of state of a particular parameter produces a change in the state of a second parameter.

Most accounts of action representation have focused on the representation of action form , such as motor patterns, schemas and automated procedures (Anderson, 1982 ; Buxbaum, 2001 ; Fridland, 2021 ; Pacherie & Mylopoulos, 2020 ; Schmidt, 1975 ; Wolpert et al., 1995 ). These theories propose that, when provided with a goal in a particular context, the motor system predicts what action structure will achieve the goal and then produces that structure. Crucially, there is no representation of the causal relation between the action structure and the goal, or between components of the action structure. In contrast, causal theories claim that action control incorporates explicit representation of causal relations. For instance, the individual might use awareness of the weight of an object in order to estimate how much force to use in picking it up, or awareness of the mechanical properties of a knife blade to control its manipulation when using it as a prying lever. Thus, Goldenberg ( 2013 ) proposes that action control employs a mechanical problem-solving system that represents objects and the body in terms of parts and properties relevant to action problems. Pavese ( 2021 ) argues that these representations of causal principles are practical concepts, or concepts used for intentional control of action. Somewhat similarly to Goldenberg, we suggest that causal control models are employed in action control which explicitly represent causal structure involved in action and help to identify control acts that can achieve goal states (Christensen & Bicknell, 2019 ; Christensen et al., 2015 ).

It is plausible that cognitive action representations include representations of both action forms and causal structure, but causal representation is crucial for intentional control and flexible problem solving. Intentional control of action characteristically involves producing an action with particular features because an action with these features will bring about a goal. The representation of instrumental relations is based on the representation of causal relations. Flexible problem solving involves representing the causal structure of novel problems and finding a means to produce a causal intervention which will bring about a goal state. 5

We can further illustrate the role of causal control models in action control using the example of braking. A causal control model involved in the control of braking will represent key causal factors such as braking strength , grip , speed , and braking distance as distinct, interrelated components of braking. This allows the individual to formulate a wide range of braking strategies, and adopt strategies appropriate to the conditions and their goals. Some of the possible strategies include early braking , in which gentle braking is applied far from the point at which halting or a desired speed is attained, and late braking , in which a high speed is maintained until relatively close proximity to the target point and speed is rapidly reduced by means of hard braking. A much more advanced example of the use of causal representation in formulating action strategies can be seen in a video lesson by the climber Tomoa Narasaki. 6 Narasaki is one of the best boulderers in the world, and has a dramatic style which involves frequent use of leaps between climbing positions that are far apart. These moves are called 'dynos'. In this video Narasaki explains his technique for performing a particular kind of dyno. What is of most relevance here is that he gives a detailed rationale for each component of the technique that is based on a deep causal understanding of the technique. This causal representation includes principles that can be used, not just for this particular technique, but for refining other techniques and formulating new strategies.

Our notion of causal control models is related to Pacherie's (Mylopoulos & Pacherie, 2017 ; Pacherie, 2011 ) concept of executable action concepts . Pacherie ( 2011 ) illustrated the idea of executable action concepts by contrasting them with observational action concepts which may not be executable. Thus, a spectator at an ice-skating competition may acquire the concept of a triple-axel by watching it being performed, but is unlikely to be able to perform it themselves. Pacherie argues that, since possession of the observational concept doesn't guarantee the ability to perform the action, in order to possess an executable action concept the individual must already possess motor representations capable of producing the movement. Mylopoulos and Pacherie ( 2017 ) argue that executable action concepts are executable in virtue of being linked to motor schemas which are acquired through bottom-up learning processes.

A difficulty with this account, however, is that bottom-up motor learning in most cases depends on the action being first produced intentionally. Indeed, it has been a standard assumption that skill learning involves an initial phase in which the action is produced intentionally (Anderson, 1983 ; Fitts & Posner, 1967 ). There are possible exceptions in which the structure of the movement is produced incidentally as part a larger action and consolidated by bottom-up learning (Sun et al., 2001 ). Sequence learning tasks such as the serial reaction time task (SRTT) are designed to exploit this possibility as a means for studying implicit learning. In the SRTT the participant presses buttons in response to cues (Robertson, 2007 ). They are not informed that the sequence of cues/button presses contains a pattern. On subsequent tests participants are faster at the task, indicating they have some learning of the sequence. It was hoped that tasks like this would reveal purely implicit learning, operationally measured as speeded response combined with lack of explicit awareness of the sequence. However, participants do learn some of the sequence structure explicitly while performing the task and this appears to fully explain speed improvements (Krakauer et al., 2019 ). Thus, even in tasks specifically designed to elicit implicit, bottom-up learning it has proven difficult to do so. Masters and colleagues have attempted to develop training methods which allow the movement patterns of a skill to be learned largely or entirely implicitly (Masters, 2000; Poolton et al., 2006). However, it has proved difficult to apply these methods to complex skills (e.g. Poolton & Zachry, 2007). For most complex real-world skills like performing a dance step or changing gear in a manual car there is no other practical way to initially generate the action than by intentional control.

Thus, for the most part, the individual must already be able to intentionally produce the action before bottom-up motor learning can start to occur. Bottom-up motor learning refines and consolidates movement patterns that are intentionally produced. It doesn't construct novel movement patterns. Pacherie is right that to develop an executable action concept the individual must already possess motor representations capable of producing (at least an approximation of) the reference movement pattern. But in the initial stages of motor skill acquisition the individual does not have an integrated motor representation that is specific to the movement pattern being learned. The individual usually needs to construct a cognitive representation of the desired movement as an integrated structure assembled from intentionally controllable motor components.

This brings us to a crucial phenomenon that any theory of action and skill must accommodate, namely the ability to intentionally produce novel movement patterns. The basic level of control in intentional action is not the ability to produce 'basic actions', in the philosophical sense, it is the ability to intentionally control movement parameters such as postural parameters, direction, distance, speed, force, and so on. To intentionally produce novel movement patterns as functionally integrated wholes it is necessary to represent causal interdependencies amongst at least some of these parameters, such as between position, distance, speed, time, and force. 7 Thus, causal control models of the same kind as we described for braking are used in the fundamental control of movement.

Infants and young children learn a repertoire of basic coordinated actions, including pointing, reaching, grasping, manipulating, stepping, and so on. These actions are basic in the sense that they come to function as units which will be employed in the construction of more complex actions. They incorporate stereotyped movement patterns and their control is likely to incorporate linked conceptual and motor schema representations in the way that the Mylopoulos and Pacherie model describes. But they are intentionally controllable , in the sense that their parameters can be intentionally adjusted to achieve a variety of goals. To explain this we need to supplement the Mylopoulos and Pacherie model of executable action concepts with the account of causal control models that we are proposing. Typically, in skill acquisition, such as when learning to play a musical instrument, more basic intentionally controlled movement capacities are adapted for the specific demands of the skill. During skill learning cognition leads in the construction of new actions to suit the task demands. Once a novel action structure has been constructed, consolidation and refinement will occur across the whole control system, including the formation of integrated motor schemas and the formation of integrated causal control models.

Translation between representational systems

Theories of action control face the problem of understanding translation between and within representational systems during action control, including multiple perceptual modalities, visual and verbal linguistic representations, emotion experience, gestures, computer and web interface 'languages', the iconography and signaling conventions of driving on roads, maps, music representational systems such as notation and tab, and so on. 8 Hierarchical models of intentional control, such as that of Mylopoulos and Pacherie ( 2018 ), must explain translation across different levels of abstraction. Translation across all these representational systems and levels plays a central role in problem solving and flexibility. Abstract goals and plans must be interpreted in more concrete situational terms. Flexibility hinges on being able to vary the way actions are performed in relation to features of the situation while realising the features of action critical to achieving the goals. Learning involves abstracting action features from instances in a way that allows varied concrete implementations. Recent philosophical theories of the architecture of action control, such as the DPM and Mesh models, have not so far addressed these issues but there is a long tradition of work on them in other fields (Fitch & Martins, 2014; Lashley, 1951; MacKay, 1982; Ondobaka & Bekkering, 2012). 9

A connected issue that has received recent attention in philosophy is that of the perspective of the representations involved in action control. Pavese ( 2019 ) develops the idea that some representations have a distinctive practical mode of presentation or practical perspective . She argues that these are imperative representations which specify a method of performing a task in terms of the abilities of a system that can implement the method. She claims that motor commands and motor schemas are examples of this kind of representation. We agree this is an important form of practical perspective, but we need to also understand the form of practical perspective of the representations used in the problem solving by which schemas and motor commands are formulated and evaluated. We'll call this the perspective of control . The perspective of control encompasses all of the phases, levels and aspects of control, many of which have their own perspectival characters, including those of distal decision-making and proximal control of execution.

