psychosocial competency problem solving

• Provide Psychosocial Skills Training and Cognitive Behavioral Interventions

What to Know

Psychosocial skills training and cognitive behavioral interventions teach specific skills to students to help them cope with challenging situations, set goals, understand their thoughts, and change behaviors using problem-solving strategies.

Psychosocial skills training asks students to explore whether their behaviors align with their personal values. Cognitive behavioral interventions teach students to identify their own unhelpful thoughts and replace them with thoughts that are more helpful. Students might practice helpful coping behaviors and find positive activities to try. Doing these things can improve their mood and other symptoms of mental distress.

Districts and schools can deliver interventions in one-on-one settings, small groups, and classrooms. Some interventions focus on concepts that are also taught in social skill and emotional development programs, like self-control and decision-making. A counselor or therapist can lead these programs.

What Can Schools Do?

Promote acceptance and commitment to change.

Schools can help promote acceptance and positive behavior change for students through psychosocial skills training and dialectical behavior therapy. Psychosocial skills training asks students to explore whether their behaviors align with their personal values. Students who see that their behavior does not match their values can decide to make behavior changes. These trainings also help students accept what they cannot change and focus on what they can change. Dialectical behavior therapy teaches mindfulness, acceptance, and commitment skills.

Approaches using acceptance and commitment to change are associated with increases in students’ coping skills and decreases in depression and physical symptoms of depression.

Provide Cognitive Behavioral Interventions

Cognitive behavioral interventions for schools often include multiple sessions. They can be used for one student or a small group. Sessions often follow a standardized manual of activities to help students examine their own thoughts and behaviors. The interventions can include asking students to share what they learn about their thoughts and behaviors with their parents and other people. In some interventions, session leaders focus on a specific topic. Other interventions target mental health symptoms, like depression, anxiety, or post-traumatic stress.

Cognitive behavioral interventions can improve students’ mental health in many ways, including decreasing anxiety, depression, and symptoms related to post-traumatic stress.

• LARS & LISA
• Tools for Getting Along Curriculum—Behavior Management Resource Guide
• Cognitive Behavioral Intervention for Trauma in Schools (CBITS )
• Bounce Back
• Brief Intervention for School Clinicians
• Skills for Academic and Social Success
• Building Confidence

Engage Students in Coping Skills Training Groups

Coping skills training groups use principles of cognitive behavioral intervention to teach students skills to help them handle specific problems. Students can also use these skills to help them cope when their lives are changing. Similar to social, emotional, and behavioral learning programs, coping skills training often focuses on building resilience, or being able to “bounce back” when bad things happen. Students can practice skills outside of the small group, like they would with social skills and emotional development lessons.

Coping skills training groups can increase coping skills for students and decrease anxiety and depression.

• Journey of Hope
• High School Transition Program

Focus on Equity

Students who have been exposed to trauma may receive trauma-focused or trauma-informed interventions in school. Cognitive behavioral interventions that are trauma-informed meet the unique needs of students exposed to traumatic experiences. These interventions teach problem-solving and relaxation techniques and help reduce trauma-related symptoms, including behavioral challenges. Trauma-informed interventions can also improve students’ coping strategies.

Implementation Tips

Cognitive behavioral interventions and psychosocial skills training help with many kinds of student needs. They can be used at multiple grade levels. Leaders can:

• Work with school mental health staff to find ways for students to practice their new behaviors and coping skills.
• Use the Multitiered Systems of Support (MTSS) framework to ensure that students are appropriately matched with classroom, small-group, or individual interventions that meet their needs.

Want to Learn More?

For more details on MTSS and providing psychosocial skills training and cognitive behavioral interventions, see Promoting Mental Health and Well-Being in Schools: An Action Guide for School Administrators [PDF - 3 MB]

• Increase Students’ Mental Health Literacy
• Promote Mindfulness
• Promote Social, Emotional, and Behavioral Learning
• Enhance Connectedness Among Students, Staff, and Families
• Support Staff Well-Being

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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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Further Reading

Baron, J. ( 2008 ). Thinking and deciding (4th ed). New York: Cambridge University Press.

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

Holyoak, K. J. , & Morrison, R. G. ( 2005 ). The Cambridge handbook of thinking and reasoning . New York: Cambridge University Press.

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

Sternberg, R. J. , & Ben-Zeev, T. ( 2001 ). Complex cognition: The psychology of human thought . New York: Oxford University Press.

Weisberg, R. W. ( 2006 ). Creativity . New York: Wiley.

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Resilience: Psychosocial competencies

• Description

We are facing a mental (ill) health crisis – but unfortunately the focus when it comes to support is biased towards treatment only, rather than prevention. Even then, without having had the opportunity to learn the skills needed, coming to them especially at the point of crisis can feel overwhelming.  As such, many clients drop out of therapy, and others find other, more damaging ways to regulate. 

  In contrast, where resilience, emotional fortitude and regulation, self-value and self-compassion is taught from the bottom up, parents and children recognise a greater sense of fulfilment, happiness and even problem solving.    

The World Health Organisation sets out ten criteria for psychosocial competence: 

• Critical Thinking 
• Creative Thinking 
• Decision Making 
• Problem Solving 
• Effective Communication 
• Self-Awareness 
• Interpersonal relationships 
• Coping with stress 
• Coping with emotion.

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Developing Social Competence Through a Resilience Model

• First Online: 01 January 2014

Cite this chapter

• Mary K. Alvord Ph.D. 5 ,
• Brendan A. Rich Ph.D. 6 &
• Lisa H. Berghorst Ph.D. 5  

Part of the book series: The Springer Series on Human Exceptionality ((SSHE))

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Social deficits are ubiquitous across childhood psychopathology, and impaired social functioning in childhood is associated with a multitude of negative outcomes throughout youth and into adulthood. In contrast, social competence, a key component of resilience, is associated with multiple positive outcomes. In this chapter, we discuss the nature of childhood resilience and how psychotherapeutic interventions may enhance resilience. The primary components of resilience, including proactive orientation, self-regulation, connections and attachments, special interests and talents, community, and proactive parenting, are reviewed. We then describe the Resilience Builder Program ® (RBP ® ), a comprehensive resilience-based manualized group therapy for children and adolescents with prominent social competence deficits. Finally, we discuss efforts to evaluate the effectiveness of the RBP ® in a private clinical practice, and we present pilot data in youth with ADHD, anxiety, and autism spectrum disorders.

• Autism Spectrum Disorder
• Anxiety Disorder
• Social Competence
• Social Deficit

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Alvord, M.K., Rich, B.A., Berghorst, L.H. (2014). Developing Social Competence Through a Resilience Model. In: Prince-Embury, S., Saklofske, D. (eds) Resilience Interventions for Youth in Diverse Populations. The Springer Series on Human Exceptionality. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0542-3_15

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Problem-solving skills training may improve parental psychosocial outcomes

by Elana Gotkine

For parents of children with chronic health conditions (CHCs), problem-solving skills training (PSST) is associated with improvement in parental, pediatric, and family psychosocial outcomes, according to a review published online Jan. 2 in JAMA Pediatrics .

Tianji Zhou, Ph.D., from the Xiangya School of Nursing at Central South University in Changsha, China, and colleagues conducted a systematic review of randomized clinical trials (RCTs) to examine the associations of PSST for parents of children with CHCs with parental, pediatric, and family psychosocial outcomes. Twenty-three RCTs involving 3,141 parents were included in the systematic review ; 21 were eligible for meta-analysis.

The researchers found that PSST was significantly associated with improvements in parental outcomes, including problem-solving skills, depression, distress, posttraumatic stress, parenting stress, and quality of life (QOL; standardized mean differences [SMDs], 0.43, −0.45, −0.61, −0.39, −0.62, and 0.45, respectively).

PSST was associated with better QOL and fewer mental problems for children (SMD, 0.76 and −0.51, respectively) and with less parent-child conflict (SMD, −0.38). PSST was more efficient for parents of children aged 10 years or younger or who were newly diagnosed with a CHC in subgroup analysis. PSST delivered online was associated with significant improvements in most outcomes.

"Our findings on children- and intervention-level characteristics may guide the design and delivery of future PSST by presenting information on factors associated with effectiveness," the authors write.

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What Is Psychosocial Rehabilitation?

A Holistic, Person-Centered Approach to Mental Health Care

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

Steven Gans, MD is board-certified in psychiatry and is an active supervisor, teacher, and mentor at Massachusetts General Hospital.

