The Psychology of Problem Solving: Navigating Challenges with Diverse Approaches and Techniques

I. Introduction to the Landscape of Problem Solving

Problem solving is a fundamental cognitive activity that permeates nearly every aspect of human endeavor, from mundane daily choices to groundbreaking scientific discoveries. Its psychological underpinnings are complex and multifaceted, involving a dynamic interplay of cognitive processes, motivational states, and environmental interactions. Understanding the psychology of problem solving is not merely an academic exercise; it offers profound implications for enhancing individual and collective efficacy in navigating an increasingly intricate world.

A. Defining Problem Solving: A Psychological Perspective

From a psychological standpoint, problem solving is defined as a motivational drive to reach a definite “goal” from a present situation or condition that is either not moving toward that goal, is distant from it, or requires more complex logical analysis for finding a missing description of conditions or steps toward that goal.¹ It is the process of achieving a goal by overcoming obstacles, a frequent component of most activities, ranging from simple personal tasks, such as how to operate an appliance, to complex issues in business, science, and technical fields.² This definition is pivotal as it immediately frames problem solving not just as a sequence of cognitive operations but as an activity imbued with motivation. This motivational element is a recurring theme in understanding the engagement, persistence, and success in problem-solving endeavors.

The systematic study of human and animal problem-solving processes has yielded significant insights into our conscious experience and has concurrently fueled advancements in diverse fields such as computer science and artificial intelligence.¹ Indeed, a substantial portion of contemporary cognitive science is dedicated to investigating how individuals consciously and unconsciously make decisions and solve problems when confronted with various situations, such as processing large volumes of information or troubleshooting complex systems.¹

B. The Spectrum of Problems: From Well-Defined to Ill-Defined

Problems encountered by individuals can be broadly categorized along a spectrum from well-defined to ill-defined. Well-defined problems are characterized by specific goals, clearly defined solution paths, and clear expected solutions.¹ Examples include solving a mathematical equation or playing a game like the Tower of Hanoi, where the initial state, permissible moves (operators), and desired final state are explicit.³ These types of problems generally allow for more extensive initial planning.²

In contrast, ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions.¹ Examples might include designing a sustainable urban environment, resolving a complex social issue, or formulating a novel artistic concept. Problem solving in such contexts often incorporates pragmatics (logical reasoning within context) and semantics (interpretation of meanings), and frequently necessitates abstract thinking and creativity to even articulate the problem adequately before attempting to find novel solutions.¹

This distinction between well-defined and ill-defined problems is fundamental because the nature of the problem profoundly influences the entire subsequent problem-solving cascade. It dictates the most appropriate strategies, the cognitive resources demanded, and can even shape the emotional experience of the problem solver. The inherent clarity of goals and solution paths in well-defined problems typically reduces the cognitive load associated with problem representation and ambiguity. Conversely, the ambiguity inherent in ill-defined problems tends to increase cognitive load and may evoke feelings of uncertainty or frustration if not effectively managed, thereby impacting persistence and strategic choices. Thus, the initial classification of a problem is not merely descriptive; it carries predictive weight for the cognitive and affective journey involved in its resolution. This understanding has significant implications for educational approaches, suggesting that cultivating strategies for managing ambiguity is paramount when tackling ill-defined challenges.

C. Core Cognitive Components in the Problem-Solving Cycle

The process of problem solving, regardless of the problem’s nature, generally involves several core components, often conceptualized as a cycle. This cycle typically begins with problem finding (also known as problem analysis or discovery), where the problem is identified and understood, and problem shaping, where the organization and structuring of the problem occur, simplifying it for cognitive engagement.¹

Following these initial stages, the problem solver moves to generating alternative strategies, which involves brainstorming and developing various approaches to tackle the problem. Subsequently, one or more of these strategies are chosen for the implementation of attempted solutions. The final key component is the verification of the selected solution, which involves evaluating whether the implemented solution has effectively resolved the problem and achieved the desired goal.¹ These components highlight that problem solving is often an iterative process, particularly for complex or ill-defined problems, where the solver may cycle through these stages multiple times, refining their understanding and approach.

D. The Significance of Problem Solving in Human Cognition and Daily Life

Problem solving is recognized as a higher-order cognitive process and a critical intellectual function that requires the modulation and control of more routine or fundamental cognitive skills.² It is a pervasive aspect of human activity, integral to navigating both simple personal tasks and complex professional challenges.² The ability to effectively solve problems allows individuals to adapt to their environments, overcome obstacles, and achieve their objectives.

The study of problem solving holds immense significance for understanding conscious experience and has been a driving force behind advancements in artificial intelligence and cognitive science.¹ Many professions, such as law, medicine, engineering, and consultancy, are fundamentally centered around problem-solving, requiring specialized technical skills and knowledge beyond general competence.² The pervasiveness and critical importance of problem solving underscore the value of understanding its psychological underpinnings. Such understanding is essential not only for advancing scientific knowledge but also for developing methods to enhance this vital human skill. The very definition of problem solving as a “motivational drive” ¹ challenges purely computational interpretations, suggesting that affective and motivational factors are not merely secondary modulators but are integral to the process. This implies that understanding the impetus to solve a problem is as crucial as understanding the cognitive steps involved, and interventions aimed at improving problem-solving should address these motivational and emotional dimensions alongside cognitive strategies.

II. Foundational Theories of Problem Solving

The psychological study of problem solving has been shaped by several influential theoretical perspectives, each offering unique insights into the mental processes involved. Early theories laid the groundwork for later, more nuanced understandings, and their core concepts continue to inform contemporary research.

A. The Gestalt Approach: Insight, Restructuring, and Mental Representation

Emerging in the early 20th century, Gestalt psychology, founded by figures such as Max Wertheimer, Kurt Koffka, and Wolfgang Köhler, provided one of the first dominant frameworks for understanding problem solving.² A central tenet of the Gestalt approach is that problem solving often involves a process called restructuring. This occurs when an individual reorganizes their mental representation of a problem’s elements, leading to a new understanding and, often, a solution.³

A key concept within this framework is insight, characterized by the sudden realization of a problem’s solution, frequently accompanied by an “Aha!” experience.³ Insight problems typically require novel and non-obvious approaches, distinguishing them from problems solvable through reproductive thinking, which involves applying previously learned responses.³ Instead, insight relies on productive thinking, where new solutions are generated.

The mental representation of a problem—how it is modeled in the solver’s mind, including its objects, predicates, potential states, available operators, and solution criteria—is paramount.³ Gestalt psychologists argued that re-analyzing a problem or shifting from one representation to another can be the key to unlocking a solution.³

Key figures and their contributions include:

• Karl Duncker, who in his work The Psychology of Productive Thinking (1935), explored how prior experience and problem presentation can affect solutions. He is particularly known for the concept of functional fixedness, the tendency to perceive an object only in terms of its most common use, which can impede problem solving (e.g., his famous candle problem or the X-ray problem).²
• Max Wertheimer distinguished between productive (insightful) thinking and reproductive thinking.⁵ His earlier work on the phi phenomenon, demonstrating apparent motion from static lights, established the Gestalt principle that perception is holistic—the whole is different from the sum of its parts—a concept that extends to how problems are perceived and understood.⁵
• Wolfgang Köhler’s experiments with chimpanzees demonstrated that animals could solve problems through “sudden insight” rather than solely through trial and error or incremental learning.⁵ His apes, for example, would suddenly realize how to use tools to reach bananas that were out of reach, illustrating a restructuring of their perception of the problem elements.

Recent advancements in cognitive neuroscience have lent support to some core Gestalt ideas. Studies using techniques like pupillometry have shown that pupil diameter often increases shortly before an individual reports an “Aha!” moment, suggesting a physiological correlate to the subjective experience of insight.⁷ This, along with findings on the role of the visual system in marking a switch of knowledge into awareness, suggests a shared neural mechanism for perceptual reorganization and the cognitive restructuring central to insight problem-solving.⁷

B. The Information Processing Paradigm: Problem Solving as Search

Beginning in the 1950s and gaining prominence through the 1970s, the information processing paradigm, pioneered by Allen Newell and Herbert A. Simon, offered a new way to conceptualize problem solving, heavily influenced by the advent of computer science.² This approach views the human mind as an information-processing system, and problem solving as a systematic search through a problem space.⁹

The problem space is defined by several components:

1. Initial State: The problem’s starting condition.
2. Goal State: The desired end state or solution.
3. Operators: Permissible actions or rules that can transform one problem state into another.
4. Path Constraints: Limitations or rules that must be adhered to during the solution process.⁹

Newell and Simon’s General Problem Solver (GPS) was a computer model designed to simulate human problem-solving behavior.¹⁰ The GPS worked by recursively applying heuristics, most notably means-ends analysis. This heuristic involves identifying the difference between the current state and the goal state and then selecting an operator (a “means”) to reduce that difference. This often involves breaking the main problem into a series of smaller, more manageable subgoals.¹⁰ The GPS could solve a variety of well-defined problems, such as logical proofs and puzzles like the Tower of Hanoi.¹⁰

The information processing framework has been extended to encompass a wider range of phenomena.

• Dual-space search, proposed by Simon and Lea (1974), suggests that problem solving can involve searching in two distinct but related spaces: an instance space (containing the possible states of the problem) and a rule space (containing possible rules or principles governing the problem).⁹ This is particularly relevant for tasks involving induction or learning new rules.
• Hayes and Simon (1974) emphasized the importance of an initial understanding process. They argued that problem solvers must first interpret and represent the problem, and this understanding process then drives the subsequent search process.⁹

Despite their differing terminologies and methodologies, both the Gestalt and Information Processing theories converge on the critical importance of problem representation. For Gestalt psychologists, achieving insight hinges on restructuring this mental representation. For Information Processing theorists, the initial “understanding process” ⁹ defines the problem space, which subsequently dictates the search strategy. An inadequate or flawed initial representation in either framework is likely to lead to inefficient or unsuccessful problem-solving efforts. This commonality underscores that a core competence in problem solving is the ability to accurately and flexibly construct a mental model of the problem, a skill that could be a valuable target for educational interventions.