The structure of control

In addition to causal control models, previous explications of Mesh have identified two further components of action control: forms of higher order performance and metacognitive awareness. Before describing these in detail, however, it will help to clarify the structure of control. Mesh is similar to the DPM model of Mylopoulos and Pacherie ( 2018 ) in depicting action control as involving a hierarchical structure. Mesh has not yet been very specific about the details of the nature of the control involved in the hierarchy, whereas the DPM model, based on Bratman's account of intentions (along with Searle ( 1983 ), Brand ( 1984 ), and Mele ( 1992 )), specifies a control organisation that involves multiple levels of intentions which are responsible for specific aspects of action control. In particular, a distal intention, commonly formed outside the action context, represents the overarching goal of the action. Proximal intentions are formed which specify how the distal intention is to be implemented in the context of performance. Motor intentions specify the motoric means by which proximal intentions are implemented. Here we extend Mesh by specifying the structure of control in more detail. This account shares with the DPM model the idea that intentional action often involves a hierachical goal structure, but departs from it in certain respects which in part stem from a departure from Bratman's model of intentions. 10

One way to conceptualise control is as the ability of the agent to achieve its goals. We'll call this the goal-based conception of control. Mylopoulos and Pacherie ( 2018 ) and Shepherd ( 2021 ) employ this conception. 11 A different way to conceptualise control is as the ability of an agent to solve the problems that it faces. We'll call this the problem-based conception of control. Both concepts of control are useful but the problem-based concept is important for understanding adaptive control systems and the structure of control in skill learning. Thus, when we perform a full analysis of a biological control system we need to determine both the proximal goals (the represented goals) and the ultimate goals, which are solutions to adaptive problems faced by the biological agent. These problems are to a significant degree independent of and prior to the explicit goals of the control system. Solving them is often obligatory or very difficult to avoid. The relationship between proximal goals and adaptive problems will often be imperfect, and evolution will generally tend to bring the represented goals of organisms into alignment with their adaptive problems. Proximal criteria used in the control of eating include satisfying hunger and enjoyment of the experiences of eating. The primary adaptive goal is nutrition. Humans can adopt conceptualised nutrition as an explicit goal of eating but they need not. The proximal control criteria for eating can be satisfied while the adaptive problem is not. In cases where conceptualised nutrition is a goal of eating it may correspond imperfectly to objective nutrition. Thus, goal-based and problem-based control can be dissociated.

Humans are a highly social species and are exceptionally flexible in developing varied lifestyles and technologies which have allowed the colonisation of almost every kind of terrestrial environment on earth. This flexibility in lifestyles is founded on an exceptional capacity for flexible skill learning. Human evolution has thus endowed us with skill learning capacities which are extremely good at solving the ecological and social problems we face. Uncertainty plays a central role in this flexibility. Humans face a fundamental and pervasive uncertainty concerning their goals. Their goals correspond imperfectly to their problems and they must learn about the structure of the problems that they have. Problem discovery thus plays a central role in skill learning. Skill learners typically begin with poor representations of their problems. Their goals correspond imperfectly to their problems and they must learn about the structure of the problems that they have, and learn to form better goals. This learning occurs at every level, from the specific problems involved in performing particular actions up to and including self-conception, whether to engage in the skilled activity at all, and to what degree.

More specifically, uncertainty and problem discovery play a key role in the structure of action evaluation. On a goal-based hierarchical model of control, such as the DPM model, performance at a given level of control is evaluated with respect to the goal at that level and to higher level goals. Thus, the success of motor performance is evaluated with respect to whether it achieves the goal specified by the M-intention, and whether this satisfies the goal specified by the P-intention. However, there are certain phenomena which arise quite commonly during skill learning which don't fit this model very well. An action can go according to plan yet be assessed negatively. For example, an inexperienced guitarist might perform with a band at a gig in a way that they have planned to, and which they consider to be aligned with their norms for playing well, yet later evaluate their performance negatively when they review a recording. This later evaluation may be based on performance norms they had not previously considered, but which are highlighted when they assess their performance from the perspective of a listener and compare it to performances of more advanced players they admire. For example, they might realise that their playing was overly busy, failing to complement the song, and too loud, overshadowing the rest of the band. 12

An action can also go contrary to plan yet be assessed positively; a mistake which proves to be a 'happy accident'. For instance, you might accidentally shake out more hotsauce on your eggs than intended, yet regard the outcome as superior to the intended quantity of hotsauce.

These possibilities can't be explained if the only evaluative criteria are the goals specified by the intentions.

The action evaluation system

To understand these phenomena we need to recognise a broader set of evaluative criteria. While it is often the case that a specific explicit goal operates as a primary focus of action selection and regulation processes, this goal is only one item amongst a complex set of criteria used to evaluate the action. Some criteria are low level and generalised. Thus, all actions are evaluated for efficiency, regardless of whether efficiency is an explicit constituent of the content of the goal of the action. Other criteria are higher level and also generalised. A bluegrass musician will evaluate their playing according to their internalised aesthetic norms for bluegrass music. Some norms are specific to the action type, such as technique criteria. Some norms are specific to an individual, such as a personal playing style. In the performance of any given action an ensemble of criteria will be operative in evaluation processes. Criteria other than the primary goal can be used to evaluate the primary goal and its implementation. These additional criteria are themselves imperfect and subject to learning. A novice has evaluative criteria for the skill which are impoverished and poorly reflect the norms of the skill domain. Experts often have very rich, articulated evaluative criteria. For this reason, instruction and other forms of social feedback can play a vital role in guiding learners. Techniques for self-assessment which use an external perspective, such as recording and analysing performances, are also very valuable because they allow the individual to better apply performance norms they have acquired from an observer's perspective to their own performances.

Thus, we add to Mesh the proposal that skilled action evaluation is based on an action evaluation system (AES) which develops during skill learning. 13 The AES plays a role in the cognitive processes of intention formation and in the control of action execution. Action evaluation is holistic: no single criterion has strict dominance (e.g., there is no strict master goal) and the weighting of criteria can vary across contexts. The breadth and depth of evaluation will vary across contexts, but a complex set of criteria are often operative in the control of action execution. 14

In this respect the account departs from Bratman's model of intentions. As described above, Bratman's model has a strongly punctate structure in which there is a phase of deliberation which culminates in commitment to an intention, followed by a phase in which cognitive processes are focused on implementation of the intention and evaluation of it is bracketed. Bratman's rationale for the bracketing of intention evaluation is based on cognitive resource limitations: he claims that it is not possible to continuously determine the best course of action at each point in time. But while it is true that it isn't possible to perform a comprehensive analysis of the best course of action at each point in time, this doesn't imply that intention evaluation must have the punctate structure of his model. Bratman recognises that intentions may be reconsidered when stakes are high and 'new information comes in', but he regards this as exceptional. He says that it is reasonable to have a default presumption in favour of plan stability rather than reconsideration. Concerning the circumstances in which reconsideration is reasonable, he writes:

Sometimes the stakes are quite high, and there is an opportunity for calm and careful reconsideration of one's prior plan. It seems plausible to suppose that it is in the long-run interests of an agent occasionally to reconsider what he is up to, given such opportunities for reflection and given that the stakes are high, as long as the resources used in the process of such reconsideration are themselves modest ( 1987 , p. 67).

Our model is very different. It is common to have highly imperfect information and it is hence adaptive to continue to evaluate intentions after they have been adopted, including during action execution. This allows them to be flexibly modified and abandoned as more information is gained and as circumstances change. Here we need to distinguish between evaluation of implementation intentions involved in carrying out a plan and evaluation of the overarching intention. We claim that evaluation occurs at every level. The breadth and depth of evaluation varies, and it is certainly true that there is greater opportunity for deep and wide evaluation before and after performance compared with during, but nevertheless, higher levels of control can be 'in play' during performance. Thus a professional bike rider might, during a race, re-evaluate their ability, re-evaluate their strategy for a particular obstacle, re-evaluate their race strategy, or pacing plan (Christensen & Bicknell, 2019 ; Sutton & Bicknell, 2020 ). More broadly, an athlete may re-evaluate their strategy for the season, and might even re-evaluate their commitment to racing at this level. For instance, an older rider near the end of their career might switch during a race from assessing themselves as still being competitive at the highest level to no longer being competitive, and decide on this basis to retire. At the other end of the skill career time line, we can expect that evaluation of commitment to the skill to commonly occur during performance during early phases of acquisition and at key career stages.

The basis for such evaluation is the individual's AES. A well-developed, adaptive AES represents relevant evaluative criteria at various stages of intention formation and action performance.

This model of control differs from the DPM model. In keeping with Bratman's model, on the DPM model distal intentions are ascribed the function of terminating practical reasoning about what to do. Evaluation of success is goal-based and top-down. In contrast, our model places more weight on bottom-up processes in which higher-level goals are revised in response to information gained during action execution. Evaluation of intentions does not necessarily terminate with their adoption. Evaluation of success is not only with respect to achieving the goals specified by intentions. We think the DPM model can be readily amended to accommodate the phenomena we're describing, but these are nonetheless features of control that have high significance because they play important roles in learning and flexibility.

Performance and metacognitive awareness

Performance and metacognitive forms of awareness play a key role in action evaluation. In contrast, on Bratman's account reconsideration is based on habits and dispositions, deliberation, or by policies. He thus fails to recognise the importance of such forms of awareness. Confidence, for example, can have performance and metacognitive forms. Performance confidence is awareness of the likelihood of action success. Metacognitive confidence is awareness of the extent to which sufficient information is available for effective decision-making and control. When both kinds of confidence are high, as they are likely to be when a philosophy professor makes a plan to go to the library to borrow a book, depth of evaluation can be low during decision making and performance. When these forms of confidence are much lower, as they will be when learning a new mountain bike riding technique, depth of evaluation will tend to be higher in all stages of action.