• Who Can Benefit
• Effectiveness

People with mental illness sometimes need assistance in different aspects of their lives—including their work, living, social, and learning environments. One treatment approach that can help these individuals manage their symptoms and better function is psychosocial rehabilitation.

Psychosocial rehabilitation is designed to improve the lives of people with mental illness by giving them the emotional, cognitive, and social skills needed to live and work in their communities as independently as possible. Here we explore this approach in greater detail, from its history to its effectiveness.

Verywell / Brianna Gilmartin

History of Psychosocial Rehabilitation

Before the 1960s and 1970s, it was common for people with serious mental illnesses to be institutionalized. The treatment approach for mental health issues has changed considerably since then and led to de-institutionalization.

Today, there is a greater emphasis on helping people with mental health conditions live as independently as possible and become fully integrated into the communities in which they live.

While a stigma surrounding mental illness still exists, psychosocial rehabilitation strives to help reduce prejudice and foster social inclusion. This approach uses what is known as the recovery model of mental illness .

Full recovery is frequently the goal, but it is seen as a process rather than an outcome. Psychosocial rehabilitation is centered on the person's recovery potential. It is focused on providing them with empowerment, social inclusion, support, and coping skills.

Everyone's journey with mental illness is individual and unique. Psychosocial rehabilitation can help individuals find meaning, hope, and growth—regardless of their abilities or the effects of their condition.

Goals of Psychosocial Rehabilitation

The core goals of a psychosocial rehabilitation program include helping the participant feel:

• Empowered : Each individual should feel that they can set their own goals and that they have the power and autonomy to pursue those aims.
• Hopeful : People with mental health conditions often feel demoralized. Psychosocial rehabilitation focuses on helping them feel hopeful about the future.
• Skilled : This form of rehabilitation aims to teach people skills to help them manage their condition and live the life they want to live. This includes life skills, work skills, social skills, and others.
• Supported : Mental health professionals offer support and help individuals build relationships and social connections in their community.

The time following the diagnosis of a mental health condition is a period of major transition. Patients may lose some functionality, but new approaches can allow them to manage their condition better.

Their illness may have made it difficult to go to school or work, or to maintain supportive relationships with others. Many aspects of life can be affected, including the person's employment status, housing situation, and family life.

Principles of Psychosocial Rehabilitation

Several key principles help guide how mental health professionals in this field approach their work. These are aligned with a social model of care versus focusing solely on a medical model of care.

Some overarching psychosocial rehabilitation principles include:

• Each person's needs are different, but all people have potential that can be developed.
• People have a right to self-determination .
• An individual's strengths should be emphasized rather than their symptoms.
• The present is more central to recovery than fixating on the past.
• Professional services should be committed and occur in as normalized an environment as possible.

A Multidisciplinary, Whole-Person Approach

Psychosocial rehabilitation treatments are multidisciplinary. This perspective recognizes that mental illness impacts multiple areas of life, including the biological, social, and psychological systems. Not only are each of these systems affected by mental health, but they are also inextricably interlinked.

When something affects one area, it is bound to influence other areas as well. In light of this, psychosocial rehabilitation takes a whole-person approach. It recognizes that other mental health professionals and physicians may be needed to make contributions to the treatment process.

For example, a person with a mental illness may need psychosocial rehabilitation services that target basic living and social skills training . But they might also need treatment involving medication and psychotherapy. The treatment plan targets the person’s specific symptoms, while rehabilitation focuses on the recovery and reintegration process.

A team approach ensures that the person has access to the tools and resources needed to achieve their goals.

Who Can Benefit From Psychosocial Rehabilitation?

Many people can benefit from psychosocial rehabilitation, but not all people with mental illness require it. For some, medication, therapy, or a combination of the two may be sufficient to restore functioning.

Rehabilitation can be useful when people need additional recovery assistance to help them restore functioning. Those who might benefit from psychosocial rehabilitation include:

• People who need help restoring their full functioning after treatment
• Those who are disabled and need ongoing assistance in multiple life domains
• Individuals who, while functional, feel a need for support and assistance
• People who lack the supportive environment and resources they need to achieve full-functioning

People with chronic and severe psychiatric conditions can benefit from psychosocial rehabilitation services. It can help them learn basic skills that allow them to function and cope with their condition. People with intellectual and cognitive disabilities can also benefit from gaining life, social, and self-care skills.

Once the underlying condition has been addressed through treatment, psychosocial rehabilitation focuses on helping people develop the skills and support they need to live full, satisfying lives.

Approaches Used in Psychosocial Rehabilitation

Psychosocial rehabilitation is based on the idea that people are motivated to achieve independence and capable of adapting to achieve their goals . It uses a combination of evidence-based best practices and emerging, promising practices that focus on restoring social and psychological functioning. Here are some of the approaches used.

Builds on Strengths

Rather than focusing on areas of weakness, psychosocial rehabilitation empowers clients and builds on their existing capabilities. Their abilities help form a foundation upon which other important life skills can be developed through observation, modeling, education, and practice.

Some specific areas that psychosocial rehabilitation might address include skills, training, and experiences designed to boost:

• Resilience and mental toughness
• Problem-solving ability
• Self-esteem
• Social skills
• Stress management

Building these strengths might be accomplished through one-on-one educational sessions that focus on specific skills, or it might involve incorporating training and experience in other life domains such as cooking or recreation. Such experiences allow people to practice their abilities in a safe environment, with supervision and support from a psychosocial rehabilitation professional.

Psychosocial rehabilitation strives to address areas of the person’s life that contribute to their overall physical and psychological well-being . Professionals who work in this field provide a range of individual and community-based psychological services.

In determining each patient's needs, mental health professionals look at the physical and social environment, develop a service plan, and collaborate with other professionals.

Psychosocial rehabilitation providers look at each client's situation and help determine what they need to live and function as independently as possible. This frequently involves locating those services in the community and coordinating their delivery.

Specific psychosocial rehabilitation treatments can vary considerably from case to case depending upon a person's needs and the resources available. The process is highly individualized, person-centered, and collaborative.

Person-Oriented

The client plays a role in setting goals for what they hope to accomplish in psychosocial rehabilitation. Each client’s goals are individualized based upon their specific needs or concerns.

The rehabilitation process is not about the therapist deciding what the client's goals should be. Instead, the client determines what they want to achieve. The focus is then on providing the support and resources they need to make these goals a reality.

Psychosocial Rehabilitation Activities

Psychosocial rehabilitation activities include those related to basic living skills, family relationships, peer and social relationships , employment, education, recreation, health, and wellness.

Working is beneficial for mental wellness and can help people feel productive. This is why vocational assistance is an important component of psychosocial rehabilitation.

Finding and maintaining work can often improve social connections, boost self-esteem , and improve one's overall quality of life.

Psychosocial rehabilitation workers can assist clients with finding and maintaining employment. This might include helping them develop vocational skills, connecting the client to employment services in the community, assisting with career planning, and providing transportation assistance.

Another activity related to this aspect of the psychosocial rehabilitation process is assistance with filling out job applications or practicing job interviews . In other instances, clients may work in temporary or supported work settings where they can develop and practice these skills.

Psychosocial rehabilitation may involve connecting clients with safe, affordable, and appropriate housing. Clients may live independently in their own homes or in family homes. Other housing situations may include group homes , residential services, and apartments.

Depending on the client's needs, housing support exists on a continuum. It ranges from fully staffed, round-the-clock supportive care to minimally staffed or fully independent living.

Relationships

Social skills and interpersonal functioning are important parts of psychosocial rehabilitation. Skills training may focus on activities designed to help clients better function in their social worlds, including family, work, school, friendships, and romance.

This is accomplished by teaching clients skills related to emotional understanding. They're also exposed to skills that enhance their interpersonal problem-solving , verbal and conversational abilities, and nonverbal communication .

Community Functioning

One of the overriding goals of psychosocial rehabilitation is to help those with mental illness become better integrated within their community. Rehabilitation professionals often work with clients in community settings and locations.

For example, a child receiving psychosocial rehabilitation services may work with mental health professionals in school settings but also spend time on social outings to local businesses, doctor's offices, libraries, and other locations. Practicing social and life skills in these settings allows the child to gain experience and rehearse interactions they might face as part of daily life.

