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Cognitive Systems Research
On the cognitive process of human problem solving.
One of the fundamental human cognitive processes is problem solving. As a higher-layer cognitive process, problem solving interacts with many other cognitive processes such as abstraction, searching, learning, decision making, inference, analysis, and synthesis on the basis of internal knowledge representation by the object–attribute-relation (OAR) model. Problem solving is a cognitive process of the brain that searches a solution for a given problem or finds a path to reach a given goal. When a problem object is identified, problem solving can be perceived as a search process in the memory space for finding a relationship between a set of solution goals and a set of alternative paths. This paper presents both a cognitive model and a mathematical model of the problem solving process. The cognitive structures of the brain and the mechanisms of internal knowledge representation behind the cognitive process of problem solving are explained. The cognitive process is formally described using real-time process algebra (RTPA) and concept algebra. This work is a part of the cognitive computing project that designed to reveal and simulate the fundamental mechanisms and processes of the brain according to Wang’s layered reference model of the brain (LRMB), which is expected to lead to the development of future generation methodologies for cognitive computing and novel cognitive computers that are capable of think, learn, and perceive.
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Problem-Solving Strategies and Obstacles
Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.
Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.
JGI / Jamie Grill / Getty Images
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
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.
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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.
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By Kendra Cherry Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.
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Problem-Solving in Cognitive Psychology
Cognitive skills that a person acquires throughout one’s life shape a personal background and allow interacting with other people through the experience of communication to overcome various barriers. Problem-solving is valuable attainment, and cognitive psychology is the industry that studies this phenomenon from the perspective of drivers and incentives to make decisions in favor of specific actions or ideas.
From a neurological perspective, problem-solving is characterized by the nature of the human desire to fill the space and identify the best methods to overcome specific barriers. At the same time, this skill may be applied to other areas where the experience gained is a crucial self-determining factor, for instance, differential or educational psychology. The problem-solving attainment is of high importance from the perspective of gaining individual adaptive and social habits. The abilities to analyze and make the right decision based on the proposed circumstances are the skills that distinguish the human species from most other living beings.
Neurological Foundations and Processes Related to Problem-Solving
Problem-solving is an active neurological process that occurs at the initiative of a person oneself and does not belong to the category of automatic and reflex properties. Any task requiring a solution is associated with the work of various cognitive skills that need to be applied to solve an individual problem (“Cognitive psychology,” 2020). This form of behavior is goal-directed and serves as a tool for performing specific actions but not as a ready-made set of behavioral reflexes (“Cognitive psychology,” 2020).
The abilities to find flexible solutions, adapt to the current conditions, divide tasks in accordance with the spectrum of their significance, assess specific actions or solutions adequately, and other attainments shape the neurological background of problem-solving. Brace (2014) lists various problem-solving strategies and notes that building a sequence of actions in a specific order to achieve the desired goal is evidence of cognitive development, which varies depending on complexity. Thus, the effectiveness of problem-solving may depend on the criteria of the complexity of a particular issue and the tools available to overcome it.
The ability to control cognitive functions to direct them towards solving a specific problem is a skill that is established from an early age. As one grows older and acquires new cognitive skills, the complexity of potentially solvable problems increases. A person learns to combine existing knowledge, for instance, in the context of problem-solving by analogy, which Brace (2014) describes as a process related to experience rather than knowledge. As Kolbert (2017) argues, collaborative groups, play a significant role in this process and stimulate solving different problems through the application of previously learned attainments. In this regard, one can conclude about the neurological connection between problem-solving and social adaptation.
Filling the space that has arisen due to the urgent need to overcome a specific obstacle does not carry unconditioned reflexes and is based on a conscious choice to search for optimal solutions. When a person analyzes, draws analogies, divides tasks into subtasks, and performs other actions related to problem-solving, cognitive skills are activated (“Cognitive psychology,” 2020). Unwillingness to deviate from the intended plan characterizes the innate ability to overcome barriers to achieve the desired goal. A baby who crawls towards one’s toy despite obstacles on the floor does this consciously. Thus, problem-solving may be characterized not only as a cognitive process that develops as people grow older and socialize but also as an integral and conscious personality trait.
Criticism of the Problem-Solving Theory
Despite the fact that problem-solving is the subject of cognitive psychology research and a recognized concept, certain aspects of this theory are questioned due to the similarity with other psychological models. In particular, Servant-Miklos (2019) argues that problem-solving and knowledge acquisition are processes that have much in common and are often discussed as related phenomena. As a result, contradictions between each of these theories arise. This context is based on the understanding of what knowledge is since the ability to use accumulated cognitive skills may be interpreted from the perspectives of both intelligence and a set of problem-solving attainments.
According to Servant-Miklos (2019), “both approaches are the product of the Cognitive Revolution in psychology,” but their differences presuppose the ability to use knowledge (p. 622). As a justification, the author draws attention to the generation of the late 20th century and notes that the emergence of computer technology has eliminated the urgent need to utilize knowledge for problem-solving (Servant-Miklos, 2019). Therefore, this interpretation of the theoretical foundations is the argument in favor of the approach in which problem-solving skills in cognitive psychology prevail over knowledge acquisition.
At the same time, despite conflicting positions regarding problem-solving and knowledge acquisition, evaluating these concepts from a critical perspective allows finding the relationship between them. Lieto et al. (2019) consider problem-solving through the prism of the goal-directed approach when the final task is the main one to achieve through overcoming appropriate obstacles. In this regard, the researchers consider this process “is based on the availability of novel, additional, knowledge that can be then used to select novel sub-goals or novel operations” (Lieto et al., 2019, p. 305).
In other words, an algorithm that involves searching for effective solutions and methods to overcome specific problems is inextricably linked with the acquisition of new knowledge that will subsequently be transformed into experience. According to Servant-Miklos (2019), the psychology of learning is built on the constant processing of information that comes through communication and personal drive to overcome barriers. The better the information studied, the higher the likelihood that the problem-solving process will be faster and more successful. Therefore, despite the criticism and differentiation of the concepts of problem-solving and knowledge acquisition, these two models are rather interrelated than separated.
Application of Problem-Solving to Other Fields
Problem-solving is a concept that finds its application not only in cognitive psychology but also in other fields. For instance, Xiong and Proctor (2018) state that this model fits into the area of educational psychology.
This is an approach that allows building the educational process based on the search for evidence and justification. In modern pedagogical practice, this technique is widely used because the trend to stimulate student activity through the development of critical thinking involves the ability to solve various problems on one’s own. Kovacs and Conway (2019), in turn, draw attention to differential psychology as the area in which problem-solving can be actively applied. In this field, the search for arguments for obtaining reasonable alternative conclusions shapes the basis of the cognitive process. As a result, the more successful an individual utilizes problem-solving skills, the higher the likelihood of the objective assessment of specific phenomena or challenges to overcome.
Problem-solving, as a methodological concept, is used not only in various branches of psychology but also in other areas where the assessment of cognitive processes is indirect. For instance, Kovacs and Conway (2019) analyze this approach for practical purposes and provide an example of recruiting tests used in hiring employees. Job applicants, as a rule, are asked to answer questions related to the assessment of individual situations, and the use of critical thinking skills to apply problem-solving attainments is a common approach.
Another area in which this concept is applied is computer technology. As Xiong and Proctor (2018) note, modern AI algorithms are built due to the methods that aim to train AI to overcome various problems through problem-solving. Advances in this area may prove that acquired information accumulated through knowledge is an objective and effective methodology to overcome barriers. Computers combine and synthesize different data, thereby transforming them into efficient problem-solving algorithms. Therefore, this concept finds its application in various fields as a necessary and relevant technique.
Problem-solving is a subject of study not only in cognitive psychology but also in other areas since this concept characterizes the individual from different perspectives and distinguishes people from other living beings. Applying critical thinking and combining experience with knowledge shape the basis of this model. Despite the existing criticism, the separation of problem-solving from knowledge acquisition is irrelevant because these theories are interrelated.
Utilizing appropriate skills in computer technology confirms that the collection and accumulation of valuable information is the core of the development of problem-solving skills. Therefore, further research on this topic can be devoted to a deeper analysis of such attainments in the technology industry, in particular, artificial intelligence, to identify basic algorithms and compare them with those in humans.
Brace, N. (2014). Thinking and problem-solving. In D. Groome (Ed.), An introduction to cognitive psychology: Processes and disorders (3 rd ed., pp. 241-271). Psychology Press.
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Kolbert, E. (2017). Why facts don’t change our minds . The New Yorker . Web.
Kovacs, K., & Conway, A. R. (2019). A unified cognitive/differential approach to human intelligence: Implications for IQ testing. Journal of Applied Research in Memory and Cognition , 8 (3), 255-272. Web.
Lieto, A., Perrone, F., Pozzato, G. L., & Chiodino, E. (2019). Beyond subgoaling: A dynamic knowledge generation framework for creative problem solving in cognitive architectures . Cognitive Systems Research , 58 , 305-316. Web.
Servant-Miklos, V. F. (2019). Problem solving skills versus knowledge acquisition: The historical dispute that split problem-based learning into two camps . Advances in Health Sciences Education , 24 (3), 619-635. Web.
Xiong, A., & Proctor, R. W. (2018). Information processing: The language and analytical tools for cognitive psychology in the information age. Frontiers in Psychology , 9 , 1270. Web.
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On the cognitive process of human problem solving
International Center for Cognitive Informatics (ICfCI) and Theoretical and Empirical Software Engineering Research Centre, Department of Electrical and Computer Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive, NW, Calgary, Alberta, Canada T2N 1N4
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Cognitive Systems Research
One of the fundamental human cognitive processes is problem solving. As a higher-layer cognitive process, problem solving interacts with many other cognitive processes such as abstraction, searching, learning, decision making, inference, analysis, and synthesis on the basis of internal knowledge representation by the object-attribute-relation (OAR) model. Problem solving is a cognitive process of the brain that searches a solution for a given problem or finds a path to reach a given goal. When a problem object is identified, problem solving can be perceived as a search process in the memory space for finding a relationship between a set of solution goals and a set of alternative paths. This paper presents both a cognitive model and a mathematical model of the problem solving process. The cognitive structures of the brain and the mechanisms of internal knowledge representation behind the cognitive process of problem solving are explained. The cognitive process is formally described using real-time process algebra (RTPA) and concept algebra. This work is a part of the cognitive computing project that designed to reveal and simulate the fundamental mechanisms and processes of the brain according to Wang's layered reference model of the brain (LRMB), which is expected to lead to the development of future generation methodologies for cognitive computing and novel cognitive computers that are capable of think, learn, and perceive.
Knowledge representation and reasoning
Philosophical/theoretical foundations of artificial intelligence
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Copyright © Elsevier B.V. © 2008
Elsevier Science Publishers B. V.
- Published: 1 March 2010
- Cognitive processes
- Brain informatics
- Reference model of the brain
- Mathematical model
- Cognitive computing
- Problem solving
- Computational intelligence
- Cognitive informatics
- Concept algebra
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Virtually all cognitive activity resembles problem solving , the task of moving a system from its current state A to a goal state B. Any successful cognitive act (retrieving a memory, perceiving a scene, understanding a passage) can be seen as a goal-directed behavior.
In visual perception, the goal is to come up with a construction that accurately describes the sensory world. For example, in our description of visual scene analysis, the goal was to find a way to interpret visual clues like surfaces and edges in which all the data fits together into one coherent interpretation. That ws the constraint-satisfaction approach.
In language comprehension, the problem is to reconstruct the author's intended meaning. Again, the product of cognition is guided by multiple sources of information. Ambiguous words must be resolved in a process very much like analyzing a visual scene: all the clues must fit together.
In motor activity, the problem is to arrive at a destination or manipulate an object in a particular way. To solve the problem, one must find a sequence of intermediary actions that results in the goal state.
In what sense does all cognition require problem solving?
Here are two examples of problem solving from very different realms. They are similar processes in that each presents the brain with the dilemma of how to move from state A to state B.