According to Mesh, causal representation contributes to performance and metacognitive awareness. A causal control model represents the causal features of the situation relevant to action decisions and control. In the case of braking this will include causal features such as the nature of the surface, the amount of grip, and the amount of braking force that can be applied. Thus, the causal control model is the basis for awareness of the performance envelope , or range of performance states that are available. In this case, awareness of the performance envelope includes awareness of the range of braking forces that can be applied without losing grip. Awareness of the performance envelope serves as a basis for evaluating whether to continue with an action during performance. If a breakdown is likely it may be best to abandon the action. At a more finegrained level, awareness of the performance envelope allows the formulation and modification of action strategies. If grip proves to be unexpectedly high, for instance when using a new type of tire, braking strategies can be modified accordingly. When the individual is uncertain they may adopt a conservative strategy and attempt to gather more information (Christensen & Bicknell, 2019 ). Thus, if they are unsure of how powerful their brakes are, for example if they are on a new or recently serviced bike, they might use early braking or ride at a slower speed as they assess the performance of the brakes. If the individual is confident they may operate closer to the edges of the envelope.

Social and cultural learning and the degrees of freedom problem

The standard approach to skill is individualistic. When seeking to understand advanced skills the focus is on the autonomous abilities of individual experts. When seeking to understand skill learning the focus is on the processes by which an individual's abilities are transformed from novice to expert. Of course, it is understood that teaching and other forms of social learning play a role in skill learning. It's understood that some skills, such as theatre, dance, music, and team sports, involve collective action. Indeed, there is burgeoning transdisciplinary interest in collaborative experiences of, and influences on, skilled performance (Bicknell & Sutton, 2022 ). Nevertheless, skill theories treat social phenomena as secondary, or subtopics of skill. Mesh has followed this individualistic orientation (but see Christensen & Sutton, 2018 ).

Attention to the larger evolutionary and ecological context indicates that we should see individual and social aspects of skill as fundamentally interwoven. Human skills are exceptionally flexible, complex, and are generally acquired and practiced in highly social ways. These associations are not accidental. The flexibility of human skill is founded on a sensorimotor system capable of many 'degrees of freedom', being able to adopt an extremely large number of configurations that can be structured in many ways over time. The diversity and complexity of human skills, in comparison with other species, is possible only because of this underlying potential. But the high dimensionality of the human sensorimotor system, combined with the complexity of many skills, presents difficult problems for learning and control. The learner confronts an extremely large problem space in which solutions must be found. The degrees of freedom of the sensorimotor system must be steered in ways that realise solutions (Bernstein, 1996 ). Learning thus presents extremely difficult search and control problems.

One way that learning is made tractable is to acquire skill progressively, beginning with basic abilities that present relatively simple problems and moving to progressively more complex abilities that build on the simpler abilities (Bryan & Harter, 1899 ). Another way that learning is made tractable is by making it social. Experts and peers provide models of high quality solutions. Teachers can guide learners through the extended pathways to complex solutions. A skill community is able to explore the space of possibilities and solutions far more effectively than a lone individual. When a member of a community discovers a superior solution or other form of valuable skill knowledge, this can be propagated through the community (Goodwin, 1994 ). Many discoveries can be combined into complex, sophisticated methods.

Rival expectations

Based on the preceding discussion we can distinguish between two main contrasting sets of expectations for the situation we are investigating. Based on the classical view we should expect major changes to technique and equipment to be highly disruptive for two reasons. Firstly, automated forms of flexibility should be unable to cope with these kinds of changes because they require qualitatively new sensorimotor patterns. Secondly, cognitive processes should also struggle to cope because they employ general purpose representations and problem solving methods. They are hence poorly suited to skilled action control, and should be overwhelmed by the alterations to the complex relations involved in action production. Mesh yields a different set of expectations. An individual with a significant amount of experience will have developed mechanisms for the cognitive control of action which allow relatively fluent coping based on problem solving. This problem solving will be based on causal representation and an action evaluation system employing a complex set of criteria. Control will be more flexible than depicted by Bratman's model, with continuous evaluation even at higher intentional levels. This problem solving will be imperfect, however, especially in an individual whose technical abilities are fairly basic. Social guidance from an expert can supplement individual problem solving by directing the learner to better solutions.

The nature of our study

We conducted a field study investigating responses to major changes in a rider with several years mountain biking experience but beginner-level technique.

We employed a researcher-practitioner approach, in which the authors served the dual roles of investigators and participants (see Bicknell, 2021 ; Downey, 2022 ; Downey et al., 2015 ; McIlwain & Sutton, 2014 , 2015 ; Nemani & Thorpe 2016 ; Olive et al. 2016 ; Ravn, 2022 ; Samudra, 2008 ; Spinney, 2006 ; Sutton & Bicknell, 2020 ). This approach brings attention to theoretically and ecologically significant aspects of skilled action in contexts that are difficult to capture in the laboratory, from the armchair, or when the researcher is unfamiliar with the nuances of a particular community of practice. Our experiences were undoubtedly shaped by our theoretical interests, and the evidence should be viewed as exploratory and tentative. Validation of the kinds of phenomena we describe is needed using other methods. These include broader ecological sampling and laboratory investigation. It is especially important that ecological methods be employed which use structured data gathering in close temporal proximity to performance with theoretically naïve participants. But it must be emphasized that all methods have strengths and limitations. The best overall research strategy is to use a large methodological toolkit and seek to buttress each investigative mode with convergent evidence from others.

The two authors of this paper have differing levels of mountain bike expertise. Kath has been a mountain bike rider for over twenty years. She has worked for global cycling media for more than ten years, taught skills clinics, raced domestically and internationally, and has written academic papers and a PhD on the sport. Wayne, in contrast, has very limited mountain bike riding experience. He is not a raw novice; he has extensive experience of recreational and commuting riding on roads and about fifteen years previously he spent about a year mountain biking regularly, riding once or twice a week. This experience included twisty 'singletrails', tracks roughly the width of a foot trail, with rutting and differences in grip due to the type of dirt underneath his wheels (eg. loose and skatey or smoother ‘hardpack’). He had largely avoided more 'technical' trails including features like ‘rock gardens’ and logs. With respect to mountain bike riding he was self-taught and as a result had not acquired some important basic mountain bike riding techniques. As part of research for a previous paper (Christensen et al., 2015 ), he read a mountain bike instruction book and gained some familiarity with basic mountain bike techniques this way. Kath had also given him some instruction during the study. He had not, however, spent a significant amount of time practicing these techniques or received any further ‘live’ riding instruction.

The fieldwork session was designed to explore and document Wayne’s experience of the trails through an initial ride with no input from Kath, followed by two major changes. After observing Wayne ride an initial series of beginner-intermediate singletrails, Kath provided instruction on core mountain bike riding techniques, which Wayne then attempted to employ. Secondly, after riding the track on his own bike, Wayne then switched to Kath’s bike, which was a more modern and capable design.

In more detail, at the time of the study Wayne’s bike was approximately ten years old, an aluminium ‘cross country’-style hardtail (meaning no rear suspension), with 26″ wheels, hydraulic disc brakes, and basic front suspension in need of a service. Kath’s ‘trail’-style bike was a few months old. The design reflected substantial changes in bike technology, trends and manufacturing materials. These included: larger 29″ wheels with wide 2.4″ tubeless tyres, which roll over obstacles with more ease and traction compared to Wayne’s smaller wheels with narrower tyres; a more stable and relaxed geometry, which adds traction and confidence on climbs and descents; far more sophisticated front and rear suspension for better traction and compliance, and other modern features such as a 1 × 12 drive train (so no shifting is needed with the left hand) and a dropper seat post which allows the rider to press a lever on the handlebars and move the seat downwards so it doesn’t catch on their thighs when they move their body toward the rear of the bike while descending. The brakes were far more powerful, the frame material (carbon) more compliant, and the handlebars substantially wider, again providing enhanced stability and control. Kath and Wayne are a similar height, meaning they both ‘fit’ the same size frame. However, when Wayne switched to Kath’s bike the contact points were adjusted for Wayne, with the seat height being modified and his own pedals used.

The trail used for this investigation, a popular cross-country loop at the Ourimbah trail network in New South Wales, Australia, was chosen on the basis that Wayne could tackle it with reasonable safety, with guidance from Kath, but which contained obstacles that were more challenging than Wayne's prior experience made him comfortable with. During the ride, Kath gave Wayne the kind of instruction and induction into the mountain bike subculture that would be characteristic of an experienced rider taking a friend on a ride for the first or second time. For example, when Wayne was concerned about riding over a log obstacle she explained and demonstrated key body movements and the amount of speed needed to do it safely, but also encouraged him to walk the obstacle and try it again later if he preferred.

We took photos and recorded video of Wayne’s successive attempts at challenging obstacles on both bikes, and recorded video of Wayne describing his immediate responses to these experiences. We met the next day to write notes on the experience.

Riding the Ourimbah cross-country track

There were two aspects that stood out as especially noteworthy in Wayne’s experience: a change in technique that dramatically improved descending steeper trails, and adaptations to the increased performance capabilities provided by the second bike, particularly due to its stability over rough terrain.

At the beginning of our fieldwork session, Wayne rode a short loop of ‘singletrails’ without instruction or interference from Kath, who rode behind him, watching and observing. These trails included several relatively steep descending sections of trail, linked together by narrow, winding, rocky connections and the occasional smooth section for the rider to relax and catch their breath. (Understandably) Wayne was riding somewhat nervously and cautiously. He felt that his approach to riding these trails was reasonable given his limited overall experience and that he had not ridden a mountain bike trail in a number of years. Riding behind him, however, Kath could identify specific technical problems. She could see and hear the rear wheel skidding and noticed that Wayne’s body position (and centre of gravity) was quite far forward on the bike. This puts a lot of pressure on the front wheel, which causes several problems while descending, the most severe of which is that it increases the risk of flipping over the front of the bike. In the mountain biking subculture this is referred to as an ‘OTB’ (over the bars)—the standardization of the term suggesting it is a fairly common experience but one to be wary of.