Effectiveness of Psychosocial Rehabilitation

Research investigating the outcomes and effectiveness of psychosocial rehabilitation treatments is still ongoing, but there is evidence indicating these approaches have an overall beneficial effect.

Improved Life Skills

A study of people with schizophrenia and affective disorders found that psychosocial rehabilitation was linked to significant benefits in a variety of areas—including family relations, communication, community participation, self-care, money management, transportation, and vocational abilities.

Greater Overall Wellness

Research has also shown that psychosocial rehabilitation can help improve a client's well-being. In one study published in the International Journal of Mental Health , individuals engaged in this type of program reported a higher sense of respect, autonomy, and purpose, along with feeling at peace.

May Help With Serious Psychiatric Conditions

A review of psychosocial treatments suggests that these approaches show promise in both bipolar disorder and schizophrenia recovery . Strategies often used in psychosocial rehabilitation, such as social skills training and cognitive remediation, can help address social functioning, work recovery, and independent living.

Effective rehabilitation involves a comprehensive plan that addresses the client’s life and functioning. A psychosocial rehabilitation professional is usually only one part of the process. The plan is often overseen by a psychiatrist, psychologist, or counselor and typically involves working with the client individually and in community settings.

The goal of psychosocial rehabilitation is to help clients engage in their communities as fully as they possibly can, and many of the strategies used in the process are aimed at helping clients become fully integrated. Doing this not only improves a client's quality of life but also helps create a network of ongoing social support .

Psychosocial rehabilitation is not always necessary, but it can be a helpful part of a comprehensive treatment program. By promoting recovery, improving quality of life, and fostering community integration, this approach can be an essential resource for those who have been diagnosed with a mental health condition.

Such services can help individuals develop skills, identify strengths, and improve their capacity to be successful in their lives, work, and relationships.

Keynejad R, Semrau M, Toynbee M, et al. Building the capacity of policy-makers and planners to strengthen mental health systems in low- and middle-income countries: A systematic review .  BMC Health Serv Res . 2016;16(1):601. doi:10.1186/s12913-016-1853-0

Stein DJ, Szatmari P, Gaebel W, et al. Mental, behavioral and neurodevelopmental disorders in the ICD-11: An international perspective on key changes and controversies .  BMC Med . 2020;18(1):21. doi:10.1186/s12916-020-1495-2

De Weert GH, Markus W, Kissane DW, De Jong CAJ. Demoralization in patients with substance use and co-occurring psychiatric disorders . J Dual Diagn . 2017;13(2):136-143. doi:10.1080/15504263.2017.1287457

Mutschler C, Rouse J, McShane K, Habal-Brosek C. Developing a realist theory of psychosocial rehabilitation: the Clubhouse model . BMC Health Serv Res . 2018;18:442. doi:10.1186/s12913-018-3265-9

Evans J, Wilton R. Well enough to work? Social enterprise employment and the geographies of mental health recovery . Ann Amer Assoc Geograph . 2019;109(1):87-103. doi:10.1080/24694452.2018.1473753

Spaulding WD, Sullivan ME. Treatment of cognition in the schizophrenia spectrum: The context of psychiatric rehabilitation .  Schizophr Bull . 2016;42 Suppl 1(Suppl 1):S53–S61. doi:10.1093/schbul/sbv163

Rouse J, Mutschler C, McShane K, Habal-Brosek C. Qualitative participatory evaluation of a psychosocial rehabilitation program for individuals with severe mental illness . Int J Mental Health . 2017;46(2):139-156. doi:10.1080/00207411.2017.1278964

Yildiz M. Psychosocial rehabilitation interventions in the treatment of schizophrenia and bipolar disorder . Noro Psikiyatr Ars . 2021;58(Suppl 1):S77-S82. doi:10.29399/npa.27430

King R, Lloyd C, Meehan T. Handbook of Psychosocial Rehabilitation .

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

Psychological Steps Involved in Problem Solving

A mental process or a phenomenon dedicated towards solving problems by discovering and analyzing the problem is referred to as problem-solving. It is a process dedicated to finding not just any solution, but the best solution to resolve any problems. There is no such thing as one best way to solve every kind of problem, since there are unique problems depending upon the situation there are unique solutions too.

In psychology, problem solving doesn’t necessarily refer to solving psychological/mental issues of the brain. The process simply refers to solving every kind of problems in life in a proper manner. The idea of including the subject in psychology is because psychology deals with the overall mental process. And, tactfully using our thought process is what leads to the solution of any problems.

There are number of rigid psychological steps involved in problem solving, which is also referred as problem-solving cycle. The steps are in sequential order, and solving any problem requires following them one after another. But, we tend to avoid following this rigid set of steps, which is why it often requires us to go through the same steps over and over again until a satisfactory solution is reached.

Here are the steps involved in problem solving, approved by expert psychologists.

1. Identifying the Problem

Identifying the problem seems like the obvious first stem, but it’s not exactly as simple as it sounds. People might identify the wrong source of a problem, which will render the steps thus carried on useless.

For instance , let’s say you’re having trouble with your studies. identifying the root of your failure is your first priority. The problem here could be that you haven’t been allocating enough time for your studies, or you haven’t tried the right techniques. But, if you make an assumption that the problem here is the subject being too hard, you won’t be able to solve the problem.

2. Defining/Understanding the Problem

It’s vital to properly define the problem once it’s been identified. Only by defining the problem, further steps can be taken to solve it. While at it, you also need to take into consideration different perspectives to understand any problem; this will also help you look for solutions with different perspectives.

Now, following up with the previous example . Let’s say you have identified the problem as not being able to allocate enough time for your studies. You need to sort out the reason behind it. Have you just been procrastinating? Have you been too busy with work? You need to understand the whole problem and reasons behind it, which is the second step in problem solving.

3. Forming a Strategy

Developing a strategy is the next step to finding a solution. Each different situation will require formulating different strategies, also depending on individual’s unique preferences.

Now, you have identified and studied your problem. You can’t just simply jump into trying to solve it. You can’t just quit work and start studying. You need to draw up a strategy to manage your time properly. Allocate less time for not-so-important works, and add them to your study time. Your strategy should be well thought, so that in theory at least, you are able to manage enough time to study properly and not fail in the exams.

4. Organizing Information

Organizing the available information is another crucial step to the process. You need to consider

• What do you know about the problem?
• What do you not know about the problem?

Accuracy of the solution for your problem will depend on the amount of information available.

The hypothetical strategy you formulate isn’t the all of it either. You need to now contemplate on the information available on the subject matter. Use the aforementioned questions to find out more about the problem. Proper organization of the information will force you to revise your strategy and refine it for best results.

5. Allocating Resources

Time, money and other resources aren’t unlimited. Deciding how high the priority is to solve your problem will help you determine the resources you’ll be using in your course to find the solution. If the problem is important, you can allocate more resources to solving it. However, if the problem isn’t as important, it’s not worth the time and money you might spend on it if not for proper planning.

For instance , let’s consider a different scenario where your business deal is stuck, but it’s few thousand miles away. Now, you need to analyze the problem and the resources you can afford to expend to solve the particular problem. If the deal isn’t really in your favor, you could just try solving it over the phone, however, more important deals might require you to fly to the location in order to solve the issue.

6. Monitoring Progress

You need to document your progress as you are finding a solution. Don’t rely on your memory, no matter how good your memory is. Effective problem-solvers have been known to monitor their progress regularly. And, if they’re not making as much progress as they’re supposed to, they will reevaluate their approach or look for new strategies.

Problem solving isn’t an overnight feat. You can’t just have a body like that of Brad Pitt after a single session in the gym. It takes time and patience. Likewise, you need to work towards solving any problem every day until you finally achieve the results. Looking back at the previous example , if everything’s according to plan, you will be allocating more and more time for your studies until finally you are confident that you’re improving. One way to make sure that you’re on a right path to solving a problem is by keeping track of the progress. To solve the problem illustrated in the first example, you can take self-tests every week or two and track your progress.

7. Evaluating the Results

Your job still isn’t done even if you’ve reached a solution. You need to evaluate the solution to find out if it’s the best possible solution to the problem. The evaluation might be immediate or might take a while. For instance , answer to a math problem can be checked then and there, however solution to your yearly tax issue might not be possible to be evaluated right there.