C. Evolving Perspectives: Complex Problem Solving (CPS)

Research into Complex Problem Solving (CPS) emerged in the 1970s, spurred by a growing recognition that many real-world problems—such as managing economic systems, addressing environmental crises, or navigating political instability—were far more dynamic, interconnected, and opaque than the well-defined puzzles typically studied in laboratories.¹¹

Dietrich Dörner is a key figure in CPS research. He and his colleagues pioneered the use of computer simulations as a research methodology.¹¹ These simulations, such as Lohhausen (which required participants to manage a small town) or Moroland (involving the organization of developmental aid for a fictional country), allowed researchers to observe how individuals learn, make decisions, and strategize in complex, interactive environments that changed over time, often in response to the participant’s actions.¹¹

This research yielded significant findings about human performance in complex situations. Dörner’s group identified common errors people make when dealing with complexity, including:

• Ignoring trends or feedback delays.
• Underestimating exponential growth.
• Thinking in linear causal chains instead of understanding interconnected causal networks.¹¹

Furthermore, by comparing successful and unsuccessful problem solvers, Dörner (1989, 1996) identified several characteristics of effective CPS. Good problem solvers tended to:

• Make more decisions simultaneously and consider more aspects of the system.
• Focus on central, underlying causes early in the process, rather than getting bogged down in superficial effects.
• Engage in more hypothesis testing and ask more questions about causal relationships.
• Be less distracted by unimportant subproblems.
• Demonstrate greater consistency in their decision-making over time.
• More actively structure, reflect upon, criticize, and modify their own hypotheses and behaviors.¹¹

CPS research highlighted the limitations of studying only simple, well-defined problems and underscored the importance of factors like knowledge acquisition, dynamic strategy formation, and self-regulation in tackling complex scenarios. It also initiated a lively debate on the relationship between CPS skills and traditional measures of general intelligence, and whether CPS represented a distinct cognitive ability.¹¹ While early CPS simulations faced psychometric criticisms, later work focused on improving their reliability and validity, leading to the inclusion of CPS tasks in large-scale assessments like the Programme for International Student Assessment (PISA).¹¹

The evolution from Gestalt and early Information Processing theories towards CPS research reflects a broader trend in psychology: a move towards greater ecological validity and the study of cognition in more complex, realistic contexts. The limitations of simple laboratory tasks, such as the Tower of Hanoi ², became apparent when attempting to understand how individuals solve multifaceted problems like managing a simulated city.¹¹ This shift acknowledged that real-world problems are often ill-defined, dynamic, involve numerous interacting variables, and necessitate continuous learning and adaptation—features not readily captured by simpler, static tasks. Consequently, findings from simpler tasks may not always generalize to the intricacies of real-world problem solving, underscoring the need for specific research into CPS.

Moreover, the characteristics of effective complex problem solvers identified by Dörner—such as focusing on central causes, robust hypothesis testing, and reflective self-modification of strategies ¹¹—resonate strongly with later discussions on the nature of expertise (see Section V.B.1) and the role of metacognition (see Section IV.E). Effective performance in CPS appears to be a confluence of deep domain understanding (implicit in the ability to discern central causes from superficial effects) and sophisticated self-regulatory skills (evident in hypothesis testing and reflective practice). This suggests that the abilities Dörner observed are not isolated traits but likely manifestations of developing expertise and strong metacognitive capabilities applied within a dynamic and complex domain, pointing towards potential avenues for improving CPS through fostering these underlying capacities.

III. A Toolkit of Problem-Solving Strategies and Techniques

Problem solvers employ a diverse array of strategies and techniques, ranging from systematic procedures to intuitive shortcuts and creative explorations. The choice of strategy often depends on the nature of the problem, the available resources, and the individual’s own cognitive preferences and experiences.

A. Algorithmic vs. Heuristic Approaches

A primary distinction in problem-solving strategies lies between algorithms and heuristics.

• Algorithms are step-by-step procedures or methodical, logical rules that guarantee a solution if applied correctly and if an algorithm exists for the problem type.¹² Examples include mathematical formulas, a recipe for baking a cake, or systematically trying every possible combination to open a lock.¹² While algorithms ensure accuracy, they can be time-consuming and are not always available or practical, especially for ill-defined or complex problems where the steps to a solution are not clear.¹²
• Heuristics, in contrast, are mental shortcuts, rules of thumb, or educated guesses that are often useful for finding a solution quickly and efficiently, but they do not guarantee a correct or optimal outcome.¹ Heuristics are particularly valuable when time is limited, information is scarce or overwhelming, the decision is unimportant, or an appropriate heuristic readily comes to mind.¹ Examples include the availability heuristic (judging the likelihood of an event by how easily examples come to mind), the representativeness heuristic (judging something based on how well it matches a prototype, potentially ignoring base rates), and the anchoring and adjustment heuristic (relying heavily on an initial piece of information—the anchor—and then adjusting insufficiently from that point).¹²

The selection between an algorithmic or heuristic approach is rarely arbitrary. It often represents a meta-cognitive decision influenced by the problem’s characteristics (well-defined problems are more amenable to algorithms, while ill-defined ones may necessitate heuristics ¹), the availability of resources (such as time and information ¹), and the acceptable margin for error. The problem solver implicitly or explicitly weighs the potential “cost” of using a heuristic (risk of error or sub-optimal solution) against the “cost” of an algorithm (time, effort, and its applicability to the specific problem). This selection process itself is a crucial problem-solving skill, reflecting an understanding of one’s own cognitive limitations and the demands of the task.

B. Common Heuristics and Methods

Beyond the general distinction, several specific heuristics and methods are commonly employed:

1. Trial and Error: This strategy involves attempting different potential solutions sequentially and eliminating those that prove unsuccessful until a working solution is found.¹ It is one of the most basic problem-solving approaches.

• Examples: Restarting a malfunctioning phone by trying various actions (turning off WiFi, Bluetooth), checking ink levels or paper jams in a printer, or Thomas Edison’s extensive experimentation to find a suitable filament for the light bulb.¹³ While simple, trial and error can be inefficient for problems with a large number of possibilities.

2. Means-Ends Analysis and Subgoaling: A powerful heuristic central to Newell and Simon’s General Problem Solver, means-ends analysis involves identifying the ultimate goal (“end”) and then determining the appropriate actions or strategies (“means”) to reduce the difference between the current state and the goal state.¹ This often requires breaking the main problem down into a series of smaller, more manageable subgoals. Achieving each subgoal brings the solver closer to the final solution.

• Examples: The Tower of Hanoi puzzle is solved by creating subgoals to move individual discs according to rules.¹ Writing a research paper can be approached by setting subgoals such as brainstorming, developing a thesis, conducting research, outlining, drafting, and revising.¹ The Missionary-Cannibal problem also exemplifies this strategy, requiring careful planning of moves (subgoals) to transport everyone across a river under constraints.¹

3. Working Backward: This heuristic involves starting from the known or desired goal state and working in reverse to determine the sequence of steps or initial conditions that must have led to it.¹ It is particularly useful when the initial state is complex or has many possibilities, but the end state is clear.

• Examples: Planning attendance at an event by starting with the arrival time and working backward to calculate departure time, preparation time, and preceding activities.¹ Solving certain mathematical problems by starting with the result and reversing the operations.

4. Hill Climbing: In this heuristic, the problem solver, at each decision point, chooses the action that appears to lead most directly towards the goal state, similar to climbing a hill by always taking a step in the upward direction.¹⁷ While it provides a sense of continuous progress, a significant disadvantage is the risk of getting trapped on a “local maximum”—a state that is better than its immediate neighbors but is not the overall optimal solution for the entire problem space. The solver can only see one step ahead and may miss a better solution that requires an initial move away from the apparent goal.

• Examples: Navigating a maze by consistently choosing paths that seem to reduce the distance to the exit.¹⁷ In artificial intelligence, hill climbing algorithms are used for optimization problems, such as finding the shortest route in the Traveling Salesman Problem, though they may not always find the global optimum.²⁰

5. Analogical Reasoning: Leveraging Past Experience: This strategy involves using the solution of a previously encountered problem (the source problem) that is similar or analogous in structure to the current problem (the target problem).¹ Effective analogical reasoning typically involves three steps: (1) Noticing that an analogical connection exists between the source and target problems; (2) Mapping the corresponding parts of the two problems onto each other; and (3) Applying the mapping to generate a parallel solution for the target problem.²¹

• Examples: Karl Duncker’s classic radiation problem (destroying a tumor with rays without harming healthy tissue) can often be solved when individuals are presented with the analogous “General and Fortress Problem” (capturing a fortress by dispatching small groups of soldiers down multiple roads simultaneously).²¹ In everyday life, one might decide whether to invest in a new business venture by comparing its characteristics and potential outcomes to those of previous successful or unsuccessful investments.²²

Many of these seemingly distinct problem-solving strategies are, in practice, specific applications or variations of more fundamental cognitive principles. For instance, Means-Ends Analysis, Working Backward, and the structural approach of Problem Decomposition (discussed below) all leverage the core idea of breaking a complex goal or problem into smaller, more manageable parts, essentially navigating a problem space through hierarchical structuring. Similarly, some creative techniques aim to disrupt established mental representations to foster new perspectives, a concept that echoes the Gestalt notion of “restructuring.” Recognizing these shared cognitive underpinnings allows for a more flexible and integrated application of these techniques, enabling a solver to, for example, use problem decomposition to identify sub-problems and then apply lateral thinking to generate novel solutions for a particularly challenging sub-problem.

C. Creative and Divergent Techniques

When standard heuristics or algorithms fail, or when problems are particularly ill-defined, creative techniques that promote divergent thinking become essential.

1. Brainstorming: A widely used technique, especially in group settings, aimed at generating a large quantity of ideas related to a problem.¹ The core principle is to encourage free-flowing thought and defer judgment on the feasibility or quality of ideas during the generation phase.

• Key rules for effective brainstorming include: (1) Defer Judgment (avoid criticism); (2) Encourage Wild Ideas (the more unconventional, the better); (3) Build on the Ideas of Others (use “and” instead of “but”); (4) Stay Focused on the Topic; (5) One Conversation at a Time; (6) Be Visual (use notes, drawings); and (7) Go for Quantity (aim for a high number of ideas).²³
• Variations: While traditional brainstorming is verbal and group-based, variations include brainwriting (where individuals write down ideas before sharing, ensuring quieter members contribute), mind mapping (visually structuring ideas), SWOT analysis, rolestorming (adopting different personas), starbursting (focusing on questions), the “five whys” (iterative questioning to find root causes), and stop-and-go-brainstorming (alternating idea generation and evaluation).²³

2. Lateral Thinking (Edward de Bono): An approach to problem solving that involves deliberately moving away from obvious, direct, and logical (or “vertical”) lines of thought in favor of indirect, oblique, or unexpected perspectives.¹ Lateral thinking, also called horizontal thinking, emphasizes generating many different ideas and possibilities (divergent thinking) rather than deeply analyzing a single approach.