We paused on a long flat section of fire road to discuss the experience of the first section of trails. Worried that Wayne was going to injure himself, Kath provided instructions that would help him ride the section more smoothly and safely on the next attempt. She explained a technique for descending steep obstacles, which involves keeping the feet balanced evenly on the pedals while the rider moves their bodyweight rearward on the bike to maintain balance and stability. She explained this to Wayne verbally, along with an arm gesture showing the effect of weight on the bike in relation to the terrain. She used the cue words ‘butt back’ and ‘weight back’ as a shorthand way to emphasize and direct this technique after the initial description of what to do. Taking advantage of the less threatening and challenging terrain provided by the wide, flat fire road, Kath showed Wayne an exercise which encouraged him to experiment with how far he could move his body rearwards while maintaining momentum on the bike. This involved riding in a straight line at a moderate speed, moving his butt behind the saddle and allowing it to graze the rear tyre. This exercise was designed to increase his awareness of how much space he had to move rearward on the bike, what this felt like in practice, and how this sensation differed to what Wayne thought was the near-maximum amount he could get his bodyweight behind the bike. 15 The sound and feel of grazing the tire provide aural and kinaesthetic cues that signify the rider has succeeded in the task when it is not possible to see, visually, how far back they have reached.

We then rode the same short sequence of trails again. Wayne now focused on getting behind the saddle during any steep downward sections of trail. The result was a dramatic improvement in the controllability of the bike. This transformed the experience of sustained descents and short, sharp drops or ‘rolldowns’. Rather than feeling threatening, the experience of riding these obstacles felt relatively comfortable—it felt less steep, less rough, less like he was about to have a crash. After applying the technique cautiously to a rocky ‘stepdown’, Wayne immediately began to apply the same technique to other steep, downward sections of the trails: log rolls, steep downward corners, rocky rolldowns, anything where the front of the bike is much lower than the rear of the bike while riding a trail obstacle.

After a longer lap of the trail on Wayne’s bike, Kath gave him her own bike to use for the second lap. She had another bike waiting in the car to facilitate this exercise. The technological differences described above between Kath’s bike and Wayne’s older model bike indicate that Kath’s bike would be more stable, compliant, absorbent and confidence inspiring. While this makes sense on paper, Wayne was nevertheless astonished at how much more capable the bike was in practice. The most immediately striking feature of the bike to him was its greater stability, and the fact that this allowed much better low speed control than his own bike. In comparison, the relative instability of Wayne’s own bike meant it would often feel like it was going to tip over at slow speeds.

The combination of greatly enhanced stability and compliance had a dramatic effect on Wayne’s experience riding the trail. He was able to ride faster on bumpier sections, with the bike soaking up rocks and gaps between them that would produce strong jarring on his own bike. Within 10–20 min of riding this bike his confidence greatly increased. Many descents and ascents he had struggled on while riding a lap of the trails on his own bike—rooty straights, rocky windy uphills, small rocky step-ups, uphill corners, rutted entries into corners, descents littered with a messy array of small obstacles—were experienced as being much more ‘ridable’ than they had been earlier that same day. The bike maintained traction more easily allowing Wayne to pedal and guide it through the obstacle with more control, confidence and ease. He continued to approach some obstacles cautiously, however, and Kath spent some time teaching him to ride over a log, which looked difficult to him but in fact was not. His main difficulty was simply overcoming his fear of the obstacle so that his approach was fast enough to carry him over the rocky ramp that led to the log itself. We make no claims that Wayne was able to ride all sections of the trail, or ride flawlessly ever after. He subsequently crashed when he misjudged a rocky section later in the day, bruising his ankle and wrist and acquiring some grazing.

Finding theory in action

In this section we use the theoretical concepts introduced in Sect. 2.2 to characterise the processes by which Wayne adjusted to the new technique and the new bike. Wayne was familiar with these concepts, which makes it easy for him to describe his riding experiences in these terms. This familiarity also undoubtedly influenced Wayne's experiences during our field study. However, based on Kath’s extensive experience teaching skills clinics, and riding with mountain bikers at a diverse range of skillsets, we think that the kinds of problem solving Wayne engaged in are not unusual. In particular, his experiences of identifying control problems and experimenting with solutions were in many respects fairly typical for a beginner rider.

Simple forms of adaptation

Wayne adapted rapidly to the new technique and new bike. Some of this adaptation involved relatively simple forms of flexibility. Simple calibration changes in important parameters, such as braking forces and braking timing, played a role. Both of the major changes improved stability, which had the effect of making feedback control more tolerant or less 'twitchy'. Feedback control processes quickly recalibrated for the new tolerances. As riding became more manageable Wayne could relax more, and reduced bodily stiffness is likely to have made control easier; bumps and other perturbations which might have been jarring and disruptive would now be absorbed more effectively through his limbs. Experience selectively highlighted key parameters, allowing control to be more focused.

Problem solving using causal knowledge and metacognition

Nevertheless, the changes in technique and bike were large enough to require adjustments by means of strategies formulated using problem solving. Wayne's ability to adapt to large changes hinged critically on an ability to formulate and implement new action strategies 'on the fly'. We can illustrate this by describing in detail a change in riding strategy associated with the technique change of getting behind the saddle. Although Kath wasn’t aware of it, the rear wheel skidding that she observed during Wayne’s initial ride was partly the result of a deliberate braking strategy that he thinks of as ‘tail dragging’, which involves using primarily the rear brake. After adopting the behind-the-saddle technique Wayne switched to an equalized front-rear braking strategy. Wayne was familiar with rear-wheel-based braking from riding as a child, with this experience including riding ‘back pedal’ brake bikes and with using the rear brake to skid out the back wheel on loose surfaces when coming to a halt, a satisfying and popular maneuver. He knew, however, that equalized braking is regarded as the superior technique and he had generally used it in his previous mountain bike riding. He nevertheless initially used rear-biased braking as an improvised strategy in response to control problems that he was experiencing. Wayne wasn’t aware that his weight was too far forward, but he was aware of some of the consequences of this. The load on the front wheel caused instability and had the potential to cause the front wheel to lose grip and slide out, resulting in a crash (which Wayne thought of as a ‘washout’). 16 Wayne felt that the wheel was most likely to lose grip under braking and using a rear-biased braking strategy helped to reduce this risk.

Thus, causal awareness played a key role in the adoption of the tail-dragging strategy and the later switch to equalized braking. Here we should note that Wayne's perception of the most immediate and important risk that he faced differed from Kath's assessment. Wayne was preoccupied with the danger of a washout due to heavy front braking, whereas Kath viewed the primary risk in Wayne's riding during this phase as being a front wheel washout or OTB crash caused by insufficient rearward weight. Other riders in a similar situation might have interpreted their risks differently and adopted different strategies. Other strategies which reduce the risk of loss of control when riding a difficult descent include putting one or both feet on the ground and scooting down, using both brakes fairly heavily and ‘inching’ down the obstacle (generally ill-advised), avoiding braking all together and focusing on body position, balance and looking ahead to the exit of the obstacle, or getting off the bike and walking (or sliding) the bike down the obstacle.

Metacognition can also be seen in this example. While Wayne thought there was a danger of the front wheel sliding out, he didn’t know in detail in what conditions this could occur. He was still adjusting to the ‘feel’ of the bike on the terrain and was uncertain about the amount of grip available and the braking forces that could be used. That is to say, Wayne was aware that he lacked sufficient information for good control. Estimating these action parameters is complicated by the fact that they are strongly affected by the nature of the surface, which was variable, and by the fact that in a washout the loss of grip tends to be abrupt. In the face of this uncertainty, tail dragging combined with low speed was a relatively safe, conservative strategy. And it worked! Wayne did manage to ride these difficult sections of trail without crashing. Kath’s intervention was to help Wayne ride them more smoothly, more safely and, ultimately, more enjoyably.

Metacognition also influenced Wayne’s use of tail dragging in another way. Tail dragging is a simple strategy to employ because there is no need to precisely coordinate front and rear braking pressures. Wayne was experiencing high cognitive load because he needed to pick a line with care over the deep rutting of the trail to ensure that the front wheel did not glance off the side of a rut and get channeled down it, resulting in a crash. In addition, Wayne was experiencing significant jarring through the handlebars, and he was concerned that if he hit a bump while braking he might accidentally grab the front brake too hard. Tail dragging simplified the cognitive demands of braking and allowed him to direct more attention to line choice. That is, the choice of strategy was based in part on awareness of excessive cognitive load and the need to reduce this load.

One of the main problems with tail dragging is that it reduces effective braking power because braking force is provided by only one wheel, and because it often results in the rear wheel skidding. This in turn means that speed must be kept low. Partly for this reason Wayne maintained a fairly low speed during the descents, but he preferred to ride at a relatively low speed in any case to allow more time for line choice and to minimize the consequences of a crash. He thus didn’t regard the speed limitations of tail dragging as a reason to avoid it in this context.

