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

Introduction.

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

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

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

General Overviews

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

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Problem-Solving Strategies and Obstacles

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

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

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality .  Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition .  Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

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

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The Role of Motivation in Complex Problem Solving

C. dominik güss.

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

Madison Lee Burger

Dietrich dörner.

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

The role of motivation in complex problem solving

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

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

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

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

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

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

Previous research on motivation and CPS

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

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

CPS assessment

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

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

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

Psychological theories of motivation and their application to CPS

Mcclelland's human motivation theory.

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

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

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

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

Maslow's hierarchy of needs

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

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

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

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

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

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

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

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

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

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

Summary and evaluation

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

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

Scope/ Breadth	+	++	++
Applicability to CPS	+	+	++
Adaptability of needs	−	−	+
Incorporation of emotion	++	−	++
Individual differences	++	−	++
.

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

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

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

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

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

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

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

Author contributions

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

Conflict of interest statement

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

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Problem-solving concepts and theories

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• 1 Mississippi StateUniversity, College of Veterinary Medicine, USA. [email protected]
• PMID: 14648495
• DOI: 10.3138/jvme.30.3.226

Many educators, especially those involved in professional curricula, are interested in problem solving and in how to support students' development into successful problem solvers. The following article serves as an overview of educational research on problem solving. Several concepts are defined and the transition from one theory to another is discussed. Educational theories describing problem solving in the context of behavioral, cognitive, and information-processing pedagogy are discussed. The final section of the article describes prior findings regarding expert-novice differences in problem solving of various kinds.

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Problem-Solving Theory: The Task-Centred Model

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• Blanca M. Ramos 5 &
• Randall L. Stetson 6  

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

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

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

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Target may have solved one of retail's biggest problems: theft.

Target ( TGT ) is hitting its goals on inventory shrink.

On a call with reporters, Its CFO and COO Michael Fiddelke told Yahoo Finance the company has hit a plateau when it comes to shrink, including retail theft.

"[Inventory shrink] was one of the tailwinds to profit in the quarter, and as we stepped into the year, our aim was to have shrink plateau, and so to improve from the deterioration we've seen over the last couple of years, two quarters in — we're achieving that and then some," Fiddelke said.

Shrink can be the result of theft, damage, or poor record keeping, among other factors.

In its second quarter report, Target's 28.9% gross profit margin beat estimates, up from 27% a year ago.

Read more: Best credit cards for back-to-school shopping at Target (August 2024)

Target said shrink increased by more than $500 million last year compared to 2022, "representing about 50 basis points of incremental rate pressure," Fiddelke said on the company's Q4 earnings call in March.

Profits took a $700 million hit from the issue in 2022. From 2019 to 2023, the company said shrink costs reduced its operating margin rate by a "cumulative 1.2 percentage points."

Collaboration with local officials, expanding locked cases

"The things that we feel good about are the progress we're seeing in our partnerships at the federal and state and local level," Fiddelke said.

But the work is ongoing, and the company is hoping to keep making progress in the quarters ahead.

Part of the strategy included closing nine stores at the end of last October .

"We cannot continue operating these stores because theft and organized retail crime are threatening the safety of our team and guests, and contributing to unsustainable business performance," the company said in a statement at the time.

The closed stores included one in Harlem, New York City; two in Seattle; three near San Francisco and Oakland, Calif.; and three in Portland, Ore.

At some hard-hit stores, Target also installed locking cases for "prone to theft" merchandise.

Other tactics include investing in additional security members and third-party guard services and training store leaders and employees to "protect themselves and de-escalate potential safety issues associated with organized retail crime incidents," the company said at the time .

It also planned to partner with the investigations division of the US Department of Homeland Security to develop cyber defense technology. The tech could create custom tools that analyze fraud and other crimes.

Other retailers have also shared progress on solving the issue.

Last week, Walmart ( WMT ) CFO John David Rainey told investors on its earnings call that in its "core merchandise mix," the company saw "a little bit of benefit from improved shrink in the quarter," a trend that started in Q1.

Dollar General ( DG ) converted 12,000 of its stores away from self-checkout this year.

"While this represents a significant change in our stores, we believe this is the right course of action to drive increased customer engagement while also better positioning us to begin reducing shrink in the back half of '24 with a more material positive impact expected in 2025," CEO Todd Vasos said during its Q1 earnings call.

TJX Companies, Inc. ( TJX ), the parent company of TJ Maxx, Marshall's, and Home Goods, said during Q1 that it plans for shrink to be flat year over year.

At the end of 2023, the discount retailer introduced body cameras for its loss prevention associates.

"When somebody comes in, it's sort of — it's almost like a deescalation where people are less likely to do something when they're being videotaped, so we definitely feel that that's playing a role," CFO John Klinger told investors.

Brooke DiPalma is a senior reporter for Yahoo Finance. Follow her on X at @ BrookeDiPalma or email her at [email protected].

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Mathematics > Analysis of PDEs

Title: solving schiffer's problem in inverse scattering theory almost surely.