• De Bono’s techniques for fostering lateral thinking include: (1) Awareness: Recognizing the brain’s tendency to rely on established patterns; (2) Random Stimulation: Introducing unrelated or random inputs to disrupt set patterns and spark new connections; (3) Alternatives: Deliberately seeking out multiple alternative solutions or perspectives, even if one seems adequate; and (4) Alteration: Systematically changing or reversing elements of the problem or assumed relationships to see what new possibilities emerge.²⁵

D. Structural Approaches

For highly complex problems, strategies that focus on the problem’s structure can be invaluable.

1. Problem Decomposition (Divide and Conquer): This strategy involves breaking down a large, complex problem into smaller, more manageable, and often independent sub-problems.¹ Each sub-problem can then be tackled individually, and their solutions can be combined or integrated to solve the original overarching problem. This is a common method for reducing the perceived difficulty of structured problems.²⁷

• Steps typically involve: Identifying the core issue, dividing it into smaller components, prioritizing these components based on urgency or importance, understanding the interconnections between components, developing specific strategies for each component, integrating the individual solutions, and finally, assessing and refining the overall solution.²⁸

Effective problem solving often involves a dynamic interplay between strategies that emphasize divergent thinking (generating a wide range of possibilities, as seen in brainstorming and lateral thinking) and those that emphasize convergent thinking (narrowing down options to arrive at the best or most logical solution, as in means-ends analysis or the application of an algorithm). The general problem-solving cycle itself (Section I.C) reflects this, moving from generating alternative strategies (a divergent phase) to selecting, implementing, and verifying a particular solution (a convergent phase). The ability to flexibly shift between these modes of thinking is a hallmark of skilled problem solvers.

The following table provides a comparative overview of these diverse strategies:

Table 1: Summary of Problem-Solving Strategies

Strategy Name	Core Principle/Description	Type (Algorithm/Heuristic/Creative/Structural)	Common Applications/Examples	Key Advantages	Key Limitations/Considerations
Algorithm Use	Step-by-step procedure guaranteeing a correct solution if followed accurately. 12	Algorithm	Mathematical formulas, recipes, systematic search of all combinations (e.g., combination lock). 12	Guarantees a correct solution if applicable and executed correctly. 12	Can be time-consuming; not available for all problem types (especially ill-defined ones); requires all steps to be known. 12
Trial and Error	Trying different solutions sequentially and eliminating those that do not work. 1	Heuristic	Troubleshooting a malfunctioning device, Edison’s filament experiments. 13	Simple to implement; may eventually find a solution.	Can be inefficient for complex problems with many possibilities; no guarantee of finding optimal solution. 1
Means-Ends Analysis	Reducing the difference between the current state and the goal state by setting subgoals. 1	Heuristic	Tower of Hanoi, Missionary-Cannibal problem, planning a research paper. 1	Effective for complex problems; provides a structured approach to reaching goals.	Can be complex to apply if subgoals are hard to identify or achieve.
Working Backward	Starting from the goal and working in reverse to identify necessary preceding steps. 10	Heuristic	Planning event schedules, solving certain math problems. 1	Useful when the end state is clear and the initial state is complex.	Not suitable for all problems, especially those with unclear end states or irreversible steps.
Hill Climbing	At each step, choosing the action that appears to move closest to the goal. 17	Heuristic	Solving mazes, AI optimization problems (e.g., Traveling Salesman). 17	Provides a sense of continuous progress; simple to implement.	Risk of getting stuck on local optima; limited foresight (only sees one step ahead). 17
Analogical Reasoning	Using a solution from a similar past problem to solve a current problem. 1	Heuristic/Creative	Duncker’s radiation problem (using General/Fortress analogy), business investment decisions. 21	Can lead to novel solutions quickly by leveraging existing knowledge.	Finding an appropriate analogy can be difficult; surface similarities can be misleading. 21
Brainstorming	Generating a large quantity of ideas, deferring judgment, and encouraging wild ideas. 1	Creative	Idea generation for new products, marketing campaigns, solving organizational problems. 23	Fosters creativity; generates many diverse options; encourages group participation.	Can be unfocused if not managed well; quality of ideas may vary; dominant individuals can stifle others. 23
Lateral Thinking	Approaching problems indirectly and creatively, forgoing obvious logical paths. 1	Creative	Innovation, finding unconventional solutions, puzzles requiring non-obvious thinking. 25	Can uncover highly innovative solutions; overcomes mental blocks.	May seem counterintuitive; requires deliberate effort to move beyond vertical thinking. 25
Problem Decomposition	Breaking down large, complex problems into smaller, more manageable sub-problems. 1	Structural	Project management, software development, complex system design. 27	Simplifies complex problems; allows for focused effort on sub-components.	Requires careful identification of sub-problems and their interconnections; integration of solutions can be challenging. 28

IV. The Cognitive Architecture of Problem Solving

Effective problem solving relies on a sophisticated interplay of fundamental cognitive processes. These processes, from initial perception and representation to memory retrieval, reasoning, and metacognitive oversight, form the underlying architecture that supports our ability to navigate and resolve challenges.

A. The Role of Perception and Mental Representation

The journey of problem solving begins with perception, the cognitive process of interpreting sensory information to understand the environment and, crucially, to identify that a problem exists.²⁹ This involves intricate perceptual processing, including the encoding of sensory input, extraction of relevant features, and recognition of patterns.³⁰

Once a problem is perceived, a mental representation of it is constructed. This internal model, comprising the problem’s objects, their properties (predicates), the current state, possible future states, available operators (actions to change states), and criteria for a solution, is critical to how the problem is understood and approached.³ The nature of this representation, heavily influenced by prior knowledge and experience, can significantly impact the difficulty of solving the problem. As emphasized by Gestalt psychologists, restructuring this mental representation—viewing the problem from a different angle or organizing its elements in a new way—can be the key to unlocking insight and finding a solution.³

The way a problem is presented or framed also profoundly influences its mental representation and, consequently, the strategies selected and the ultimate performance.³¹ Research has shown that framing a task with an opportunity-focus (emphasizing potential gains) can enhance working memory performance by minimizing threat appraisal, whereas a risk-focused framing (highlighting potential losses) can impair performance by increasing threat appraisal and negative affect.³² Another perceptual aspect relevant to problem solving is affordance detection, which involves perceiving the potential actions or interactions that the environment offers in relation to the solver’s goals (e.g., seeing a chair not just as an object, but as something that “affords” sitting).³⁰

The quality and effectiveness of this initial problem representation are not formed in a vacuum; they are critically dependent on the subsequent cognitive processes of attentional allocation and working memory capacity. If attention is not appropriately directed towards the most relevant elements of the problem, or if working memory is overloaded and unable to adequately hold and manipulate the necessary information, the mental representation formed will likely be impoverished, inaccurate, or incomplete. Such a flawed representation will inevitably undermine subsequent reasoning processes and render metacognitive strategies less effective, as these higher-order functions would be operating on a distorted model of the problem. This highlights that interventions aimed at improving problem representation must also consider strategies for enhancing attentional control and managing working memory load.

B. Attention’s Gateway: Focusing Cognitive Resources

Attention is the cognitive mechanism that allows individuals to selectively concentrate on specific information from the environment or internal thought processes while ignoring distractions. It is a cornerstone of effective problem solving, crucial for learning, decision-making, and maintaining focus on the task at hand.²⁹

Attention can be conceptualized as a filter (as in Broadbent’s early model, which proposed that unattended information is largely blocked) or as an attenuator (as in Treisman’s model, suggesting that unattended information is weakened but not entirely excluded).38 Regardless of the precise model, attention plays a vital role in managing cognitive resources.

Different types of attention contribute to problem solving:

• Sustained attention is the ability to maintain concentration on a task over an extended period.
• Selective attention allows focus on relevant stimuli while filtering out irrelevant distractors.
• Divided attention (though less detailed in the provided materials, it is a recognized component) refers to the capacity to attend to multiple tasks or pieces of information simultaneously.³⁷

Attention is indispensable for identifying the core elements of a problem, comprehending its nuances, generating potential solutions, and encoding relevant information into memory.³⁵ Attentional mechanisms serve to enforce the relevance of information, select pertinent stimuli from the environment or from memory, and crucially, allow for shifts in focus, enabling adaptive responses to new information or changing priorities in the problem-solving context.³⁶

C. Memory Systems in Action: Working Memory and Long-Term Memory Retrieval

Memory plays a dual role in problem solving, with both working memory and long-term memory being essential.

• Working Memory (WM): This is a limited-capacity system responsible for temporarily holding and actively manipulating information that is immediately relevant to the task at hand, such as reasoning, comprehension, and learning.³⁴ It functions as a “mental chalkboard” where information is held and processed during problem solving.³⁹ Research consistently shows a positive correlation between working memory capacity and problem-solving ability.⁴⁰ For instance, in solving mathematical word problems, WM is used to store numbers, understand the question, recall relevant formulas, and track solution steps.³⁹ Interventions designed to reduce the cognitive load on WM, such as teaching students to underline key information or use diagrams, can improve problem-solving performance, especially for individuals who struggle with a particular domain.³⁹ Working memory is also implicated in various phases of insight problem solving, facilitating the representational changes that can lead to sudden solutions.⁴⁰
• Long-Term Memory (LTM): LTM provides the vast repository of knowledge—facts, concepts, procedures, and past experiences—that is drawn upon during problem solving.²⁹

• Declarative memory (explicit memory) includes semantic memory (general world knowledge, facts, concepts) and episodic memory (personal experiences and events). Semantic memory provides the contextual understanding and factual basis for a problem, while episodic memory allows solvers to recall similar problems encountered in the past and the strategies used to solve them.⁴¹
• Procedural memory (implicit memory) stores knowledge about how to perform tasks and skills, including learned problem-solving procedures, heuristics, and other executive skills.⁴¹ The way knowledge is accessed and applied from LTM during problem solving is as critical as the knowledge itself. Passive storage of information is insufficient; knowledge must be actively and flexibly retrieved in a context-appropriate manner. Research on the retrieval practice effect (the finding that actively testing oneself on material enhances long-term retention more than passive restudying) underscores the importance of active retrieval for making declarative knowledge usable.⁴² While research on its direct benefit for learning problem-solving skills from worked examples is mixed ⁴², the general principle that active engagement with knowledge promotes its utility is highly relevant. Experts, for example, excel not just in the quantity of their knowledge but in its sophisticated organization and efficient retrieval for application (see Section V.B.1). This suggests that effective problem solving relies on an LTM that is not only extensive but also well-structured to support efficient and contextually relevant access to information.