1. Problem: get a college degree . The problem is to move yourself from state A (where you are now) to state B (completing your degree requirements) so you can graduate from State U or wherever you are going to school. This is done in a series of steps: completing basic courses, selecting a major, selecting appropriate higher-level courses in the major, and so on, removing each impediment to graduation, one by one.
2. Problem: interpret your view of the room after closing your eyes and rolling your head back then opening your eyes again. The problem is to come up with a coherent interpretation of your visual world after performing a disorienting maneuver. Your brain has to go from state A (opening your eyes and experiencing an unusual visual pattern) to state B (figuring out what you are looking at, getting oriented, perceiving the room).
If you can see how both of these as examples are problem solving, then you understand what it means to say that, in a sense, all cognition is problem solving. It is all goal-directed activity.
Puzzles are problems that are difficult to solve because they require some unusual insight or unexpected mental operation. By definition, this means they do not succumb to the first mode of attack. They have proven difficult for at least some people.
Puzzles played a role in the history of cognitive psychology because they were simple to bring into a lab, standardized, and people differed dramatically in their speed of solving them. They were commonly used in mid-20th Century studies of problem-solving.
Example: Duncker's Candle Problem
Suppose you were presented with a tabletop containing a box full of tacks, a candle, and a matchbook. Your challenge is to find some way to use these materials to mount a candle on the wall and illuminate the room. How can you do it?
Most people start thinking of typical ways to use the objects, such as pinning the candle to the wall...but that won't work...or lighting the candle and dripping wax onto the wall...but that won't work...
The solution, ultimately, involves reconceptualizing the container of the tacks as something other than a container. Treat it as a potential platform for the candle.
That is the trick for solving this puzzle. One can empty the box, use a tack to fasten the box to the wall, then drip some wax onto the box and mount the candle on the box. (Several hours later the room will be in flames, but Duncker never discussed that.)
Duncker used the term functional fixity to describe the tendency of people to regard a certain object as having one, fixed function. A box is for containing things. To solve the puzzle, one must break out of functional fixity and use the box in an unusual way, as a platform.
What is Duncker's candle problem? What was Duncker's "functional fixity" concept?
In an example of how simple puzzles like this could inspire research, Higgins and Chaires (1980) showed that subjects could be unconsciously primed to find the correct solution to the candle problem.
First they were asked to participate in a study about long-term memory. They saw slides of common objects.
For one group, these objects were described using the word of (for example, "a carton of eggs"). For the other group, the same objects were described using the word and (for example, "a carton and eggs").
Then both these groups and several control groups were asked to solve the Duncker's candle problem. Only 20% of subjects in the "of" group could solve the candle problem within 10 minutes. A full 80% of subjects in the "and" group were able to solve the problem within 10 minutes.
How was Duncker's candle problem used in research?
Why did changing one word have such a profound effect? Evidently the "and" group was led to think of objects presented together as separate entities. The "of" group was led to think of objects presented together as interacting wholes.
Neither group was aware that they had been primed for the puzzle-solving part of the experiment, so this is an example of how an unconscious or automatic form of processing can influence which ideas enter attention. If it is true.
I say "if it is true" because, writing in 2017 after the priming brouhaha , I am primed to wonder about possible failures in replicating priming studies. The effect is large (80% to 20%) to the point of being almost incredible for such a subtle verbal cue.
So there is a project for an ambitious psychology major: replicate the Higgens and Chaires (1980) study. See if you can arrange a double-blind version in which experimenters do not know who is in the "and" or "of" group, to eliminate any effects of expectancy.
In general, solving a puzzle requires (1) ignoring obvious solutions that do not work, and (2) trying out unusual approaches. To solve the problem one must locate a low-probability solution.
Not all puzzles are equally revealing of intelligence. Sternberg and Davidson (1982) point out that puzzles commonly require that you find a "trick," and that is not necessarily a sign of deep intelligence.
Puzzles that correlate with high IQ scores (they suggested) are those that present both relevant and irrelevant clues, requiring the puzzle solver to ignore obvious but irrelevant clues while trying out unusual solutions.
Thinking Outside the Box with the 9-Dot Problem
Here is another classic puzzle, the 9-dot problem. To a person who encounters it for the first time, it can be puzzling indeed.
The problem is to connect 9 dots (three evenly spaced rows of three) with four lines, without lifting your pencil from the paper . If you do not know the solution to this puzzle, you should try to solve it now, using trial and error, before you read further.
Again, to solve the puzzle, step outside the normal or expected pattern of responses. One must try unusual or low-probability alternatives.
All of this is logical if you think about what defines a puzzle. A puzzle is a problem for which the obvious response does not work .
Otherwise the situation would not be puzzling. So a puzzle always requires a person to think "outside the box."
Why is it logical that puzzle solving often requires a low-probability response?
In this case, the solution is to violate the common assumption that one must stay within the square defined by the dots. When you start experimenting with lines that extend outside the square, the answer usually comes quickly.
Here is one solution. If the dots are numbered 1 through 9, then draw a line from dot 1 through 5 to 9, then up through 6 and 3 and beyond, then back down through 2 and 4, then through 7 and 8.
The General Problem Solver
Before the modern era of cognitive research, problem solving was studied mainly through examination of humans with puzzles. The modern era of computer-based research on problem solving started with Newell and Simon (1963). They designed a computer program called the General Problem Solver (GPS).
Newell and Simon defined each problem as a space. At one end of the space is the starting point. On the other side is the goal.
In the General Problem Solver, the program tests various actions (called operators by Newell and Simon) to see which would take it closer to the goal state. An operator is any activity that changes the state of the system.
The General Problem Solver always chose the operator that would bring it closer to its goal. This tactic is called hill climbing , because it resembles the tactic of always heading uphill, if your goal is to climb a mountain.
How did the GPS (General Problem Solver) solve problems?
Similarly, humans struggle toward long-term objectives one step at a time. As you complete each phase of the project, you take one step closer to the goal. (You may recognize here the pattern of deviation-reducing feedback, discussed earlier in the context of motor activity.)
Hill climbing is a simple strategy, but it does not always work efficiently. One potential trap is the foothill problem .
What is hill-climbing? What is the foothill problem?
Suppose your goal is to climb a mountain. You could start far away from the mountain and simply select whatever step takes you uphill. But you might end up climbing a foothill that lies between yourself and the mountain.
That would be foolish because it would ignore a much more efficient procedure: go around the foothill. In other words, if you go straight toward a goal without flexibility, you may pay a steep price, waste a lot of energy, or cause more work for yourself without contributing to the long-term goal.
More sophisticated problem-solving programs look ahead many steps to locate potential problems in advance. Then they can evade hidden traps and inefficient foothills, to more efficiently climb the mountain.
Advice for Human Problem Solvers
Cognitive psychologist Wayne Wickelgren wrote a little book called How to Solve Problems (1974). It was based on a popular course on problem solving which he developed at MIT (the Massachusetts Institute of Technology).
The aim of the course was to present students with useful problem-solving principles. Here is a summary of the principles he developed. Of course, this summary is very compressed. Professor Wickelgren spent a whole semester conveying these points.
- Use inference . The information required to solve a problem is probably hidden, not obvious, otherwise it would not be a problem. Be ready to go beyond the information given, looking for solutions or partial solutions.
- variations in time management (altering your schedule, setting aside times to study, etc.)
- variations in environment (you might try the library, or a quiet room)
- variations in study tactics (write out answers, or read more slowly, or read more than once)
- variations in test-day tactics (relaxing yourself before a test, getting a good sleep the night before, preparing yourself with helpful self-coaching statements).
What does it mean to classify action sequences?
- Do "hill climbing." Hill climbing occurs when you keep a goal in mind and approach it step by step. It is a long-term strategy for accomplishing a larger goal by performing smaller actions that move you in the right direction. For example, a successful diet or exercise program requires many small decisions and actions. The cumulative effect is large, if all lead in the same direction.
- Make subgoals . Often problems are best solved by breaking them into pieces. Then you can try to solve each piece of the problem by itself. A student might have to take a few lower-level courses to strengthen basic skills, before tackling a tough course in the major.
- Try contradiction . "Cultivate the habit of seeing the alternative." When stuck on a problem, sometimes it helps to consider an opposite viewpoint.
- Try working backward . Sometimes a problem is easier to solve if you start with the goal, then work backwards from it. Isaac Asimov, a prolific science fiction writer, said he commonly started with a conclusion in mind, then wrote a story leading to it.
- Seek relations between different problems . A solution to a problem might be discovered by examining similar problems from the past. Consulting an expert often helps. The expert is likely to be acquainted with a wide range of similar situations and can point to a relevant example or case history.
Constraint Satisfaction as a Problem-Solving Approach
Sometimes a problem requires picking the best option from available choices. A good general-purpose problem solving technique is this: list the constraints of a situation (negative constraints, like limitations, and positive or desirable elements wanted in the final solution). Then pick the choice that satisfies most of the constraints.
For example, suppose your first house is newly constructed and has no landscaping around it. You might identify these factors as relevant to good solutions to the landscaping problems:
- The grass, trees, or bushes should be hardy in your climate. You do not want them dying after a few years.
- The plants should not be too expensive, if you are on a budget.
- The trees and bushes should not require too much care, if you are not spending all your time gardening or working in the yard.
- Trees should shade the house during the summer (especially if you live in a warm climate) or let sun through in the winter (especially if you are in a cold climate).
- Trees and bushes might should look attractive and/or proivide fruit or nuts.
- Some plants are much better than others for privacy hedges or providing cover for small animals like rabbits.
- There might be forms of wildlife in your area that you wish not to attract, so you avoid certain plants.
- If you are putting plants along your foundation, you don't want plants that will outgrow their space in a few years; perhaps they should be dwarf species or comfortable with being cut back (etc).
How can constraint satisfaction be employed as a general problem solving technique?
As you evaluate landscaping alternatives, run through your checklist. See which of the available alternatives will meet the largest number of constraints.
A solution that satisfies multiple constraints at the same time is likely to be esthetically pleasing. It will be an elegant solution, and that will be satisfying.
Duncker, K. (1945). On problem solving. Psychological Monographs, 58, 1-113.
Higgins, E. T., & Chaires, W. M. (1980). Accessibility of interrelational constructs: Implications for stimulus encoding and creativity. Journal of Experimental Social Psychology, 16, 348-361.
Newell, A., Shaw, J. C., & Simon, H. A. (1959). Report on a general problem-solving program. Proceedings of the International Conference on Information Processing . Pp.256-264.
Sternberg, R. J. & Davidson, J. E. (1982, June). The mind of the puzzler. Psychology Today , 37~4.
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Cognitive Processes in Problem Solving
- Cognitive Processes in Problem Solving Definition
Cognitive processes are various tasks that the brain performs continuously. These procedures process all the information we receive from different sources or points. Cognitive processes allow us to explore the world.
- Overview of Cognitive Processes In Problem Solving
The cognitive process is mainly used for human problem-solving. The steps of the cognitive process involve abstraction, exploring, learning, decision making, inference, analysis, and synthesis as a step by step procedure. Problem-solving is also one of the broad processes and finds the solution to the problem presented in front of the human mind. The path is established by the cognitive processes towards the goal leading to the solution of the problem.
Got a question on this topic?
What you'll learn:, how do cognitive processes work, hurdles in cognitive processes of problem-solving:.
Let’s take an example, imagine you are watching TV. Even though the show is interesting and you are engrossed, still, if you smell something burning, then the first thing your brain will do is to center all of your brain’s attention towards the possible danger. You will start to remember that what can be burning and you remember that you have put the pizza in the oven. You will run fast towards the oven and will switch it off. The series of movements here are automatically coordinated by the brain. You will immediately wear gloves and take the pizza out of the oven. If Pizza is not fully burnt then you will decide if you want to eat unburnt parts. Finally, you again get back to your TV show. Thus, cognitive processes are serialized in such a manner that you sense the problem and then you take a few steps, in a certain chronology to solve the problem. This process has guided you in the whole problematic scenario. Interactions and harmony between cognitive processes are an essential basis for the analysis of reality and adapting to it. Our mental processes are very flexible to alterations and demands of the situation. The cognitive processes work as our executive functions. On the other note, even though we think that the processes in the example above acted together, in reality, they act separately. The process of sensing a danger was different, then it transformed into taking actual action, and the final relief of solving the problem was different.