• Take time to identify the possible sources of the problem. It’s better to spend a substantial amount of time on something right, than on something completely opposite.
• Ask yourself questions like What, Why, How to figure out the causes of the problem. Only then can you move forward on solving it.
• Carefully outline the methods to tackle the problem. There might be different solutions to a problem, record them all.
• Gather all information about the problem and the approaches. More, the merrier.
• From the outlined methods, choose the ones that are viable to approach. Try discarding the ones that have unseen consequences.
• Track your progress as you go.
• Evaluate the outcome of the progress.

What are other people reading?

Divergent Thinking

Convergent Thinking

Convergent Vs Divergent Thinking

Pave the Way for Self-regulation and Problem-solving With Social-emotional Learning

Posted: April 3, 2024

Problem-solving is a social-emotional learning (SEL) skill children need for lifelong success. Effective problem-solving skills support children's ability to self-regulate, focus on tasks, think flexibly and creatively, work with others, and generate multiple ways to solve problems. When young children develop and build these skills, it positively impacts their interactions with others, grows their capacity to manage challenges, and boosts a sense of competence.

A group of school-age children are stacking plastic blocks with an educator.

The foundation for effective social problem-solving is grounded in self-regulation, or the ability to regulate emotions when interacting with others. It is easier to focus on one's feelings and the feelings and perspectives of others and to work cooperatively toward solutions when a child can self-regulate and calm down. Children develop self-regulation skills over time, with practice and with adult guidance. Equally important is how an adult models emotion regulation and co-regulation. 

"Caregivers play a key role in cultivating the development of emotion regulation through co-regulation, or the processes by which they provide external support or scaffolding as children navigate their emotional experiences" (Paley & Hajal, 2022, p. 1).

When adults model calm and self-regulated approaches to problem-solving, it shows children how to approach problems constructively. For example, an educator says, "I'm going to take a breath and calm down so I can think better." This model helps children see and hear a strategy to support self-regulation.

Problem-solving skills help children resolve conflicts and interact with others as partners and collaborators. Developing problem-solving skills helps children learn and grow empathy for others, stand up for themselves, and build resilience and competence to work through challenges in their world. 

Eight strategies to support problem-solving 

• Teach about emotions and use feeling words throughout the day. When children have more words to express themselves and their feelings, it is easier to address and talk about challenges when they arise. 
• Recognize and acknowledge children's feelings throughout the day. For example, when children enter the classroom during circle time, mealtime, and outside time, ask them how they feel. Always acknowledge children's feelings, both comfortable and uncomfortable, to support an understanding that all feelings are OK to experience.  
• Differentiate between feelings and behaviors. By differentiating feelings from behaviors, educators contribute to children’s understanding that all feelings are OK, but not all behaviors are OK. For example, an educator says, "It looks like you may be feeling mad because you want the red blocks, and Nila is playing with them. It's OK to feel mad but not OK to knock over your friend’s blocks."
• Support children's efforts to calm down. When children are self-regulated, they can think more clearly. For example, practice taking a breath with children as a self-regulation technique during calm moments. Then, when challenges arise, children have a strategy they have practiced many times and can use to calm down before problem-solving begins.  
• Encourage children's efforts to voice the problem and their feelings after they are calm. For example, when a challenge arises, encourage children to use the phrase, "The problem is_______, and I feel______." This process sets the stage to begin problem-solving.
• Acknowledge children's efforts to think about varied ways to solve problems. For example, an educator says, "It looks like you and Nila are trying to work out how to share the blocks. What do you think might work so you can both play with them? Do you have some other ideas about how you could share?"
• Champion children's efforts as they problem-solve. For example, "You and Nila thought about two ways you could share. One way is to divide the red blocks so you can each build, and the other is to build a tower together. Great thinking, friends!"
• Create opportunities for activities and play that offer problem-solving practice. For example, when children play together in the block area, it provides opportunities to negotiate plans for play and role-play, build perspective, talk about feelings, and share. The skills children learn during play, along with adult support, enhance children’s ability to solve more complex and challenging social problems and conflicts when they occur in and out of the early learning setting.

References: 

Paley, B., & Hajal, N. J. (2022). Conceptualizing emotion regulation and coregulation as family-level phenomena. Clinical Child and Family Psychology Review ,  25 (1), 19-43.

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Analysing Complex Problem-Solving Strategies from a Cognitive Perspective: The Role of Thinking Skills

1 MTA-SZTE Digital Learning Technologies Research Group, Center for Learning and Instruction, University of Szeged, 6722 Szeged, Hungary

Gyöngyvér Molnár

2 MTA-SZTE Digital Learning Technologies Research Group, Institute of Education, University of Szeged, 6722 Szeged, Hungary; uh.degezs-u.yspde@ranlomyg

Associated Data

The data used to support the findings cannot be shared at this time as it also forms part of an ongoing study.

Complex problem solving (CPS) is considered to be one of the most important skills for successful learning. In an effort to explore the nature of CPS, this study aims to investigate the role of inductive reasoning (IR) and combinatorial reasoning (CR) in the problem-solving process of students using statistically distinguishable exploration strategies in the CPS environment. The sample was drawn from a group of university students (N = 1343). The tests were delivered via the eDia online assessment platform. Latent class analyses were employed to seek students whose problem-solving strategies showed similar patterns. Four qualitatively different class profiles were identified: (1) 84.3% of the students were proficient strategy users, (2) 6.2% were rapid learners, (3) 3.1% were non-persistent explorers, and (4) 6.5% were non-performing explorers. Better exploration strategy users showed greater development in thinking skills, and the roles of IR and CR in the CPS process were varied for each type of strategy user. To sum up, the analysis identified students’ problem-solving behaviours in respect of exploration strategy in the CPS environment and detected a number of remarkable differences in terms of the use of thinking skills between students with different exploration strategies.

1. Introduction

Problem solving is part and parcel of our daily activities, for instance, in determining what to wear in the morning, how to use our new electronic devices, how to reach a restaurant by public transport, how to arrange our schedule to achieve the greatest work efficiency and how to communicate with people in a foreign country. In most cases, it is essential to solve the problems that recur in our study, work and daily lives. These situations require problem solving. Generally, problem solving is the thinking that occurs if we want “to overcome barriers between a given state and a desired goal state by means of behavioural and/or cognitive, multistep activities” ( Frensch and Funke 1995, p. 18 ). It has also been considered as one of the most important skills for successful learning in the 21st century. This study focuses on one specific kind of problem solving, complex problem solving (CPS). (Numerous other terms are also used ( Funke et al. 2018 ), such as interactive problem solving ( Greiff et al. 2013 ; Wu and Molnár 2018 ), and creative problem solving ( OECD 2010 ), etc.).

CPS is a transversal skill ( Greiff et al. 2014 ), operating several mental activities and thinking skills (see Molnár et al. 2013 ). In order to explore the nature of CPS, some studies have focused on detecting its component skills ( Wu and Molnár 2018 ), whereas others have analysed students’ behaviour during the problem-solving process ( Greiff et al. 2018 ; Wu and Molnár 2021 ). This study aims to link these two fields by investigating the role of thinking skills in learning by examining students’ use of statistically distinguishable exploration strategies in the CPS environment.

1.1. Complex Problem Solving: Definition, Assessment and Relations to Intelligence

According to a widely accepted definition proposed by Buchner ( 1995 ), CPS is “the successful interaction with task environments that are dynamic (i.e., change as a function of users’ intervention and/or as a function of time) and in which some, if not all, of the environment’s regularities can only be revealed by successful exploration and integration of the information gained in that process” ( Buchner 1995, p. 14 ). A CPS process is split into two phases, knowledge acquisition and knowledge application. In the knowledge acquisition (KAC) phase of CPS, the problem solver understands the problem itself and stores the acquired information ( Funke 2001 ; Novick and Bassok 2005 ). In the knowledge application (KAP) phase, the problem solver applies the acquired knowledge to bring about the transition from a given state to a goal state ( Novick and Bassok 2005 ).

Problem solving, especially CPS, has frequently been compared or linked to intelligence in previous studies (e.g., Beckmann and Guthke 1995 ; Stadler et al. 2015 ; Wenke et al. 2005 ). Lotz et al. ( 2017 ) observed that “intelligence and [CPS] are two strongly overlapping constructs” (p. 98). There are many similarities and commonalities that can be detected between CPS and intelligence. For instance, CPS and intelligence share some of the same key features, such as the integration of information ( Stadler et al. 2015 ). Furthermore, Wenke et al. ( 2005 ) stated that “the ability to solve problems has featured prominently in virtually every definition of human intelligence” (p. 9); meanwhile, from the opposite perspective, intelligence has also been considered as one of the most important predictors of the ability to solve problems ( Wenke et al. 2005 ). Moreover, the relation between CPS and intelligence has also been discussed from an empirical perspective. A meta-analysis conducted by Stadler et al. ( 2015 ) selected 47 empirical studies (total sample size N = 13,740) which focused on the correlation between CPS and intelligence. The results of their analysis confirmed that a correlation between CPS and intelligence exists with a moderate effect size of M(g) = 0.43.