D. Reasoning and Inference: Inductive and Deductive Processes

Reasoning is the cognitive process of using existing knowledge and information to form conclusions, make judgments, or draw inferences. It is essential for making sense of the information perceived from the problem statement and retrieved from memory, for weighing different solution options, and for considering potential outcomes.29 Reasoning is a key component of executive functions, which are higher-level cognitive processes that manage and control thought and action.37

Two primary forms of reasoning are employed in problem solving:

• Inductive Reasoning: This is a “bottom-up” approach where specific observations, details, or instances are used to construct broader generalizations, hypotheses, or theories.⁴³ In problem solving, inductive reasoning is valuable for identifying patterns in data, formulating potential explanations for a problem (hypothesis generation), and discerning potential root causes, especially when faced with novel or poorly understood situations.
• Deductive Reasoning: This is a “top-down” approach that starts with general principles, premises, or theories and applies them to specific instances to derive logical conclusions or test hypotheses.⁴³ In problem solving, deductive reasoning is useful for applying known rules or principles to a specific problem, testing the validity of a proposed solution by examining its logical consequences, and systematically working through possibilities.

In practice, complex problem solving often involves an iterative interplay between inductive and deductive reasoning.⁴⁴ One might use inductive reasoning to generate a hypothesis about a problem’s cause and then use deductive reasoning to test the predictions derived from that hypothesis.

E. Metacognition: Thinking About Thinking in Problem Solving

Metacognition refers to an individual’s awareness and understanding of their own cognitive processes (self-monitoring) and their ability to control and regulate these processes (self-regulation) for the purpose of learning and problem solving.⁴⁵ It is, in essence, “thinking about thinking.” A robust body of research links stronger metacognitive skills to improved problem-solving performance and academic achievement.⁴⁵

Metacognition encompasses several key activities:

• Planning: Strategizing how to approach a problem or learning task.
• Monitoring: Tracking one’s understanding, progress towards a goal, the relevance of information, the presence of confusion, and the correctness of one’s thinking and actions.
• Evaluating: Assessing the outcome of one’s efforts, the effectiveness of chosen strategies, and the overall achievement of the goal.⁴⁵

Metacognition helps problem solvers to accurately identify the given information and constraints, clearly define the goal state, select appropriate strategies, recognize and overcome obstacles, and critically revise their approaches as needed.⁴⁵ The process monitoring theory, for instance, suggests that metacognitive monitoring and control abilities allow individuals to constantly assess the discrepancy between their current state and the target state, prompting adjustments in cognitive strategies to facilitate creative problem solving.⁴⁷

Rather than being just one cognitive process among others, metacognition functions as a higher-order executive controller. It actively directs and manages other cognitive resources—such as perception, attention, memory retrieval, and reasoning—specifically in service of the problem-solving goal. For example, metacognitive monitoring prompts questions like, “Am I focusing on the most important information?” (directing attention), “Do I fully understand this aspect of the problem?” (evaluating problem representation), “What strategies have I used before for similar problems?” (guiding LTM retrieval), and “Is this line of reasoning leading me closer to a solution?” (assessing reasoning). This directive and integrative role makes metacognition a pivotal target for interventions aimed at improving overall problem-solving ability.

F. Interplay of Core Cognitive Processes (Abstraction, Analysis, Synthesis)

Problem solving, as a higher-layer cognitive process, involves the coordinated interaction of several other fundamental cognitive operations ⁴:

• Abstraction: Identifying and focusing on the essential features of a problem while disregarding irrelevant details. This helps in simplifying complex situations and recognizing underlying patterns.
• Analysis: Breaking down a complex problem into smaller, more manageable components or sub-problems to understand their individual characteristics and their relationships to one another.
• Synthesis: Combining different pieces of information, ideas, or partial solutions into a new, coherent, and integrated whole, often leading to the final solution.
• Searching: Navigating the mental problem space, or external information sources, to find pathways between the initial problem state and the desired goal state, or to locate relevant information and potential solutions.
• Learning: Encoding the problem-solving experience, including successful strategies and outcomes, into long-term memory. This learning allows for more efficient problem solving in future similar situations.
• Decision Making: Evaluating various potential solution paths or strategies and selecting the most promising one(s) to pursue based on criteria such as likelihood of success, efficiency, and resource availability.

These processes are not necessarily sequential but are often iterative and interactive, with the problem solver dynamically engaging them as needed throughout the problem-solving endeavor.

V. Modulators of Problem-Solving Efficacy: Obstacles and Facilitators

The path to a solution is rarely straightforward; it is often influenced by a variety of factors that can either impede progress or facilitate success. Understanding these modulators—both the common pitfalls and the key enablers—is crucial for optimizing problem-solving performance.

A. Common Obstacles to Effective Problem Solving

Several cognitive and situational factors can act as barriers, making problem solving more difficult or leading to suboptimal solutions.

1. Functional Fixedness: This cognitive bias refers to the tendency to perceive objects solely in terms of their most common or customary functions, thereby overlooking alternative, less conventional uses that might be instrumental in solving a problem.² It is a specific type of mental set that limits the perceived utility of objects.

• Example: In Duncker’s famous candle problem, participants often struggle to see a thumbtack box as a potential platform for the candle because they are “fixed” on its function as a container for tacks. Similarly, the String Problem requires using pliers not for gripping, but as a weight to create a pendulum, a solution often missed due to functional fixedness.⁸

2. Mental Set (Einstellung): A mental set is the predisposition to approach problems using strategies, methods, or solutions that have proven successful in the past, even when those approaches are not the most appropriate or efficient for the current, different problem.² While relying on past experience can be adaptive, an overly rigid mental set can stifle creativity and prevent the discovery of simpler or more innovative solutions.

• Example: Luchins’ water jar problems effectively demonstrate this. After solving a series of problems using a specific, somewhat complex sequence of filling and emptying jars, participants often persist in applying this same complex method to subsequent problems where a much simpler solution is available, thus failing to see the more direct route.⁸

3. Cognitive Biases: These are systematic patterns of deviation from norm or rationality in judgment, often leading to perceptual distortion, inaccurate judgment, or illogical interpretation.

• Confirmation Bias: The tendency to seek out, interpret, favor, and recall information that confirms or supports one’s pre-existing beliefs, hypotheses, or expectations, while simultaneously downplaying or ignoring contradictory evidence.² This can lead to entrenched errors in problem definition and solution evaluation.
• Anchoring Bias: An over-reliance on the first piece of information encountered when making decisions or judgments. This initial “anchor” can unduly influence subsequent thought processes, even if the anchor itself is arbitrary or irrelevant.⁸
• Hindsight Bias: The tendency, after an event has occurred, to see the event as having been predictable, despite there having been little or no objective basis for predicting it beforehand (“I knew it all along”).¹⁶

4. Irrelevant Information: Problems are sometimes presented with extraneous information that is not necessary for finding the solution. Individuals often mistakenly assume that all provided information must be utilized, which can distract from the core elements of the problem and lead to inefficient or incorrect solution paths.⁸
5. Unnecessary Constraints: This barrier arises when problem solvers impose limitations or rules on themselves that are not actually part of the problem’s conditions. These self-imposed constraints can artificially narrow the solution space, making the problem seem more difficult or even impossible to solve.⁸

• Example: The classic nine-dot puzzle, which requires connecting nine dots arranged in a square with four straight lines without lifting the pen, often stumps people because they unnecessarily assume they must stay within the implied boundary of the square formed by the dots. Solutions typically require extending lines beyond this perceived boundary.⁸

6. Groupthink: In the context of group problem solving, groupthink refers to a phenomenon where the desire for harmony or conformity within the group results in an irrational or dysfunctional decision-making outcome. Group members may avoid expressing dissenting opinions or critically evaluating ideas to prevent conflict or maintain group cohesion, thereby stunting creativity, limiting the range of solutions considered, and reducing the quality of the final decision.⁴⁸

The following table summarizes these common obstacles and suggests potential mitigation strategies:

Table 2: Common Obstacles to Problem Solving and Mitigation Strategies

Obstacle Name	Description	Psychological Mechanism	Example	Potential Mitigation Strategies
Functional Fixedness	Perceiving objects only in terms of their most common uses. 2	Limited perception of object functions due to prior experience.	Duncker’s candle problem; inability to use pliers as a pendulum weight. 8	Actively consider alternative uses for all objects; reframe the problem; break down objects into their components and properties.
Mental Set (Einstellung)	Tendency to use problem-solving strategies that have worked in the past, even if suboptimal. 2	Over-reliance on familiar procedures; cognitive inertia.	Luchins’ water jar problems. 8	Consciously seek alternative strategies; take a break to disrupt the set; explicitly define the current problem’s unique features.
Confirmation Bias	Seeking or interpreting information to confirm preexisting beliefs. 2	Motivated reasoning; selective attention and memory retrieval.	Ignoring data that contradicts a favored hypothesis; interpreting ambiguous information as supportive. 16	Actively seek disconfirming evidence; consider alternative hypotheses; engage in perspective-taking; use structured analytical techniques.
Irrelevant Information	Information included in a problem that is not needed for the solution. 8	Assumption that all given information is relevant; difficulty in filtering.	Word problems with extraneous numerical data. 8	Carefully analyze the problem statement to identify essential vs. non-essential information; create a simplified representation of the problem.
Unnecessary Constraints	Assuming rules or limitations that don’t actually exist. 8	Misinterpretation of problem boundaries; implicit assumptions.	Nine-dot puzzle (assuming lines must stay within the dot square). 8	Explicitly question all assumed constraints; “think outside the box”; redefine problem boundaries.
Groupthink	Desire for group conformity overrides critical evaluation and realistic appraisal of alternatives. 48	Social pressure; desire for cohesion; fear of dissent.	Decisions made by highly cohesive groups without critical debate (e.g., Bay of Pigs invasion planning).	Encourage dissent and critical evaluation (e.g., assign a devil’s advocate); seek external opinions; leader refrains from stating preference early.