Types of Cognitive Processes:
Basic Cognitive Processes: Cognitive processes working towards problem-solving have various types. They are ‘Sensation and perception of problematic stimuli’, ‘filtering information’, ‘interpretation of stimuli’, ‘Attention to stimuli’, where we give the highest attention to a particular problem, and not to things like how we walk, talk, and others. ‘Memory’ is a further step. In problem-solving, we try to remember the information we have learned till now, how we or someone else have faced the situation in the past or how we should take further situations.
Complex Cognitive Processes: ‘Intelligence’ is a higher cognitive process. Emotional intelligence is equally important to keep a person emotionally balanced in stress for solving a problem. The logical and rational outcome is derived through intelligent analysis. ‘Thought’ is another level of the process, which is used for reasoning, decision-making, divergent thinking, and creative thinking. Also, cognitive biases and cognitive distortions are a product of positive or negative thoughts that we hold about the situation. ‘Language’ is important for comprehending different verbal responses in a problematic situation. Someone in danger to life will shout ‘help’. In case of fire, someone will call the fire brigade. Thus, communication is also part of the cognitive process.
Getting stuck: The problem solver’s attempt to solve and proceed further if fails repeatedly. The solver has no idea what to do and he is panicked and frustrated to think of a problem.
Unconscious search: Solver tries to search for a solution unconsciously, without knowing the direction. It is similar to searching for a thing in the dark. Solver either experience-less or novice to a problem or fails to have calm thinking.
Dilemmas: The dilemmas are faced by people while problem-solving and are common. The confusion created in choosing which process is appropriate is a major hurdle.
Not thinking out of the box: Many times solvers constrain themselves to what they know and what they can do. But in reality, thinking out of the box to arrive at a solution adds ease and novelty to it. Even a grave issue sometimes needs a simple solution that may not be found in a regular grid. The major example given here is ‘dot problem’ which simplifies the ‘out of the box’ concept.
Strategies to Tackle Problem-solving
Abstraction or solving the problem as a model
Analogy or finding a solution to a similar problem.
Brainstorming for the possible domains.
The divide problem is small parts and goals to be solved.
Hypothesis testing, making and rejecting assumptions.
Connecting means and ends, which connects the process.
Hitting the root-cause analysis of the current problem.
Trial and error to find a suitable solution.
What to learn next based on college curriculum
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Hypothesis and theory article, real world problem-solving.
- Human-Robot Interaction Laboratory, Department of Computer Science, Tufts University, Medford, MA, United States
Real world problem-solving (RWPS) is what we do every day. It requires flexibility, resilience, resourcefulness, and a certain degree of creativity. A crucial feature of RWPS is that it involves continuous interaction with the environment during the problem-solving process. In this process, the environment can be seen as not only a source of inspiration for new ideas but also as a tool to facilitate creative thinking. The cognitive neuroscience literature in creativity and problem-solving is extensive, but it has largely focused on neural networks that are active when subjects are not focused on the outside world, i.e., not using their environment. In this paper, I attempt to combine the relevant literature on creativity and problem-solving with the scattered and nascent work in perceptually-driven learning from the environment. I present my synthesis as a potential new theory for real world problem-solving and map out its hypothesized neural basis. I outline some testable predictions made by the model and provide some considerations and ideas for experimental paradigms that could be used to evaluate the model more thoroughly.
In the Apollo 13 space mission, astronauts together with ground control had to overcome several challenges to bring the team safely back to Earth ( Lovell and Kluger, 2006 ). One of these challenges was controlling carbon dioxide levels onboard the space craft: “For 2 days straight [they] had worked on how to jury-rig the Odysseys canisters to the Aquarius's life support system. Now, using materials known to be available onboard the spacecraft—a sock, a plastic bag, the cover of a flight manual, lots of duct tape, and so on—the crew assembled a strange contraption and taped it into place. Carbon dioxide levels immediately began to fall into the safe range” ( Team, 1970 ; Cass, 2005 ).
The success of Apollo 13's recovery from failure is often cited as a glowing example of human resourcefulness and inventiveness alongside more well-known inventions and innovations over the course of human history. However, this sort of inventive capability is not restricted to a few creative geniuses, but an ability present in all of us, and exemplified in the following mundane example. Consider a situation when your only suit is covered in lint and you do not own a lint remover. You see a roll of duct tape, and being resourceful you reason that it might be a good substitute. You then solve the problem of lint removal by peeling a full turn's worth of tape and re-attaching it backwards onto the roll to expose the sticky side all around the roll. By rolling it over your suit, you can now pick up all the lint.
In both these examples (historic as well as everyday), we see evidence for our innate ability to problem-solve in the real world. Solving real world problems in real time given constraints posed by one's environment are crucial for survival. At the core of this skill is our mental capability to get out of “sticky situations” or impasses, i.e., difficulties that appear unexpectedly as impassable roadblocks to solving the problem at hand. But, what are the cognitive processes that enable a problem solver to overcome such impasses and arrive at a solution, or at least a set of promising next steps?
A central aspect of this type of real world problem solving, is the role played by the solver's surrounding environment during the problem-solving process. Is it possible that interaction with one's environment can facilitate creative thinking? The answer to this question seems somewhat obvious when one considers the most famous anecdotal account of creative problem solving, namely that of Archimedes of Syracuse. During a bath, he found a novel way to check if the King's crown contained non-gold impurities. The story has traditionally been associated with the so-called “Eureka moment,” the sudden affective experience when a solution to a particularly thorny problem emerges. In this paper, I want to temporarily turn our attention away from the specific “aha!” experience itself and take particular note that Archimedes made this discovery, not with his eyes closed at a desk, but in a real-world context of a bath 1 . The bath was not only a passive, relaxing environment for Archimedes, but also a specific source of inspiration. Indeed it was his noticing the displacement of water that gave him a specific methodology for measuring the purity of the crown; by comparing how much water a solid gold bar of the same weight would displace as compared with the crown. This sort of continuous environmental interaction was present when the Apollo 13 engineers discovered their life-saving solution, and when you solved the suit-lint-removal problem with duct tape.
The neural mechanisms underlying problem-solving have been extensively studied in the literature, and there is general agreement about the key functional networks and nodes involved in various stages of problem-solving. In addition, there has been a great deal of work in studying the neural basis for creativity and insight problem solving, which is associated with the sudden emergence of solutions. However, in the context of problem-solving, creativity, and insight have been researched as largely an internal process without much interaction with and influence from the external environment ( Wegbreit et al., 2012 ; Abraham, 2013 ; Kounios and Beeman, 2014 ) 2 . Thus, there are open questions of what role the environment plays during real world problem-solving (RWPS) and how the brain enables the assimilation of novel items during these external interactions.
In this paper, I synthesize the literature on problem-solving, creativity and insight, and particularly focus on how the environment can inform RWPS. I explore three environmentally-informed mechanisms that could play a critical role: (1) partial-cue driven context-shifting, (2) heuristic prototyping and learning novel associations, and (3) learning novel physical inferences. I begin first with some intuitions about real world problem solving, that might help ground this discussion and providing some key distinctions from more traditional problem solving research. Then, I turn to a review of the relevant literature on problem-solving, creativity, and insight first, before discussing the three above-mentioned environmentally-driven mechanisms. I conclude with a potential new model and map out its hypothesized neural basis.
2. Problem Solving, Creativity, and Insight
2.1. what is real world problem-solving.
Archimedes was embodied in the real world when he found his solution. In fact, the real world helped him solve the problem. Whether or not these sorts of historic accounts of creative inspiration are accurate 3 , they do correlate with some of our own key intuitions about how problem solving occurs “in the wild.” Real world problem solving (RWPS) is different from those that occur in a classroom or in a laboratory during an experiment. They are often dynamic and discontinuous, accompanied by many starts and stops. Solvers are never working on just one problem. Instead, they are simultaneously juggling several problems of varying difficulties and alternating their attention between them. Real world problems are typically ill-defined, and even when they are well-defined, often have open-ended solutions. Coupled with that is the added aspect of uncertainty associated with the solver's problem solving strategies. As introduced earlier, an important dimension of RWPS is the continuous interaction between the solver and their environment. During these interactions, the solver might be inspired or arrive at an “aha!” moment. However, more often than not, the solver experiences dozens of minor discovery events— “hmmm, interesting…” or “wait, what?…” moments. Like discovery events, there's typically never one singular impasse or distraction event. The solver must iterate through the problem solving process experiencing and managing these sorts of intervening events (including impasses and discoveries). In summary, RWPS is quite messy and involves a tight interplay between problem solving, creativity, and insight. Next, I explore each of these processes in more detail and explicate a possible role of memory, attention, conflict management and perception.
2.2. Analytical Problem-Solving
In psychology and neuroscience, problem-solving broadly refers to the inferential steps taken by an agent 4 that leads from a given state of affairs to a desired goal state ( Barbey and Barsalou, 2009 ). The agent does not immediately know how this goal can be reached and must perform some mental operations (i.e., thinking) to determine a solution ( Duncker, 1945 ).
The problem solving literature divides problems based on clarity (well-defined vs. ill-defined) or on the underlying cognitive processes (analytical, memory retrieval, and insight) ( Sprugnoli et al., 2017 ). While memory retrieval is an important process, I consider it as a sub-process to problem solving more generally. I first focus on analytical problem-solving process, which typically involves problem-representation and encoding, and the process of forming and executing a solution plan ( Robertson, 2016 ).
2.2.1. Problem Definition and Representation
An important initial phase of problem-solving involves defining the problem and forming a representation in the working memory. During this phase, components of the prefrontal cortex (PFC), default mode network (DMN), and the dorsal anterior cingulate cortex (dACC) have been found to be activated. If the problem is familiar and well-structured, top-down executive control mechanisms are engaged and the left prefrontal cortex including the frontopolar, dorso-lateral (dlPFC), and ventro-lateral (vlPFC) are activated ( Barbey and Barsalou, 2009 ). The DMN along with the various structures in the medial temporal lobe (MTL) including the hippocampus (HF), parahippocampal cortex, perirhinal and entorhinal cortices are also believed to have limited involvement, especially in episodic memory retrieval activities during this phase ( Beaty et al., 2016 ). The problem representation requires encoding problem information for which certain visual and parietal areas are also involved, although the extent of their involvement is less clear ( Anderson and Fincham, 2014 ; Anderson et al., 2014 ).
18.104.22.168. Working memory
An important aspect of problem representation is the engagement and use of working memory (WM). The WM allows for the maintenance of relevant problem information and description in the mind ( Gazzaley and Nobre, 2012 ). Research has shown that WM tasks consistently recruit the dlPFC and left inferior frontal cortex (IC) for encoding an manipulating information; dACC for error detection and performance adjustment; and vlPFC and the anterior insula (AI) for retrieving, selecting information and inhibitory control ( Chung and Weyandt, 2014 ; Fang et al., 2016 ).
While we generally have a sense for the brain regions that are functionally influential in problem definition, less is known about how exactly events are represented within these regions. One theory for how events are represented in the PFC is the structured event complex theory (SEC), in which components of the event knowledge are represented by increasingly higher-order convergence zones localized within the PFC, akin to the convergence zones (from posterior to anterior) that integrate sensory information in the brain ( Barbey et al., 2009 ). Under this theory, different zones in the PFC (left vs. right, anterior vs. posterior, lateral vs. medial, and dorsal vs. ventral) represent different aspects of the information contained in the events (e.g., number of events to be integrated together, the complexity of the event, whether planning, and action is needed). Other studies have also suggested the CEN's role in tasks requiring cognitive flexibility, and functions to switch thinking modes, levels of abstraction of thought and consider multiple concepts simultaneously ( Miyake et al., 2000 ).
Thus, when the problem is well-structured, problem representation is largely an executive control activity coordinated by the PFC in which problem information from memory populates WM in a potentially structured representation. Once the problem is defined and encoded, planning and execution of a solution can begin.