However, after Wayne began getting fully behind the seat while descending he switched to equalized braking. This was because the control problems that prompted the tail dragging strategy had been largely eliminated. Independently of any detailed causal understanding, the rearward riding posture leads to several changes in the feel and handling of the bike which provide greater sense of control on steep sections of trail. Cues indicating instability are reduced and handling is improved. The arms are more extended, which reduces unwanted side-to-side rotation of the handlebars and, consequently, the front wheel (compared to the freedom of movement that comes with a larger bend at the elbows). But Wayne was more specifically aware that with his weight now towards the rear there was a greatly reduced risk that the front wheel would lock up under braking. The risk of an over-the-bars crash was also much lower. As noted, this danger had not been at the forefront of Wayne's mind but he was aware of it (he had experienced such a crash previously). Now that his weight was positioned rearwards, and the bike could rotate forwards without pitching him forwards, he became aware that an OTB crash was a lot less likely.

Indeed, the front wheel could now rise and fall much more easily as it tracked over obstacles. This made line choice less critical because there was less chance that the front wheel would glance sideways when it struck the side of a rut. This reduced cognitive load. There was less jarring through the handlebars, making it easier to judge and execute braking pressures. With braking distributed between front and rear, overall grip was increased and there was less chance of either wheel skidding. Wayne became more confident about applying much stronger braking pressures than he had previously. And since the improved handling made similar riding problems more tractable, he became more generally confident about tackling various kinds of descent obstacles. There were distinct limits to these improvements, however, and there were some descents that he still regarded as too challenging. For these he would dismount and walk.

We can illustrate changes in strategy in response to the new bike with the example of a decision to tackle a particular ascent. It was short, relatively steep and had a somewhat loose surface. Wayne tackled it several times on his own bike and once on Kath’s. On his own bike Wayne found the ascent challenging because he needed to begin with high momentum in order to climb it. There were two problems that contributed to this. One was that he had relatively little grip because of the geometry of his bike and the tires. Specifically, on this slope, with its loose surface, if his speed became too slow while using high power pedal strokes the rear wheel could lose traction and 'spin out'. The other was that his riding position on this bike had a relatively high and forward center of gravity, which meant that the bike felt unstable and 'tippy' when riding at slow speeds. If Wayne was going too slow he needed to come to a complete halt and dismount, or he would fall over. The approach to the ascent was downhill, and each time he made the approach he needed to quickly decide whether he had the right line and was going fast enough to make the ascent successfully. He made it up the first time on his bike but stopped on the second attempt because he didn’t think he was going fast enough.

On Kath’s bike Wayne decided to tackle the ascent even though his approach was slow. This point is worth emphasizing because it highlights the way that the different capacities of the new bike led him to use altered riding strategies for obstacles that he had not yet experienced on the bike. Had Wayne been on his own bike he would not have attempted the ascent with the approach that he had at this point. He did attempt the climb because he was confident that the low speed stability of the bike and its grip would allow him to ride it slowly, with less risk of falling over and less risk of losing traction. This proved to be the case. He found that he could come to a near halt during the climb without falling over, and the increased grip of the tires meant that he could use slow, high power pedal strokes without the rear wheel spinning out.

To sum up, Wayne was able to construct riding strategies ‘on the fly’ based on causal and metacognitive awareness. He could form, evaluate and modify strategies based on awareness of factors such as instability and threatened loss of grip. The strategies could take into account multiple factors, reflecting an awareness of how causal factors interrelate in riding. Wayne also selected and adjusted strategies based on sensed uncertainty and risk. This problem solving ability extended to large changes in causal relations associated with major changes in technique and equipment, and hence allowed him to cope with these changes.

It's important to note that Wayne's adaptations went beyond the formulation of specific strategies for particular problems. Wayne showed generalised learning in the sense that each major change allowed him to solve new classes of control problems. As he formulated and implemented new strategies he was also learning about the underlying causal structure of control. He was, thus, extending his causal control model as well as refining it.

Difficulties in adaptation

Difficulties and limitations in Wayne's adjustments are also revealing.

The new bike had only a rear derailleur rather than front and rear. This simplified changing gears but Wayne had well-entrenched gear changing methods which involved coordinated shifting of front and rear derailleurs. It's worth emphasising just how important gear changing is in mountain bike riding. With frequent, rapid changes in gradient and other trail features, it's necessary to change gears often. Smooth, fast riding depends on anticipative gear shifts, especially when the change in gear is large. When encountering a steep slope, for instance, the rider may need to shift from a high to a low gear, and be in the right gear to effectively apply power as speed slows. It's desirable to maintain as much speed and momentum as possible. Wayne's technique for such a situation involved making several shifts in sequence. An initial anticipative shift selects the middle or small front chain ring (lower range gears) and a rear gear that is medium-to-low but high enough to 'catch' the initial phase of slow-down and extend the speed and momentum. Multiple subsequent shifts downward are then made, using the rear derailleur, as slow-down continues, until the right gear for sustained climb is reached. Selecting the wrong gear for a shift disrupts the smooth progression. When the gear is too high or too low the rider will 'bog down' or spin, and either way lose speed and momentum. A further consideration on Wayne's bike was that his gears would sometimes not shift under heavy load, making it important to shift before high power output was required. This was not the case with Kath's bike, which shifted smoothly during high-power pedaling on climbs.

On Kath's bike Wayne had to inhibit his urge to operate the front gear system and reorganise the way that he made anticipative gear shifts. This required heightened attention. An especially attention-drawing feature of the alteration was that in the location where Wayne would operate his front derailleur there was a lever to activate the 'dropper' post. This, in combination with pressure (or lack of) on the saddle, lowered and raised the seat. Lowering the seat during descents gives more freedom to move backwards and forwards as needed. But having the seat drop is not something which the rider will want to happen unexpectedly when trying to change gears or pedal up a hill. When raised the seat would spring upwards to its normal position, and was, in effect, a spring-loaded piston driving towards the rider's crotch. This bike feature was unlike any that Wayne had previously experienced and he found it somewhat disconcerting.

Wayne was able to modify his gear change method and learn to use the dropper post, but these adjustments were more effortful and less smooth than those described in the previous section. Why this should be so raises interesting questions. In general, it's reasonable to expect that some modifications to control are easier to make than others because the control system is better prepared to handle some kinds of change than others. Piaget's ( 2015 ) distinction between assimilation and accommodation is one expression of this idea. In the Piagetian picture increasingly powerful/flexible forms of problem solving ability develop in a progressive sequence as more abstract/deep concepts are learned. The Einstellung (Luchins, 1942 ) and functional fixedness effects (Duncker, 1945 ) are manifestations of the somewhat contrary-seeming phenomenon of increases in rigidity with learning. There is no deep conflict, however. Learning can involve increases in rigidity with respect to some aspects of control together with increases in flexibility with respect to others.

We can develop a preliminary explanation for differences in difficulty in this case which draws on the resources developed in Sect. 2.2 . With respect to the new bike, changes in attributes such as stability and grip were relatively easy for Wayne to incorporate into his riding in at least an initial, basic way. This may be because, although the parameter values were substantially different to his own bike, the parameters themselves, and their role in control, were reasonably familiar. He could therefore adjust his existing methods relatively smoothly. But other differences involved more substantial changes in causal relations and more extensive changes in control operations. Thus, a familiar operation needed to be 'remapped' to a different mechanism with drastically different causal effects, along lines such as {[L-LEVER-OP → F-GEAR-OP] ⇒ [L-LEVER-OP → SEAT-OP]}. Since the operations involved considerable novel structure, the structure needed to be composed in working memory, with implementation and monitoring requiring greater attention than more familiar control operations.

More generally, based on the causal control model account we could expect that skill learning will often exhibit a somewhat Piagetian pattern of increases in generalisation and flexibility which arise as the learner learns to solve varied causal problems. More generalised causal representations develop which capture deeper structure, and more powerful and flexible forms of control develop in order to efficiently manage varied problems.

An even stronger limitation in Wayne's ability to solve the riding problems he was facing is evident in the fact that he needed instruction on the correct implementation of the behind-the-seat technique. During the initial ride he was aware that he was experiencing control problems and rode cautiously for this reason. But he was unable to diagnose the source of these problems to specific technical flaws. At this point he assumed that he simply needed more experience in order to improve calibration and refinement, as opposed to making large technical changes.

This failure in problem solving is all the more striking because he understood the technique abstractly and believed he was implementing it. When Kath explained verbally the technique of getting behind the saddle during descents, the information was already familiar. He had not known of the technique when he was mountain bike riding by himself many years previously, but he had since learned of it from a mountain bike instruction book. He knew that good riding technique involves shifting one’s weight backwards during a descent to maintain even weight distribution across both wheels. What he didn’t realize is that he was implementing this technique incorrectly. More specifically, he didn’t realize that he wasn’t moving nearly as far backwards as he could and should. From his perspective it seemed like he was moving backwards to about the limits of rearward movement for his body. This was far from being the case.

To understand how Wayne could be as mistaken as he was about this it will help to note that in riding on roads—which was the bulk of his riding experience—there is relatively little need for front-rear body movement. Consequently, a relatively small amount of rearwards movement felt like a lot. Moreover, although Wayne knew that it was important to maintain even weight distribution across the front and rear wheels, he was not used to maintaining this form of awareness and had been preoccupied by line choice. There is a distinctive ‘feel’ to a weight distribution that is too far forward in a descent, which notably involves pressure on the hands and wrists. Wayne had not yet learned to efficiently identify this and respond appropriately.