Abstract: In this short note, we present a probabilistic perspective on the Schiffer's problem in the inverse scattering theory, which asks whether one can uniquely determine the shape of an unknown obstacle by a single far-field measurement. It is a longstanding problem and has received considerable studies in the literature. We show that this conjecture holds true in more general settings in the probability sense. Our new perspective has important implications from the practical viewpoint and also points an interesting direction of research for broader inverse problems.

Subjects:	Analysis of PDEs (math.AP)
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OSP Hosted Webinar: The RPPR Matrix – Decoding and Problem Solving the NIH Progress Report System

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The RPPR Matrix – Decoding and Problem Solving the NIH Progress Report System

September 30, 2024 12:00 – 1:30 pm MT * Webinar 1:35 – 2:30 pm ET * After the Show * Talk with the Faculty Directly!

Completing an RPPR can be a daunting challenge especially if one is new to the process. This session will go through an actual Progress Report (RPPR), section by section in detail explaining the requirements that NIH will review. The session will go over addressing the common errors and warnings and how to avoid the common pitfalls that result in a late submission or a non-compliant RPPR that can result in further inquiry from NIH. This session will go over the difference between SNAP and Non-SNAP RPPRs, Multiple component RPPRs, completion of the Budget Section H for applicable activity codes and dive into HSS/ASSIST for Human Subjects reporting requirements. Difference between Annual, Interim, and Final reports will also be discussed.

Learning Objectives

By the end of this webinar, participants will be able to:

• Navigate and become familiar with each section of the RPPR
• Troubleshoot error and warning messages
• Correctly report personnel effort and unobligated balance
• Advise PI on other reporting components
• Understanding the process of preparing budgets in section H

Format of webinar: 90-minute presentation, followed by 55 minutes of discussion.

If you, another faculty member, or your department administrator or business manager are interested in attending this webinar, please complete this sign-up form . You do not need to be an NCURA member in order to register. We look forward to learning alongside you!

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Rubik's Cube, Special Retro 50th Anniversary Edition, Original 3x3 Color-Matching Puzzle Classic Problem-Solving Challenging Brain Teaser Fidget Toy, for Adults & Kids Ages 8+

• SPECIAL 50TH ANNIVERSARY CUBE: Go retro with a Rubik’s Cube that looks and feels like it’s a toy from the past, complete with classic boxy edges, slower turning, stickers, gold side, and special anniversary logo, presented in a retro plastic display case.
• THE ORIGINAL RUBIK’S CUBE: A combination of math, art and science, the iconic Rubik’s Cube challenges minds and problem-solving skills. The classic 3x3 is one of the world’s best-known puzzles since 1980.
• TURN, TWIST & REPEAT: The Rubik’s Cube features six different colored sides of nine squares each. Once the faces are jumbled, twist, turn, and rotate until each of the six faces has only one color.
• A MUST HAVE FOR PUZZLE LOVERS: This original cube has 43,252,003,274,489,856,000 combinations, but only one solution. Do you have what it takes to solve the world’s favorite puzzle?
• CLASSIC PUZZLE-SOLVING GAMEPLAY: This challenging puzzle is the same retro toy that you remember from childhood. Brain teaser, fidget toy, or travel puzzle, this brain puzzle is your new go-to cube.
• Includes 1 Rubik’s Cube
• Covered by the Spin Master Care Commitment. See below for full details

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Product information

Product Dimensions	2.24 x 2.24 x 0.04 inches
Item Weight	5.4 ounces
ASIN	B0CCW4F1CH
Item model number	6068726
Manufacturer recommended age	8 years and up
Best Sellers Rank	#1,405 in Toys & Games ( ) #10 in
Customer Reviews	4.7 out of 5 stars
Release date	November 30, 2023
Manufacturer	Spin Master

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Product Description

Launched to celebrate Rubik’s 50th anniversary, the special edition Rubik’s Cube looks and feels like it came right out of a time capsule! Fans of fidget toys and vintage toys will love this classic toy modeled after the first edition Rubik’s Cubes, complete with sharp edges, clunky turning, standard stickers. The Rubik’s Cube is a classic color-matching puzzle that can be enjoyed at home or on the move. The original, classic 3x3 cube is a highly addictive brain teaser that has fascinated fans all around the world for decades. The Rubik’s Cube features six different sides, each made up of nine colorful squares. A must for puzzle lovers and fans of puzzles for adults and kids puzzles, the aim is to try twist and turn the Rubik’s Cube to its original state, with every side having one solid color. There are 43,252,003,274,489,856,000 ways of arranging the squares, and only one of these is the solution. Turn and twist away – can you solve it? The retro plastic display case with throwback logo and design as well as the Rubik’s Cube whole collection make the perfect gifts for men, gifts for women, and gifts for teens. Celebrate 50 years of puzzle solving with Rubik’s Cube.