The central executive network (CEN), particularly the PFC, is largely involved in plan formation and in plan execution. Planning is the process of generating a strategy to advance from the current state to a goal state. This in turn involves retrieving a suitable solution strategy from memory and then coordinating its execution.
22.214.171.124. Plan formation
The dlPFC supports sequential planning and plan formation, which includes the generation of hypothesis and construction of plan steps ( Barbey and Barsalou, 2009 ). Interestingly, the vlPFC and the angular gyrus (AG), implicated in a variety of functions including memory retrieval, are also involved in plan formation ( Anderson et al., 2014 ). Indeed, the AG together with the regions in the MTL (including the HF) and several other regions form a what is known as the “core” network. The core network is believed to be activated when recalling past experiences, imagining fictitious, and future events and navigating large-scale spaces ( Summerfield et al., 2010 ), all key functions for generating plan hypotheses. A recent study suggests that the AG is critical to both episodic simulation, representation, and episodic memory ( Thakral et al., 2017 ). One possibility for how plans are formulated could involve a dynamic process of retrieving an optimal strategy from memory. Research has shown significant interaction between striatal and frontal regions ( Scimeca and Badre, 2012 ; Horner et al., 2015 ). The striatum is believed to play a key role in declarative memory retrieval, and specifically helping retrieve optimal (or previously rewarded) memories ( Scimeca and Badre, 2012 ). Relevant to planning and plan formation, Scimeca & Badre have suggested that the striatum plays two important roles: (1) in mapping acquired value/utility to action selection, and thereby helping plan formation, and (2) modulation and re-encoding of actions and other plan parameters. Different types of problems require different sets of specialized knowledge. For example, the knowledge needed to solve mathematical problems might be quite different (albeit overlapping) from the knowledge needed to select appropriate tools in the environment.
Thus far, I have discussed planning and problem representation as being domain-independent, which has allowed me to outline key areas of the PFC, MTL, and other regions relevant to all problem-solving. However, some types of problems require domain-specific knowledge for which other regions might need to be recruited. For example, when planning for tool-use, the superior parietal lobe (SPL), supramarginal gyrus (SMG), anterior inferior parietal lobe (AIPL), and certain portions of the temporal and occipital lobe involved in visual and spatial integration have been found to be recruited ( Brandi et al., 2014 ). It is believed that domain-specific information stored in these regions is recovered and used for planning.
126.96.36.199. Plan execution
Once a solution plan has been recruited from memory and suitably tuned for the problem on hand, the left-rostral PFC, caudate nucleus (CN), and bilateral posterior parietal cortices (PPC) are responsible for translating the plan into executable form ( Stocco et al., 2012 ). The PPC stores and maintains “mental template” of the executable form. Hemispherical division of labor is particularly relevant in planning where it was shown that when planning to solve a Tower of Hanoi (block moving) problem, the right PFC is involved in plan construction whereas the left PFC is involved in controlling processes necessary to supervise the execution of the plan ( Newman and Green, 2015 ). On a separate note and not the focus of this paper, plan execution and problem-solving can require the recruitment of affective and motivational processing in order to supply the agent with the resolve to solve problems, and the vmPFC has been found to be involved in coordinating this process ( Barbey and Barsalou, 2009 ).
During the gestalt movement in the 1930s, Maier noted that “most instances of “real” problem solving involves creative thinking” ( Maier, 1930 ). Maier performed several experiments to study mental fixation and insight problem solving. This close tie between insight and creativity continues to be a recurring theme, one that will be central to the current discussion. If creativity and insight are linked to RWPS as noted by Maier, then it is reasonable to turn to the creativity and insight literature for understanding the role played by the environment. A large portion of the creativity literature has focused on viewing creativity as an internal process, one in which the solvers attention is directed inwards, and toward internal stimuli, to facilitate the generation of novel ideas and associations in memory ( Beaty et al., 2016 ). Focusing on imagination, a number of researchers have looked at blinking, eye fixation, closing eyes, and looking nowhere behavior and suggested that there is a shift of attention from external to internal stimuli during creative problem solving ( Salvi and Bowden, 2016 ). The idea is that shutting down external stimuli reduces cognitive load and focuses attention internally. Other experiments studying sleep behavior have also noted the beneficial role of internal stimuli in problem solving. The notion of ideas popping into ones consciousness, suddenly, during a shower is highly intuitive for many and researchers have attempted to study this phenomena through the lens of incubation, and unconscious thought that is internally-driven. There have been several theories and counter-theories proposed to account specifically for the cognitive processes underlying incubation ( Ritter and Dijksterhuis, 2014 ; Gilhooly, 2016 ), but none of these theories specifically address the role of the external environment.
The neuroscience of creativity has also been extensively studied and I do not focus on an exhaustive literature review in this paper (a nice review can be found in Sawyer, 2011 ). From a problem-solving perspective, it has been found that unlike well-structured problems, ill-structured problems activate the right dlPFC. Most of the past work on creativity and creative problem-solving has focused on exploring memory structures and performing internally-directed searches. Creative idea generation has primarily been viewed as internally directed attention ( Jauk et al., 2012 ; Benedek et al., 2016 ) and a primary mechanism involved is divergent thinking , which is the ability to produce a variety of responses in a given situation ( Guilford, 1962 ). Divergent thinking is generally thought to involve interactions between the DMN, CEN, and the salience network ( Yoruk and Runco, 2014 ; Heinonen et al., 2016 ). One psychological model of creative cognition is the Geneplore model that considers two major phases of generation (memory retrieval and mental synthesis) and exploration (conceptual interpretation and functional inference) ( Finke et al., 1992 ; Boccia et al., 2015 ). It has been suggested that the associative mode of processing to generate new creative association is supported by the DMN, which includes the medial PFC, posterior cingulate cortex (PCC), tempororparietal juntion (TPJ), MTL, and IPC ( Beaty et al., 2014 , 2016 ).
That said, the creativity literature is not completely devoid of acknowledging the role of the environment. In fact, it is quite the opposite. Researchers have looked closely at the role played by externally provided hints from the time of the early gestalt psychologists and through to present day studies ( Öllinger et al., 2017 ). In addition to studying how hints can help problem solving, researchers have also looked at how directed action can influence subsequent problem solving—e.g., swinging arms prior to solving the two-string puzzle, which requires swinging the string ( Thomas and Lleras, 2009 ). There have also been numerous studies looking at how certain external perceptual cues are correlated with creativity measures. Vohs et al. suggested that untidiness in the environment and the increased number of potential distractions helps with creativity ( Vohs et al., 2013 ). Certain colors such as blue have been shown to help with creativity and attention to detail ( Mehta and Zhu, 2009 ). Even environmental illumination, or lack thereof, have been shown to promote creativity ( Steidle and Werth, 2013 ). However, it is important to note that while these and the substantial body of similar literature show the relationship of the environment to creative problem solving, they do not specifically account for the cognitive processes underlying the RWPS when external stimuli are received.
2.4. Insight Problem Solving
Analytical problem solving is believed to involve deliberate and conscious processing that advances step by step, allowing solvers to be able to explain exactly how they solved it. Inability to solve these problems is often associated with lack of required prior knowledge, which if provided, immediately makes the solution tractable. Insight, on the other hand, is believed to involve a sudden and unexpected emergence of an obvious solution or strategy sometimes accompanied by an affective aha! experience. Solvers find it difficult to consciously explain how they generated a solution in a sequential manner. That said, research has shown that having an aha! moment is neither necessary nor sufficient to insight and vice versa ( Danek et al., 2016 ). Generally, it is believed that insight solvers acquire a full and deep understanding of the problem when they have solved it ( Chu and Macgregor, 2011 ). There has been an active debate in the problem solving community about whether insight is something special. Some have argued that it is not, and that there are no special or spontaneous processes, but simply a good old-fashioned search of a large problem space ( Kaplan and Simon, 1990 ; MacGregor et al., 2001 ; Ash and Wiley, 2006 ; Fleck, 2008 ). Others have argued that insight is special and suggested that it is likely a different process ( Duncker, 1945 ; Metcalfe, 1986 ; Kounios and Beeman, 2014 ). This debate lead to two theories for insight problem solving. MacGregor et al. proposed the Criterion for Satisfactory Progress Theory (CSPT), which is based on Newell and Simons original notion of problem solving as being a heuristic search through the problem space ( MacGregor et al., 2001 ). The key aspect of CSPT is that the solver is continually monitoring their progress with some set of criteria. Impasses arise when there is a criterion failure, at which point the solver tries non-maximal but promising states. The representational change theory (RCT) proposed by Ohlsson et al., on the other hand, suggests that impasses occur when the goal state is not reachable from an initial problem representation (which may have been generated through unconscious spreading activation) ( Ohlsson, 1992 ). In order to overcome an impasse, the solver needs to restructure the problem representation, which they can do by (1) elaboration (noticing new features of a problem), (2) re-encoding fixing mistaken or incomplete representations of the problem, and by (3) changing constraints. Changing constraints is believed to involve two sub-processes of constraint relaxation and chunk-decomposition.
The current position is that these two theories do not compete with each other, but instead complement each other by addressing different stages of problem solving: pre- and post-impasse. Along these lines, Ollinger et al. proposed an extended RCT (eRCT) in which revising the search space and using heuristics was suggested as being a dynamic and iterative and recursive process that involves repeated instances of search, impasse and representational change ( Öllinger et al., 2014 , 2017 ). Under this theory, a solver first forms a problem representation and begins searching for solutions, presumably using analytical problem solving processes as described earlier. When a solution cannot be found, the solver encounters an impasse, at which point the solver must restructure or change the problem representation and once again search for a solution. The model combines both analytical problem solving (through heuristic searches, hill climbing and progress monitoring), and creative mechanisms of constraint relaxation and chunk decomposition to enable restructuring.
Ollingers model appears to comprehensively account for both analytical and insight problem solving and, therefore, could be a strong candidate to model RWPS. However, while compelling, it is nevertheless an insufficient model of RWPS for many reasons, of which two are particularly significant for the current paper. First, the model does explicitly address mechanisms by which external stimuli might be assimilated. Second, the model is not sufficiently flexible to account for other events (beyond impasse) occurring during problem solving, such as distraction, mind-wandering and the like.
So, where does this leave us? I have shown the interplay between problem solving, creativity and insight. In particular, using Ollinger's proposal, I have suggested (maybe not quite explicitly up until now) that RWPS involves some degree of analytical problem solving as well as the post-impasse more creative modes of problem restructuring. I have also suggested that this model might need to be extended for RWPS along two dimensions. First, events such as impasses might just be an instance of a larger class of events that intervene during problem solving. Thus, there needs to be an accounting of the cognitive mechanisms that are potentially influenced by impasses and these other intervening events. It is possible that these sorts of events are crucial and trigger a switch in attentional focus, which in turn facilitates switching between different problem solving modes. Second, we need to consider when and how externally-triggered stimuli from the solver's environment can influence the problem solving process. I detail three different mechanisms by which external knowledge might influence problem solving. I address each of these ideas in more detail in the next two sections.
3. Event-Triggered Mode Switching During Problem-Solving
When solving certain types of problems, the agent might encounter an impasse, i.e., some block in its ability to solve the problem ( Sprugnoli et al., 2017 ). The impasse may arise because the problem may have been ill-defined to begin with causing incomplete and unduly constrained representations to have been formed. Alternatively, impasses can occur when suitable solution strategies cannot be retrieved from memory or fail on execution. In certain instances, the solution strategies may not exist and may need to be generated from scratch. Regardless of the reason, an impasse is an interruption in the problem solving process; one that was running conflict-free up until the point when a seemingly unresolvable issue or an error in the predicted solution path was encountered. Seen as a conflict encountered in the problem-solving process it activates the anterior cingulate cortex (ACC). It is believed that the ACC not only helps detect the conflict, but also switch modes from one of “exploitation” (planning) to “exploration” (search) ( Quilodran et al., 2008 ; Tang et al., 2012 ), and monitors progress during resolution ( Chu and Macgregor, 2011 ). Some mode switching duties are also found to be shared with the AI (the ACC's partner in the salience network), however, it is unclear exactly the extent of this function-sharing.