Thus, although Wayne was able to detect the front wheel instability and formulate a compensatory strategy, he failed to autonomously find a much more effective strategy. This stemmed from a poor representation of weight and balance and a poor awareness of his ability to adjust balance. He failed to properly relate the instability to a forward weight distribution and solve this by moving far enough rearwards. This is despite the fact that he knew the correct technique abstractly. A poor on-the-bike representation of balance contributed to a failure to properly interpret the abstract instructions.

We can interpret these points in terms of the concepts of causal control models, action evaluation systems, and problem discovery. Wayne experienced cues to poor control in his initial ride which prompted him to ride cautiously. But his ability to represent the causes of these problems was underdeveloped and so, while he found a solution that achieved the goal of riding the obstacle, he failed to find a more optimal (smoother, safer, speedier) solution. Once he had learned the superior technique his causal control model was altered and his capacity for action evaluation improved. He became aware of an expanded range of body movements and as he experimented with this range he gained new information about the interrelations between weight distribution, stability and handling. He could now interpret high pressure through the wrists as a sign of weight being too far forward. He could better interpret perceptual cues related to balance and perform bodily adjustments to modify weight distribution more appropriately. Putting this in more general terms, he had acquired a revised understanding of balance control on the bike which yielded a generalised improvement in his ability to solve riding problems.

The problem of translating between representational systems

The difficulties Wayne experienced involved a failure to properly translate between abstract and situated representational systems. As such, they help to reveal how these mappings are constructed. In the earliest stages of skill learning the individual must laboriously construct concrete interpretations of abstract action descriptions. This is hampered by two factors. Firstly, the individual lacks systematic representations of skill-specific phenomena at the level of concrete control of execution. Secondly, the individual lacks well-developed systematic mappings from abstract to concrete representations. In this case Wayne lacked a fully-developed systematic representation of the range of positions he could take on the bike and their relations to balance. Once he had learned to move his body backwards, and experienced the technique in an approximation of its correct form, he developed an awareness of balance and stability which he could relate to his abstract knowledge of the structure of the technique. He had thus developed a representation of the structure of the technique from the perspective of control which he could use for control. One way to describe this is that he had now acquired a relatively well-structured executable action concept for the technique. However, much more practice would be needed to consolidate this concept in relation to a well-developed causal control model for implementation.

Improvements in the structure of control

Wayne experienced a significant degree of uncertainty throughout the ride. His intentions, in particular the riding strategies he adopted, involved commitment that was always qualified and evaluated during performance. He maintained awareness of opportunities to abort actions and he did so on several occasions, such as the one described above where he initiated an ascent but stopped part way for fear of losing traction at a higher section of the ascent and falling over. He modified strategies both prior to and during execution to reduce problems, increase the chances of success, and, later, to exploit improved capabilities. His intentions were thus much more labile than Bratman's model recognises. This lability was based on an action evaluation system which could evaluate intentions against a complex ensemble of further criteria represented by the AES. Indeed, the learning process hinged on this.

Wayne's uncertainty was especially high in the initial stages of the ride. He was unsure of which trail sections he could and could not ride safely and he was unsure of whether his riding strategies would be effective in negotiating obstacles and avoiding crashes. His ability to evaluate his performance was also limited, as evident in his flawed diagnosis of the stability problems he was experiencing. Thus, his control ability was relatively poor in both the goal-based and problem-based senses. His ability to achieve the goals that he had was modest and not reliable enough to provide reasonable confidence. But he was also uncertain about his goals, and not able to form all of the right goals, because he lacked a good understanding of his riding problems.

Wayne’s control ability improved over the course of the ride in both the goal-based and problem-based senses. He became better able to achieve the goals that he had, and he became better able to solve the riding problems that he faced. This was based in part on improvements in his understanding of his riding problems, which included greater ability to evaluate action strategies and performance, and form appropriate goals. Improvements in evaluation ability, with enhanced ability to manage uncertainty, are critical to mountain biking, which routinely involves riding unfamiliar, challenging trails.

The technical improvements in particular involved a relatively deep form of problem discovery. As Wayne learned how to properly implement the behind-the-seat technique he was learning both technique-specific and more generalised representations. He was refining a technique-specific concept linked to a causal control model for the technique. These representations incorporated more generalised representations, such as of body position on the bike, balance state, terrain, grip, speed, and so on. These more generalised representations allowed improved representation of a larger set of riding problems. This enabled the formulation of an expanded range of riding strategies which were more effective. These representations also improved the ability to interrelate techniques and strategies by means of common features. Thus, when one strategy is succeeded by another, such as a descent followed by the negotiation of a corner, features of each can be related to each other and adjusted to provide good fit. The speed and line of the descent can be shaped to set up a good entry to the corner and an efficient cornering line, for instance. Action-specific representations are thus integrated into a global state-space of control which represents the situation, performance state, and action possibilities. This state-space can be more or less well integrated, and the more integrated it is, the better able the individual will be to produce coherent complex action.

Social and cultural influences

Wayne's prior mountain bike riding experience was not insignificant, involving about a year of riding one or more times a week on a mixed set of singletrack and fire trails. This provided him with enough skill to engage in the problem-solving described above. But his learning was based largely on solo discovery, adapting skills from road riding and casual BMX-style riding in childhood. The kind of flaws in we’ve described in Wayne's technique, and the limitations in his problem solving ability, are common in individuals who attempt to teach themselves complex skills. Rich engagement with teachers and a skill community can scaffold skill development, allowing the individual to develop solutions and an expanded sense of what is possible (Aggerholm & Hølbjerre-Larsen, 2017 ).

One of the most important ways that a skill community can guide individual learning is by furnishing skill norms. As we described above, during the initial ride Wayne was aware that he was experiencing control problems but thought his riding was reasonable given his experience and the context. This is an example of a general phenomenon: learners tend to possess impoverished norms for the skill domain, and this hampers their ability to evaluate and improve their performance. In this case, Wayne did not have a good grasp of what kind of performance he should be able to achieve, given his base skill level. In fact, at that point he could relatively easily achieve a much higher level of performance. In general, it is difficult for learners to know what performance standards could be expected for their level and experience. This in turn limits their ability to diagnose problems in their methods.

Skill communities often have highly developed performance norms which orient individuals. In mountain biking, speed is a highly valued performance norm. Wayne was not especially concerned with speed at this point, and Kath found it amusing that Wayne’s initial reactions to the new bike were primarily focused on its improved low speed handling. Speed, though, is only one element of a set of norms for assessing quality of performance. Smoothness and efficiency are also valued. These attributes are integrated into an umbrella concept of flow , 17 which serves as a goal for riders and trail builders (Bicknell, 2016 ). Other norms concern safety and risk management. In this respect, a feature of the risk norms for mountain biking that is striking to Wayne is the acceptance that there is a fairly high level of risk that is ineliminable and must simply be accepted. Crashes and injuries are simply part of mountain biking. Thus, through social interaction learners acquire concepts for normatively characterising performance which help them to evaluate their own performances and set goals. Group riding, both social and competition, exposes the individual directly to the performance abilities and conventions of others, providing further information for self-evaluation and goal setting.

The ability to use social information is itself skill-dependent. For example, in riding with Kath, Wayne was aware that she was a more capable rider. However, from this he gained little information that was useful for his own riding. Because Kath was so much more advanced, her performance ability did not serve as a useful benchmark for him and he was unable to identify the structure of her methods in a way that would allow him to copy them. Individuals with more advanced skill are often much better at identifying the structure of methods used by others (Bicknell, 2010 , 2011 ). This can allow them to copy and adapt them for themselves, or identify problems which should be avoided or corrected. Teaching can scaffold learners through this limitation. The learner's limited action evaluation system is supplemented by the much more sophisticated action evaluation system of the teacher. In such situations, the causal control model of the more experienced rider can help to develop the causal control model of the learner.

The mountain bike community routinely scaffolds the experiences of the individual in other ways, too. The difficulty and type of experience that riders have is shaped by trail and bike design. Trail grading gives riders information about the difficulty of particular trails which allows riders to decide in advance whether a trail will be within their ability. Grading systems like this also provide individuals with benchmarks for assessing performance. If an individual finds an intermediate trail difficult they are able to locate themselves within the spectrum of abilities within the community. This can in turn guide goal setting for learning and performance. An individual having difficulties at a particular level can seek to identify technical limitations that are holding them back, and work on those, for example. At a more immediate level, signage on trails alerts riders to the required skill level needed to ride specific, upcoming obstacles. Double- or triple-downward arrows before a particularly steep section of trail that isn’t clearly visible on approach serve this function on some trails, alerting the rider to challenging terrain they typically cannot see until they are already riding it. In other trail communities a sign saying ‘warning’ may be used. An alternative convention is signs pointing to A-, B- or C-lines, indicating the technical difficulty of upcoming sections of trail and encouraging riders to make a decision about which line to take (Fig. (Fig.1 1 ).

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Trail sign, Ourimbah cross-country mountain bike track. This sign prompts riders to prepare for the jump line on the right, or to veer left to avoid it. Importantly, it is placed on an unremarkable section of track, at eye height, to catch the rider’s attention with enough time to make a decision about how to approach the upcoming section of trail, without having to stop riding in order to do so. Photo by Kath Bicknell.