B. Key Facilitators of Successful Problem Solving

Conversely, numerous factors can enhance problem-solving effectiveness, enabling individuals and groups to overcome obstacles and achieve desired outcomes.

1. The Power of Expertise and Organized Knowledge:
   Experts in a particular domain demonstrate significantly superior problem-solving capabilities compared to novices within that domain.3 This advantage stems not merely from possessing more knowledge, but from how that knowledge is structured and utilized. Experts have extensive, well-organized, and highly integrated knowledge bases, typically structured around the deep principles and underlying concepts of their field, rather than superficial features.49 This sophisticated knowledge organization allows them to quickly recognize patterns, efficiently retrieve relevant information, and accurately represent complex problems.49 Experts also tend to spend more time analyzing a problem before attempting a solution, leading to the selection of more appropriate and efficient strategies.49 The acquisition of such expertise is typically the result of extensive deliberate practice—challenging activities specifically designed to improve performance and target weaknesses.50
2. Creativity, Insight, and the Role of Incubation:

• Creativity in problem solving involves the generation of solutions that are both novel and useful.¹ It often requires abstract thinking, the ability to see connections between seemingly disparate ideas, and divergent thinking—exploring multiple possible solutions.
• Insight, as discussed by Gestalt psychologists, is the sudden realization or understanding of a problem’s solution, often occurring after a period of impasse where the solver feels stuck.³ This “Aha!” moment is typically associated with a restructuring of the problem’s mental representation.
• Incubation is a phenomenon where stepping away from consciously working on a problem for a period can facilitate the emergence of a solution.⁴ During this period, implicit cognitive processes may continue to work on the problem, or the break may allow for the dissipation of misleading mental sets or the integration of new information. Factors influencing incubation effectiveness include the length of the incubation period, the nature of preparatory activities before incubation, and the presence of relevant clues during or after incubation.⁵³

3. Motivational Drivers: Self-Efficacy, Interest, and Goal Orientation:
   Motivation is a critical engine for problem-solving efforts, determining the energization and direction of behavior.1

• Self-efficacy, an individual’s belief in their own capability to successfully execute the actions required to solve a problem, is a strong predictor of the effort they will invest and their persistence in the face of difficulties.⁴⁵
• Intrinsic task interest, or finding the problem itself engaging, enjoyable, or meaningful, fuels sustained effort and deep engagement.⁵⁵
• Broader motivational theories also apply. For example, McClelland’s theory of needs suggests that individual needs for achievement, power, or affiliation can influence their problem-solving approach and goals.⁵⁶ Maslow’s hierarchy of needs posits that fundamental needs (e.g., for safety, certainty, or competence) must be sufficiently met before individuals can effectively engage in higher-level problem solving.⁵⁶
• Self-regulation models of learning integrate these motivational beliefs with metacognitive processes, showing how motivation instigates and sustains problem-solving efforts, and how the outcomes of these efforts reciprocally modify motivational beliefs.⁵⁵

4. The Influence of Emotional States: Arousal, Stress, and Affect:
   Emotions are not mere byproducts of cognition but are deeply intertwined with cognitive processes, significantly influencing attention, memory, reasoning, and problem solving.2

• High arousal or stress can have detrimental effects, particularly on complex problem solving. It can narrow attention, reduce available working memory resources (as the prefrontal cortex’s executive functions are impaired), and promote reliance on habitual or automatic responses rather than flexible, goal-directed thinking.⁵⁷ Severe stress can lead to “emotional flooding,” impairing rational thought.⁵⁷
• Conversely, positive affect is often associated with broadened attention, enhanced creativity, and more flexible thinking (though less detailed in the provided sources, this is a common finding often contrasted with the impact of negative affect). For instance, positive emotions can lead to increased risk-taking behavior by enhancing the perception of potential rewards.⁵⁸
• Negative affect, such as anxiety or sadness, can lead to risk aversion.⁵⁸ Poor emotional control can disrupt focus, impede problem resolution, and contribute to negative outcomes like fatigue and inertia.² The amygdala (central to emotional processing) and the prefrontal cortex (key for executive functions and emotional regulation) are crucial brain regions mediating these complex interactions between emotion and cognition.⁵⁸

5. Cognitive Styles and Personality Traits:

• Cognitive Styles refer to an individual’s habitual or preferred modes of perceiving, thinking, remembering, and solving problems.⁶¹

• The Visualizer-Verbalizer dimension describes preferences for processing information pictorially versus linguistically, with neuroimaging studies showing distinct patterns of brain activity associated with these styles.⁶²
• The Wholist-Analytic dimension (which includes constructs like field-dependence/independence) differentiates between global, context-sensitive processing and detail-oriented, context-independent processing, influencing attentional focus.⁶²
• Research on Integrated versus Split cognitive styles found that female undergraduates with an integrated style (combining logical analysis with intuitive thought) demonstrated better problem-solving abilities.⁶³
• Personality Traits, particularly those from the Big Five model, also predict aspects of problem-solving ability:

• Conscientiousness emerges as the most consistent positive predictor, associated with positive problem orientation, rational problem solving, and lower levels of negative orientation, impulsivity, and avoidance.³³
• Neuroticism is strongly linked to a negative problem orientation (viewing problems as threats, doubting one’s ability) and generally predicts lower problem-solving ability.³³
• Openness to Experience tends to predict higher problem-solving ability, associated with a positive orientation and rational approaches.³³
• Extraversion shows mixed results, sometimes associated with impulsivity in problem solving, while its positive links to constructive problem solving might be mediated by positive affectivity.⁶⁴
• Agreeableness has less consistent relationships with measured problem-solving dimensions.⁶⁴

6. The Social Context: Group Dynamics, Collaboration, and Competition:
   Much problem solving, especially in organizational and real-world settings, occurs in social contexts.

• Cooperative goal structures, where group members are positively interdependent (i.e., they must rely on one another for success), can enhance engagement, effort, and achievement in group problem solving.⁶⁵
• Group norms, the shared rules and expectations for behavior within a group, influence member commitment and can significantly impact group effectiveness. Adherence to productive norms is generally beneficial, but the presence of “dissidents” who constructively challenge potentially harmful norms can actually improve group performance and innovation.⁶⁶
• The quality of social interactions is critical. Deep discussions, constructive debate around ideas (task conflict or process conflict), and mutual support predict better outcomes than superficial interactions or interpersonal (relationship) conflict.⁶⁵
• However, the demands of social interaction can also consume cognitive resources that might otherwise be available for individual information processing and problem analysis.⁶⁵

7. Impact of Task Framing and Problem Representation:
   As introduced in Section IV.A, how a task is framed (e.g., as an opportunity for gain versus a risk of loss) significantly influences cognitive appraisals (challenge versus threat), subsequent affective responses, and ultimately, working memory performance and problem-solving outcomes.32 Similarly, the initial mental representation of a problem—how it is understood and structured by the solver—is a critical determinant of strategy selection and overall success.3 Salient features of the task often guide this initial representation.31

The facilitators of problem solving are often deeply interconnected rather than independent factors. For example, the development of expertise (V.B.1) typically requires sustained deliberate practice, which is fueled by motivation (V.B.3). This expertise, in turn, leads to more efficient cognitive processing (Section IV), making creative solutions and insights (V.B.2) more probable. Positive emotional states (V.B.4) can foster the cognitive flexibility conducive to creativity and enhance motivation. This suggests that interventions aimed at bolstering problem-solving capabilities should consider a holistic approach that nurtures multiple facilitators concurrently.

Furthermore, the effectiveness of these facilitators can be context-dependent, and some may even become obstacles in different situations. Expertise, while generally a powerful asset, can occasionally lead to mental sets or functional fixedness if an expert becomes overly reliant on past successful strategies when faced with a truly novel problem that requires a different approach. Similarly, strong group cohesion, a facilitator of collaboration, can degrade into groupthink if critical evaluation is suppressed for the sake of unanimity. This implies that even beneficial factors have optimal ranges or may require balancing mechanisms, such as experts consciously cultivating openness to new ideas or cohesive groups implementing procedures to encourage critical dissent.

Underlying many of these modulators is the pervasive role of cognitive appraisal—how an individual interprets a problem, its context, and their own ability to cope. Task framing directly influences appraisal (e.g., interpreting a situation as a threat versus a challenge), which then impacts working memory and performance.³² Emotional states themselves (V.B.4) often arise as a consequence of such appraisals. Moreover, an individual’s problem orientation, a component of social problem-solving linked to personality traits (V.B.5), is essentially a characteristic style of appraisal (e.g., a tendency to view problems as significant threats versus manageable challenges). This suggests that an individual’s appraisal processes act as a central hub through which various internal factors (like personality and motivation) and external factors (like task framing and social context) exert their influence on the problem-solving trajectory. Consequently, interventions that target appraisal styles, such as cognitive restructuring techniques, could have broad positive effects on problem-solving efficacy.

VI. Cultivating Problem-Solving Prowess

Given the critical role of problem solving in virtually all aspects of life, developing and enhancing these skills is a worthwhile endeavor. Psychological research offers several avenues for cultivating problem-solving prowess, ranging from fostering critical thinking to employing specific visualization techniques and adopting structured approaches.

A. Strategies for Developing Critical Thinking Skills

Critical thinking is defined as the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action.67 It is foundational to effective problem solving.

Key steps and characteristics involved in developing and applying critical thinking include 67:

• Identifying the problem or question accurately: Clearly defining the issue is the first step.
• Gathering relevant information: Collecting data from diverse and credible sources.
• Analyzing and evaluating data: Assessing the reliability, significance, and potential biases of the information. This includes examining evidence and analyzing assumptions.
• Considering alternative points of view and biases: Actively challenging one’s own assumptions and seeking out different interpretations. This involves avoiding emotional reasoning and oversimplification.
• Drawing logical conclusions: Forming well-reasoned judgments based on the evidence.
• Tolerating ambiguity: Recognizing that not all problems have simple, clear-cut solutions.