Even though it is debatable if impasses are a necessary component of insight, they are still important as they provide a starting point for the creativity ( Sprugnoli et al., 2017 ). Indeed, it is possible that around the moment of impasse, the AI and ACC together, as part of the salience network play a crucial role in switching thought modes from analytical planning mode to creative search and discovery mode. In the latter mode, various creative mechanisms might be activated allowing for a solution plan to emerge. Sowden et al. and many others have suggested that the salience network is potentially a candidate neurobiological mechanism for shifting between thinking processes, more generally ( Sowden et al., 2015 ). When discussing various dual-process models as they relate to creative cognition, Sowden et al. have even noted that the ACC activation could be useful marker to identify shifting as participants work creative problems.
3.2. Defocused Attention
As noted earlier, in the presence of an impasse there is a shift from an exploitative (analytical) thinking mode to an exploratory (creative) thinking mode. This shift impacts several networks including, for example, the attention network. It is believed attention can switch between a focused mode and a defocused mode. Focused attention facilitates analytic thought by constraining activation such that items are considered in a compact form that is amenable to complex mental operations. In the defocused mode, agents expand their attention allowing new associations to be considered. Sowden et al. (2015) note that the mechanism responsible for adjustments in cognitive control may be linked to the mechanisms responsible for attentional focus. The generally agreed position is that during generative thinking, unconscious cognitive processes activated through defocused attention are more prevalent, whereas during exploratory thinking, controlled cognition activated by focused attention becomes more prevalent ( Kaufman, 2011 ; Sowden et al., 2015 ).
Defocused attention allows agents to not only process different aspects of a situation, but to also activate additional neural structures in long term memory and find new associations ( Mendelsohn, 1976 ; Yoruk and Runco, 2014 ). It is believed that cognitive material attended to and cued by positive affective state results in defocused attention, allowing for more complex cognitive contexts and therefore a greater range of interpretation and integration of information ( Isen et al., 1987 ). High attentional levels are commonly considered a typical feature of highly creative subjects ( Sprugnoli et al., 2017 ).
4. Role of the Environment
In much of the past work the focus has been on treating creativity as largely an internal process engaging the DMN to assist in making novel connections in memory. The suggestion has been that “individual needs to suppress external stimuli and concentrate on the inner creative process during idea generation” ( Heinonen et al., 2016 ). These ideas can then function as seeds for testing and problem-solving. While true of many creative acts, this characterization does not capture how creative ideas arise in many real-world creative problems. In these types of problems, the agent is functioning and interacting with its environment before, during and after problem-solving. It is natural then to expect that stimuli from the environment might play a role in problem-solving. More specifically, it can be expected that through passive and active involvement with the environment, the agent is (1) able to trigger an unrelated, but potentially useful memory relevant for problem-solving, (2) make novel connections between two events in memory with the environmental cue serving as the missing link, and (3) incorporate a completely novel information from events occuring in the environment directly into the problem-solving process. I explore potential neural mechanisms for these three types of environmentally informed creative cognition, which I hypothesize are enabled by defocused attention.
4.1. Partial Cues Trigger Relevant Memories Through Context-Shifting
I have previously discussed the interaction between the MTL and PFC in helping select task-relevant and critical memories for problem-solving. It is well-known that pattern completion is an important function of the MTL and one that enables memory retrieval. Complementary Learning Theory (CLS) and its recently updated version suggest that the MTL and related structures support initial storage as well as retrieval of item and context-specific information ( Kumaran et al., 2016 ). According to CLS theory, the dentate gyrus (DG) and the CA3 regions of the HF are critical to selecting neural activity patterns that correspond to particular experiences ( Kumaran et al., 2016 ). These patterns might be distinct even if experiences are similar and are stabilized through increases in connection strengths between the DG and CA3. Crucially, because of the connection strengths, reactivation of part of the pattern can activate the rest of it (i.e., pattern completion). Kumaran et al. have further noted that if consistent with existing knowledge, these new experiences can be quickly replayed and interleaved into structured representations that form part of the semantic memory.
Cues in the environment provided by these experiences hold partial information about past stimuli or events and this partial information converges in the MTL. CLS accounts for how these cues might serve to reactivate partial patterns, thereby triggering pattern completion. When attention is defocused I hypothesize that (1) previously unnoticed partial cues are considered, and (2) previously noticed partial cues are decomposed to produce previously unnoticed sub-cues, which in turn are considered. Zabelina et al. (2016) have shown that real-world creativity and creative achievement is associated with “leaky attention,” i.e., attention that allows for irrelevant information to be noticed. In two experiments they systematically explored the relationship between two notions of creativity— divergent thinking and real-world creative achievement—and the use of attention. They found that attentional use is associated in different ways for each of the two notions of creativity. While divergent thinking was associated with flexible attention, it does not appear to be leaky. Instead, selective focus and inhibition components of attention were likely facilitating successful performance on divergent thinking tasks. On the other hand, real-world creative achievement was linked to leaky attention. RWPS involves elements of both divergent thinking and of real-world creative achievement, thus I would expect some amount of attentional leaks to be part of the problem solving process.
Thus, it might be the case that a new set of cues or sub-cues “leak” in and activate memories that may not have been previously considered. These cues serve to reactivate a diverse set of patterns that then enable accessing a wide range of memories. Some of these memories are extra-contextual, in that they consider the newly noticed cues in several contexts. For example, when unable to find a screwdriver, we might consider using a coin. It is possible that defocused attention allows us to consider the coin's edge as being a potentially relevant cue that triggers uses for the thin edge outside of its current context in a coin. The new cues (or contexts) may allow new associations to emerge with cues stored in memory, which can occur during incubation. Objects and contexts are integrated into memory automatically into a blended representation and changing contexts disrupts this recognition ( Hayes et al., 2007 ; Gabora, 2016 ). Cue-triggered context shifting allows an agent to break-apart a memory representation, which can then facilitate problem-solving in new ways.
4.2. Heuristic Prototyping Facilitates Novel Associations
It has long been the case that many scientific innovations have been inspired by events in nature and the surrounding environment. As noted earlier, Archimedes realized the relationship between the volume of an irregularly shaped object and the volume of water it displaced. This is an example of heuristic prototyping where the problem-solver notices an event in the environment, which then triggers the automatic activation of a heuristic prototype and the formation of novel associations (between the function of the prototype and the problem) which they can then use to solve the problem ( Luo et al., 2013 ). Although still in its relative infancy, there has been some recent research into the neural basis for heuristic prototyping. Heuristic prototype has generally been defined as an enlightening prototype event with a similar element to the current problem and is often composed of a feature and a function ( Hao et al., 2013 ). For example, in designing a faster and more efficient submarine hull, a heuristic prototype might be a shark's skin, while an unrelated prototype might be a fisheye camera ( Dandan et al., 2013 ).
Research has shown that activating the feature function of the right heuristic prototype and linking it by way of semantic similarity to the required function of the problem was the key mechanism people used to solve several scienitific insight problems ( Yang et al., 2016 ). A key region activated during heuristic prototyping is the dlPFC and it is believed to be generally responsible for encoding the events into memory and may play an important role in selecting and retrieving the matched unsolved technical problem from memory ( Dandan et al., 2013 ). It is also believed that the precuneus plays a role in automatic retrieval of heuristic information allowing the heuristic prototype and the problem to combine ( Luo et al., 2013 ). In addition to semantic processing, certain aspects of visual imagery have also been implicated in heuristic prototyping leading to the suggestion of the involvement of Broadman's area BA 19 in the occipital cortex.
There is some degree of overlap between the notions of heuristic prototyping and analogical transfer (the mapping of relations from one domain to another). Analogical transfer is believed to activate regions in the left medial fronto-parietal system (dlPFC and the PPC) ( Barbey and Barsalou, 2009 ). I suggest here that analogical reasoning is largely an internally-guided process that is aided by heuristic prototyping which is an externally-guided process. One possible way this could work is if heuristic prototyping mechanisms help locate the relevant memory with which to then subsequently analogize.
4.3. Making Physical Inferences to Acquire Novel Information
The agent might also be able to learn novel facts about their environment through passive observation as well as active experimentation. There has been some research into the neural basis for causal reasoning ( Barbey and Barsalou, 2009 ; Operskalski and Barbey, 2016 ), but beyond its generally distributed nature, we do not know too much more. Beyond abstract causal reasoning, some studies looked into the cortical regions that are activated when people watch and predict physical events unfolding in real-time and in the real-world ( Fischer et al., 2016 ). It was found that certain regions were associated with representing types of physical concepts, with the left intraparietal sulcus (IPS) and left middle frontal gyrus (MFG) shown to play a role in attributing causality when viewing colliding objects ( Mason and Just, 2013 ). The parahippocampus (PHC) was associated with linking causal theory to observed data and the TPJ was involved in visualizing movement of objects and actions in space ( Mason and Just, 2013 ).
5. Proposed Theory
I noted earlier that Ollinger's model for insight problem solving, while serving as a good candidate for RWPS, requires extension. In this section, I propose a candidate model that includes some necessary extensions to Ollinger's framework. I begin by laying out some preliminary notions that underlie the proposed model.
5.1. Dual Attentional Modes
I propose that the attention-switching mechanism described earlier is at the heart of RWPS and enables two modes of operation: focused and defocused mode. In the focused mode, the problem representation is more or less fixed, and problem solving proceeds in a focused and goal directed manner through search, planning, and execution mechanisms. In the defocused mode, problem solving is not necessarily goal directed, but attempts to generate ideas, driven by both internal and external items.
At first glance, these modes might seem similar to convergent and divergent thinking modes postulated by numerous others to account for creative problem solving. Divergent thinking allows for the generation of new ideas and convergent thinking allows for verification and selection of generated ideas. So, it might seem that focused mode and convergent thinking are similar and likewise divergent and defocused mode. They are, however, quite different. The modes relate less to idea generation and verification, and more to the specific mechanisms that are operating with regard to a particular problem at a particular moment in time. Convergent and divergent processes may be occurring during both defocused and focused modes. Some degree of divergent processes may be used to search and identify specific solution strategies in focused mode. Also, there might be some degree of convergent idea verification occuring in defocused mode as candidate items are evaluated for their fit with the problem and goal. Thus, convergent and divergent thinking are one amongst many mechanisms that are utilized in focused and defocused mode. Each of these two modes has to do with degree of attention placed on a particular problem.
There have been numerous dual-process and dual-systems models of cognition proposed over the years. To address criticisms raised against these models and to unify some of the terminology, Evans & Stanovich proposed a dual-process model comprising Type 1 and Type 2 thought ( Evans and Stanovich, 2013 ; Sowden et al., 2015 ). Type 1 processes are those that are believed to be autonomous and do not require working memory. Type 2 processes, on the other hand, are believed to require working memory and are cognitively decoupled to prevent real-world representations from becoming confused with mental simulations ( Sowden et al., 2015 ). While acknowledging various other attributes that are often used to describe dual process models (e.g., fast/slow, associative/rule-based, automatic/controlled), Evans & Stanovich note that these attributes are merely frequent correlates and not defining characteristics of Type 1 or Type 2 processes. The proposed dual attentional modes share some similarities with the Evans & Stanovich Type 1 and 2 models. Specifically, Type 2 processes might occur in focused attentional mode in the proposed model as they typically involve the working memory and certain amount of analytical thought and planning. Similarly, Type 1 processes are likely engaged in defocused attentional mode as there are notions of associative and generative thinking that might be facilitated when attention has been defocused. The crucial difference between the proposed model and other dual-process models is that the dividing line between focused and defocused attentional modes is the degree of openness to internal and external stimuli (by various networks and functional units in the brain) when problem solving. Many dual process models were designed to classify the “type” of thinking process or a form of cognitive processing. In some sense, the “processes” in dual process theories are characterized by the type of mechanism of operation or the type of output they produced. Here, I instead characterize and differentiate the modes of thinking by the receptivity of different functional units in the brain to input during problem solving.