Indeed, the mountain bike community has a rich set of community-specific caretaking practices which manage awareness, decision making and problem solving. Additional practices include:

‘Pre-riding’ (looking at a trail slowly, with an explorative mindset, before riding it at speed);
‘Sessioning an obstacle’ (stopping to look at and practice an obstacle before riding it at speed);
‘Riding and scoping’ (eg. riding around a jump while looking at it sideways during the first run of a trail and deciding whether it is safe to attempt on the next lap of that section of trail);
Building up ‘reserve techniques’ (which can help to regain control if the speed, shape or pitch of the bike mid-obstacle indicates a crash is imminent).

Communication methods are also used to manage problem solving. For example, the question, ‘Is it rollable?’ is one that a skilled rider may ask another before attempting a trail for the first time. If a trail is ‘rollable’ it means there are no gaps that need to be jumped—as long as balance and momentum are maintained everything is ‘rideable’. The trail may well be frighteningly steep and require a high skillset in a number of other areas, but it will be manageable for a rider with a particular set of abilities.

To sum up, skill communities scaffold learning and performance in many ways, allowing higher levels of performance to be achieved and a better, safer quality of experience. The practices which achieve this do so to a significant degree by enhancing the decision-making and problem solving of the individual. Indeed, the engaging nature of sports like mountain biking rests on achieving a complex balance between approachability, challenge, and safety. Mountain biking has been very successful in this respect, and is a fast-growing sport (eg. Latz, 2020 ). This point is worth emphasising because it helps make the case that the phenomena we’ve been describing are not marginal or unimportant—they’re integral to many skills and can be crucial to their success.

The ability to formulate action strategies and control their execution is a central issue for understanding action and skill, yet there is very little work on it. Here we found that even an individual with relatively modest skill experience can be capable of fairly complex, fast-paced construction and control of action strategies. Our results need to be validated by further ecological and laboratory-based investigation but we are confident that the core phenomena we've described are real, and that the use of strategies and problem solving is very common in skilled action. The kind of problem solving we found, together with its flaws, is likely to be fairly typical for individuals in relatively early stages of skill learning. But in skills which require significant levels of flexibility—such as mountain biking and climbing—problem solving is also likely to be central to the most advanced levels of skill. It is consequently of high importance that we develop a better understanding of the mechanisms which support these abilities and the way they develop during skill learning. We've argued that causal representation, performance awareness, metacognitive awareness and action evaluation all play important roles and operate together in a complex, integrated action control system. Our account of these mechanisms goes beyond previous work and adds to the Mesh theory of skill a more detailed model of action control.

Acknowledgements

We thank John Sutton, John Michael, Josh Shepherd, Chiara Brozzo, Cynthia Siew, Gaye Camm, Tom McClelland, Doris McIlwain, and the generosity of colleagues and students in the Cognitive Ecologies and Microethnography Labs at Macquarie University, Sydney, Australia. An earlier version of this paper was presented as a keynote at the ‘Actions: The Mental and the Bodily’ conference at the University of Warwick, UK, and in a shorter form at the ‘Cognitive Futures in the Arts and Humanities: Paradigms of Understanding—Sharing Cognitive Worlds’ conference in Mainz, Germany. We thank the audiences for their questions, provocations and enthusiasm for this work.

Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research was funded by European Research Council starting Grant 757698, awarded under the Horizon 2020 program for research and innovation, and the Australian Research Council Discovery Project grants DP130100756 ‘Mindful Bodies in Action: a philosophical study of skilled movement’, awarded to Doris McIlwain and John Sutton (2013–2015) and DP180100107 ‘The Cognitive Ecologies of Collaborative Embodied Skills’, awarded to John Sutton (2018–2020).

Declarations

The authors report no conflict of interest.

1 See Preston ( 2013 ) for a related discussion of Bratman’s account.

2 See Chisholm ( 2008 ) for an in-depth exploration of the relationship between bodily characteristics, technique and environment in climbing.

3 This video shows six different strategies used to solve a particular problem at the 2021 World Championships: https://www.instagram.com/p/CT9pAfTpMmm/ .

4 A video of squirrels engaging in this kind of problem solving can be seen here: https://theconversation.com/we-used-peanuts-and-a-climbing-wall-to-learn-how-squirrels-judge-their-leaps-so-successfully-and-how-their-skills-could-inspire-more-nimble-robots-165524 .

5 Nanay (2020) and Fridland ( 2021 ) argue that action control is based on imagistic representation, drawing on evidence that practice using mental imagery can be highly beneficial. Causal control models should be differentiated from mental images. Imagistic representations do not represent causal relations per se, although causal representation can be incorporated into imagistic representations. Nor is causal representation necessarily imagistic. It is the representation of causal relations specifically that plays a foundational enabling role in the intentional control of action.

6 https://www.youtube.com/watch?v=IqsNJv2VROs .

7 Not all parameter relations need be represented as causally related since the motor system can sometimes ‘fill-in’ some parameters when given others as explicit goals. Indeed, because of the limits of attention capacity learners must often rely on some degree of ‘filling-in’ because they can’t continuously attend to the full structure of the technique for a novel action while performing it. For instance, when learning a new chord the learner might initially attend primarily to landing finger locations then switch to correcting overall hand posture, while largely ignoring timing. But these kinds of cases illustrate limitations of automated ‘filling-in’ because the filled-in parameters will often not correspond to good technique. Focusing on finger locations while neglecting hand posture when learning a new chord is likely to result in poor posture. Once an individual has developed a high level of skill automated filling-in will tend to better correspond to good technique, but this is because the techniques have already been intentionally learned. We thank a referee for prompting this clarification.

8 We’re using the term ‘translation’ in a broad sense which involves the construction of alternative representations of the same, similar or related content (see Christensen, 2020). This includes translation between alternative expressions within a representational system such as a language. An alternative approach would be to restrict ‘translation’ to content re-representations and interpretations across representational systems with distinct formats and use an alternative concept such as ‘mapping’ for such content relating processes within a representational system, such as between levels of abstraction (we thank a reviewer for this suggestion). This raises a complex set of issues. We agree that there may be reasons to adopt a more restricted concept of translation but we think it is unclear how this should be done. In general, we think that philosophers and cognitive scientists have been overly focused on the idea that mental representational systems are discrete, static systems defined by a distinct, unchanging format Evidence from cognitive neuroscience suggests that the brain has an extremely flexible ability to construct representational systems, that representational systems with different formats can overlap (auditory, visual, and haptic representational systems use shared spatial representations), that multiple formats can be encompassed in an integrated representational system (working memory is an integrated workspace which includes auditory, visual and other subcomponents), and so on (see Author 2020 for an extended discussion). Consequently, we doubt that it will be possible to draw a clear distinction between within-system and between-system content-relating processes. More specifically, it’s likely that content-relating and construction processes that operate within cognitive representational systems also play a role in constructing new representational systems and building relations across existing systems when this becomes functionally beneficial. These points have strong implications for understanding skill learning, which, we suggest, involves the construction of multiple interlinked domain-specific representational systems. In future work we’ll develop the idea that the processes we described here as translating between levels of abstraction play a key role in the formation of new representational systems for skill control.

9 Recent philosophical discussion has been preoccupied with a narrower 'interface problem' formulated by Butterfill and Sinigaglia (2014). The idea is that there is a special difficulty understanding how cognitive and motor representations can interact which stems from the supposed impossibility of translation between their formats. However, Christensen (2020) argues that the theoretical rationale for rejecting translation is unsound and that there is extensive empirical evidence that the brain translates across many representational formats, including motor and cognitive.

10 We won't engage in a comprehensive analysis of the DPM model here. Brozzo (2021) criticises the distinction between present- and future-directed intentions. Christensen (2020) gives an alternative account of motor representations and their interface with higher level intentions.

11 Although it should be noted that Shepherd's account includes a discussion of the role of domain norms in action evaluation which brings it closer to the problem-based conception.

12 This example reflects common advice to, and complaints about, inexperienced musicians. The following article provides a fairly typical illustration: https://www.premierguitar.com/articles/print/28953-last-call-space-is-music-too .

13 Our use of the term ‘system’ here may suggest that we have in mind a Fodorian module. However, we are adopting a different, non-Fodorian conception of modules and systems which is based in a biological framework. By ‘system’ we mean a network of structures and processes that show a degree of somewhat specific functional integration and perform one or more somewhat specific functional roles (in this case, action evaluation). A cognitive system in this sense can integrate with, and overlap with, other cognitive systems. The AES will be a ‘system of systems’ which encompasses multiple lower and higher level evaluative systems, for instance including both reward and efficiency evaluation systems.

14 In this respect our account can be contrasted with that of the predictive processing framework, which claims that behaviour is governed by a single dominant goal, namely predictive error minimization. Our account thus avoids the ‘dark room’ problem facing the predictive coding approach, which is that predictive error minimization can be achieved by placing oneself in a highly predictable environment (Sun & Firestone, 2020). We thank a referee for this point.

15 Drawing on Kath’s experience of teaching this exercise to beginner riders at skills clinics, many riders think they are almost about the graze the tyre when they are still approximately 20 cm away from reaching it. This was also true of Wayne. Kath communicated this to him verbally during the exercise, showed the gap with a hand gesture, and demonstrated the correct vs incorrect technique. In response, Wayne exaggerated his attempt at the task and was able to graze the rear tyre. Both riders were delighted!