Due to the strong link between CPS and intelligence, assessments of these two domains have been connected and have overlapped to a certain extent. For instance, Beckmann and Guthke ( 1995 ) observed that some of the intelligence tests “capture something akin to an individual’s general ability to solve problems (e.g., Sternberg 1982 )” (p. 184). Nowadays, some widely used CPS assessment methods are related to intelligence but still constitute a distinct construct ( Schweizer et al. 2013 ), such as the MicroDYN approach ( Greiff and Funke 2009 ; Greiff et al. 2012 ; Schweizer et al. 2013 ). This approach uses the minimal complex system to simulate simplistic, artificial but still complex problems following certain construction rules ( Greiff and Funke 2009 ; Greiff et al. 2012 ).

The MicroDYN approach has been widely employed to measure problem solving in a well-defined problem context (i.e., “problems have a clear set of means for reaching a precisely described goal state”, Dörner and Funke 2017, p. 1 ). To complete a task based on the MicroDYN approach, the problem solver engages in dynamic interaction with the task to acquire relevant knowledge. It is not possible to create this kind of test environment with the traditional paper-and-pencil-based method. Therefore, it is currently only possible to conduct a MicroDYN-based CPS assessment within the computer-based assessment framework. In the context of computer-based assessment, the problem-solvers’ operations were recorded and logged by the assessment platform. Thus, except for regular achievement-focused result data, logfile data are also available for analysis. This provides the option of exploring and monitoring problem solvers’ behaviour and thinking processes, specifically, their exploration strategies, during the problem-solving process (see, e.g., Chen et al. 2019 ; Greiff et al. 2015a ; Molnár and Csapó 2018 ; Molnár et al. 2022 ; Wu and Molnár 2021 ).

Problem solving, in the context of an ill-defined problem (i.e., “problems have no clear problem definition, their goal state is not defined clearly, and the means of moving towards the (diffusely described) goal state are not clear”, Dörner and Funke 2017, p. 1), involved a different cognitive process than that in the context of a well-defined problem ( Funke 2010 ; Schraw et al. 1995 ), and it cannot be measured with the MicroDYN approach. The nature of ill-defined problem solving has been explored and discussed in numerous studies (e.g., Dörner and Funke 2017 ; Hołda et al. 2020 ; Schraw et al. 1995 ; Welter et al. 2017 ). This will not be discussed here as this study focuses on well-defined problem solving.

1.2. Inductive and Combinatorial Reasoning as Component Skills of Complex Problem Solving

Frensch and Funke ( 1995 ) constructed a theoretical framework that summarizes the basic components of CPS and the interrelations among the components. The framework contains three separate components: problem solver, task and environment. The impact of the problem solver is mainly relevant to three main categories, which are memory contents, dynamic information processing and non-cognitive variables. Some thinking skills have been reported to play an important role in dynamic information processing. We can thus describe them as component skills of CPS. Inductive reasoning (IR) and combinatorial reasoning (CR) are the two thinking skills that have been most frequently discussed as component skills of CPS.

IR is the reasoning skill that has been covered most commonly in the literature. Currently, there is no universally accepted definition. Molnár et al. ( 2013 ) described it as the cognitive process of acquiring general regularities by generalizing single and specific observations and experiences, whereas Klauer ( 1990 ) defined it as the discovery of regularities that relies upon the detection of similarities and/or dissimilarities as concerns attributes of or relations to or between objects. Sandberg and McCullough ( 2010 ) provided a general conclusion of the definitions of IR: it is the process of moving from the specific to the general.

Csapó ( 1997 ) pointed out that IR is a basic component of thinking and that it forms a central aspect of intellectual functioning. Some studies have also discussed the role of IR in a problem-solving environment. For instance, Mayer ( 1998 ) stated that IR will be applied in information processing during the process of solving general problems. Gilhooly ( 1982 ) also pointed out that IR plays a key role in some activities in the problem-solving process, such as hypothesis generation and hypothesis testing. Moreover, the influence of IR on both KAC and KAP has been analysed and demonstrated in previous studies ( Molnár et al. 2013 ).

Empirical studies have also provided evidence that IR and CPS are related. Based on the results of a large-scale assessment (N = 2769), Molnár et al. ( 2013 ) showed that IR significantly correlated with 9–17-year-old students’ domain-general problem-solving achievement (r = 0.44–0.52). Greiff et al. ( 2015b ) conducted a large-scale assessment project (N = 2021) in Finland to explore the links between fluid reasoning skills and domain-general CPS. The study measured fluid reasoning as a two-dimensional model which consisted of deductive reasoning and scientific reasoning and included inductive thinking processes ( Greiff et al. 2015b ). The results drawing on structural equation modelling indicated that fluid reasoning which was partly based on IR had significant and strong predictive effects on both KAC (β = 0.51) and KAP (β = 0.55), the two phases of problem solving. Such studies have suggested that IR is one of the component skills of CPS.

According to Adey and Csapó ’s ( 2012 ) definition, CR is the process of creating complex constructions out of a set of given elements that satisfy the conditions explicitly given in or inferred from the situation. In this process, some cognitive operations, such as combinations, arrangements, permutations, notations and formulae, will be employed ( English 2005 ). CR is one of the basic components of formal thinking ( Batanero et al. 1997 ). The relationship between CR and CPS has frequently been discussed. English ( 2005 ) demonstrated that CR has an essential meaning in several types of problem situations, such as problems requiring the systematic testing of alternative solutions. Moreover, Newell ( 1993 ) pointed out that CR is applied in some key activities of problem-solving information processing, such as strategy generation and application. Its functions include, but are not limited to, helping problem solvers to discover relationships between certain elements and concepts, promoting their fluency of thinking when they are considering different strategies ( Csapó 1999 ) and identifying all possible alternatives ( OECD 2014 ). Moreover, Wu and Molnár ’s ( 2018 ) empirical study drew on a sample (N = 187) of 11–13-year-old primary school students in China. Their study built a structural equation model between CPS, IR and CR, and the result indicated that CR showed a strong and statistically significant predictive power for CPS (β = 0.55). Thus, the results of the empirical study also support the argument that CR is one of the component skills of CPS.

1.3. Behaviours and Strategies in a Complex Problem-Solving Environment

Wüstenberg et al. ( 2012 ) stated that the creation and implementation of strategic exploration are core actions of the problem-solving task. Exploring and generating effective information are key to successfully solving a problem. Wittmann and Hattrup ( 2004 ) illustrated that “riskier strategies [create] a learning environment with greater opportunities to discover and master the rules and boundaries [of a problem]” (p. 406). Thus, when gathering information about a complex problem, there may be differences between exploration strategies in terms of efficacy. The MicroDYN scenarios, a simplification and simulation of the real-world problem-solving context, will also be influenced by the adoption and implementation of exploration strategies.

The effectiveness of the isolated variation strategy (or “Vary-One-Thing-At-A-Time” strategy—VOTAT; Vollmeyer et al. 1996 ) in a CPS environment has been hotly debated ( Chen et al. 2019 ; Greiff et al. 2018 ; Molnár and Csapó 2018 ; Molnár et al. 2022 ; Wu and Molnár 2021 ; Wüstenberg et al. 2014 ). To use the VOTAT strategy, a problem solver “systematically varies only one input variable, whereas the others remain unchanged. This way, the effect of the variable that has just been changed can be observed directly by monitoring the changes in the output variables” ( Molnár and Csapó 2018, p. 2 ). Understanding and using VOTAT effectively is the foundation for developing more complex strategies for coordinating multiple variables and the basis for some phases of scientific thinking (i.e., inquiry, analysis, inference and argument; Kuhn 2010 ; Kuhn et al. 1995 ).