This, however, raises a different question of the relationship between these attentional modes and conscious vs. unconscious thinking. It is clear that both the conscious and unconscious are involved in problem solving, as well as in RWPS. Here, I claim that a problem being handled is, at any given point in time, in either a focused mode or in a defocused mode. When in the focused mode, problem solving primarily proceeds in a manner that is available for conscious deliberation. More specifically, problem space elements and representations are tightly managed and plans and strategies are available in the working memory and consciously accessible. There are, however, secondary unconscious operations in the focused modes that includes targeted memory retrieval and heuristic-based searches. In the defocused mode, the problem is primarily managed in an unconscious way. The problem space elements are broken apart and loosely managed by various mechanisms that do not allow for conscious deliberation. That said, it is possible that some problem parameters remain accessible. For example, it is possible that certain goal information is still maintained consciously. It is also possible that indexes to all the problems being considered by the solver are maintained and available to conscious awareness.
5.2. RWPS Model
Returning to Ollinger's model for insight problem solving, it now becomes readily apparent how this model can be modified to incorporate environmental effects as well as generalizing the notion of intervening events beyond that of impasses. I propose a theory for RWPS that begins with standard analytical problem-solving process (See Figures 1 , 2 ).
Figure 1 . Summary of neural activations during focused problem-solving (Left) and defocused problem-solving (Right) . During defocused problem-solving, the salience network (insula and ACC) coordinates the switching of several networks into a defocused attention mode that permits the reception of a more varied set of stimuli and interpretations via both the internally-guided networks (default mode network DMN) and externally guided networks (Attention). PFC, prefrontal cortex; ACC, anterior cingulate cortex; PCC, posterior cingulate cortex; IPC, inferior parietal cortex; PPC, posterior parietal cortex; IPS, intra-parietal sulcus; TPJ, temporoparietal junction; MTL, medial temporal lobe; FEF, frontal eye field.
Figure 2 . Proposed Model for Real World Problem Solving (RWPS). The corresponding neural correlates are shown in italics. During problem-solving, an initial problem representation is formed based on prior knowledge and available perceptual information. The problem-solving then proceeds in a focused, goal-directed mode until the goal is achieved or a defocusing event (e.g., impasse or distraction) occurs. During focused mode operation, the solver interacts with the environment in directed manner, executing focused plans, and allowing for predicted items to be activated by the environment. When a defocusing event occurs, the problem-solving then switches into a defocused mode until a focusing event (e.g., discovery) occurs. In defocused mode, the solver performs actions unrelated to the problem (or is inactive) and is receptive to a set of environmental triggers that activate novel aspects using the three mechanisms discussed in this paper. When a focusing event occurs, the diffused problem elements cohere into a restructured representation and problem-solving returns into a focused mode.
5.2.1. Focused Problem Solving Mode
Initially, both prior knowledge and perceptual entities help guide the creation of problem representations in working memory. Prior optimal or rewarding solution strategies are obtained from LTM and encoded in the working memory as well. This process is largely analytical and the solver interacts with their environment through focused plan or idea execution, targeted observation of prescribed entities, and estimating prediction error of these known entities. More specifically, when a problem is presented, the problem representations are activated and populated into working memory in the PFC, possibly in structured representations along convergence zones. The PFC along with the Striatum and the MTL together attempt at retrieving an optimal or previously rewarded solution strategy from long term memory. If successfully retrieved, the solution strategy is encoded into the PPC as a mental template, which then guides relevant motor control regions to execute the plan.
5.2.2. Defocusing Event-Triggered Mode Switching
The search and solve strategy then proceeds analytically until a “defocusing event” is encountered. The salience network (AI and ACC) monitor for conflicts and attempt to detect any such events in the problem-solving process. As long as no conflicts are detected, the salience network focuses on recruiting networks to achieve goals and suppresses the DMN ( Beaty et al., 2016 ). If the plan execution or retrieval of the solution strategy fails, then a defocusing event is detected and the salience network performs mode switching. The salience network dynamically switches from the focused problem-solving mode to a defocused problem-solving mode ( Menon, 2015 ). Ollinger's current model does not account for other defocusing events beyond an impasse, but it is not inconceivable that there could be other such events triggered by external stimuli (e.g., distraction or an affective event) or by internal stimuli (e.g., mind wandering).
5.2.3. Defocused Problem Solving Mode
In defocused mode, the problem is operated on by mechanisms that allow for the generation and testing of novel ideas. Several large-scale brain networks are recruited to explore and generate new ideas. The search for novel ideas is facilitated by generally defocused attention, which in turn allows for creative idea generation from both internal as well as external sources. The salience network switches operations from defocused event detection to focused event or discovery detection, whereby for example, environmental events or ideas that are deemed interesting can be detected. During this idea exploration phase, internally, the DMN is no longer suppressed and attempts to generate new ideas for problem-solving. It is known that the IPC is involved in the generation of new ideas ( Benedek et al., 2014 ) and together with the PPC in coupling different information together ( Simone Sandkühler, 2008 ; Stocco et al., 2012 ). Beaty et al. (2016) have proposed that even this internal idea-generation process can be goal directed, thereby allowing for a closer working relationship between the CEN and the DMN. They point to neuroimaging evidence that support the possibility that the executive control network (comprising the lateral prefrontal and inferior parietal regions) can constrain and direct the DMN in its process of generating ideas to meet task-specific goals via top down monitoring and executive control ( Beaty et al., 2016 ). The control network is believed to maintain an “internal train of thought” by keeping the task goal activated, thereby allowing for strategic and goal-congruent searches for ideas. Moreover, they suggest that the extent of CEN involvement in the DMN idea-generation may depend on the extent to which the creative task is constrained. In the RWPS setting, I would suspect that the internal search for creative solutions is not entirely unconstrained, even in the defocused mode. Instead, the solver is working on a specified problem and thus, must maintain the problem-thread while searching for solutions. Moreover, self-generated ideas must be evaluated against the problem parameters and thereby might need some top-down processing. This would suggest that in such circumstances, we would expect to see an increased involvement of the CEN in constraining the DMN.
On the external front, several mechanisms are operating in this defocused mode. Of particular note are the dorsal attention network, composed of the visual cortex (V), IPS and the frontal eye field (FEF) along with the precuneus and the caudate nucleus allow for partial cues to be considered. The MTL receives synthesized cue and contextual information and populates the WM in the PFC with a potentially expanded set of information that might be relevant for problem-solving. The precuneus, dlPFC and PPC together trigger the activation and use of a heuristic prototype based on an event in the environment. The caudate nucleus facilitates information routing between the PFC and PPC and is involved in learning and skill acquisition.
5.2.4. Focusing Event-Triggered Mode Switching
The problem's life in this defocused mode continues until a focusing event occurs, which could be triggered by either external (e.g., notification of impending deadline, discovery of a novel property in the environment) or internal items (e.g., goal completion, discovery of novel association or updated relevancy of a previously irrelevant item). As noted earlier, an internal train of thought may be maintained that facilitates top-down evaluation of ideas and tracking of these triggers ( Beaty et al., 2016 ). The salience network switches various networks back to the focused problem-solving mode, but not without the potential for problem restructuring. As noted earlier, problem space elements are maintained somewhat loosely in the defocused mode. Thus, upon a focusing event, a set or subset of these elements cohere into a tight (restructured) representation suitable for focused mode problem solving. The process then repeats itself until the goal has been achieved.
5.3. Model Predictions
5.3.1. single-mode operation.
The proposed RWPS model provides several interesting hypotheses, which I discuss next. First, the model assumes that any given problem being worked on is in one mode or another, but not both. Thus, the model predicts that there cannot be focused plan execution on a problem that is in defocused mode. The corollary prediction is that novel perceptual cues (as those discussed in section 4) cannot help the solver when in focused mode. The corollary prediction, presumably has some support from the inattentional blindness literature. Inattentional blindness is when perceptual cues are not noticed during a task (e.g., counting the number of basketball passes between several people, but not noticing a gorilla in the scene) ( Simons and Chabris, 1999 ). It is possible that during focused problem solving, that external and internally generated novel ideas are simply not considered for problem solving. I am not claiming that these perceptual cues are always ignored, but that they are not considered within the problem. Sometimes external cues (like distracting occurrences) can serve as defocusing events, but the model predicts that the actual content of these cues are not themselves useful for solving the specific problem at hand.
When comparing dual-process models Sowden et al. (2015) discuss shifting from one type of thinking to another and explore how this shift relates to creativity. In this regard, they weigh the pros and cons of serial vs. parallel shifts. In dual-process models that suggest serial shifts, it is necessary to disengage one type of thought prior to engaging the other or to shift along a continuum. Whereas, in models that suggest parallel shifts, each of the thinking types can operate in parallel. Per this construction, the proposed RWPS model is serial, however, not quite in the same sense. As noted earlier, the RWPS model is not a dual-process model in the same sense as other dual process model. Instead, here, the thrust is on when the brain is receptive or not receptive to certain kinds of internal and external stimuli that can influence problem solving. Thus, while the modes may be serial with respect to a certain problem, it does not preclude the possibility of serial and parallel thinking processes that might be involved within these modes.
5.3.2. Event-Driven Transitions
The model requires an event (defocusing or focusing) to transition from one mode to another. After all why else would a problem that is successfully being resolved in the focused mode (toward completion) need to necessarily be transferred to defocused mode? These events are interpreted as conflicts in the brain and therefore the mode-switching is enabled by the saliency network and the ACC. Thus, the model predicts that there can be no transition from one mode to another without an event. This is a bit circular, as an event is really what triggers the transition in the first place. But, here I am suggesting that an external or internal cue triggered event is what drives the transition, and that transitions cannot happen organically without such an event. In some sense, the argument is that the transition is discontinuous, rather than a smooth one. Mind-wandering is good example of when we might drift into defocused mode, which I suggest is an example of an internally driven event caused by an alternative thought that takes attention away from the problem.
A model assumption underlying RWPS is that events such as impasses have a similar effect to other events such as distraction or mind wandering. Thus, it is crucial to be able to establish that there exists of class of such events and they have a shared effect on RWPS, which is to switch attentional modes.
5.3.3. Focused Mode Completion
The model also predicts that problems cannot be solved (i.e., completed) within the defocused mode. A problem can be considered solved when a goal is reached. However, if a goal is reached and a problem is completed in the defocused mode, then there must have not been any converging event or coherence of problem elements. While it is possible that the solver arbitrarily arrived at the goal in a diffused problem space and without conscious awareness of completing the task or even any converging event or problem recompiling, it appears somewhat unlikely. It is true that there are many tasks that we complete without actively thinking about it. We do not think about what foot to place in front of another while walking, but this is not an instance of problem solving. Instead, this is an instance of unconscious task completion.
5.3.4. Restructuring Required
The model predicts that a problem cannot return to a focused mode without some amount of restructuring. That is, once defocused, the problem is essentially never the same again. The problem elements begin interacting with other internally and externally-generated items, which in turn become absorbed into the problem representation. This prediction can potentially be tested by establishing some preliminary knowledge, and then showing one group of subjects the same knowledge as before, while showing the another group of subjects different stimuli. If the model's predictions hold, the problem representation will be restructured in some way for both groups.
There are numerous other such predictions, which are beyond the scope of this paper. One of the biggest challenges then becomes evaluating the model to set up suitable experiments aimed at testing the predictions and falsifying the theory, which I address next.
6. Experimental Challenges and Paradigms
One of challenges in evaluating the RWPS is that real world factors cannot realistically be accounted for and sufficiently controlled within a laboratory environment. So, how can one controllably test the various predictions and model assumptions of “real world” problem solving, especially given that by definition RWPS involves the external environment and unconscious processing? At the expense of ecological validity, much of insight problem solving research has employed an experimental paradigm that involves providing participants single instances of suitably difficult problems as stimuli and observing various physiological, neurological and behavioral measures. In addition, through verbal protocols, experimenters have been able to capture subjective accounts and problem solving processes that are available to the participants' conscious. These experiments have been made more sophisticated through the use of timed-hints and/or distractions. One challenge with this paradigm has been the selection of a suitable set of appropriately difficult problems. The classic insight problems (e.g., Nine-dot, eight-coin) can be quite difficult, requiring complicated problem solving processes, and also might not generalize to other problems or real world problems. Some in the insight research community have moved in the direction of verbal tasks (e.g., riddles, anagrams, matchstick rebus, remote associates tasks, and compound remote associates tasks). Unfortunately, these puzzles, while providing a great degree of controllability and repeatability, are even less realistic. These problems are not entirely congruent with the kinds of problems that humans are solving every day.