16 Also called a ‘front wheel washout’. There are some differences in the way that ‘washout’ is conceptualised in the mountain bike community. The version of the concept Wayne was using treats it as any case in which the front wheel loses traction and slides out from underneath the rider, causing a crash.

17 This folk concept of flow should be differentiated from the concept used in psychology (Csikszentmihalyi 1990 ).

S.I.: Minds in Skilled Performance.

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Contributor Information

Wayne Christensen, Email: [email protected] .

Kath Bicknell, Email: moc.llenkcibhtak@liame .

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Cognitive Model of Problem Solving

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The Journal of International Educational Sciences

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Bu calismada cevrimici araclarin, lise matematik egitimine entegresiyle, problem cozerken ayni zamanda iletisim ve isbirligi olanaklarini artirma yoluyla ogrencilere daha fazla ogrenme firsati sunulmasi amaclanmistir. Harmanlanmis bir matematik egitimi ortaminda yapilan kanita dayali bu calismada ogrenci-ogrenci, ogrenci-ogretmen ve ogrenci-icerik iliskileri incelenmektedir. Calismaya Ameriaka Birlesik Devletlerinin guneydogu bolgesindeki bir lisede gorev yapan iki ogretmen ve ayni lisede ogrenim goren 35 ogrenci katilmistir. Calismada nitel arastirma yontemleri kullanilmistir. Veri toplama araclarini ogretmen ve ogrenci gorusmeleri ve ogrencilerin cevrimici araclardaki katilimlari olusturmaktadir. Calismanin veri toplama, duzenleme ve analiz asamalarinda iki modelden yararlanilmistir: Stahl (2006)’in Isbirlikci Bilgiyi Insa Modeli (Model of Collaborative Knowledge-Building) ve Anderson (2008)’in Cevrimici Ogrenme Teorisi (Theory of Online Learning). Bu iki modelin sentezlenmesi ile...

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The aims of the study are to specify the academic achievement of the fifth, sixth, seventh and eighth grade students in proportional reasoning problems, to determine how the academic achievement of these students change according to problem types, to examine their solution strategies in these problems, and to reveal how these strategies diversify from fifth to eighth grade. To collect data in order to achieve these aims, a proportional reasoning test were prepared. The study was designed as a mixed study. It was carried out with a total of 858 students- 255 fifth, 209 sixth, 256 seventh and 138 eighth grade students- studying at a public school in Mamak district of Ankara in the fall semester of the 2018-2019 academic year. The data were obtained from all students in the quantitative part of the study. In the qualitative part of the study, the data were collected from 80 students in total. These students were 20 students with the highest score in proportional reasoning test at each ...

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The purpose of this study is to determine to what extent problem-solving skill contributes to the prediction of lateral thinking. The sample of the research consisted of 475 undergraduate students, more specifically 357 female (75.2%) and 118 male (24.8%) students, attending the Faculty of Education at Çanakkale Onsekiz Mart University in Çanakkale, Turkey. The Problem-Solving Inventory-developed by Heppner and Petersen (1982)-and the Lateral Thinking Scale-developed by Semerci (2016)-were employed in the study to collect data. The descriptive statistics (frequency, percentage, arithmetic mean, and standard deviation) and multiple regression analysis were used to analyze the obtained data. According to the findings of the study, the lateral thinking levels of the teacher candidates were high, and their problem-solving skills were at a positive medium level. The teacher candidates' confidence in problem-solving ability and approach-avoidance scores positively affected their lateral thinking levels, on which their personal control scores exerted negative effects. In addition, the participating pre-service teachers' total scores of problem-solving skills significantly predicted their lateral thinking scores. ÖZ: Bu araştırmanın amacı, yanal düşünmenin yordanmasında problem çözme becerisinin ne düzeyde katkıda bulunduğunu belirlemektir. Araştırmanın çalışma grubunu Çanakkale Onsekiz Mart Üniversitesi Eğitim Fakültesi'ne devam eden 357 kız (%75.2), 118 erkek (%24.8) toplam 475 üniversite öğrencisi oluşturmuştur. Araştırmada veri toplamak amacıyla Heppner ve Petersen (1982) tarafından geliştirilen Problem Çözme Envanterive Semerci (2016) tarafından geliştirilen Yanal Düşünme Ölçeği kullanılmıştır. Araştırmada elde edilen verilerin analizinde betimsel istatistikler (frekans, yüzde, aritmetik ortalama ve standart sapma) ve çoklu regresyon analizi kullanılmıştır. Araştırmada ulaşılan bulgulara göre, öğretmen adaylarının yanal düşünme düzeyleri yüksek, problem çözme becerileri pozitif orta düzeydedir. Öğretmen adaylarının problem çözme yeteneğine güven ve yaklaşma-kaçınma puanları, yanal düşünme düzeyini olumlu yönde etkilerken, kişisel kontrol puanları olumsuz yönde etkilemektedir. Ayrıca öğretmen adaylarının problem çözme becerisi toplam puanları, yanal düşünme puanlarını anlamlı olarak yordamaktadır. Anahtar kelimeler: Yanal düşünme, problem çözme, öğretmen yetiştirme, öğretmen adayları.

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LEONIDAS CHYTIRIS

Psych 256: Cognitive Psychology, 002, SP24

Making connections between theory and reality., reflection and creative problem solving.

Have you ever tried to solve a problem in a way that seemed unconventional? You may have participated in creative problem-solving. This is when you are thinking of a large number of solutions that are original, but useful as well (pg. 377). I work with children, and I constantly have to think of new ways to solve children’s problems such as unwanted behaviors they are displaying or maybe an issue they are having with a friend. Some strategies work with certain children and other strategies do not so this is where I have to get creative. Now, have you ever wanted to solve that problem in an unconventional way, but the more you reflected it seemed unreasonable? There were times when I wanted to try a different approach with a child, but I was stuck in my way because the strategies I used beforehand all worked with other children. Instead of thinking of creative ways to help this child, I stuck to what I knew, and this did not benefit them. Eventually, I did change my approach and it benefited the child greatly. There is research that suggests that reflecting on how people solve problems is important to their learning. Reflection is when you take the time to examine your thoughts and feelings. Researchers Rosseel and Anseel (2021), want to show and examine the effects of reflection on creative problem-solving to see if there are any discrepancies with the previous research.

One reason why they are questioning the effectiveness of reflection in creative problem-solving is that uncertainty is a defining factor of the creative process (Rosseel & Anseel, 2021). If you are taking the time to think if your idea is good, then this can hinder what makes it a creative idea. Creative solutions are not always the most logical and overthinking can lead to a hinderance of that. The next reason is that reflection is assumed to lead to better task performance. If you have a schema for how to solve a certain task, then you can reflect on that previous situation and use that schema to solve the current problem. This limits creativity because you are not coming up with new ways to solve a problem, but utilizing previous schemas that you know have worked before. Sometimes these schemas do not always work and do not allow for the flexibility that creative problem-solving might need since some situations are unique.

This article examines two different studies the researchers conducted. The first study asked participants to complete two creative problem-solving tasks and reflect on their creative approach in between all while being timed. They found that “task reflection without imaginative reflection hindered idea generation” (Rosseel & Anseel, 2021). Imaginative reflection is when individuals think about what other approaches, they could have used to solve a problem. The second study looks at how people can learn by elaborating on others’ experiences and they use the term “vicarious elaboration”. They are trying to make sense of others’ experiences by watching their behaviors and the consequences that they experienced. The researchers found that vicarious experience did not improve creative problem-solving. Both studies found that this did not lead to better outcomes than no reflection at all. This means that reflection can hinder our creative problem-solving abilities.

Rosseel, J., & Frederik, A. (2022). When reflection hinders creative problem-solving: A test of alternative reflection strategies. Journal of Business and Psychology, 37 (2), 429-441

Goldstein, E. B. (2021). Cognitive psychology: Connecting mind, research, and everyday experience. Cengage. 376-380.

One thought on “ Reflection and Creative Problem Solving ”

Hi, I enjoyed reading your blog. I also admire the works you contributed to benefiting the kids. It reminds me that every individual is unique, and there are no one-size-fits-all plans. Especially for psychology majors like us, we emphasize the uniqueness of each individual and trying different approaches if one does not work out. I understand the difficulties you had when attempting to address behaviors or social concerns that are unique to each child. Even though I’m not a professional, I do help babysit relatives’ children, so I have some experience with kids. Though, I find it challenging to deal with each child’s unique personality characteristics. Every child has a unique temperament, and I had to come up with several creative techniques to calm them down at times. For example, I recently met a three-year-old girl who gets upset when things don’t go her way. She would act out and then walk away by herself. I’ve tried different methods to calm her down or get her to listen more, but none of them have worked, even if they’ve worked on other children. As I read about your experiences, I recalled the moments when I was afraid to attempt new things or try different approaches to problems. Even thinking about it makes me anxious because I would think about consequences if it didn’t work out. As you mentioned, I sometimes become stuck in my own habits since they’ve previously worked. The study by Rossel and Anseel (2021) that you shared was interesting as well; it emphasizes how uncertainty may encourage and hinder creativity. It’s similar to approaching an issue from two different perspectives, one emphasizing what has already been accomplished and the other what might be possible. I find creativity to be critical in problem solving situations; like I mentioned, when I think about new things, I weigh down the drawbacks but also potential advantages. Therefore I am more prone to making alternative plans or back up plans if one does not work out.

Good work! -Linda