Some previous studies have indicated that students who are able to apply VOTAT are more likely to achieve higher performance in a CPS assessment ( Greiff et al. 2018 ), especially if the problem is a well-defined minimal complex system (such as MicroDYN) ( Fischer et al. 2012 ; Molnár and Csapó 2018 ; Wu and Molnár 2021 ). For instance, Molnár and Csapó ( 2018 ) conducted an empirical study to explore how students’ exploration strategies influence their performance in an interactive problem-solving environment. They measured a group (N = 4371) of 3rd- to 12th-grade (aged 9–18) Hungarian students’ problem-solving achievement and modelled students’ exploration strategies. This result confirmed that students’ exploration strategies influence their problem-solving performance. For example, conscious VOTAT strategy users proved to be the best problem-solvers. Furthermore, other empirical studies (e.g., Molnár et al. 2022 ; Wu and Molnár 2021 ) achieved similar results, thus confirming the importance of VOTAT in a MicroDYN-based CPS environment.

Lotz et al. ( 2017 ) illustrated that effective use of VOTAT is associated with higher levels of intelligence. Their study also pointed out that intelligence has the potential to facilitate successful exploration behaviour. Reasoning skills are an important component of general intelligence. Based on Lotz et al. ’s ( 2017 ) statements, the roles IR and CR play in the CPS process might vary due to students’ different strategy usage patterns. However, there is still a lack of empirical studies in this regard.

2. Research Aims and Questions

Numerous studies have explored the nature of CPS, some of them discussing and analysing it from behavioural or cognitive perspectives. However, there have barely been any that have merged these two perspectives. From the cognitive perspective, this study explores the role of thinking skills (including IR and CR) in the cognition process of CPS. From the behavioural perspective, the study focuses on students’ behaviour (i.e., their exploration strategy) in the CPS assessment process. More specifically, the research aims to fill this gap and examine students’ use of statistically distinguishable exploration strategies in CPS environments and to detect the connection between the level of students’ thinking skills and their behaviour strategies in the CPS environment. The following research questions were thus formed.

• (RQ1) What exploration strategy profiles characterise the various problem-solvers at the university level?
• (RQ2) Can developmental differences in CPS, IR and CR be detected among students with different exploration strategy profiles?
• (RQ3) What are the similarities and differences in the roles IR and CR play in the CPS process as well as in the two phases of CPS (i.e., KAC and KAP) among students with different exploration strategy profiles?

3.1. Participants and Procedure

The sample was drawn from one of the largest universities in Hungary. Participation was voluntary, but students were able to earn one course credit for taking part in the assessment. The participants were students who had just started their studies there (N = 1671). 43.4% of the first-year students took part in the assessment. 50.9% of the participants were female, and 49.1% were male. We filtered the sample and excluded those who had more than 80% missing data on any of the tests. After the data were cleaned, data from 1343 students were available for analysis. The test was designed and delivered via the eDia online assessment system ( Csapó and Molnár 2019 ). The assessment was held in the university ICT room and divided into two sessions. The first session involved the CPS test, whereas the second session entailed the IR and CR tests. Each session lasted 45 min. The language of the tests was Hungarian, the mother tongue of the students.

3.2. Instruments

3.2.1. complex problem solving (cps).

The CPS assessment instrument adopted the MicroDYN approach. It contains a total of twelve scenarios, and each scenario consisted of two items (one item in the KAC phase and one item in the KAP phase in each problem scenario). Twelve KAC items and twelve KAP items were therefore delivered on the CPS test for a total of twenty-four items. Each scenario has a fictional cover story. For instance, students found a sick cat in front of their house, and they were expected to feed the cat with two different kinds of cat food to help it recover.

Each item contains up to three input and three output variables. The relations between the input and output variables were formulated with linear structural equations ( Funke 2001 ). Figure 1 shows a MicroDYN sample structure containing three input variables (A, B and C), three output variables (X, Y and Z) and a number of possible relations between the variables. The complexity of the item was defined by the number of input and output variables, and the number of relations between the variables. The test began with the item with the lowest complexity. The complexity of each item gradually increased as the test progressed.

A typical MicroDYN structure with three input variables and three output variables ( Greiff and Funke 2009 ).

The interface of each item displays the value of each variable in both numerical and figural forms (See Figure 2 ). Each of the input variables has a controller, which makes it possible to vary and set the value between +2 (+ +) and −2 (− −). To operate the system, students need to click the “+” or “−” button or use the slider directly to select the value they want to be added to or subtracted from the current value of the input variable. After clicking the “Apply” button in the interface, the input variables will add or subtract the selected value, and the output variables will show the corresponding changes. The history of the values for the input and output variables within the same problem scenario is displayed on screen. If students want to withdraw all the changes and set all the variables to their original status, they can click the “Reset” button.

Screenshot of the MicroDYN item Cat—first phase (knowledge acquisition). (The items were administered in Hungarian.)

In the first phase of the problem-solving process, the KAC phase, students are asked to interact with the system by changing the value of the input variables and observing and analysing the corresponding changes in the output variables. They are then expected to determine the relationship between the input and output variables and draw it in the form of (an) arrow(s) on the concept map at the bottom of the interface. To avoid item dependence in the second phase of the problem-solving process, the students are provided with a concept map during the KAP phase (see Figure 3 ), which shows the correct connections between the input and output variables. The students are expected to interact with the system by manipulating the input variables to make the output variables reach the given target values in four steps or less. That is, they cannot click on the “Apply” button more than four times. The first phase had a 180 s time limit, whereas the second had a 90 s time limit.

Screenshot of the MicroDYN item Cat—second phase (knowledge application). (The items were administered in Hungarian).

3.2.2. Inductive Reasoning (IR)

The IR instrument (see Figure 4 ) was originally designed and developed in Hungary ( Csapó 1997 ). In the last 25 years, the instrument has been further developed and scaled for a wide age range ( Molnár and Csapó 2011 ). In addition, figural items have been added, and the assessment method has evolved from paper-and-pencil to computer-based ( Pásztor 2016 ). Currently, the instrument is widely employed in a number of countries (see, e.g., Mousa and Molnár 2020 ; Pásztor et al. 2018 ; Wu et al. 2022 ; Wu and Molnár 2018 ). In the present study, four types of items were included after test adaptation: figural series, figural analogies, number analogies and number series. Students were expected to ascertain the correct relationship between the given figures and numbers and select a suitable figure or number as their answer. Students used the drag-and-drop operation to provide their answers. In total, 49 inductive reasoning items were delivered to the participating students.

Sample items for the IR test. (The items were administered in Hungarian.).

3.2.3. Combinatorial Reasoning (CR)

The CR instrument (see Figure 5 ) was originally designed by Csapó ( 1988 ). The instrument was first developed in paper-and-pencil format and then modified for computer use ( Pásztor and Csapó 2014 ). Each item contained figural or verbal elements and a clear requirement for combing through the elements. Students were asked to list every single combination based on a given rule they could find. For the figural items, students provided their answers using the drag-and-drop operation; for the verbal items, they were asked to type their answers in a text box provided on screen. The test consisted of eight combinatorial reasoning items in total.

Sample item for the CR test. (The items were administered in Hungarian).

3.3. Scoring

Students’ performance was automatically scored via the eDia platform. Items on the CPS and IR tests were scored dichotomously. In the first phase (KAC) of the CPS test, if a student drew all the correct relations on the concept map provided on screen within the given timeframe, his/her performance was assigned a score of 1 or otherwise a score of 0. In the second phase (KAP) of the CPS test, if the student successfully reached the given target values of the output variables by manipulating the level of the input variables within no more than four steps and the given timeframe, then his/her performance earned a score of 1 or otherwise a score of 0. On the IR test items, if a student selected the correct figure or number as his/her answer, then he or she received a score of 1; otherwise, the score was 0.

Students’ performance on the CR test items was scored according to a special J index, which was developed by Csapó ( 1988 ). The J index ranges from 0 to 1, where 1 means that the student provided all the correct combinations without any redundant combinations on the task. The formula for computing the J index is the following:

x stands for the number of correct combinations in the student’s answer,

T stands for the number of all possible correct combinations, and

y stands for the number of redundant combinations in the student’s answer.

Furthermore, according to Csapó ’s ( 1988 ) design, if y is higher than T, then the J index will be counted as 0.