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Customer Reviews
Difficulty	Beginner	Intermediate	Advanced	Intermediate	Beginner	Beginner
Feature	Don’t let the size fool you – with over 3.6 million possible permutations and only one solution, this is a brain teaser that will challenge you again and again.	The classic 3x3 Rubik’s Cube is the world’s best-known addictive puzzle and has fascinated fans since its launch in 1980. A true icon.	This 4x4 puzzle is made up of 56 small cubes, but the center pieces move in relation to each other, making it even more difficult.	Go retro with a Rubik’s Cube that looks and feels like it’s a toy from the past, complete with classic boxy edges, slower turning, stickers, gold side, and special anniversary logo, presented in a retro plastic display case.	Play a new twist on the classic Rubik’s Cube with a game inspired by the iconic brain teaser made to challenge your flexible thinking, speed, and problem-solving skills.	This Amazon Exclusive Race game has 6 added tiles and an added layer of complexity, making it the perfect puzzle gift for any Rubik’s enthusiast in your life!

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Customer reviews.

• 5 star 4 star 3 star 2 star 1 star 5 star 83% 10% 4% 1% 2% 83%
• 5 star 4 star 3 star 2 star 1 star 4 star 83% 10% 4% 1% 2% 10%
• 5 star 4 star 3 star 2 star 1 star 3 star 83% 10% 4% 1% 2% 4%
• 5 star 4 star 3 star 2 star 1 star 2 star 83% 10% 4% 1% 2% 1%
• 5 star 4 star 3 star 2 star 1 star 1 star 83% 10% 4% 1% 2% 2%

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

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

Customers say

Customers like the smoothness of movement of the puzzle. They say it's fun to solve and engaging for kids. They also appreciate the value for money. However, some customers have reported that the fit of the cube is loose. Opinions are mixed on quality.

AI-generated from the text of customer reviews

Customers like the smoothness of movement of the puzzle. They say the rows and columns swivel seamlessly and are durable enough to withstand the hands of most.

"...The movement of the cube is seamless , with each turn feeling smooth and secure...." Read more

" Super easy to rotate and super cool looking. Also love that it doesn’t have stickers so it won’t wear over time. My new go to Rubik’s cube." Read more

"...This one is not as expected it is not smooth actions Jerry does like to lineup...." Read more

"...CONS:1. Not really a con, but while this is a super smooth cube , it is not a speed-cube like that you see real experts use...." Read more

Customers find the puzzle fun, engaging for kids, and fun to solve. They also say it's a great toy that keeps them entertained for a good while and makes them think. Customers also mention the step-by-step moves and interesting Rubik's Cube fun facts.

"...Not only does it add a layer of sophistication and modernity to the iconic cube, but it also provides an intriguing look into the inner workings of..." Read more

"...Not too big or small.The saturation of the colors makes it more enticing to use . The quality of the cubes itself is great!..." Read more

"...It keeps her mind busy and sharp . Great price too!!" Read more

"...although it is lighter than it was in the 80’s, it is still fun to fiddle around with ." Read more

Customers appreciate the value of the puzzle. They mention it's sturdy, works well for the price, and is not cheap.

"...for hours, days, even months of fun...definitely the best investment for the money .4. High quality...." Read more

"...It keeps her mind busy and sharp. Great price too!!" Read more

"The kids love it, it's sturdy, good value for the money , it's fun, fits in your purse, and it's pretty." Read more

"...Slick movement easy to use, well put together. Would highly recommend good price too." Read more

Customers are satisfied with the performance of the puzzle. They mention that it works extremely well, is functional, and turns smoothly. Some say that the product is constructed better and functions better than knockoffs. Overall, most are happy with the quality and performance of this product.

"...4. High quality. I have been using it for months now and it is still working great ..." Read more

"Its a standard rubix cube. Sturdy and functional . Has held up well with three little kids" Read more

"Purchased the Rubik's cube and am very satisfied with the product ." Read more

" This thing is great ! Really brings back old memories of being a kid!" Read more

Customers are mixed about the quality of the puzzle. Some mention it's good quality all around, well put together, and sturdy. Others say that it'd break easily, wobble at first, and feel a little sloppy after a lot of use.

"...The build quality is excellent , ensuring that even after multiple solves, the cube maintains its integrity and the colors remain as vibrant as ever,..." Read more

"Super easy to rotate and super cool looking . Also love that it doesn’t have stickers so it won’t wear over time. My new go to Rubik’s cube." Read more

"...The rest are poor quality. They would pop pieces out when you turn them." Read more

"PROS:1. Inexpensive.2. Stand is a nice bonus for display ...." Read more

Customers are dissatisfied with the fit of the puzzle. They mention that the pieces on the cube are very loose, and the turning mechanism is loose. Some say that the product is sturdy enough for their needs, but some feel that it loses its lubrication.

"It’s a good cube but my only problem was that the pieces on the cube were very loose and to the point it felt like it was going to come apart" Read more

"...although at times this becomes its downside as the "smoothness" can be a bit loos and cause parts that you do not intend, turn...." Read more

"This cube feels a little bit worse than the standard rubiks brand 3x3 with tiles...." Read more

"...This one is seamless! Easy to use and the size is perfect ! Not too big or small.The saturation of the colors makes it more enticing to use...." Read more

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