The other challenge with insight experiments is the selection of appropriate performance and process tracking measures. Most commonly, insight researchers use measures such as time to solution, probability of finding solution, and the like for performance measures. For process tracking, verbal protocols, coded solution attempts, and eye tracking are increasingly common. In neuroscientific studies of insight various neurological measures using functional magnetic resonance imaging (fMRI), electroencephalography (EEGs), transcranial direct current stimulation (tDCS), and transcranial magnetic stimulation (tMS) are popular and allow for spatially and temporally localizing an insight event.
Thus, the challenge for RWPS is two-fold: (1) selection of stimuli (real world problems) that are generalizable, and (2) selection of measures (or a set of measures) that can capture key aspects of the problem solving process. Unfortunately, these two challenges are somewhat at odds with each other. While fMRI and various neuroscientific measures can capture the problem solving process in real time, it is practically difficult to provide participants a realistic scenario while they are laying flat on their back in an fMRI machine and allowed to move nothing more than a finger. To begin addressing this conundrum, I suggest returning to object manipulation problems (not all that different from those originally introduced by Maier and Duncker nearly a century ago), but using modern computing and user-interface technologies.
One pseudo-realistic approach is to generate challenging object manipulation problems in Virtual Reality (VR). VR has been used to describe 3-D environment displays that allows participants to interact with artificially projected, but experientially realistic scenarios. It has been suggested that virtual environments (VE) invoke the same cognitive modules as real equivalent environmental experience ( Foreman, 2010 ). Crucially, since VE's can be scaled and designed as desired, they provide a unique opportunity to study pseudo-RWPS. However, a VR-based research approach has its limitations, one of which is that it is nearly impossible to track participant progress through a virtual problem using popular neuroscientific measures such as fMRI because of the limited mobility of connected participants.
Most of the studies cited in this paper utilized an fMRI-based approach in conjunction with a verbal or visual task involving problem-solving or creative thinking. Very few, if any, studies involved the use physical manipulation, and those physical manipulations were restricted to limited finger movements. Thus, another pseudo-realistic approach is allowing subjects to teleoperate robotic arms and legs from inside the fMRI machine. This paradigm has seen limited usage in psychology and robotics, in studies focused on Human-Robot interaction ( Loth et al., 2015 ). It could be an invaluable tool in studying real-time dynamic problem-solving through the control of a robotic arm. In this paradigm a problem solving task involving physical manipulation is presented to the subject via the cameras of a robot. The subject (in an fMRI) can push buttons to operate the robot and interact with its environment. While the subjects are not themselves moving, they can still manipulate objects in the real world. What makes this paradigm all the more interesting is that the subject's manipulation-capabilities can be systematically controlled. Thus, for a particular problem, different robotic perceptual and manipulation capabilities can be exposed, allowing researchers to study solver-problem dynamics in a new way. For example, even simple manipulation problems (e.g., re-arranging and stacking blocks on a table) can be turned into challenging problems when the robotic movements are restricted. Here, the problem space restrictions are imposed not necessarily on the underlying problem, but on the solver's own capabilities. Problems of this nature, given their simple structure, may enable studying everyday practical creativity without the burden of devising complex creative puzzles. Crucial to note, both these pseudo-realistic paradigms proposed demonstrate a tight interplay between the solver's own capabilities and their environment.
While the neural basis for problem-solving, creativity and insight have been studied extensively in the past, there is still a lack of understanding of the role of the environment in informing the problem-solving process. Current research has primarily focused on internally-guided mental processes for idea generation and evaluation. However, the type of real world problem-solving (RWPS) that is often considered a hallmark of human intelligence has involved both a dynamic interaction with the environment and the ability to handle intervening and interrupting events. In this paper, I have attempted to synthesize the literature into a unified theory of RWPS, with a specific focus on ways in which the environment can help problem-solve and the key neural networks involved in processing and utilizing relevant and useful environmental information. Understanding the neural basis for RWPS will allow us to be better situated to solve difficult problems. Moreover, for researchers in computer science and artificial intelligence, clues into the neural underpinnings of the computations taking place during creative RWPS, can inform the design the next generation of helper and exploration robots which need these capabilities in order to be resourceful and resilient in the open-world.
The author confirms being the sole contributor of this work and approved it for publication.
The research for this Hypothesis/Theory Article was funded by the authors private means. Publication costs will be covered by my institution: Tufts University, Medford, MA, USA.
Conflict of Interest Statement
The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
I am indebted to Professor Matthias Scheutz, Professor Elizabeth Race, Professor Ayanna Thomas, and Professor. Shaun Patel for providing guidance with the research and the manuscript. I am also grateful for the facilities provided by Tufts University, Medford, MA, USA.
1. ^ My intention is not to ignore the benefits of a concentrated internal thought process which likely occurred as well, but merely to acknowledge the possibility that the environment might have also helped.
2. ^ The research in insight does extensively use “hints” which are, arguably, a form of external influence. But these hints are highly targeted and might not be available in this explicit form when solving problems in the real world.
3. ^ The accuracy of these accounts has been placed in doubt. They often are recounted years later, with inaccuracies, and embellished for dramatic effect.
4. ^ I use the term “agent” to refer to the problem-solver. The term agent is more general than “creature” or “person” or “you" and is intentionally selected to broadly reference humans, animals as well as artificial agents. I also selectively use the term “solver.”
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Keywords: creativity, problem-solving, insight, attention network, salience network, default mode network
Citation: Sarathy V (2018) Real World Problem-Solving. Front. Hum. Neurosci . 12:261. doi: 10.3389/fnhum.2018.00261
Received: 03 August 2017; Accepted: 06 June 2018; Published: 26 June 2018.
Copyright © 2018 Sarathy. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Vasanth Sarathy, [email protected]
By the end of this section, you will be able to:
- Describe problem solving strategies
- Define algorithm and heuristic
- Explain some common roadblocks to effective problem solving
People face problems every day—usually, multiple problems throughout the day. Sometimes these problems are straightforward: To double a recipe for pizza dough, for example, all that is required is that each ingredient in the recipe be doubled. Sometimes, however, the problems we encounter are more complex. For example, say you have a work deadline, and you must mail a printed copy of a report to your supervisor by the end of the business day. The report is time-sensitive and must be sent overnight. You finished the report last night, but your printer will not work today. What should you do? First, you need to identify the problem and then apply a strategy for solving the problem.
The study of human and animal problem solving processes has provided much insight toward the understanding of our conscious experience and led to advancements in computer science and artificial intelligence. Essentially much of cognitive science today represents studies of how we consciously and unconsciously make decisions and solve problems. For instance, when encountered with a large amount of information, how do we go about making decisions about the most efficient way of sorting and analyzing all the information in order to find what you are looking for as in visual search paradigms in cognitive psychology. Or in a situation where a piece of machinery is not working properly, how do we go about organizing how to address the issue and understand what the cause of the problem might be. How do we sort the procedures that will be needed and focus attention on what is important in order to solve problems efficiently. Within this section we will discuss some of these issues and examine processes related to human, animal and computer problem solving.
When people are presented with a problem—whether it is a complex mathematical problem or a broken printer, how do you solve it? Before finding a solution to the problem, the problem must first be clearly identified. After that, one of many problem solving strategies can be applied, hopefully resulting in a solution.
Problems themselves can be classified into two different categories known as ill-defined and well-defined problems (Schacter, 2009). Ill-defined problems represent issues that do not have clear goals, solution paths, or expected solutions whereas well-defined problems have specific goals, clearly defined solutions, and clear expected solutions. Problem solving often incorporates pragmatics (logical reasoning) and semantics (interpretation of meanings behind the problem), and also in many cases require abstract thinking and creativity in order to find novel solutions. Within psychology, problem solving refers to a motivational drive for reading 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. Processes relating to problem solving include problem finding also known as problem analysis, problem shaping where the organization of the problem occurs, generating alternative strategies, implementation of attempted solutions, and verification of the selected solution. Various methods of studying problem solving exist within the field of psychology including introspection, behavior analysis and behaviorism, simulation, computer modeling, and experimentation.
A problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them (table below). For example, a well-known strategy is trial and error. The old adage, “If at first you don’t succeed, try, try again” describes trial and error. In terms of your broken printer, you could try checking the ink levels, and if that doesn’t work, you could check to make sure the paper tray isn’t jammed. Or maybe the printer isn’t actually connected to your laptop. When using trial and error, you would continue to try different solutions until you solved your problem. Although trial and error is not typically one of the most time-efficient strategies, it is a commonly used one.
Another type of strategy is an algorithm. An algorithm is a problem-solving formula that provides you with step-by-step instructions used to achieve a desired outcome (Kahneman, 2011). You can think of an algorithm as a recipe with highly detailed instructions that produce the same result every time they are performed. Algorithms are used frequently in our everyday lives, especially in computer science. When you run a search on the Internet, search engines like Google use algorithms to decide which entries will appear first in your list of results. Facebook also uses algorithms to decide which posts to display on your newsfeed. Can you identify other situations in which algorithms are used?
A heuristic is another type of problem solving strategy. While an algorithm must be followed exactly to produce a correct result, a heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. A “rule of thumb” is an example of a heuristic. Such a rule saves the person time and energy when making a decision, but despite its time-saving characteristics, it is not always the best method for making a rational decision. Different types of heuristics are used in different types of situations, but the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
- When one is faced with too much information
- When the time to make a decision is limited
- When the decision to be made is unimportant
- When there is access to very little information to use in making the decision
- When an appropriate heuristic happens to come to mind in the same moment
Working backwards is a useful heuristic in which you begin solving the problem by focusing on the end result. Consider this example: You live in Washington, D.C. and have been invited to a wedding at 4 PM on Saturday in Philadelphia. Knowing that Interstate 95 tends to back up any day of the week, you need to plan your route and time your departure accordingly. If you want to be at the wedding service by 3:30 PM, and it takes 2.5 hours to get to Philadelphia without traffic, what time should you leave your house? You use the working backwards heuristic to plan the events of your day on a regular basis, probably without even thinking about it.
Another useful heuristic is the practice of accomplishing a large goal or task by breaking it into a series of smaller steps. Students often use this common method to complete a large research project or long essay for school. For example, students typically brainstorm, develop a thesis or main topic, research the chosen topic, organize their information into an outline, write a rough draft, revise and edit the rough draft, develop a final draft, organize the references list, and proofread their work before turning in the project. The large task becomes less overwhelming when it is broken down into a series of small steps.
Further problem solving strategies have been identified (listed below) that incorporate flexible and creative thinking in order to reach solutions efficiently.
Additional Problem Solving Strategies :
- Abstraction – refers to solving the problem within a model of the situation before applying it to reality.
- Analogy – is using a solution that solves a similar problem.
- Brainstorming – refers to collecting an analyzing a large amount of solutions, especially within a group of people, to combine the solutions and developing them until an optimal solution is reached.
- Divide and conquer – breaking down large complex problems into smaller more manageable problems.
- Hypothesis testing – method used in experimentation where an assumption about what would happen in response to manipulating an independent variable is made, and analysis of the affects of the manipulation are made and compared to the original hypothesis.
- Lateral thinking – approaching problems indirectly and creatively by viewing the problem in a new and unusual light.
- Means-ends analysis – choosing and analyzing an action at a series of smaller steps to move closer to the goal.
- Method of focal objects – putting seemingly non-matching characteristics of different procedures together to make something new that will get you closer to the goal.
- Morphological analysis – analyzing the outputs of and interactions of many pieces that together make up a whole system.