Several teaching strategies can promote critical thinking skills in educational and training contexts ⁶⁷:

• Cooperative Learning Strategies: Placing individuals in group learning situations where they can engage in active, critical thinking with peer support and feedback.
• Case Study/Discussion Method: Presenting realistic cases without explicit solutions and guiding learners through discussion to construct conclusions.
• Reciprocal Peer Questioning: Having learners generate and ask each other questions about material, promoting deeper processing.
• Writing Assignments: Requiring learners to argue for multiple sides of an issue, thereby developing dialectic reasoning.
• Analysis of Dialogues: Having learners analyze discussions for biases, evidence (or lack thereof), alternative interpretations, and errors in reasoning.
• Introducing Ambiguity: Presenting conflicting information or ill-structured problems that learners must navigate and resolve.

B. Mind Mapping and Other Visualization Techniques

Visualizing problems and potential solutions can significantly aid understanding and creativity.

• Tony Buzan’s Mind Mapping: This technique involves creating a visual diagram that starts with a central idea or problem, with main themes radiating outward as branches, and further sub-branches representing associated concepts, details, or potential solutions.⁶⁹ Key elements of Buzan’s approach include:

• Starting with a central image that is impressive and defines the core idea.
• Using colors throughout the map to differentiate ideas and enhance visual appeal.
• Creating curved, organic branches rather than straight lines.
• Using single keywords or very short phrases on each branch.
• Incorporating images, icons, and symbols to replace or supplement words wherever possible, as visuals are often processed more powerfully by the brain.⁶⁹ The benefits of mind mapping for problem solving include enhanced creativity (due to its non-linear structure), improved memory and recall of information, better organization of complex thoughts, and a clearer visualization of connections between different aspects of a problem, which can spark new insights and solution pathways.⁶⁹
• Flow Charts: For problems amenable to a more sequential or algorithmic approach, creating flow charts can be beneficial. This involves mapping out each potential solution path, its likely consequences, and the subsequent steps or decision points, providing a clear visual representation of the problem-solving process.⁷¹

C. Practical Steps for Improving Problem-Solving Abilities (General Framework)

A general framework for approaching problem solving in a more systematic way includes the following steps ⁷¹:

1. Recognize that a problem exists: The first step is to identify and acknowledge the signs that indicate an issue requiring resolution.
2. Decide to solve the problem: Make a conscious commitment to engage in the process of finding a solution.
3. Seek to fully understand the issue: Analyze the problem thoroughly, examining it from multiple perspectives. Consider how others involved might interpret the situation and how one’s own actions might be contributing.
4. Research potential options and generate alternatives: Employ various problem-solving strategies (as discussed in Section III) to brainstorm and research potential solutions. Create a list of these options.
5. Evaluate alternatives: Consider the pros and cons of each potential solution. Assess what would be required to implement each option.
6. Take action: Select the best possible solution based on the evaluation and implement it.
7. Evaluate outcomes and iterate if needed: If the chosen solution does not work, do not give up. Either restart the problem-solving process, perhaps with a new understanding gained from the failed attempt, or try another viable option. Working through a problem from different angles can also help overcome fixed ways of thinking.

Many of these techniques for improving problem-solving skills, such as the steps involved in critical thinking (e.g., “analyzing assumptions and biases” ⁶⁷ or “challenging the assumptions you’re making” ⁶⁸) or the structured visualization offered by mind mapping, implicitly target the development and refinement of metacognitive abilities (see Section IV.E). They encourage individuals to become more aware of their own thought processes, to monitor their understanding and progress, and to regulate their strategies. For instance, critical thinking demands self-assessment and the recasting of thinking in an improved form.⁶⁷ Mind mapping helps to externally organize thoughts, which can aid the internal metacognitive processes of structuring and comprehending one’s own knowledge related to the problem. The practical steps outlined by VeryWellMind ⁷¹—such as “fully understand the issue” and “research potential options”—necessitate self-awareness of current knowledge gaps and deliberate planning for information gathering, both of which are metacognitive functions. Therefore, these improvement strategies are not merely about learning new “tricks” but about cultivating a more reflective, aware, and self-directed approach to thinking itself.

The effectiveness of these improvement techniques is also likely contingent upon an individual’s existing foundational cognitive skills, such as working memory capacity and attentional control, as well as their motivation and willingness to engage in effortful cognitive processing. Critical thinking, for example, is described as an “intellectually disciplined process” ⁶⁷, implying that it requires sustained cognitive effort and potentially dedicated training to overcome more automatic, heuristic-based modes of thought. Higher-order skills like analysis, synthesis, and evaluation draw heavily upon resources like attention (to focus on relevant evidence) and working memory (to hold and manipulate information during analysis). If these underlying resources are limited or poorly managed, the application of sophisticated problem-solving strategies will be less effective. Similarly, techniques like detailed mind mapping or creating comprehensive flow charts require sustained attention and mental effort. This suggests that a comprehensive approach to improving problem-solving might sometimes necessitate a two-pronged strategy: direct training in specific techniques and exercises or strategies aimed at bolstering underlying cognitive capacities or teaching methods to manage cognitive load more effectively.

VII. The Evolving Frontier: Current Trends and Future Directions in Problem-Solving Research

The psychological study of problem solving is a dynamic field, continuously evolving with advances in methodology, theory, and interdisciplinary collaboration. Current research is pushing the boundaries of our understanding, exploring the neural underpinnings of problem solving, leveraging computational power to model cognitive processes, and increasingly focusing on how these skills manifest in complex, real-world scenarios.

A. Neuroscientific Insights into Problem Solving

Cognitive neuroscience is providing increasingly detailed insights into the brain mechanisms that support problem solving. Researchers are investigating the neural correlates of different stages in the problem-solving process, such as representing the problem, planning and executing strategies, and monitoring outcomes.⁷² Functional neuroimaging techniques (e.g., fMRI, EEG) are used to identify brain regions and networks involved in these activities.

Notably, neuroscientific evidence has lent support to some long-standing concepts from Gestalt psychology, particularly regarding insight. Studies have linked the “Aha!” moment to specific neural markers, such as distinct patterns of brain activity (e.g., a burst of high-frequency gamma-band activity) and physiological responses like pupil dilation immediately preceding the reported insight.⁷ There is also evidence for the involvement of the visual system in the perceptual reorganization that often accompanies insight.⁷

Research continues to map the brain regions crucial for the various cognitive processes integral to problem solving. For instance, attention relies on a network including the prefrontal cortex, inferior frontal gyrus, and dorsal striatum; reasoning engages the frontoparietal network, dorsolateral prefrontal cortex (DLPFC), and inferior frontal gyrus (IFG); and various memory functions (working memory, episodic memory) involve interactions between the prefrontal cortex, parietal cortex, and hippocampus.³⁴

A particularly exciting recent development involves the creation of neuromorphic architectures—computational systems modeled on the structure and function of the human brain (neurons and synapses). Some current research is exploring how these architectures, when combined with principles from quantum mechanics (such as Fowler-Nordheim annealers that use quantum tunneling for search), can solve highly complex optimization problems and even “discovery” problems where new and unknown solutions are sought.⁷³ The NeuroSA project is an example of such an architecture, aiming to bridge neurobiology and quantum computation to achieve superior problem-solving capabilities.⁷³ While these are AI systems, their brain-inspired design and success in finding novel solutions may offer new perspectives on human creative problem solving and the potential mechanisms underlying discovery.

B. Computational Modeling of Problem-Solving Processes

Computational modeling remains a central methodology in cognitive science for developing and testing formal theories of how humans solve problems.74 These models aim to provide precise, mechanistic accounts of the cognitive steps, representations, and learning processes involved.

Three broad classes of computational models are influential:

1. Symbolic approaches: These models, exemplified by Newell and Simon’s General Problem Solver (GPS), represent knowledge and problem states using symbols and manipulate these symbols according to defined rules or operators.⁹ They excel at modeling well-defined problems and heuristic search.
2. Neural networks (Connectionist models): Inspired by the brain’s structure, these models consist of interconnected nodes (artificial neurons) that process information in parallel. They are particularly adept at pattern recognition, learning from data, and capturing aspects of implicit cognition.⁷⁵
3. Probabilistic and statistical models (including Bayesian approaches): These models frame cognition in terms of probability distributions and statistical inference. They are useful for understanding how humans deal with uncertainty, make predictions, and learn from incomplete or noisy information.⁷⁵

By building and testing computational models, researchers can simulate human performance, explore the consequences of different theoretical assumptions, and generate new hypotheses about the intricacies of problem solving.

C. Problem Solving in Authentic, Real-World Contexts (RWPS)

There is a growing emphasis in problem-solving research on moving beyond simplified laboratory tasks to study how people solve problems in authentic, real-world contexts (RWPS).⁷² RWPS is characterized by its dynamic, often ill-defined nature, requiring flexibility, resilience, resourcefulness, and creativity.⁷⁶ Unlike many lab tasks, real-world problems involve continuous interaction with a complex and often changing environment, where the environment itself can be a source of information, inspiration, or further complications.⁷⁶ Solvers in the real world typically juggle multiple problems simultaneously and must adapt to unexpected interruptions or new information.⁷⁶

A common theme in current research is the domain specificity of problem-solving skills, recognizing that expertise in one area does not always transfer readily to another, and that the context in which a problem is embedded heavily influences the solution process.⁷² Applied psychology, for instance, leverages problem-solving research to address tangible issues in workplaces, schools, healthcare settings, and the legal system.⁷⁷ To study RWPS more effectively while maintaining some experimental control, researchers are exploring innovative methodologies such as using virtual reality (VR) to create immersive and interactive problem scenarios, or employing teleoperation of robots to study dynamic physical problem solving.⁷⁶

D. The Role of Artificial Intelligence and Technology

Artificial intelligence (AI) and technology are increasingly intertwined with the study and practice of problem solving. Historically, research into human problem solving, particularly the information processing approach, informed early AI development, such as the use of heuristic methods in automated theorem proving.1

Today, AI is transforming various fields, including psychology, with tools like AI-powered chatbots being developed for preliminary symptom identification in mental health, and behavioral analytics being used to predict mental health trends from large datasets.78 As AI tools become more sophisticated, research is also focusing on human-AI interaction, including how humans develop trust in AI systems, the ethical implications of using AI in sensitive domains like mental healthcare (addressing issues of data privacy, empathy, and potential misuse), and how AI can serve as an aid or collaborator in human problem-solving endeavors.78

E. Future Perspectives for Research and Application

Looking ahead, several key directions and perspectives are shaping the future of problem-solving research:

• There is an urgent need to modernize perspectives on the teaching and learning of problem solving, taking into account the complex, interconnected, and technologically infused nature of problems in the 21st century.⁷² This includes a focus on how to effectively equip students with the skills needed to be adaptive problem solvers and how to design instruction that promotes the transfer of learned skills to novel problems.⁷²
• Substantive theory development is considered long overdue.⁷⁹ One promising direction is the “models and modeling perspective” (MMP), which views problem solving as an iterative process where individuals develop, test, and revise mental models or conceptual tools to make sense of a situation. MMP emphasizes the co-development of mathematical (or other domain) concepts alongside problem-solving processes, metacognitive functions, beliefs, and emotions.⁷⁹
• Continued exploration of the roles of emotion, metacognition, and incubation in creative and complex problem solving is crucial.⁴⁵ Understanding how these factors interact and how they can be harnessed to improve performance remains a key research area.