3.4. Coding and Labelling the Logfile Data

Beyond concrete answer data, students’ interaction and manipulation behaviour were also logged in the assessment system. This made it possible to analyse students’ exploration behaviour in the first phase of the CPS process (KAC phase). Toward this aim, we adopted a labelling system developed by Molnár and Csapó ( 2018 ) to transfer the raw logfile data to structured data files for analysis. Based on the system, each trial (i.e., the sum of manipulations within the same problem scenario which was applied and tested by clicking the “Apply” button) was modelled as a single data entity. The sum of these trials within the same problem was defined as a strategy. In our study, we only consider the trials which were able to provide useful and new information for the problem-solvers, whereas the redundant or operations trials were excluded.

In this study, we analysed students’ trials to determine the extent to which they used the VOTAT strategy: fully, partially or not at all. This strategy is the most successful exploration strategy for such problems; it is the easiest to interpret and provides direct information about the given variable without any mediation effects ( Fischer et al. 2012 ; Greiff et al. 2018 ; Molnár and Csapó 2018 ; Wüstenberg et al. 2014 ; Wu and Molnár 2021 ). Based on the definition of VOTAT noted in Section 1.3 , we checked students’ trials to ascertain if they systematically varied one input variable while keeping the others unchanged, or applied a different, less successful strategy. We considered the following three types of trials:

• “Only one single input variable was manipulated, whose relationship to the output variables was unknown (we considered a relationship unknown if its effect cannot be known from previous settings), while the other variables were set at a neutral value like zero […]
• One single input variable was changed, whose relationship to the output variables was unknown. The others were not at zero, but at a setting used earlier. […]
• One single input variable was changed, whose relationship to the output variables was unknown, and the others were not at zero; however, the effect of the other input variable(s) was known from earlier settings. Even so, this combination was not attempted earlier” ( Molnár and Csapó 2018, p. 8 )

We used the numbers 0, 1 and 2 to distinguish the level of students’ use of the most effective exploration strategy (i.e., VOTAT). If a student applied one or more of the above trials for every input variable within the same scenario, we considered that they had used the full VOTAT strategy and labelled this behaviour 2. If a student had only employed VOTAT on some but not all of the input variables, we concluded that they had used a partial VOTAT strategy for that problem scenario and labelled it 1. If a student had used none of the trials noted above in their problem exploration, then we determined that they had not used VOTAT at all and thus gave them a label of 0.

3.5. Data Analysis Plan

We used LCA (latent class analysis) to explore students’ exploration strategy profiles. LCA is a latent variable modelling approach that can be used to identify unmeasured (latent) classes of samples with similarly observed variables. LCA has been widely used in analysing logfile data for CPS assessment and in exploring students’ behaviour patterns (see, e.g., Gnaldi et al. 2020 ; Greiff et al. 2018 ; Molnár et al. 2022 ; Molnár and Csapó 2018 ; Mustafić et al. 2019 ; Wu and Molnár 2021 ). The scores for the use of VOTAT in the KAC phase (0, 1, 2; see Section 3.4 ) were used for the LCA analysis. We used Mplus ( Muthén and Muthén 2010 ) to run the LCA analysis. Several indices were used to measure the model fit: AIC (Akaike information criterion), BIC (Bayesian information criterion) and aBIC (adjusted Bayesian information criterion). With these three indicators, lower values indicate a better model fit. Entropy (ranging from 0 to 1, with values close to 1 indicating high certainty in the classification). The Lo–Mendell–Rubin adjusted likelihood ratio was used to compare the model containing n latent classes with the model containing n − 1 latent classes, and the p value was the indicator for whether a significant difference could be detected ( Lo et al. 2001 ). The results of the Lo–Mendell–Rubin adjusted likelihood ratio analysis were used to decide the correct number of latent classes in LCA models.

ANOVA was used to analyse the performance differences for CPS, IR and CR across the students from the different class profiles. The analysis was run using SPSS. A path analysis (PA) was employed in the structural equation modelling (SEM) framework to investigate the roles of CR and IR in CPS and the similarities and differences across the students from the different exploration strategy profiles. The PA models were carried out with Mplus. The Tucker–Lewis index (TLI), the comparative fit index (CFI) and the root-mean-square error of approximation (RMSEA) were used as indicators for the model fit. A TLI and CFI larger than 0.90 paired with a RMSEA less than 0.08 are commonly considered as an acceptable model fit ( van de Schoot et al. 2012 ).

4.1. Descriptive Results

All three tests showed good reliability (Cronbach’s α: CPS: 0.89; IR: 0.87; CR: 0.79). Furthermore, the two sub-dimensions of the CPS test, KAC and KAP, also showed satisfactory reliability (Cronbach’s α: KAC: 0.86; KAP: 0.78). The tests thus proved to be reliable. The means and standard deviations of students’ performance (in percentage) on each test are provided in Table 1 .

The means and standard deviations of students’ performance on each test.

4.2. Four Qualitatively Different Exploration Strategy Profiles Can Be Distinguished in CPS

Based on the labelled logfile data for CPS, we applied latent class analyses to identify the behaviour patterns of the students in the exploration phase of the problem-solving process. The model fits for the LCA analysis are listed in Table 2 . Compared with the 2 or 3 latent class models, the 4 latent class model has a lower AIC, BIC and aBIC, and the likelihood ratio statistical test (the Lo–Mendell–Rubin adjusted likelihood ratio test) confirmed it has a significantly better model fit. The 5 and 6 latent class models did not show a better model fit than the 4 latent class model. Therefore, based on the results, four qualitatively different exploration strategy profiles can be distinguished, which covered 96% of the students.

Fit indices for latent class analyses.

The patterns for the four qualitatively different exploration strategy profiles are shown in Figure 6 . In total, 84.3% of the students were proficient exploration strategy users, who were able to use VOTAT in each problem scenario independent of its difficulty level (represented by the red line in Figure 5 ). In total, 6.2% of the students were rapid learners. They were not able to apply VOTAT at the beginning of the test on the easiest problems but managed to learn quickly, and, after a rapid learning curve by the end of the test, they reached the level of proficient exploration strategy users, even though the problems became much more complex (represented by the blue line). In total, 3.1% of the students proved to be non-persistent explorers, and they employed VOTAT on the easiest problems but did not transfer this knowledge to the more complex problems. Finally, they were no longer able to apply VOTAT when the complexity of the problems increased (represented by the green line). In total, 6.5% of the students were non-performing explorers; they barely used any VOTAT strategy during the whole test (represented by the pink line) independent of problem complexity.

Four qualitatively different exploration strategy profiles.

4.3. Better Exploration Strategy Users Showed Better Performance in Reasoning Skills

Students with different exploration strategy profiles showed different kinds of performance in each reasoning skill under investigation. Results (see Table 3 ) showed that more proficient strategy users tended to have higher achievement in all the domains assessed as well as in the two sub-dimensions in CPS (i.e., KAC and KAP; ANOVA: CPS: F(3, 1339) = 187.28, p < 0.001; KAC: F(3, 1339) = 237.15, p < 0.001; KAP: F(3, 1339) = 74.91, p < 0.001; IR: F(3, 1339) = 48.10, p < 0.001; CR: F(3, 1339) = 28.72, p < 0.001); specifically, students identified as “proficient exploration strategy users” achieved the highest level on the reasoning skills tests independent of the domains. On average, they were followed by rapid learners, non-persistent explorers and, finally, non-performing explorers. Tukey’s post hoc tests revealed more details on the performance differences of students with different exploration profiles in each of the domains being measured. Proficient strategy users proved to be significantly more skilled in each of the reasoning domains. They were followed by rapid learners, who outperformed non-persistent explorers and non-performing explorers in CPS. In the domains of IR and CR, there were no achievement differences between rapid learners and non-persistent explorers, who significantly outperformed non-performing strategy explorers.

Students’ performance on each test—grouped according to the different exploration strategy profiles.

4.4. The Roles of IR and CR in CPS and Its Processes Were Different for Each Type of Exploration Strategy User

Path analysis was used to explore the predictive power of IR and CR for CPS and its processes, knowledge acquisition and knowledge application, for each group of students with different exploration strategy profiles. That is, four path analysis models were built to indicate the predictive power of IR and CR for CPS (see Figure 7 ), and another four path analyses models were developed to monitor the predictive power of IR and CR for the two empirically distinguishable phases of CPS (i.e., KAC and KAP) (see Figure 8 ). All eight models had good model fits, the fit indices TLI and CFI were above 0.90, and RMSEA was less than 0.08.

Path analysis models (with CPS, IR and CR) for each type of strategy user; * significant at 0.05 ( p   <  0.05); ** significant at 0.01 ( p   <  0.01); N.S.: no significant effect can be found.