- Proof – trying to prove that a problem cannot be solved. Where the proof fails becomes the starting point or solving the problem.
- Reduction – adapting the problem to be as similar problems where a solution exists.
- Research – using existing knowledge or solutions to similar problems to solve the problem.
- Root cause analysis – trying to identify the cause of the problem.
The strategies listed above outline a short summary of methods we use in working toward solutions and also demonstrate how the mind works when being faced with barriers preventing goals to be reached.
One example of means-end analysis can be found by using the Tower of Hanoi paradigm . This paradigm can be modeled as a word problems as demonstrated by the Missionary-Cannibal Problem :
Three missionaries and three cannibals are on one side of a river and need to cross to the other side. The only means of crossing is a boat, and the boat can only hold two people at a time. Your goal is to devise a set of moves that will transport all six of the people across the river, being in mind the following constraint: The number of cannibals can never exceed the number of missionaries in any location. Remember that someone will have to also row that boat back across each time.
Hint : At one point in your solution, you will have to send more people back to the original side than you just sent to the destination.
The actual Tower of Hanoi problem consists of three rods sitting vertically on a base with a number of disks of different sizes that can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top making a conical shape. The objective of the puzzle is to move the entire stack to another rod obeying the following rules:
- 1. Only one disk can be moved at a time.
- 2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack or on an empty rod.
- 3. No disc may be placed on top of a smaller disk.
Figure 7.02. Steps for solving the Tower of Hanoi in the minimum number of moves when there are 3 disks.
Figure 7.03. Graphical representation of nodes (circles) and moves (lines) of Tower of Hanoi.
The Tower of Hanoi is a frequently used psychological technique to study problem solving and procedure analysis. A variation of the Tower of Hanoi known as the Tower of London has been developed which has been an important tool in the neuropsychological diagnosis of executive function disorders and their treatment.
GESTALT PSYCHOLOGY AND PROBLEM SOLVING
As you may recall from the sensation and perception chapter, Gestalt psychology describes whole patterns, forms and configurations of perception and cognition such as closure, good continuation, and figure-ground. In addition to patterns of perception, Wolfgang Kohler, a German Gestalt psychologist traveled to the Spanish island of Tenerife in order to study animals behavior and problem solving in the anthropoid ape.
As an interesting side note to Kohler’s studies of chimp problem solving, Dr. Ronald Ley, professor of psychology at State University of New York provides evidence in his book A Whisper of Espionage (1990) suggesting that while collecting data for what would later be his book The Mentality of Apes (1925) on Tenerife in the Canary Islands between 1914 and 1920, Kohler was additionally an active spy for the German government alerting Germany to ships that were sailing around the Canary Islands. Ley suggests his investigations in England, Germany and elsewhere in Europe confirm that Kohler had served in the German military by building, maintaining and operating a concealed radio that contributed to Germany’s war effort acting as a strategic outpost in the Canary Islands that could monitor naval military activity approaching the north African coast.
While trapped on the island over the course of World War 1, Kohler applied Gestalt principles to animal perception in order to understand how they solve problems. He recognized that the apes on the islands also perceive relations between stimuli and the environment in Gestalt patterns and understand these patterns as wholes as opposed to pieces that make up a whole. Kohler based his theories of animal intelligence on the ability to understand relations between stimuli, and spent much of his time while trapped on the island investigation what he described as insight , the sudden perception of useful or proper relations. In order to study insight in animals, Kohler would present problems to chimpanzee’s by hanging some banana’s or some kind of food so it was suspended higher than the apes could reach. Within the room, Kohler would arrange a variety of boxes, sticks or other tools the chimpanzees could use by combining in patterns or organizing in a way that would allow them to obtain the food (Kohler & Winter, 1925).
While viewing the chimpanzee’s, Kohler noticed one chimp that was more efficient at solving problems than some of the others. The chimp, named Sultan, was able to use long poles to reach through bars and organize objects in specific patterns to obtain food or other desirables that were originally out of reach. In order to study insight within these chimps, Kohler would remove objects from the room to systematically make the food more difficult to obtain. As the story goes, after removing many of the objects Sultan was used to using to obtain the food, he sat down ad sulked for a while, and then suddenly got up going over to two poles lying on the ground. Without hesitation Sultan put one pole inside the end of the other creating a longer pole that he could use to obtain the food demonstrating an ideal example of what Kohler described as insight. In another situation, Sultan discovered how to stand on a box to reach a banana that was suspended from the rafters illustrating Sultan’s perception of relations and the importance of insight in problem solving.
Grande (another chimp in the group studied by Kohler) builds a three-box structure to reach the bananas, while Sultan watches from the ground. Insight , sometimes referred to as an “Ah-ha” experience, was the term Kohler used for the sudden perception of useful relations among objects during problem solving (Kohler, 1927; Radvansky & Ashcraft, 2013).
Problem-solving abilities can improve with practice. Many people challenge themselves every day with puzzles and other mental exercises to sharpen their problem-solving skills. Sudoku puzzles appear daily in most newspapers. Typically, a sudoku puzzle is a 9×9 grid. The simple sudoku below (see figure) is a 4×4 grid. To solve the puzzle, fill in the empty boxes with a single digit: 1, 2, 3, or 4. Here are the rules: The numbers must total 10 in each bolded box, each row, and each column; however, each digit can only appear once in a bolded box, row, and column. Time yourself as you solve this puzzle and compare your time with a classmate.
How long did it take you to solve this sudoku puzzle? (You can see the answer at the end of this section.)
Here is another popular type of puzzle (figure below) that challenges your spatial reasoning skills. Connect all nine dots with four connecting straight lines without lifting your pencil from the paper:
Did you figure it out? (The answer is at the end of this section.) Once you understand how to crack this puzzle, you won’t forget.
Take a look at the “Puzzling Scales” logic puzzle below (figure below). Sam Loyd, a well-known puzzle master, created and refined countless puzzles throughout his lifetime (Cyclopedia of Puzzles, n.d.).
What steps did you take to solve this puzzle? You can read the solution at the end of this section.
Pitfalls to problem solving.
Not all problems are successfully solved, however. What challenges stop us from successfully solving a problem? Albert Einstein once said, “Insanity is doing the same thing over and over again and expecting a different result.” Imagine a person in a room that has four doorways. One doorway that has always been open in the past is now locked. The person, accustomed to exiting the room by that particular doorway, keeps trying to get out through the same doorway even though the other three doorways are open. The person is stuck—but she just needs to go to another doorway, instead of trying to get out through the locked doorway. A mental set is where you persist in approaching a problem in a way that has worked in the past but is clearly not working now.
Functional fixedness is a type of mental set where you cannot perceive an object being used for something other than what it was designed for. During the Apollo 13 mission to the moon, NASA engineers at Mission Control had to overcome functional fixedness to save the lives of the astronauts aboard the spacecraft. An explosion in a module of the spacecraft damaged multiple systems. The astronauts were in danger of being poisoned by rising levels of carbon dioxide because of problems with the carbon dioxide filters. The engineers found a way for the astronauts to use spare plastic bags, tape, and air hoses to create a makeshift air filter, which saved the lives of the astronauts.
Researchers have investigated whether functional fixedness is affected by culture. In one experiment, individuals from the Shuar group in Ecuador were asked to use an object for a purpose other than that for which the object was originally intended. For example, the participants were told a story about a bear and a rabbit that were separated by a river and asked to select among various objects, including a spoon, a cup, erasers, and so on, to help the animals. The spoon was the only object long enough to span the imaginary river, but if the spoon was presented in a way that reflected its normal usage, it took participants longer to choose the spoon to solve the problem. (German & Barrett, 2005). The researchers wanted to know if exposure to highly specialized tools, as occurs with individuals in industrialized nations, affects their ability to transcend functional fixedness. It was determined that functional fixedness is experienced in both industrialized and nonindustrialized cultures (German & Barrett, 2005).
In order to make good decisions, we use our knowledge and our reasoning. Often, this knowledge and reasoning is sound and solid. Sometimes, however, we are swayed by biases or by others manipulating a situation. For example, let’s say you and three friends wanted to rent a house and had a combined target budget of $1,600. The realtor shows you only very run-down houses for $1,600 and then shows you a very nice house for $2,000. Might you ask each person to pay more in rent to get the $2,000 home? Why would the realtor show you the run-down houses and the nice house? The realtor may be challenging your anchoring bias. An anchoring bias occurs when you focus on one piece of information when making a decision or solving a problem. In this case, you’re so focused on the amount of money you are willing to spend that you may not recognize what kinds of houses are available at that price point.
The confirmation bias is the tendency to focus on information that confirms your existing beliefs. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Hindsight bias leads you to believe that the event you just experienced was predictable, even though it really wasn’t. In other words, you knew all along that things would turn out the way they did. Representative bias describes a faulty way of thinking, in which you unintentionally stereotype someone or something; for example, you may assume that your professors spend their free time reading books and engaging in intellectual conversation, because the idea of them spending their time playing volleyball or visiting an amusement park does not fit in with your stereotypes of professors.
Finally, the availability heuristic is a heuristic in which you make a decision based on an example, information, or recent experience that is that readily available to you, even though it may not be the best example to inform your decision . Biases tend to “preserve that which is already established—to maintain our preexisting knowledge, beliefs, attitudes, and hypotheses” (Aronson, 1995; Kahneman, 2011). These biases are summarized in the table below.
Were you able to determine how many marbles are needed to balance the scales in the figure below? You need nine. Were you able to solve the problems in the figures above? Here are the answers.
Many different strategies exist for solving problems. Typical strategies include trial and error, applying algorithms, and using heuristics. To solve a large, complicated problem, it often helps to break the problem into smaller steps that can be accomplished individually, leading to an overall solution. Roadblocks to problem solving include a mental set, functional fixedness, and various biases that can cloud decision making skills.
Openstax Psychology text by Kathryn Dumper, William Jenkins, Arlene Lacombe, Marilyn Lovett and Marion Perlmutter licensed under CC BY v4.0. https://openstax.org/details/books/psychology
1. A specific formula for solving a problem is called ________.
a. an algorithm
b. a heuristic
c. a mental set
d. trial and error
2. Solving the Tower of Hanoi problem tends to utilize a ________ strategy of problem solving.
a. divide and conquer
b. means-end analysis
3. A mental shortcut in the form of a general problem-solving framework is called ________.
4. Which type of bias involves becoming fixated on a single trait of a problem?
a. anchoring bias
b. confirmation bias
c. representative bias
d. availability bias
5. Which type of bias involves relying on a false stereotype to make a decision?
6. Wolfgang Kohler analyzed behavior of chimpanzees by applying Gestalt principles to describe ________.
a. social adjustment
b. student load payment options
c. emotional learning
d. insight learning
7. ________ is a type of mental set where you cannot perceive an object being used for something other than what it was designed for.
a. functional fixedness
c. working memory
Critical Thinking Questions:
1. What is functional fixedness and how can overcoming it help you solve problems?
2. How does an algorithm save you time and energy when solving a problem?
Personal Application Question:
1. Which type of bias do you recognize in your own decision making processes? How has this bias affected how you’ve made decisions in the past and how can you use your awareness of it to improve your decisions making skills in the future?
trial and error
Answers to Exercises
algorithm: problem-solving strategy characterized by a specific set of instructions
anchoring bias: faulty heuristic in which you fixate on a single aspect of a problem to find a solution
availability heuristic: faulty heuristic in which you make a decision based on information readily available to you
confirmation bias: faulty heuristic in which you focus on information that confirms your beliefs
functional fixedness: inability to see an object as useful for any other use other than the one for which it was intended
heuristic: mental shortcut that saves time when solving a problem
hindsight bias: belief that the event just experienced was predictable, even though it really wasn’t
mental set: continually using an old solution to a problem without results
problem-solving strategy: method for solving problems
representative bias: faulty heuristic in which you stereotype someone or something without a valid basis for your judgment
trial and error: problem-solving strategy in which multiple solutions are attempted until the correct one is found
working backwards: heuristic in which you begin to solve a problem by focusing on the end result
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