A significant overarching trend in the field is the convergence of multiple disciplines—neuroscience, AI and computational modeling, and ecological psychology—to create a more comprehensive understanding of problem solving. We are moving beyond purely cognitive or purely behavioral explanations towards more integrated, multi-level accounts that consider neural underpinnings, computational mechanisms, and dynamic real-world interactions. The NeuroSA project, for example, explicitly merges neuromorphic (brain-inspired) architecture with quantum mechanical principles (a computational approach) to tackle complex problems ⁷³, exemplifying this interdisciplinary fusion. Future breakthroughs in understanding and enhancing problem solving will likely emerge from such synergistic approaches that can bridge these different levels of analysis.

However, as problem-solving research increasingly ventures into the domain of authentic, complex, real-world problems (RWPS) ⁷², a significant challenge arises: maintaining experimental rigor and developing generalizable theories amidst the inherent “messiness” of these situations. The ill-defined, dynamic, and multi-variable nature of RWPS makes it far more difficult to study systematically than the well-defined, controlled tasks often used in traditional laboratory settings.² Methodological innovations, such as the MMP framework ⁷⁹ which focuses on the iterative development and revision of mental models, or the use of sophisticated simulations like VR ⁷⁶, represent attempts to capture the richness of RWPS while still allowing for systematic investigation and robust theory building. The future of the field will depend on developing further such methodologies that can embrace complexity without sacrificing scientific validity.

Ultimately, the strong and growing emphasis on improving the teaching of problem-solving skills and fostering their transfer to novel situations ⁷² reflects a pressing societal need. In a world characterized by rapid change and complex, often unprecedented challenges (e.g., climate change, global health crises, socio-economic disruptions ¹¹), the capacity for adaptive and effective problem solving is more critical than ever. This has profound implications for educational curricula and pedagogical approaches worldwide, urging a fundamental shift away from rote memorization of facts towards the cultivation of critical thinking, metacognitive agility, and the ability to apply knowledge flexibly and creatively—in short, fostering adaptive expertise. The success and resilience of future societies may well depend significantly on how effectively we cultivate these sophisticated problem-solving capabilities across the population.

VIII. Conclusion: Synthesizing the Psychology of Effective Problem Solving

The psychological exploration of problem solving reveals a rich and intricate tapestry woven from cognitive processes, theoretical frameworks, diverse strategies, and a host of influencing factors. From its fundamental definition as a motivated drive to overcome obstacles, to the sophisticated neural and computational mechanisms that underpin it, problem solving stands as a cornerstone of human intelligence and adaptation.

A. Recap of Key Theoretical Approaches and Diverse Techniques

The historical journey of problem-solving research has seen a progression from the Gestalt psychologists’ emphasis on insight and the crucial role of mental restructuring, through the Information Processing paradigm’s view of problem solving as a systematic search within a defined problem space, to more contemporary investigations into Complex Problem Solving (CPS) and Real-World Problem Solving (RWPS). These later approaches acknowledge the dynamic, often ill-defined, and interactive nature of the challenges individuals face in everyday life and professional domains. Accompanying these theoretical shifts has been the identification and analysis of a broad toolkit of problem-solving strategies. This toolkit ranges from methodical algorithms that guarantee solutions for well-defined problems, to efficient heuristics like means-ends analysis and working backward, to creative techniques such as brainstorming and lateral thinking designed to foster novel solutions, and structural approaches like problem decomposition that simplify complexity. The selection and application of these techniques are often contingent upon the specific nature of the problem, the context in which it arises, and the cognitive resources available to the solver.

B. The Interwoven Fabric: Cognitive, Emotional, and Motivational Factors

A central theme emerging from the psychological study of problem solving is that it is not a purely “cold” cognitive endeavor. Instead, effective problem solving arises from a dynamic and inseparable interplay of how individuals think (their perceptual processes, attentional control, memory capacities, reasoning abilities, and metacognitive oversight), how they feel (the influence of emotional states like stress, arousal, and mood), and what drives them (their motivations, including self-efficacy, intrinsic interest, and goal orientations). Cognitive obstacles such as functional fixedness, mental sets, and various biases are common, but an understanding of their psychological bases allows for the development of strategies to mitigate their impact. Conversely, facilitators like expertise, creativity, positive emotional states, and supportive social contexts can significantly enhance problem-solving efficacy. The individual’s appraisal of the problem situation appears to be a critical mediating factor, shaping how these cognitive, emotional, and motivational elements interact.

C. The Imperative of Adaptive and Flexible Problem Solving in a Complex World

In an increasingly complex, interconnected, and rapidly changing global landscape, the ability to approach problems with flexibility, to adapt strategies in the face of new information or unforeseen obstacles, to learn from both successes and failures, and to persist despite ambiguity and uncertainty, is paramount. The psychological study of problem solving, by illuminating the intricate mechanisms and diverse factors involved, provides a crucial foundation for cultivating these essential skills. The ongoing evolution of research, particularly at the fertile intersections of cognitive psychology, neuroscience, artificial intelligence, and education, promises to further deepen our understanding and enhance our collective capacity for effective and innovative problem solving, equipping individuals and societies to better navigate the challenges and opportunities of the future.