Path analysis models (with KAC, KAP, IR and CR) for each type of strategy user; * significant at 0.05 ( p  <  0.05); ** significant at 0.01 ( p  <  0.01); N.S.: no significant effect can be found.

Students’ level of IR significantly predicted their level of CPS in all four path analysis models independent of their exploration strategy profile ( Figure 7 ; proficient strategy users: β = 0.432, p < 0.01; rapid learners: β = 0.350, p < 0.01; non-persistent explorers: β = 0.309, p < 0.05; and non-performing explorers: β = 0.386, p < 0.01). This was not the case for CR, which only proved to have predictive power for CPS among proficient strategy users (β = 0.104, p < 0.01). IR and CR were significantly correlated in all four models.

After examining the roles of IR and CR in the CPS process, we went further to explore the roles of these two reasoning skills in the distinguishable phases of CPS. The path analysis models ( Figure 8 ) showed that the predictive power of IR and CR for KAC and KAP was varied in each group. Levels of IR and CR among non-persistent explorers and non-performing explorers failed to predict their achievement in the KAC phase of the CPS process. Moreover, rapid learners’ level of IR significantly predicted their achievement in the KAC phase (β = 0.327, p < 0.01), but their level of CR did not have the same predictive power. Furthermore, the proficient strategy users’ levels of both reasoning skills had significant predictive power for KAC (IR: β = 0.363, p < 0.01; CR: β = 0.132, p < 0.01). In addition, in the KAP phase of the CPS problems, IR played a significant role for all types of strategy users, although with different power (proficient strategy users: β = 0.408, p < 0.01; rapid learners: β = 0.339, p < 0.01; non-persistent explorers: β = 0.361, p < 0.01; and non-performing explorers: β = 0.447, p < 0.01); by contrast, CR did not have significant predictive power for the KAP phase in any of the models.

5. Discussion

The study aims to investigate the role of IR and CR in CPS and its phases among students using statistically distinguishable exploration strategies in different CPS environments. We examined 1343 Hungarian university students and assessed their CPS, IR and CR skills. Both achievement data and logfile data were used in the analysis. The traditional achievement indicators formed the foundation for analysing the students’ CPS, CR and IR performance, whereas process data extracted from logfile data were used to explore students’ exploration behaviour in various CPS environments.

Four qualitatively different exploration strategy profiles were distinguished: proficient strategy users, rapid learners, non-persistent explorers and non-performing explorers (RQ1). The four profiles were consistent with the result of another study conducted at university level (see Molnár et al. 2022 ), and the frequencies of these four profiles in these two studies were very similar. The two studies therefore corroborate and validate each other’s results. The majority of the participants were identified as proficient strategy users. More than 80% of the university students were able to employ effective exploration strategies in various CPS environments. Of the remaining students, some performed poorly in exploration strategy use in the early part of the test (rapid learners), some in the last part (non-persistent explorers) and some throughout the test (non-performing explorers). However, students with these three exploration strategy profiles only constituted small portions of the total sample (with proportions ranging from 3.1% to 6.5%). The university students therefore exhibited generally good performance in terms of exploration strategy use in a CPS environment, especially compared with previous results among younger students (e.g., primary school students, see Greiff et al. 2018 ; Wu and Molnár 2021 ; primary to secondary students, see Molnár and Csapó 2018 ).

The results have indicated that better exploration strategy users achieved higher CPS performance and had better development levels of IR and CR (RQ2). First, the results have confirmed the importance of VOTAT in a CPS environment. This finding is consistent with previous studies (e.g., Greiff et al. 2015a ; Molnár and Csapó 2018 ; Mustafić et al. 2019 ; Wu and Molnár 2021 ). Second, the results have confirmed that effective use of VOTAT is strongly tied to the level of IR and CR development. Reasoning forms an important component of human intelligence, and the level of development in reasoning was an indicator of the level of intelligence ( Klauer et al. 2002 ; Sternberg and Kaufman 2011 ). Therefore, this finding has supplemented empirical evidence for the argument that effective use of VOTAT is associated with levels of intelligence to a certain extent.

The roles of IR and CR proved to be varied for each type of exploration strategy user (RQ3). For instance, the level of CPS among the best exploration strategy users (i.e., the proficient strategy users) was predicted by both the levels of IR and CR, but this was not the case for students with other profiles. In addition, the results have indicated that IR played important roles in both the KAC and KAP phases for the students with relatively good exploration strategy profiles (i.e., proficient strategy users and rapid learners) but only in the KAP phase for the rest of the students (non-persistent explorers and non-performing explorers); moreover, the predictive power of CR can only be detected in the KAC phase of the proficient strategy users. To sum up, the results suggest a general trend of IR and CR playing more important roles in the CPS process among better exploration strategy users.

Combining the answers to RQ2 and RQ3, we can gain further insights into students’ exploration strategy use in a CPS environment. Our results have confirmed that the use of VOTAT is associated with the level of IR and CR development and that the importance of IR and CR increases with proficiency in exploration strategy use. Based on these findings, we can make a reasonable argument that IR and CR are essential skills for using VOTAT and that underdeveloped IR and CR will prevent students from using effective strategies in a CPS environment. Therefore, if we want to encourage students to become better exploration strategy users, it is important to first enhance their IR and CR skills. Previous studies have suggested that establishing explicit training in using effective strategies in a CPS environment is important for students’ CPS development ( Molnár et al. 2022 ). Our findings have identified the importance of IR and CR in exploration strategy use, which has important implications for designing training programmes.

The results have also provided a basis for further studies. Future studies have been suggested to further link the behavioural and cognitive perspectives in CPS research. For instance, IR and CR were considered as component skills of CPS (see Section 1.2 ). The results of the study have indicated the possibility of not only discussing the roles of IR and CR in the cognitive process of CPS, but also exploration behaviour in a CPS environment. The results have thus provided a new perspective for exploring the component skills of CPS.

6. Limitations

There are some limitations in the study. All the tests were low stake; therefore, students might not be sufficiently motivated to do their best. This feature might have produced the missing values detected in the sample. In addition, some students’ exploration behaviour shown in this study might theoretically be below their true level. However, considering that data cleaning was adopted in this study (see Section 3.1 ), we believe this phenomenon will not have a remarkable influence on the results. Moreover, the CPS test in this study was based on the MicroDYN approach, which is a well-established and widely used artificial model with a limited number of variables and relations. However, it does not have the power to cover all kinds of complex and dynamic problems in real life. For instance, the MicroDYN approach cannot measure ill-defined problem solving. Thus, this study can only demonstrate the influence of IR and CR on problem solving in well-defined MicroDYN-simulated problems. Furthermore, VOTAT is helpful with minimally complex problems under well-defined laboratory conditions, but it may not be that helpful with real-world, ill-defined complex problems ( Dörner and Funke 2017 ; Funke 2021 ). Therefore, the generalizability of the findings is limited.

7. Conclusions

In general, the results have shed new light on students’ problem-solving behaviours in respect of exploration strategy in a CPS environment and explored differences in terms of the use of thinking skills between students with different exploration strategies. Most studies discuss students’ problem-solving strategies from a behavioural perspective. By contrast, this paper discusses them from both behavioural and cognitive perspectives, thus expanding our understanding in this area. As for educational implications, the study contributes to designing and revising training methods for CPS by identifying the importance of IR and CR in exploration behaviour in a CPS environment. To sum up, the study has investigated the nature of CPS from a fresh angle and provided a sound basis for future studies.

Funding Statement

This study has been conducted with support provided by the National Research, Development and Innovation Fund of Hungary, financed under the OTKA K135727 funding scheme and supported by the Research Programme for Public Education Development, Hungarian Academy of Sciences (KOZOKT2021-16).

Author Contributions

Conceptualization, H.W. and G.M.; methodology, H.W. and G.M.; formal analysis, H.W.; writing—original draft preparation, H.W.; writing—review and editing, G.M.; project administration, G.M.; funding acquisition, G.M. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Ethical approval was not required for this study in accordance with the national and institutional guidelines. The assessments which provided data for this study were integrated parts of the educational processes of the participating university. The participation was voluntary.

Informed Consent Statement

All of the students in the assessment turned 18, that is, it was not required or possible to request and obtain written informed parental consent from the participants.

Data Availability Statement

Conflicts of interest.

Authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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