Works cited

1. 7.3 Problem-Solving – Introductory Psychology – Open Text WSU, accessed May 9, 2025, https://opentext.wsu.edu/psych105/chapter/7-4-problem-solving/
2. Problem solving – Wikipedia, accessed May 9, 2025, https://en.wikipedia.org/wiki/Problem_solving
3. Chapter 10 Problem Solving | Cognitive Foundations – Bookdown, accessed May 9, 2025, https://bookdown.org/pilegard/cogfoundations/problem-solving.html
4. (PDF) On the cognitive process of human problem solving, accessed May 9, 2025, https://www.researchgate.net/publication/222705878_On_the_cognitive_process_of_human_problem_solving
5. Gestalt psychology – Wikipedia, accessed May 9, 2025, https://en.wikipedia.org/wiki/Gestalt_psychology
6. Understanding Gestalt Psychologists: Insights into Holistic Perception, accessed May 9, 2025, https://therapygroupdc.com/therapist-dc-blog/understanding-gestalt-psychologists-insights-into-holistic-perception/
7. Gestalt’s Perspective on Insight: A Recap Based on Recent …, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC10743969/
8. Barriers to Effective Problem Solving – MCAT Psychology …, accessed May 9, 2025, https://www.medschoolcoach.com/barriers-to-effective-problem-solving-mcat-psychology/
9. escholarship.org, accessed May 9, 2025, https://escholarship.org/content/qt0xb6p4sk/qt0xb6p4sk.pdf
10. 10.3 An Information Processing Perspective on Problem-Solving …, accessed May 9, 2025, https://nmoer.pressbooks.pub/cognitivepsychology/chapter/an-information-processing-perspective-on-problem-solving/
11. www.psychologie.uni-heidelberg.de, accessed May 9, 2025, https://www.psychologie.uni-heidelberg.de/ae/allg/mitarb/jf/Fischer%20etal%202017%20history%20of%20CPS.pdf
12. 8.2 Problem-Solving: Heuristics and Algorithms – Psychology – 1st …, accessed May 9, 2025, https://psychology.pressbooks.tru.ca/chapter/8-2-heuristics-and-algorithms/
13. media.lanecc.edu, accessed May 9, 2025, https://media.lanecc.edu/users/kime/Psy201Ch9ALBCC.pdf
14. Problem-Solving Strategies: Definition and 5 Techniques to Try, accessed May 9, 2025, https://psychcentral.com/health/problem-solving-strategies
15. courses.lumenlearning.com, accessed May 9, 2025, https://courses.lumenlearning.com/suny-fmcc-intropsychmaster/chapter/problem-solving/#:~:text=For%20example%2C%20a%20well%2Dknown,paper%20tray%20isn’t%20jammed.
16. Problem Solving | Introduction to Psychology – Brown-Weinstock – Lumen Learning, accessed May 9, 2025, https://courses.lumenlearning.com/suny-fmcc-intropsychmaster/chapter/problem-solving/
17. mercercognitivepsychology [licensed for non-commercial use only …, accessed May 9, 2025, http://mercercognitivepsychology.pbworks.com/w/page/32255746/Heuristic%20Decision%20Process%3A%20Taking%20it%20Apart
18. 6.3: Means–Ends Analysis – Social Sci LibreTexts, accessed May 9, 2025, https://socialsci.libretexts.org/Bookshelves/Psychology/Cognitive_Psychology/Cognitive_Psychology_(Andrade_and_Walker)/06%3A_Problem_Solving/6.03%3A_Means_Ends_Analysis
19. Working-backward approach – problem-solving heuristics – Britannica, accessed May 9, 2025, https://www.britannica.com/science/working-backward-approach
20. Hill Climbing in Artificial Intelligence | GeeksforGeeks, accessed May 9, 2025, https://www.geeksforgeeks.org/introduction-hill-climbing-artificial-intelligence/
21. 10.6 Problem-Solving by Analogy – Cognitive Psychology, accessed May 9, 2025, https://nmoer.pressbooks.pub/cognitivepsychology/chapter/problem-solving-by-analogy/
22. What Is Analogical Reasoning? | Definition & Examples – QuillBot, accessed May 9, 2025, https://quillbot.com/blog/reasoning/analogical-reasoning/
23. 7 Brainstorming Rules for Stronger Collaboration – IDEO U, accessed May 9, 2025, https://www.ideou.com/blogs/inspiration/7-simple-rules-of-brainstorming
24. 8 Brainstorming Techniques to Harness the Power of Teamwork, accessed May 9, 2025, https://www.betterup.com/blog/brainstorming-techniques
25. The most undervalued problem-solving tool? Lateral thinking. – Big …, accessed May 9, 2025, https://bigthink.com/neuropsych/lateral-thinking/
26. What is lateral thinking? 7 techniques to encourage creative ideas – BetterUp, accessed May 9, 2025, https://www.betterup.com/blog/what-is-lateral-thinking
27. Learning Problem Decomposition-Recomposition with Data-driven Chunky Parsons Problems within an Intelligent Logic Tutor – Educational Data Mining, accessed May 9, 2025, https://educationaldatamining.org/EDM2023/proceedings/2023.EDM-long-papers.4/index.html
28. Problem Decomposition: A Strategy for Efficient Resolution of …, accessed May 9, 2025, https://www.iienstitu.com/en/blog/problem-decomposition
29. What cognitive processes underpin real-world problem-solving and …, accessed May 9, 2025, https://www.tutorchase.com/answers/ib/psychology/what-cognitive-processes-underpin-real-world-problem-solving-and-decision-making
30. Solving the problem of perception with narrative and symbology …, accessed May 9, 2025, https://michaelsantosauthor.com/bcpjournal/solving-the-problem-of-perception-with-narrative-and-symbology/
31. Task representation and individual differences affect strategy …, accessed May 9, 2025, https://pubmed.ncbi.nlm.nih.gov/40171084/
32. Opportunity or Risk? Appraisal and Affect Mediate the … – Frontiers, accessed May 9, 2025, https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2021.615329/full
33. big five personality traits and the prediction of conflict resolution strategies – ResearchGate, accessed May 9, 2025, https://www.researchgate.net/publication/367309962_BIG_FIVE_PERSONALITY_TRAITS_AND_THE_PREDICTION_OF_CONFLICT_RESOLUTION_STRATEGIES
34. What is Cognitive Processing: Functions & Impact on Daily Life – Creyos, accessed May 9, 2025, https://creyos.com/blog/cognitive-processing
35. Articles on Trending Technologies – Tutorialspoint, accessed May 9, 2025, https://www.tutorialspoint.com/attention-and-problem-solving
36. The Role of Attention in Cognition’, accessed May 9, 2025, http://iiif.library.cmu.edu/file/Simon_box00074_fld05940_bdl0007_doc0002/Simon_box00074_fld05940_bdl0007_doc0002.pdf
37. Exploring areas of cognitive process: memory, attention, & more, accessed May 9, 2025, https://linushealth.com/blog/exploring-key-areas-of-cognitive-function
38. What role does attention play in cognitive processing? | TutorChase, accessed May 9, 2025, https://www.tutorchase.com/answers/ib/psychology/what-role-does-attention-play-in-cognitive-processing
39. Study shows addressing working memory can help students with …, accessed May 9, 2025, https://news.ku.edu/news/article/study-shows-addressing-working-memory-can-help-students-with-math-difficulty-improve-word-problem-solving-skills
40. The Role of Working Memory in Problem-solving and Decision-making, accessed May 9, 2025, https://bbejournal.com/BBE/article/view/1092
41. Long-Term Memory: What It Is, How It Works & Types, accessed May 9, 2025, https://my.clevelandclinic.org/health/articles/long-term-memory
42. Retrieval practice may not benefit mathematical word-problem solving – Frontiers, accessed May 9, 2025, https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2023.1093653/full
43. www.marcuscoetzee.com, accessed May 9, 2025, https://www.marcuscoetzee.com/inductive-and-deductive-reasoning-can-help-us-to-solve-complex-strategic-and-social-problems/#:~:text=Inductive%20reasoning%20involves%20’bottom%20up,if%20the%20theory%20is%20valid.
44. Inductive vs. Deductive Research Approach | Steps & Examples, accessed May 9, 2025, https://www.scribbr.com/methodology/inductive-deductive-reasoning/
45. Metacognition and Self-Efficacy in Action: How First-Year Students …, accessed May 9, 2025, https://www.lifescied.org/doi/10.1187/cbe.23-08-0158
46. Critical-Thinking Basics: Metacognition and Skill Building | Edmentum, accessed May 9, 2025, https://www.edmentum.com/articles/critical-thinking-basics-metacognition-and-skill-building/
47. www.frontiersin.org, accessed May 9, 2025, https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2019.02404/full#:~:text=The%20process%20monitoring%20theory%20proposed,to%20access%20creative%20problem%20solving.
48. Barriers to Effective Problem Solving | Eller Executive Education, accessed May 9, 2025, https://executive.eller.arizona.edu/news/2017/11/barriers-effective-problem-solving
49. 10.8 Applying Expertise to Problems – Cognitive Psychology, accessed May 9, 2025, https://nmoer.pressbooks.pub/cognitivepsychology/chapter/applying-expertise-to-problems/
50. The Role of Expertise Research and Human Factors in Capturing …, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC3412393/
51. Moving from Novice to Expertise and Its Implications for Instruction …, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC5738945/
52. Full article: Enhancing Problem-Solving Skills for Word Problems: Impact of Diagram and Learner Expertise – Taylor & Francis Online, accessed May 9, 2025, https://www.tandfonline.com/doi/full/10.1080/00220973.2024.2394956
53. ccn.psych.purdue.edu, accessed May 9, 2025, https://ccn.psych.purdue.edu/papers/Helie-Sun-EII.pdf
54. Problem-solving stages | EBSCO Research Starters, accessed May 9, 2025, https://www.ebsco.com/research-starters/health-and-medicine/problem-solving-stages
55. Motivating Self-Regulated Problem Solvers (Chapter 8) – The …, accessed May 9, 2025, https://www.cambridge.org/core/books/psychology-of-problem-solving/motivating-selfregulated-problem-solvers/FEC230C40B98EAB1E66DA82720B5E7BA
56. The Role of Motivation in Complex Problem Solving – PMC, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC5440455/
57. 3.5 The Impact of Emotions on Cognition – Open Educational Resources Collective, accessed May 9, 2025, https://oercollective.caul.edu.au/neuroscience-psychology-conflict/chapter/3-5-the-impact-of-emotions-on-cognition/
58. Emotion’s Integral Role in Cognitive Processing: Implications for, accessed May 9, 2025, https://www.longdom.org/open-access/emotions-integral-role-in-cognitive-processing-implications-for-behavior-and-decisionmaking-106315.html
59. The Influences of Emotion on Learning and Memory – Frontiers, accessed May 9, 2025, https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.01454/full
60. www.frontiersin.org, accessed May 9, 2025, https://www.frontiersin.org/journals/psychology/articles/10.3389/fpsyg.2017.01454/full#:~:text=Emotion%20has%20a%20substantial%20influence,as%20motivating%20action%20and%20behavior.
61. Linking Creativity with Psychological Type, accessed May 9, 2025, https://digitalcommons.buffalostate.edu/cgi/viewcontent.cgi?article=1037&context=creativeprojects
62. Cognitive Style: Time to Experiment – PMC, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC5108774/
63. (PDF) Impact of Cognitive Style on Problem solving Ability among …, accessed May 9, 2025, https://www.researchgate.net/publication/287697212_Impact_of_Cognitive_Style_on_Problem_solving_Ability_among_Undergraduates
64. (PDF) Predicting social problem solving using personality traits, accessed May 9, 2025, https://www.researchgate.net/publication/229094736_Predicting_social_problem_solving_using_personality_traits
65. Which Group Dynamics Matter: Social Predictors of Student …, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC9582812/
66. files.eric.ed.gov, accessed May 9, 2025, https://files.eric.ed.gov/fulltext/EJ1201477.pdf
67. Critical Thinking and Problem-Solving | University of Tennessee at …, accessed May 9, 2025, https://www.utc.edu/academic-affairs/walker-center-for-teaching-and-learning/teaching-resources/pedagogical-strategies-and-techniques/ct-ps
68. How to Develop Critical Thinking Skills in 7 Steps with Examples …, accessed May 9, 2025, https://asana.com/resources/critical-thinking-skills
69. Tony Buzan Mind Map: Techniques, Benefits, and How to Create One, accessed May 9, 2025, https://edrawmind.wondershare.com/mind-map/tony-buzan-mind-map.html
70. Mind Mapping and 7 Key Steps by Tony Buzan for Developing …, accessed May 9, 2025, https://www.edrawmind.com/article/tony-buzan-biography.html
71. Problem-Solving Strategies Based in Psychology – Verywell Mind, accessed May 9, 2025, https://www.verywellmind.com/problem-solving-2795008
72. Problem Solving | Oxford Research Encyclopedia of Education, accessed May 9, 2025, https://oxfordre.com/education/display/10.1093/acrefore/9780190264093.001.0001/acrefore-9780190264093-e-860?p=emailA40ryHhcEkSUY&d=/10.1093/acrefore/9780190264093.001.0001/acrefore-9780190264093-e-860
73. A neuro-quantum leap in finding optimal solutions – The Source …, accessed May 9, 2025, https://source.washu.edu/2025/05/a-neuro-quantum-leap-in-finding-optimal-solutions/
74. psychology.princeton.edu, accessed May 9, 2025, https://psychology.princeton.edu/courses/fall-2023/computational-models-cognition#:~:text=Computational%20modeling%20is%20one%20of,for%20some%20of%20these%20problems.
75. Computational Models of Cognition (EC) | Psychology, accessed May 9, 2025, https://psychology.princeton.edu/courses/fall-2023/computational-models-cognition
76. Real World Problem-Solving – PMC, accessed May 9, 2025, https://pmc.ncbi.nlm.nih.gov/articles/PMC6028615/
77. 9 Examples of Applied Psychology Solving Real-World Problems – Florida Tech Online Degrees, accessed May 9, 2025, https://www.floridatechonline.com/blog/psychology/9-examples-of-how-applied-psychology-is-solving-real-world-problems/
78. Top 12 Emerging Psychology Research Topics in 2025 – PageOn.ai, accessed May 9, 2025, https://www.pageon.ai/blog/psychology-research-topics
79. (PDF) Future directions and perspectives for problem solving …, accessed May 9, 2025, https://www.researchgate.net/publication/38183931_Future_directions_and_perspectives_for_problem_solving_research_and_curriculum_development